' ~74.'1: d,ojv. J B\SON f)ov
TR-20 (VOL.1) JUNE 1976
SHELTER DESIGN
• I :
AND ANALYSIS
l ! II
I
II I ' I
FALLOUT RADIATION SHiffiLDING
I I • l i
DEFENSE CIVIL PREPAREDNESS AGENCY
WASHINGTON, D.C.
~··· 9 0 6 ~
f~
··,,l
j\
'
PREFACE
This manual revises and supersedes TR-20 (volume 1) dated June 1968, and changes 1, 21 and 3 thereto, as well as appendix C, which may be used.
In this revision, some of the highly theoretical materials have been reduced to simple explanations in order to aid the analyst in developing a sense of qualitative interpretation unencumbered by rigorous mathematical expressions. The radiation shielding analysis methodology is developed in logical order, with many illustrative problems designed to emphasize particular stages of development and method~ for solution •. Where appro
priate, study questions and problems have been included. These have been designed to give the analyst a means for testing his knowledge.
Although most students of shielding analysis have sufficient background in nuclear physics through formal courses of instruction, a brief, basic review of the subject matter is provided in appendix A of this manual.
CONTENTS
GENERAL EFFECTS OF NUCLEAR WEAPONS
1-1 1-1
1-3
1-4
1-6
2-1 2-1 2-3 2-4 2-4 2-7 2-8 2-12
3-1 3-2 3-3 3-4 3-7 3-8 3-11 3-14 3-14 3-15
4-1 4-2 4-3 4-30 4-33 4-43 1-1 1-2 1-3 1-4 1-5
Introduction . • . • • • • • • • • • • • • •• Nuclear and Conventional Explosions Compared • • • • . Nuclear Processes • • • • • • • • • Types of Nuclear Explosions . • • • Characteristics of Nuclear Explosions . • • • . • • • •
NUCLEAR RADIATION AND FALLOUT
2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8
BASIC
3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 3-10
Introduction • . • • • •
Nuclear Radiation . • • • • • • • •
o • • • • • • •
Initial Radiation • • • • • • • • • • • • • • Residual Radiation Fa II out • • • . . Measurement of Radioactivity . . . • Dose and Dose Rate Calculations . Biological Effects of Gamma Radiation
CONCEPTS IN FALLOUT RADIATION SHIELDING
Introduction . • Radiation Emergent From a Barrier Barrier Effectiveness vsc Photon Energy Mass Thickness •.••••••••• The Standard • • . • • • • . • . • . Standard Detector Response Evaluated Qualitatively Protected Detector Response Evc:duated Qualitatively Protection Factor. • • • • • . • The Essence of Shelter Analysis Solid Angle Fraction •••••
FALLOUT SHELTER ANALYSIS OF SIMPLE BUILDINGS
4-1 4-2 4-3 4-4 4-5 4-6
Introduction • • • • • • • . .
Functional Notation and Charts
Basic Structure • • . • • • • • . • • • •
Blockhouse With Variation in Exterior Wall Mass Thickness .
One-Story Blockhouse with Interior Partitions • . • ,
Buried Structures • . • • • • • • • • • • • • • • • . •
i i
4-7 Basement Shelters • • • • • • • 4-54 4-8 Simple Multi-Story Buildings • 4-60 4-9 Wall Apertures • 4-71 4-10 Limited Fields 4-93 4-11 Summary 4-107
APPLICATION OF THE STANDARD METHOD TO COMPLEX BUILDINGS
5-1 Introduction • • 5-1 5-2 Building Conversion ••• 5-2 5-3 Overhead Contributions • 5-2 5-4 Ground Contributions • • • • • • • 5-13 5-5 Miscellaneous Complex Conditions 5-52 5-6 Decontaminated Roofs • • • 5-78
o • •
5-7 Detector Locations Adjacent to an Exterior Wall 5-81 5-8 Summary . . . o • • • • • • • • • • • • 5-86
•
SLANTING TECHNIQUES FOR FALLOUT SHELTER
o •
6-1 Introduction • • • • • • • • 6-1 6-2 "Slanting" -A Concept of Design • • • • • • • • • , 6-2 6-3 Analysis and "Slanted" Design • • • • • • • • • • • • • 6-4 6-4 Items for Consideration in "Slanting 11 6-4
HABITABILITY REQUIREMENTS FOR FALLOUT SHELTERS
o
7-1 Introduction • • • • • • • • 7-1 7-2 Environmental Considerations • 7-2 7-3 Hazards . . . • . . . . 7-8 7-4 Electrical Power •••••. 7-9
APPENDIX A. BASIC NUCLEAR PHYSICS A-1 APPENDIX B. TABLE OF MASS THICKNESSES B-1 APPENDIX c. DETAILED METHOD ANALYSIS CHARTS C-1
APPENDIX D. VENTILATION ANALYSIS METHOD FOR COMPUT
lNG EXISTING SHELTER SPACE . . . . . . . . D-1
iii
ILLUSTRATIONS
o •••••• o •••
1-1 Pressurevs.TimeataPoint •••••••• 1-10 1-2 Reflection of Blast Wave at Earth's Surface • • • • 1-12 1-3 Overpressure vs. Time Reg ion of Regular Reflection 1-13 1-4 Outward Motion of Blast Wave • • • 1-14
o • • • • 0 0 • •
2-1 Approximate Rate of Decay of Radioactivity from Fallout. 2-9
o o •• •
3-1 Radiation Emergent from a Barrier . o • • • • • • o • • • o o • 3-3
0 0 • •
3-2 Ga,mma Energy Spectrum at Different Times After Fission •••• 3-5
o •••••• o • o
3-3 Standard Unprotected Location •••• 3-8
3-4 Qualitative Dose Rate Angular Distribution (Unprotected Detector) . . . . . • • • . . . . . • • • . • . . . • . • • . .. . . .. 3-9
o • o •• o •
3-5 Coli imated Detector -Secant Effect •• . . . . . .. . . 3-10 3-6 Qualitative Dose Rate Angular Distribution (Protected Detector) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12 3-7 Solid Angle Subtending Radiation Source o ~ •• 3-16 3-8 Solid Angle Fractions • • 3-18
o o • o o o • o •
o o o o o ••••••• o • o
3-9 Solid Angle Fraction,w(W/L Z/L) • ••• 3-19
•o •• o o ••• o o o o • o o o o o
4-1 The Basic Rectangular Building •• 4~
4-6
o ••••• o ••• o • o ••••• o ••
4-2 Radiation Paths to the Detector
4-3 Actual vs. Model Overhead Contribution 4-8
4-4 Overhead Contribution, Co(X,w} .
0
o o • o •
4-5 The Thin-Walled Structure 4-14
4-6 Geometry Factors-Scatter, Gs(w) and Skyshine, Ga(w). 4-17
iv
4-7 Geometry Factor-Direct, Gd(H,w) • . • • . . • . . . • • . . . • . . . 4-18 4-8 The Thick-Walled Structure 4-21 4-9 Shape Factor E(e) ••.••. 4-24 4-10 Scatter Fraction . • .•••.•... . 4-26 4-11 Exterior Wa II Barrier Factors Be(Xe, H) 4-29 4-12 Effect of Increasing Mass Thickness on Skyshine vs. Scatter Radiation ..•.•..•.••.•••.•• . 4-32 4-13 Effect of Interior Partitions on Detector Response •.••. 4-35
I
4-14 Interior Partition Attenuation Factors, Bi(Xi) and Bi (Xi) 4-38 4-15 Effect of Partitions on C0 • • • • • • • • • • • • • • • • • • • • • • • 4-40 4-16 Partition Barrier Effect on C0 •••••••••••••••••••••• 4-42 4-17 Effect of Structure Buria I on Detector Response . . • . . . . . • . • • • 4-46 4-18 Structures for Problem 4-10 .• 4-51 4-19 Basement Detector Location •.. 4-56 4-20 Ceiling Attenuation Factor, Bc(Xc, w c) .•.• . . . . . . . . . . . . 4-58 4-21 Effect of Detector Height on Direct Contribution .4~3 4-22 Centrally Located Detector .• . 4-65 4-23 Floor Attenuation Factor Bf(Xf) • •• 4-68 4-24 Effect of Apertures on Detection Response • . • . • . . . . • . . . • .•4-72 4-25 Continuous Aperture Concept . . • . • • • ••••••......•.•4-77 4-26 Aperture Contributions . . . . • • • . • • • . . . • • • . • • • . . • • 4-78 4-27 Ceiling Shine ••.••.••••• • 4-81 4-28 Mutual Shielding and Limited Field • 4-95
v
4-29 Limited Fields -Skyshine Radiation and Back Scatter .•••· • • • • • 4-97 4-30 Limited Fields-Scatter Radiation .•••••••••••••••••• 4-99 4-31 Limited Field Barrier Factor Bs(Xe, 2 ws) ••••••••••••••.. 4-JOJ 4-32 Limited Field Height Factor •.••••••••••••••••• ~ •. • 4-102 4-33 Limited Field Solid Angle Fraction, 2 Ws ••••••• • • • •• . 4-104 5-1 Rib/Slab Mass Thickness Curve . 5-14 5-2 Wall-by-Wall Idealization •. 5-16 5-3 Az imutha I Sectors vs. Perimeter Ratios 5-19 5-4 Complex Structure Idealized for Cg • • • • • • • • • • • • • • • • • • • 5-20 5-5 Partially Shielded Wall . . . . . . . . . . . . . . . . 5-53 5-6 Idealized Limited Fields, Partially Shielded Walls . 5-55 5-7 Idealized Limited Fields, Partially Shielded Walls • 5-56 5-8 Idealized Limited Fields, Partially Shielded Walls •.••••.•••• 5-57 5-9 Upward Sloping Ground ••••••••••••••••••••••••• 5-67
5-10 Overhead Contributions Through Partitions of Different Mass ••..•. Thickness-. .....•.........._•.............. 5-72 5-11 Set-Backs . . . . . . . . . . . . . . . . . ·. . . ·· . . . . . . . . . . . 5-74 5-12 Passageways and Shafts, C(w) • • • • • • • • • • • • • • • • • . • • • 5-77 5-13 Detector at Midpoint of a Wall • . • • • • • • • • • • • • • • • • • • 5-83
5-14 Detector in Corner Location • • • • • • • • • • • • • • 5-84 7-1 Psychrometric Chart with Effective Temperature Lines 7-4 7-2 Zones of Equal Ventilation Rates in CFM Per Person . . 7-7
vi
~------~-------------------------------------------------~
A
A
p
A
z
B
B
c
B
e
B.
I
B
s
c c
a
c
a
c
g
c
0
d
LIST OF SYMBOLS The area of a structure The ratio of the area of apertures in an exterior wall to the total
wall area
Azimuthal sector, the ratio of a plane angle at the detector subtending a wall segment to 360 degrees Any barrier reduction factor Barrier reduction factor for ce.il ings Barrier reduction factor for exterior walls
Barrier reduction factor for floors
Barrier reduction factor for ground contribution through interior partitions Barrier reduction factor for overhead contribution through interior
partitions
Barrier reduction factor for scatter radiation through exterior walls subject to limited field Any contribution of radiation to a detector The contribution through an aperture strip that is completely zero
in mass· thickness The contribution through an aperture strip that is completely solid The total ground contribution to a detector The overhead contribution to a detector The dose rate received at a point at any time, t, after an explosion The dose rate received at a point one hour after an explosion
The total accumulated radiation dose over a given time interval
vii
e Eccentricity ratio, ratio of width to length of a structure
E Shape factor applied to scatter geometry
ERD Equivalent Residual (radiation) Dose
G Any geometry reduction factor
G Geometry factor for skyshine radiation
a
Geometry factor for direct radiation
Gd G Total geometry reduction factor for ground contribution
g G Geometry factor for scatter radiation
s H Height of detector above the contaminated plane
Fictitious height of air replacing an equivalent mass thickness
Hf KT Kiloton, explosive energy equivalent of one thousand tons of TNT L Length of a rectangular structure L Length of a I imited field of contamination
c MeV Mill ion electron volts
MT -Megaton, explosive energy equivalent of one million tons of TNT
p Ratio of total width of windows in an aperture strip to total perimeter a
of the aperture strip
Protection factor
pf p Perimeter ratio, ratio of the length of any wall segment to the total r perimeter of a structure R Roentgen, a unit of measurement for radiation Reduction factor, sum of a II contributions
Rf
s -Scatter fraction, fraction of wall emergent radiation that has been
w scattered in the wa II
viii
t Any time after an explosion
t. Time, after explosion, of initio I exposure to radiation
I
Time, after explosion, of final exposure to radiation Width of a rectangular structure
w Width of a limited field of contamination
c X Any mass thickness in pounds per square foot of surface area of barrier
X Mass thickness of a ceiling barrier
c X Mass thickness of an exterior wall
e
Mass thickness of a floor barrier
X. Mass thickness of an interior partition barrier
I
X Total overhead mass thickness
0
X Mass thickness of roof barrier
r
X Mass thickness of any wall in general
w z Distance from the detector to an overhead plane of contamination w A solid angle fraction at the apex of a pyramid or cone w Solid angle fraction subtended by a limited field of contamination
s
ix
•
CHAPTER I
GENERAL EFFECTS OF NUCLEAR WEAPONS
1-1 Introduction
The following description of the general effects of nuclear weapons is intended to furnish the analyst with enough background information to enable him to recognize the destructive power of nuclear detonations, and to understand the general nature of the fallout problem -why it may exist, how it is developed, its extent, its probable effects on human life, and the need for fallout protection. Further information is found in The Effects of Nuclear Weapons, published by the United States Atomic Energy Commission, April 1962, and obtainable from the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. Appendix A of this manual provides a brief review of nuclear physics for those analysts who may find it necessary for a better understanding of the material in this and following chapters.
1-2 Nuclear and Conventional Explosions Compared
1-2. 1 Derivation of Energy
All substances are made up from one or more of over 100 different kinds of materials known as elements. The smallest part of any element that can exist, and not be divisible by chemical means is called an atom.
According to present-day theory an atom contains a relatively dense central core, called the nucleus and a much less dense outer domain consisting of electrons in motion around the nucleus. Nuclei are composed ofa definite number of fundamental particles, ---principally protons and neutrons. The proton carries a positive charge of electricity. The neutron, as its name implies, is electrically uncharged. The masses of protons and neutrons are about the same. The electrons are Iight, negatively charged particles. The total charge on electrons in a normal atom, balances the total positive charge of the nucleus.
An explosion is produced when a large amount of energy is suddenly released within a limited space. This is true both for conventional and nuclear explosions; however, the energy released in each type of explosion
1-1
is produced in different ways. In conventional explosions, the energy is released as the result of chemical reactions. In a nuclear explosion, energy is produced as the result of nuclear reactions.
Electromagnetic forces (a few eV) bind atoms together to form chemical compounds. In chemical reactions, these chemical bonds are broken and new ones are formed as original compounds are converted to others. Nuclear forces (a few MeV} bi~d the constituent parts of a nucleus together. Nuclear reactions involve the breaking and forming of nuclear bonds as origi na I atoms are converted to others. Nuclear forces are so much stronger than electromagnetic forces that even like-charged particles can be bound together. For example, eight positively charged protons are contained in the small nucleus of the oxygen atom. Because of the fact that nuclear forces are several orders of magnitude greater than electromagnetic forces, it follows that the energy released from an explosion produced by nuclear reactions is several orders of magnitude greater than that from a conventional explosion resulting from chemical reactions.
1-2.2 Energy Distribution
In conventional explosions, nearly all of the energy released appears immediately. Almost all is converted via heat into blast and shock. In nuclear explosions, only about 85% of the energy released appears at once. Of this 85%, about 50% is converted into blast and shock and 35% into thermal radiation in the form of heat and light. The remaining 15% of energy is released as various nuclear radiations, 5% as "initial radiation" within the first minute after the explosion and 10% as "residual radiation" after the first minute and over a period of time.
1-2.3 Temperature and Pressure Comparisons
In conventional explosions, temperatures reach a maximum of about 9000°F. Maximum temperatures in nuclear explosions reach several million degrees. The tremendous heat generated in a nuclear explosion converts the weapon constituents into a gaseous form.
The pressures produced in conventional explosions reach a maximum of several hundred atmospheres. Those produced in the detonation of a nuclear weapon reach maximums of severoI hundred thousand atmospheres.
•
1-2
1-3 Nuclear Processes
1-3. 1 GeneraI
Many nuclear reactions are known but not all are accompanied by explosive release of energy. The release of energy in explosive quantities requires that a very large number of nuclear reactions occur essentially instantaneously.
Two nuclear processes satisfy the above condition. These are known as the fission process and the fusion process. The fission process takes place with some of the nuclei, such as those of certain isotopes of uranium and plutonium. The fusion process takes place with some of the nuclei such as those of certain hydrogen isotopes.
1-3.2 The Fission Process
Fission is the splitting of a heavy nucleus into two approximately equal parts (which are nuclei of I ighter elements) accompanied by the release of a relatively large amount of energy and generally one or more neutrons.
Fission can be caused by the absorption of a neutron by the nucleus of a fissionable atom. The neutrons released in fission are able to produce fission of more nuclei. This results in the release of more energy and more free neutrons. The process results in a continuous chain of nuclear fissions with the number of nuclei involved, and the amount of energy released, increasing at a tremendous rate.
Actually, not all the neutrons liberated in the process are available for creating more fissions. Some escape and others are lost in nonfission reactions. For simplicity, however, if one free neutron is captured by the nucleus of a uranium atom, a rd two neutrons are liberated, then each of these neutrons causes fission, the result is the release of four neutrons. The number of neutrons released doubles in each generation. In less than 90 generations, enough neutrons would have been produced to fission every nucleus in about 110 pounds of uranium resulting in the release of the same amount of energy as would result from the explosion of 1 million tons of TNT (1 meqaton). (A 1 kiloton explosion is equivalent, in energy released, to 1 000 tons of TNT . )
The time required for the actual fission process is very short. The interval between successive generations is a function of the time necessary for the released neutron to be captured by a fissionable nucleus. This time
1-3
depends, among other things, on the' energy or speed ofthe neutrons. If they are of the high energy or fast type, the interval is about one hundredth of a millionth part of a second. In this event, the ninetieth generation would be attained in about one millionth of a second. The release of the energy equivalent to a million tons of TNT in a millionth of a second would create a tremendous explosion.
1-3.3 The Fusion Process
Fusion is the formation of a heavier nucleus from two Lighter ones with the attendant release of energy. Hydrogen isotopes; i.e. protium, deuterium, and tritium, are commonly used for fusion reactions.
In order for fusion reactions to occur, the nuclei of the interaCting isotopes must have high energies. These energies can be supplied by a charged-partie le accelerator, or by temperatures in the order of severo I million degrees. Fusion reactions obtained under the latter circumstance are referred to as thermonuclear reactions.
Since a fission reaction produces temperatures of the required magnitude, a fission device can be combined with quantities of deuterium and/or tritium; and, under the proper conditions, produce thermonuclear fusion reactions, accompanied by energy evolution. The devices producing such explosions have been variously termed hydrogen bombs or thermonuclear weapons.
A comparison of the energy released in an average fusion reaction to that from a fission reaction reveals that, on a weight for weight basis, the fusion reaction produces about three times as much energy as the fission reaction.
Three of the four thermonuclear fusion reactions that are of interest in thermonuclear weapons produce free neutrons. These neutrons can cause fission of uranium to increase to the overall energy yield of the device.
1-4 Types of Nuclear Explosions
1-4.1 General
The immediate pheonomena associated with the detonation of a nuclear weapon vary with respect to the point of detonation in relation to the surface of the earth. Similar variations exist with respect to following phenomena such as the effects of shock, blast and thermal and nuclear radiation.
1-4
•
For convenience of description, nuclear bursts are sometimes categorized into five distinguishing types, although many intermediate situations can arise in the actual employment of nuclear weapons. The five types, described in a general way in this section, are high-altitude bursts, air bursts, surface bursts, underwater bursts, and underground bursts.
1-4.2 High-altitude Bursts
A burst is defined as high-altitude if the density of the air is so low that the interaction of the weapon energy with its surroundings is markedly different from that experienced when a weapon is detonated at lower altitudes.
The absence of relatively dense air causes fireball characteristics to be substantially different from those of bursts at lower altitude. The fireball is an intensely hot and luminous mass, roughly spherical in shape, that appears immediately after detonation as the weapon residue incorporates materia I from the surrounding medium.
Also, the fraction of the explosive energy converted into blast and shock is less and decreases with increasing altitude; but the fraction of thermal energy increases with altitude. The fraction of the energy of explosion emitted as nuclear radiation is independent of height. The intensity of initial nuclear radiation reaching a point on the earth 1s surface is dependent on the amount of air through which it travels. For a point equal distance from two detonations, one at high-altitude and one lower, more initial radiation will be received from the high-altitude detonation, since there is less air in which it can be attenuated. Because of the wide dispersion of the fission products in a burst that takes place in the stratosphere, residual nuclear radiation is not a significant hazard.
1-4.3 Air Bursts
An air burst is one that occurs at an altitude of less than 100,000 feet but at such height that the fireball, at maximum brilliance, does not touch the surface of the earth.
The quantitative aspects of an air burst will depend upon the actual burst height as well as the yield of the weapon. The general phenomena will be much the same in all cases. Most of the shock energy will appear as blast with, generally, only a small portion transmitted as ground shock. Thermal radiation will be of sufficient intensity to cause severe burns and fires at relatively large distances. Initial nuclear radiation will also
1-5
penetrate long distances in the air; however, its intensity will decrease very rapidly with an increase in distance.
If the burst is moderately high, the residual nuclear radiation arising from the fission products will generally be of no consequence on the ground. If, however, the burst is of relatively low altitude, the fission products may fuse with debris from the earth1s surface and part of this fused mixture may fall to earth at points near ground zero and in sufficient quantity to create a radiation hazard to I iving organisms.
1-4.4 Surface Bursts
A surface burst occurs when a weapon is detonated at or near the surface of the earth, or at such a height that the fi reba II makes contact with the surface.
Ground shock will be more pronounced than the air burst and will represent a larger portion of the total energy of shock. Of particular importance is the radiation hazard created by the enormous quantity of debris from the earth 1s surface which is fused with the fission products, and which results in a very widespread residual radiation hazard; i.e., 11 early fallout. 11
1-4.5 Subsurface Bursts
For general descriptive purposes, both underground and underwater bursts are considered as subsurface bursts. In such bursts, most of the shock energy will be transmitted through the subsurface medium. In cases where the detonation takes place at shallow depths, some of the shock energy may escape and be transmitted as air blast. Thermal and initial nuclear radiations will be absorbed within a short distance; but, again, for shallow depth bursts, some may escape to the air above. Residual nuclear radiation can be of significant consequence, since large quantities of the subsurface medium in the vicinity of the detonation will be contaminated with the radioactive fission products.
1-5 Characteristics of Nuclear Explosions
1-5. 1 General
Characteristics usually associated with surface burst nuclear explosions are: the fireball, the atomic cloud, thermal radiation, air blast
1-6
and ground shock, crater, and nuclear radiation. Surface-burst conditions are of particular interest in this manual because of emphasis on the fallout, or residual nuclear radiation problem.
Although primary concern is with radiation effects, the other
effects are of interest frorrt the point of view of background information.
This section offers a brief description of these effects.
1-5.2 The Fireball
Almost at the instant of a nuclear explosion, an intensely hot and luminous mass of air and gaseous weapon residue, roughly spherical in shape, is formed. The brilliance of this fireball is relatively independent of weapon yield. After about one millisecond it would appear, to an observer perhaps 50 or 60 miles away, on the order of 30 times more brilliant than the sun at noon.
Immediately after its formation, the fireball increases in size and engulfs more and more of the surrounding medium. As it increases in size, it decreases in temperature because of the increase in mass, and rises into the air in the manner of a hot-air balloon.
•
While the fireball is luminous, its interior temperature is at such a high level that all the weapon materials are in the vapor state. In a surface burst1 where the fireba II touches the earth •s surface, the fireba II will also contain enormous quantities of vaporized debris from the earth•s
surface. It is estimated, for example, that if only 5 percent of the energy of a 1 megaton explosion were spent in vaporizing material from the surface of the earth1 about 20,000 tons of vaporized debris would be added to the normal constituents of the fireball. In addition, the strong afterwinds at the earth1s surface will cause large quantities of debris to be sucked up as the fireball ascends. 1-5.3 The Atomic Cloud As the fireball increases in size and cools, the included vapors condense to form a cloud containing solid particles of the bomb residue and debris and small water droplets. Its color is at first red to reddish brown, changing to white as further cooling takes place and condensation of large quantities of water occurs.
The speed with which the top of the cloud ascends depends on meteorological conditions as well as weapon characteristics. The eventual
1-7
208•401 0 . 76 • 2
height to which it ascends is similarly dependent. Heights may be as high as 30 miles or more for large weapon yields. This maximum height is strongly influenced by the tropopause; i.e., the boundary between the troposphere below and the stratosphere above. When the cloud reaches the tropopause, it will spread out laterally.
The debris sucked up by the afterwinds into the cloud forms a visible stem, giving the characteristic mushroom shape to the atomic cloud.
1-5.4 Thermal Radiation
At the instant of explosion, a nuclear weapon will emit primary thermal radiation which, because of the extremely high temperatures, is largely in the form of X-rays. These are absorbed within a few feet of air and then re-emitted from the fireball as ultraviolet, visible, and infrared
rays. Thus, thermal radiation that is of interest manifests itself in the form of heat and light.
The temperature at the interior of the fireball decreases steadily. The temperature at the surface of the fireba II, curiously enough, decreases more rapidly for a small fraction of a second, then increases for a somewhat longer time after which it decreases steadily. Corresponding to the two pulses associated with the surface of the fireba II, there are two pulses of emission of thermal radiation. The first pulse emits temperatures that are very high but of very short duration. Most of the radiations emitted during the first pulse are in the ultraviolet region. Although ultraviolet rays can cause skin burns, they are readily attenuated in air. Since the pulse is of such short duration, it may be disregarded as a source of skin burns. It is, however, capable of producing permanent or temporary damage to eyesight,
particularly in individuals who may be looking in the direction of the explosion.
The second pulse, although it does not emit thermal radiation of as high a temperature as the first, lasts generally for several seconds and consists mostly of visible and infrared rays. It is this radiation that is the main hazard in producing skin burns, eye effects and fires.
For every kiloton weapon yield, about 330 billion calories of thermal radiation are released. This is equivalent to about 400,000 kilowatt-hours, and points out the important consequences that might be expected from thermal radiation.
Thermal radiation, like light, travels in a straight line and is readily attenuated by any opaque material. However, a shield that is merely placed between a target and the fireball and does not completely surround the target,
1-8
may not be entirely effective, particularly on a hazy day. Scattering of the thermal rays may cause them to reach a given point from all directions.
Whem thermal radiation impinges upon any object, part may be reflected,
part absorbed, and part may pass through. That portion absorbed produces the heat that determines the damage. Dark objects will absorb and, consequently, transmit more heat than will I ight objects. Since the amount of energy from a nuclear explosion is high and is emitted in a very short time, it impinges upon
objects with much intensity and heat is produced rapidly. Since only a small portion of the heat can be dissipated by conduction in the short time over which radiation falls upon the material, very high temperatures are generally confined to shallow depths. As a consequence, thin materials may flamE; but thick materials may merely char.
A first-degree burn over a large portion of the body, characterized by redness of the skin as in sunburn, may produce a casualty. Second-degree burns, characterized by blistering, such as in severe sunburn, will usually incapacitate the
victim if they are extensive. In third-degree burns, the full thickness of the skin is destroyed and if destruction is extensive enough, loss of I ife can occur. To enhance appreciation for the seriousness of thermal radiation, it should be observed that the potential for first-degree burns from a 1 megaton 'yield extends to a distance of about 15 miles. The potential for second-degree burns would extend to a distance of about 11 miles. A 1 megaton yield has the potential to ignite dry forest products, such as leaves, fine grass, and rotted wood, out to a distance of about 10 miles.
1-5.5 Blast
As the gases in the fireball expand rapidly outward, they push away the surrounding air with great force creating the destructive blast effects of the explosion. The front of the blast wave or shock front travels rapidly away from the fireball in all radial directions and behaves like a movin!=J wall of compressed air. It travels roughly at the speed of sound and weakens with
distance traveled from the point of detonation.
The pressure effects at a point some distance from the point of detonation are shown qualitatively by the pressure-time curve shown in Figure 1-1.
1-9
ambient pressure
TIME
FIGURE 1-1
PRESSURE VS. TIME AT A POINT
At time t0, the instant of the explosion, pressures at the point under consideration are at ambient atmospheric values and will remain so during the time necessary for the shock front to reach the point. When the shock front arrives at the location, pressures will increase virtually immediately to some peak values, magnitudes of which are primarily a function of weapon yield and distance from ground zero and, to a lesser extent, such parameters as atmospheric conditions.· Time t1 is the time at which the shock front reaches the fixed location.
Pressures are of two kinds, overpressures and dynamic pressures. Overpressures are pressures in excess of atmospheric values that may be I ike ned to pressures that would be experienced by descent into depths of water. Dynamic pressures are the result of winds following immediately behind the shock front.
Both overpressure and dynamic pressure decay rapidly with time until, at time t2, the overpressure has again reached the ambient value. The interval between times t1 and t2 is the time duration of the positive phase of the overpressures. The positive phase of the dynamic pressures, during which the winds blow away from the point of the explosion, persists for a slightly longer time than does that for the overpressures. Following the positive pressure phase, the fixed location is subjected to negative pressures in the time interval t2 to t3 . During the negative phase, the point exists in a partial vacuum. The winds reverse in direction, blowing toward the point of detonation. Negative pressures are always substantially less than the peak pressures associated with the positive phase of the pressure diagram.
"l-lO.
•
Most of the damage associated with the blast effect of nuclear weapons occurs during the positive phase of pressures. Overpressure or dynamic pressure or both may decide the extent of damage or establish the design loading criteria depending largely on structures type and location. For belowground structures, only the overpressures are of concern. An enclosed aboveground structure, with blast resistant walls and few openings, would
be subject to the full effects of both the ove~pressures and the ~ynamic
pressures. On the other hand, a structure designed with frangible walls would be reduced to a structural skeleton almost immediately; and the structural frame would be loaded primarily through the drag effect of the winds. The structure I members of the frame would be com pi etely surrounded by equal overpressures. Overpressures in the positive phase produce primarily
a crushing effect, although translation effects also exist because of the time
necessary for the overpressure wave to traverse the structure and engulf it.
Dynamic pressures are essentially translational in effect.
Definite relationships exist between peak overpressure, weapon yield, distance from the explosion, arrival time, positive and negative phase duration, etc. To develop some apprecia.tion for the magnitude of blast loading, it may
be noted that a surface-burst 1-MT detonation would result in a peak
overpressure of 100 psi at a distance of about 3500 feet. The peak
dynamic pressure would be about 180 psi, resulting from winds of about
1600 mph velocity. There is a definite relationship between peak
overpressure and the accompanying peak dynamic pressure. For peak
overpressures above about 70 psi, the peak dynamic pressures will be
higher than the peak overpressure. For overpressures below about 70 psi,
dynamic pressures will peak at lower values than wi II overpressures. For
example, a 1 MT surface burst weapon wi II produce a peak overpressure
of 20 psi at a range of about 7000 feet. The accompanying peak dynamic
pressure from winds of about 470 mph is about 8 psi.
Blast effects vary generally as the cube root of weapon yield. For example, a given peak overpressure would occur only three times as far from a 27~T (=3x3x3) burst as from a 1-MT burst.
When the blast wave from an aboveground detonation reaches the surface of the earth, it is reflected back. Figure 1-2 shows four stages in the outY!qrd motion of the blast front. lnthe first and second stages,
corresponding to times t1 and t2, the wave front has not yet reached the surface of the earth.
1-11
J?IGURE 1-2
REFLECTION OF BLAST WAVE AT EARTH'S SURFACE
At time t3, the incident wave has reached point A on the ground, and the reflected wave has also formed at point A. Point A is subject to a single shock with the total peak value of pressure the sum of those from the incident wave and the reflected wave. The point A may be considered as lying within the region of regular reflection; i.e., where the incident and reflected waves do not merge except on the surface. Pressure will decay as shown in Figure 1-3a.
At time t3, point B, in the air, is subjected to a shock from the incident wave. The peak value of overpressure begins immediately to decay in the normal way until, at time t4, point B is subjected to a second shock from the reflected wave which has now reached that point. The peak pressure from the reflected wave adds to the residual from the incident wave. The combined pressures then decay in the normal way as depicted in Figure 1-3b. Point B also I ies in the region of 11 regular11 reflections.
Since the reflected wave travels in a hotter and more dense atmosphere than does the incident wave, it will move faster. Eventually, the reflected wave will overtake the incident wave and the two wave fronts will merge to produce a single front. This process of wave interaction is called 11 Mach 11 (or irregular) reflection. The region in which the two waves have merged is co lied the Mach (or irregular) region, in contrast to the regular region where merger has not taken place.
1-12
p = incident overpressure
Pr = total overpressureafter reflection
p
t4 TIME
(b)
FIGURE 1-3
OVERPRESSURE VS. TIMEREGION OF REGULAR REFLECTION
Figure 1-4 shows several stages in the fusion of incident and reflectedwaves and the formation of the Mach stem. The intersection of the Machstem, incident wave, and reflected wave, is called the triple point. Itforms the so-called triple point path with outward motion of the blast wave.Below the path of the triple point, in the region of Mach reflection, onlysingle pressure increases are experienced. This contrasts to points abovethe path in the region of regular reflections where two distinct shocks, ashort time apart, are felt as first the incident and then the reflected wavereach a specific point-as, perhaps, the top of a high building or an aircraft.It is also of considerable importance to note that the Mach stem is essentiallyvertical. The accompanying blast wave is traveling in a horizontal directionat the surface and the transient winds are essentially parallel to ground. Thus,in the Mach region, blast forces on an aboveground structure are nearlyhorizontal and vertical surfaces are loaded more intensely than horizontalsurfaces.
1-13
R I
R = reflected wave I = incident wave
•
REGULAR
REFLECTION REGION OF MACH REFLECTIONS
REGION
FIGURE 1-4
OUTWARD MOTION OF BLAST WAVE
Obviously, in a surface burst, only a single merged wave develops, ond only one pressure increase will be experienced at all points on the ground or in the air.
It is impossible to describe structural damage that might be expected
to occur as the result of blast without more or less complete knowledge of structural features and weapon characteristics, including yield and distance. For the purpose of this section, it is sufficient to consider the expected results from the standpoint of the types of construction that exist in typical
American cities. More common structures are of brick and wood frame,
multi-story masonry bearing, light steel frames, etc. For surface burst
weapons, it would be expected that such construction would be destroyed
within radii of 3 3/4 miles and 10 miles respectively for 1 megaton and
20 megaton explosions. Within this zone of complete destruction, peak
overpressures would have ranged from about 3 psi at the edge to more
than 1000 psi toward the center. Wind velocities would vary from about
150 mph at the edge to more than 2000 mph near the center. Within a
band between 4.4 psi miles and 1.4 psi miles from a 1 MT explosion and
1-14
between 4.55 miles and 1.4 psi miles from a 20 MT explosion, damage would be so severe that extensive reconstruction would be required before the structures could be reused. Within this zone, overpressures would range from
1.5 to 5.0 psi and wind velocities from 50 to 150 mph.
Within a band between 1.4 and 0.9 psi miles from a 1 MT explosion and between 1.4 and 0. 88 miles from a 20 MT explosion, overpressures would range between 1.0 and 1.5 psi and maximum wind velocities from 33 to 51 mph. Moderate repairs would be required for most structures in this band.
Minor repairs would be required for most structures from 8 to 1/2 psi miles from a 1 MT detonation point and -1/2 psi miles from a 20 MT explosion. Wind velocities at these distances would be about 20 mph maximum and peak overpressures about 0.5 psi. Overpressures of a magnitude of from one-quarter to one-half pound per square inch will shatter ordinary window glass. Overpressures of this magnitude have been observed at distances as great as 50 miles away from nominal-yield, test shots as the result of blast waves reflected out of the sky.
1-5.6 Craters
The size of the crater is a complex function of many things, including material, height of burst, and weapon yield. As an example of crater effects, a 1 MT weapon surface burst on dry soil would result in a crater about 630x2 feet in diameter and about 2501 rock feet deep. Corresponding figures for a 20 MT explosion are 1680x2 feet and 8151 feet.
The crater effect results partly from the vaporization of material, partly from consolidation, and partly from lateral translation and heave of material to form I ips around the crater.
1-5.7 Electromagnetic Pulse
The electromagnetic pulse associated with nuclear explosions is complicated phenomenon which can only be discussed briefly here. The brief discussion here is intended only to acquaint the analyst with the phenomenon itself and its possible effects on installations of interest in certain nuclear defense areas.
The detonation of a nuclear weapon is accompanied by the immediate emission of high energy gamma rays, a form of nuclear radiation that will be discussed later.
1-15
This gamma radiation, as it penetrates into the atmosphere, interacts with molecules within the surrounding medium causing the expulsion of electrons from those molecules. These electrons move rapidly away from the point of detonation creating, in effect, a separation of electrical charges on a
•wholesale basis. A volume of positively charged molecules, defined by the
spatial extent to which the gamma rays have penetrated, is surrounded by a volume with excess negative charge represented by the departed electrons. This relative displacement of positively and negatively charged regions produces an intense electric field giving rise to the phenomenon known as the electromagnetic pulse, EMP.
Distinctly different types of source regions are created depending upon
whether the detonation is a surface burst or a high altitude or air burst. In the
case of a surface burst, the source region in which the intense electromagnetic
fields exist is limited by the atmosphere itself acting to severely reduce the
extent to which gamma rays can penetrate. A typical low-yield surface
burst may create a source region of the order of a mile in diameter. Increasing
. the weapon yield by a factor of one thousand will increase the diameter of the source region only by a factor of about three. Since, in surface bursts, the source region and damaging EMP are restricted substantially to high overpressure and thermal radiation areas, consideration of EMP, although important for hardened structures, is not of significant interest to public shelter systems which are designed primarily against fallout radiation outside the region of high intensity blast.
For high altitude bursts above the atmosphere, gamma rays can travel many miles without encountering air molecules. In such instances they will eventually affect the atmosphere over a vast region. For example, a highyield weapon detonated just above the ionosphere may create a source region in the order of a thousand miles in diameter and perhaps as much as twenty miles thick. The source region is somewhat pancake in shape as opposed to the spherica I shape from an atomospheric burst. Because of the great height of such a source region, the EMP radiated from it could appear over a substantial fraction of the earth's surface and be effective against regions that are unaffected by other nuclear effects. In such cases, the EMP could be damaging not only to power and hardened against all weapons effects but also to communications that are a part of the system of public shelter.
Whenever two opposite electrical charges are suddenly separated as
they are in the source region, nearby charges are also subjected to a similar
but somewhat diminished force or electric field. Thus, a portion of the
electric field, moving away from the displaced charges at the velocity of
Iight, can affect the position of other charges at great distances, and a strong
1-16
field can be created at some distance from the source region. These more distant fields are termed radiated fields, and this effect is called electromagnetic radiation. Electromagnetic radiation fields can cause charges to flow in distant but good conductors such as metallic structures, radio antennas or electrical wiring.
In the electromagnetic sense, the spectrum and waveform of EMP differ significantly from any other natural or man-made sources such as I ightning or radio waves. The spectrum is broad, extending from extremely low frequencies into the UHF band. The waveform indicates a higher amplitude and much faster rise time than, for example, lightning. EMP is also widely distributed, as opposed to the localized effects of lightning.
Although there are vast differences between the phenomena of EMP and lightning, both can cause the same type of damage and an analogy between the two is useful for assessing the threat of EMP in terms of a familiar phenomenon. Most damage from EMP occurs as the energy in the form of strong electromagnetic fields is converted into very large currents and voltages when it impinges on cables or other conductors. Thus, I ike lightning, EMP can cause functional damage, such as the burnout or permanent electronic damage to components, or operational upset, such as the opening of circuit breakers or the erasure of storage in the memory bank of a computer.
It is this sort of potential damage that poses EMP as a serious threat that must be considered in the design of any civil or military defense facility that must maintain operational capability in the event of a nuclear disaster.
1-17
1-6 Study Questions and Problems
I. What is the basic difference in the manner in which energy is derived
from conventional and nuclear explosions?
2.. What is the approximate percentage distribution of the various types of
energy released in a nuclear explosion?
3.
What is the basic requirements for the explosive release of energy.
4.
Describe the fission process.
5.
What is the quantitative significance of a megaton explosion? a kiloton explosion?
6.
Briefly describe the fusion process.
7.
How is the fusion process triggered in a nuclear weapon?
8.
On a weight of material basis, state the advantage of a fusion device
over a fission device.
9.
Distinguish bet':'een high-altitude, air, surface, and subsurface bursts.
(0. Briefly define the fireball.
II. Describe the formation of the atomic cloud.
12.
Describe the two-pulse phenomenon of thermal radiation, and explain why it is the second pulse that represents the most serious thermal hazard.
13.
How can thermal radiation be guarded against?
14.
Why is it that a shield, positioned between a target and a nuclear explosion, may not be completely effective in eliminating the thermal hazard?
15.
What creates the blast wave in a nuclear explosion?
16.
By means of a sketch, show the variation of overpressure with time at a point some distance removed from a nuclear explosion.
1-18
17.
What are dynamic pressures, and how do they vary with time at a
point some distance from an explosion?
18.
During what phase of the pressures does most structural damage occur?
19.
What is the approximate rule by which blast effects may be sea led with respect to weapon yield?
20.
Describe the manner in which the Mach front is formed.
21.
What is the 11 triple point11 ?
22.
Describe the phenomena that gives rise to EMP.
23.
What significant differences in the EMP threat can be expected from
high altitude as opposed to surface burst detonations?
I 24. From the damage point of view, what threat is posed by EMP against civil and/or military defense facilities?
25. Why are protective measures such as employed for lightning not appropriate for protection against EMP?
1-19
•
•
CHAPTER II
NUCLEAR RADIATION AND FALLOUT
2-1 Introduction
In Chapter I, it was stated that one of the distinguishing features of a
nuclear explosion is the delayed emission of about 15% of the total energy yield
of the weapon. This chapter will consider the nuclear radiation effects of
nuclear weapons in somewhat greater detail than that accorded the other effects.
There is no intent to minimize the importance of the latter. The intent is merely
an emphasis on the former in keeping with the purpose of this publication.
2-2 Nuclear Radiation
2-2.1 General
In the fission process, there are many different ways in which the uranium
or p,lutonium nuclei can be split up giving rise to several hundred fission fragments that are generally radioactive forms of lighter elements. Radioactivity associated with these fragments is usually manifested by the emission of beta particles and gamma radiation.
When a negatively charged beta particle is emitted, the nucleus of the radioisotope is changed into that of another element called a decay product.
The decay products may also be radioactive and, in turn, decay with the
emission of beta particles and gamma rays. About three stages of radioactivity
are required for each fission fragment to reach a stable form. At any one time
after the explosion, it is obvious that the fission product mixture will be very
complex. Over 400 different isotopes of 37 I ight elements have been identified
among the fission products.
Not all of the uranium or plutonium in a fission weapon undergoes fission. Both of these materials are, however, radioactive, and their activity consists in the emission of so-called alpha particles, gamma rays, and spontaneous fission. This activity must be considered in studying the radioactivity associated with nuclear weapons. Additionally, not all of the neutrons that are released in the fission process will interact with the fissionable constituents of the weapon and, thus, free neutrons must be considered as ionizing radiation associated with nuclear explosions when concerned with initial effects.
2-1
In fusion reactions, it is important to recognize that not all the products are radioactive fragments. Fusion reactions produce neutrons, and hydrogen and/or helium nuclei. Since an alpha particle is, in form, a helium nucleus, these particles, hydrogen and neutrons are the only forms of radioactivity
•
associated directly with a fusion reaction. It must be recalled, however, that
the triggering element of a fusion device is a fission reaction and that the free neutrons associated with a fusion reaction can be taken advantage of in producing further fuss ion.
2-2.2 Alpha Particles
Alpha particles are identical, in atomic structure, with the nuclei of helium atoms and because of their relatively large mass, they are very low in penetrating power. As a matter of fact, they can travel no more than about two inches in air before they are stopped. In any event, they are unable to penetrate even the lightest of clothing, and, consequently, they do not constitute a hazard so long as they are outside the body. If1 however, uranium or plutonium enters the body in sufficient quantity by ingestion, inhalation or other means, the internal effects can be very serious. For this reason it is important in fallout shelters to insure that fallout particles which may be brought in on clothing or by other means are brushed off and disposed of in such a manner as to minimize the possibilities of ingestion with food or water and contact with personnel.
2-2.3 Beta Particles
Except for their origin and speed, beta particles are identical to the electrons that orbit about the nuclei of atoms. They originate in the nucleus of an atom, have a small mass relative to the atom and travel at high speed. A beta particle is somewhat more penetrating than an alpha particle but still not so penetrating as to constitute a consideration in structure shielding. Beta range in air is in the order of 10 to 12 feet. They are penetrating enough to produce radiation burns if they come in contact with exposed skin and are hazardous if they are ingested. The extent to which they are a hazard depends on, among other things, the energy and concentration of the B particles. The precautions mentioned with respect to alpha particles apply as well to beta particles.
2-2.4 Gamma Rays
Gamma rays consist of streams of photons, small packets of energy, having no mass or electrical charge and traveling with the speed of light. They are quite similar to X-rays except for their origin. X-rays originate in the region of the orbiting electrons of an atom, whereas gamma rays originate in the nucleus and, in general, are somewhat higher in energy than are X-rays. They are
2-2
emitted in the fission process and in other secondary processes including decay of fission products.
Gamma rays are penetrating. They may travel in air for severo I hundred feet before interacting. Considerable mass of material is required to attenuate them. If they are absorbed by the body in sufficient quantity, either externally or internally, they constitute a very serious biological hazard. Gamma rays constitute the sole consideration in fallout shelter analysis. Structures used as protective shelter against their effect must have sufficient mass so oriented as to reduce their penetration and consequent effect on sheltered personnel to tolerable limits.
2-2.5 Neutrons
As stated earlier, neutrons are fundamental parts of the nucleus of an atom and may be released either in the fission or fusion process. They have a mass comparable to the proton and are neutrally charged.
Neutron shielding is a difficult problem different from that of shielding against gamma rays. It must be recalled that neutrons may be captured by nuclei of atoms to form new isotopes that are generally unstable and give off beta and gamma radiation. Neutrons do not cause ionization directly but, for the reason stated immediately before and as the result of other interactions, they may cause the emission of alpha, beta, and gamma radiation with the attendant biological hazard of ionization. Unreacted neutrons may undergo radioactive decay by beta emission.
As a matter of consequence is the fact that neutrons are not characteristic of radiation from fallout and are therefore not a consideration in fallout shelter analysis and design. They must, however, be considered in the design of shelters which protect against all of the effects ·of a nuclear detonation.
2-3 Initial Radiation
2-3.1 Initial vs. Residual Radiation
It is convenient for purposes of design of protective structures to consider nuclear radiation as divided into two categories, initial and residual; initial radiation is generally taken to be that which is emitted within the first minute of the explosion and residual radiation is that which is emitted following one minute after the detonation.
2-3
208-401 0 -76 -3
The somewhat arbitrary time of one minute was originally based upon the fact that the radioactive cloud from a 20-kiloton explosion will reach a height of about 2 miles in 1 minute. The effective range of gamma rays in air is roughly 2 miles and, consequently, when the height of the cloud is greater, the effect of gamma radiation on the ground is no longer significant.
For higher weapon yields it still works out that one minute is realistic. The maximum. distance over which gamma rays are effective will be greater for higher yields but so also is the rate at which the cloud will rise. A reverse situation exists for lower yields. The effective range is less as is the rate of ascent.
2-3.2 Importance of Initial Radiation
Because the effect of the initial nuclear radiation is confined to close-in locations, it becomes important in analysis and design only to a structure that is to survive close-in effects. These effects include blast pressures and thermal radiation as well as nuclear radiation. For such structures, consideration of initial nuclear radiation is important.
Fallout shelter is protective construction designed specifically to reduce the early fallout radiation hazard. No particular attention is given to blast and thermal effects although, as a matter of course and by slanting techniques, low levels of protection against these latter effects may be achieved.
2-4 Residua I Radiation
Residual radiation is defined as that emitted later than one minute after the explosion. Direct neutron effects are confined to initial radiation, but alpha and beta particles and gamma rays constitute the radioactivity that is associated with residual radiation. This activity arises mainly from fission products and products of neutron reactions other than fission. The primary hazard from residual radiations stems from the creation of early fallout particles which incorporate the radioactive elements and may be dispersed over wide areas on the earth •s surface.
2-5 Fallout
2-5. 1 Formation
As stated previously, the tremendous heat generated in. a nuclear explosion vaporizes the weapon residue. In addition, in the case of a surface burst, tons of debris from the earth 1s surface are sucked up into the fireball and, in
2-4
a vaporized or melted state, mingle with the vaporized radioactive fission products from the weapon. As the cloud ascends and cooling takes place, these vapors condense forming solid particles ranging in diameter from less than a micron (a micron is about 0.00004 inch) to several millimeters. This mixture will consist partly of particles that are comprised only of debris material from the earth, some that are a mixture of such debris and the radioactive fission products, and some that comprise condensed fission products. It is estimated that about 900/o of the radioactivity involved is associated with·. particles in the head of the cloud and about 10% with those in the stem.
2-5.2 Quantity of Fission Products
The fission products from a nuclear detonation is a complex mixture of· more than 400 different isotopes of some 35 elements most of which are radioactive. They decay by the emission of beta particles frequently accompanied by gamma rays. About 2 ounces of fission products are formed for each kiloton of fission weapon yield. The gamma ray activity of 2 ounces of fission products 1 minute after the explosion is roughly equivalent to that of 30,000 tons of radium. This, of course, decreases with time, but, if all the fission products from a one megaton explosion were to be uniformly spread over a plane surface of 5000 square miles, the radiation exposure rate at a level of 3 feet above the ground would still be 12 roentgens per hour after about 24 hours. As will be seen later, exposure to radiation of such intensity, even for a relatively short period of time, is extremely hazardous. Naturally, in an actual situation, the distribution of fallout will not be uniform, and higher levels of radiation may exist closer to the explosion than further out.
2-5.3 Early and Delayed Fallout
In article 2-5.1 it was pointed out that fallout particles range in size from less than a micron to several millimeters. Obviously the heavier particles will be deposited upon the earth relatively soon after the explosion while the very light ones will remain aloft for days,· months, or even years before they eventually settle out or are brought down with precipitation.
It is convenient to consider fallout as being divided into two parts, early and delayed. Early fallout is defined as that which returns to earth within a period of 24 hours following an explosion.
Delayed fallout, that which arrives after the first day; consists of the very fine, invisible particles which will accumulate in very low concentrations over a considerable portion of the surface of the earth. During the long time in which they are aloft, the process of decay materially reduces the intensity of
2-5
radiation that comes from them. This, together with the fact that they are widely dispersed, renders their effect as of no immediate danger to health, although there may be long time hazards that are not yet fully understood.
On the other hand, early fallout, arriving in heavy concentrations at early times while the intensity of radiation is still relatively high, represents an immediate, serious hazard to health and even life. Early fallout is the sole consideration in fallout shelters.
2-5.4 Distribution of Early Fallout
Factors affecting the distribution of early fallout particles include the height of the atomic cloud, quantity and size distribution of fallout particles, wind velocities and directions at various levels of the atmosphere through which the particles must fall, and the density of the atmosphere.
From the ever-changing pattern of parameters involved, it should be obvious that accurate predictions of fallout deposition are impossible. In general, it can be assumed that heavier concentrations will occur at points closer to ground zero and decreased concentrations as distances increase. Because of loca I variations in atmospheric conditions such as localized wind currents, updrafts, etc, it is possible that 11 hot spots 11 may be encountered at distances where, normally, low concentrations might be expected.
For planning purposes, it is possible to plot, on the basis of assumed conditions, idealized fallout patterns that might be expected to develop following a detonation at a specific location. It is also possible to assume hypothetical attacks involving specific weapons detonated on specific targets at a particular time. From a study of these attack conditions in conjunction with observed weather parameters existing at that time, a generalized view of fallout distribution on an area-wide basis can be obtained. Such studies, covering a variety of attack situations under different weather conditions, have established that no part of the United States can be considered free of a potential fallout radiation hazard in the event of a nuclear attack.
Because fallout particles descend from the head of the atomic cloud, which may reach heights of over 30 miles, even for a surface burst, a point only far enough from the explosion to escape immediate effects may not receive any fallout at all for a period of as much as 30 minutes. This is an important factor from the standpoint of moving personnel to shelter and improvisation of shelter. Points further removed will not begin to receive fallout except after longer periods of time.
2-6
Once fallout begins to arrive, at a specific location, it may continue to fall for a period of several hours. It arrives, of course, in the form of solid particles, visible, and with an average size on the order of that of fine
beach sand. Being relatively heavy, it tends to remain where it is deposited except under exceptional wind conditions which may cause some drifting. Its deposition is consequently fairly uniform. All of the early fallout, which
would result in a biological hazard, would be deposited somewhere, within a period of 24 hours from the explosion. The area affected by significant amounts of fallout from a single explosion could be several thousand square miles in extent.
2-6 Measurement of Radioactivity
2-6. 1 The Roentgen
The unit generally used to express exposure to gamma radiation is the
roentgen. A roentgen is defined as the qua9tity of gamma radiation which will give rise to the formation of 2.08 x 10 ion pairs per cubic centimeter of dry air at standard temperature and pressure. The interaction of gamma rays with matters results in ionization, or the production of ion pairs. There are
relationships between the exposure of gamma radiation in roentgens and the
biological effect that might be expected. The roentgen, then, may be considered a unit measure that can be used to relate the radiation hazard from fallout to its biological effect on human beings. It is in this sense that it is used as a unit of measure in fallout shelter analysis.
2-6.2 Dose Rate and Dose
Dose rate, for the purpose of this publication, is the rate at which radiation is being received from the field of contamination, by a detecting device that measures radiation being received from all spherical directions. The unit of measure is roentgens per hour. The reference dose rate is that which would exist one hour after the explosion. If the dose rate is known at any time after fallout has ceased to arrive, the reference dose rate can be determined and, from this, the dose rate at any other time can be predicted.
For various reasons, it is impossible to predict, with any degree of accuracy, the dose rate that might be expected at a specific location. For planning and study purposes, it has sometimes been assumed that initial dose rates in areas of heavy, medium and light concentrations of fallout are 10,000, 1,000, and 200 roentgens per hour respectively.
2-7
Dose, or totaI dose, is the integrated dose rate with respect to time . It is the quantity of radiation, expressed in roentgens, to which a point or body would be subjected in a given period of time. Total dose can be related to expected average biological effects.
•
2-7 Dose and Dose Rate Calculations
2-7. 1 Decay of Radioactivity
The half-life of a radioactive isotope is the time required for the radioactivity to decrease by one half from any initial value. In the fission products from a nuclear detonation, the many isotopes involved have half-lives ranging from a fraction of a second to milleniums. As a consequence, a study of the rate at which radioactivity from fallout decays must be considered from the standpoint of an average product containing representative fractions of all isotopes involved.
The rate of decay can be expressed by the following equation plotted in Figure 2-1. .
d . = dt1.2 1
where:
d = dose rate at H + 1 hr. {H = time of explosion)
1
d = dose rate at time t,
t =time (hours) after detonation.
A more approximate rule, which gives a more immediate appreciation of the rate of decay, is the so-called Seven-Ten rule. For every seven-fold increase in time after the explosion, there is a ten -fold decrease in dose rate. As an example, if the reference dose rate at H + 1 hrs. is taken as 1000 roentgens per hours, seven hours after the explosion the dose rate would be 100 roentgens per hour. Forty-nine hours, about 2 days, after the explosion the dose rate would be 10 roentgens per hour and 2 weeks after the explosion it would be 1 roentgen per hour.
2-7.2 Accumulated Dose
Based on the dose rate equation given in section 2-7. 1, the following expression will yield the total accumulated dose to which an exposed point or
2-8
1 10
1000
~
E-4
<
~
~
tl.l
0
Cl
...-...
1 100
1""'4
+
:I::
...........
0 ~
E-4
z
u ~
~
~
~
~ 0.1 10
E-4
<
~
~
tl.l
0
Cl
! :
-..
~
0.01 1 10 100 1000
TIME AFTER EXPLOSION(HOURS)
For times from 0.1 to 10 hours, use upper curve and read to right.
For times more than 10 hours, use lower curve and read to left.
FIGURE 2-1
APPROXIM4-TE .RATE OF DECAY
OF RADIOACTIVITY FROM FALLOUT
2-9
body will be subjected in a given time interval.
o= 5 d (t . .;.0 · 2 -t-o·2 )
1 I f
In this expression
D = dose accumulated from t i to t f
t. = time of initial exposure
I
tf = time of final exposure
Table 2-1 is given as an aid for solving dose and dose rate problems. With the aid of the data given in the table, it is observed that the toto I accumulated dose to infinite time is 5 times the initial dose rate at H+ 1 hours. Of this possible total, a point or body would accumulate about 400/o after 12 hours, 50% after 30 hours, 60% after 4 days and 70% after 2 weeks. As will be seen in subsequent paragraphs, doses absorbed in short periods of time are of extreme importance in determining the expected biological effect.
2-7.3 Example Problems
1. At a point some distance from a nuclear explosion, fallout begins to arrive at H + 4 hours and continues to fall for 8 hours. After it has ceased to fall, an observation indicates a dose rate of 50 roentgens per hour. What will the dose rate be at this location 2 days after the detonation?
Solution: (data from Table 2-1)
2
d = dtl. =50 (12) 1.2 =50 (19.73) =986 R/hr.
1
2 2
d = d +tl. = 9867(48)1. = (986)7(0.0096) = 9.5 R/hr.
1
2. Twenty hours after a detonation, the observed dose rate is 120 R/hr. A civil defense team is sent on a mission 90 hours after the detonation and remains for 5 hours. What total dose will be accumulated by the members of the team during the 5 hours on the mission?
Solution: (data from Table 2-1)
2
d = dt1.2 = 120 (20)1. = 120 (36 .41) = 4370 R/hr.
1
2-10
TABLE 2-1
VALUES FOR DOSE AND DOSE RATE FORMULAS
~ (hrs.) tl. 2 t-0.2 t (hrs) tl. 2 t-0. 2
0.1 0.063 1. 586 25 47.59 0.525
0.2 0.145 1. 381 26 49.89 0.521
0.3 0.236 1. 273 27 52.20 0.518
0.4 0.333 1. 202 28 54.52 0.514
0.5 0.435 1.149 29 56.87 0.510
0.6 0. 542 1. 110 30 59.23 0.505
0.7 0.652 1. 074 32 64.00 0.500
0.8 0.765 1.046 34 68.83 0. 494
0.9 0.881 1. 023 36 73.72 0.488
1.0 1.000 1.000 38 78.66 0.483
1.5 1. 627 0. 921 40 83.67 0.478
2.0 2.300 0.871 42 88.70 0.474
2.5 3.003 0.826 44 93.79 0. 470
3.0 3.737 0.803 46 98.93 0.465
4.0 5. 278 0. 756 48 104.1 0.461
5.0 6.899 0. 725 50 109.3 0.457
6.0 8.586 0.697 55 122.6 0.449
7.0 10.33 0.679 60 136.1 0.441
8.0 12. 13 0.660 65 149.8 0.434
I 9. a10.0 13.96 15.85 0.644 0.631 70 75 163.7 177.8 0.427 0.422
11. 0 17. 77 0.619 80 192.2 0.417
12.0 19.73 0.608 85 206.7 0. 412
13.0 21. 71 0.599 90 226.5 0.407
14.0 23.74 0. 590 95 236.2 0;402
15.0 25.78 0.582 100 251. 2 0.399
16.0 27.86 0. 574 120 312.6 0.384
17.0 29.28 0. 567 140 376.2 0. 372
18.0 32.09 0.560 160 442.5 0.362
19.0 34.23 0.555 180 508.·5 0.354
20.0 36.41 0.550 200 577.1 0.347
21.0 38.61 0.544 250 754.3 0.333
22.0 40.82 0. 539 300 938.7 0.319
23.0 43.06 0.534 336 1075. 0.313
24.0 45.3~ 0.530 720 .2683. 0.268
2-11
2 0 2
D = 5d (t~0· -t; · ) = (5)(4370)(0.407-0.402) = 109 R.
1
3. It has been determined that the H + 1 reference dose rate in an area is 1000 R/hr. If a rescue team enters the area 2 days after the detonation, how long may it remain if the accumulated dose is not to exceed 60R?
Solution: (data from Table 2-1)
0 2 2 0 2
D = 60R =~d1 ( t ~· -t;o· ) = 5ooo ( .461 -t ; · )
0 2
5ooo (t;· ) = 2305 -60 = 2245
-0.2
tf = .449; tf = 55 hrs.
stay-time = 55-48 = 7 hrs.
2-8 Biological Effects of Gamma Radiation
2-8. 1 General
Exposure to ionizing radiation, such as alpha and beta particles and gamma rays, has long been known to present a hazard to living organisms. As the result of ionization, some of the constituents, essential to the normal functioning of cells, may be altered or destroyed. Products formed may act as poisons. The action of ionization may result in breaking of the chromosones, increasing the permeability of cell membranes, destruction of cells, and inhibition of mitosis, the process of cell division necessary for. normal cell replacement in living organisms. Such cell changes may seriously alter body functions when enough cefls are affected to reduce the total function of the organs made up of such cells.
2-8.2 Acute vs. Chronic Doses
Because of the difference in biological effect, it is necessary to distinguish between an acute (short-term) exposure and a chronic (extended) exposure. It is not possible to precisely differentiate between the two but an acute dose may b_e taken for purposes of injury evaluation, as one incurred over a period of from 2 to 4 days. Although radiation from fallout persists over a long time, it is during the first few days that the dose rate is relatively high and the possible exposure more intense.
2-12
The distinction between acute and chronic doses is important because of the fact that, for doses not too large, the body can achieve partial recovery from some of the radiation injury while it is still exposed. Thus, a larger total radiation dose would be required to produce a given degree of injury, if the dose is spread over a long period of time, than would be required were the dose received in a very short period.
2-8.3 Pathology of Radiation Injury
Radiation damage results from changes induced in individual cells. Cells of different types and organs have different degrees of sensitivity to radiation. Such sensitivity decreases in the following order: lymphoid tissue and bone marrow; testes and ovaries; skin and hair; blood vessels; smooth muscle; and nerve cells. The list of items included in the above order are by no means complete.
When I iving tissue is exposed to radiation, lymph'oid cells are destroyed and disintegrate; and, lymph glands waste away with a resultant impairment of the production of lymphocytes, necessary to the function of the gland. A rapid disappearance of lymphocytes implies certain death if such disappearance is almost complete. A study of radiation casualties in Japan showed, commonly, the wasting away of lymph nodes, tonsils, appendices and spleens.
Except for lymphocytes, all other formed blood cells arise from the bone marrow. Under normal circumstances, these cells leave the marrow and enter the blood stream v-.here they remain until they are naturally destroyed or are ki lied in defense of infection. Bone marrow shows remarkable changes when irradiated. There is an immediate temporary cessation of cell division and the marrow becomes depleted of adult forms of cells and, barring regeneration, progressively wastes away. Such extreme atrophy (wasting away) of the bone marrow was common among those dying of radiation injury in Japan.
Morphologic changes in the human reproductive organs, compatible with steri Iity, are thought to occur with acute doses of from 450 to 600 roentgens. (Acute doses of such a quantity could result in death.) Temporary sterility was found among surviving men and women in Japan, but many have since produced normal children. The testes are apparently quite radiosensitive. Changes in the ovaries are less striking. Some Japanese women suffered menstrual irregularities, miscarriages and premature births. There was an apparent increase in the death rate of pregnant women.
Epilation, the loss of hair, was common among Japanese victims. In severely exposed but surviving cases, hair began to return after a few months.
2-13
•
Eyebrows, eyelashes and beards apparently were more resistant than hair on other parts of the body.
Ulcerations of intestinal linings were noted in Japanese victims. Acidsecreting cells of the stomach are lost. Mitosis stops in the intestinal glands. Bacterial invasions occur and ulcers may become fecally contaminated. Since white blood cells are simultaneously depleted and infection cannot be combated, such intestinal ulcerations become points of entry for bacteria that may kill the victim.
Hemorrhage is common after radiation exposure. This results from the depletion of blood platelets necessary for clotting. Often such hemorrhages are so widespread that severe anemia and death are the result.
The loss of protective coverings of tissues, white blood cells, and antibodies lowers the resistance of the body to bacterial and viral infections, and a patient may die of infection even from bacteria that are normally harmless. Thus, casualties may result not only directly from radiation affects but also indirectly because of the effect of radiation in impairing the normal I ife sustaining functions of the body organs.
2-8.4 Natural Radiation Doses
The human body is continually exposed to nuclear radiation from various sources. These are chronic exposures spread over the I ifetime of the individual. Certain naturally occurring radioactive substances are present in all soil and rock. Cosmic rays, originating in space, contribute to the total dose of background radiation naturally received. During an average lifetime, every human being absorbs a total dose of about 10 roentgens from natural sources.
In addition to radiation from natural sources, the human body may be exposed to further dosages from chest and dental x-rays, luminous wrist watch dials, viewing of television, etc. People engaged in occupations involving peaceful, as well as military, applications of nuclear energy are exposed to doses over and above those experienced by others. Such exposures are very carefully controlled by appropriate safeguard regulations and result in no appreciable risk to the individuals involved. Exposures from the delayed
fallout from weapons testing has added to the total exposure normally received,
but the amount received from this source has, to date, been very minute compared
even to natural background radiation.
Even though the chronic dosages from the sources enumerated above are
small in magnitude, it is nevertheless, probably true that radiation, even at a
2-14
•
low dose level, may have indeterminable long range deleterious effects, and,
aggravated exposure, even though it may not be of immediate consequence,
could be harmful.
2-8.5 Clincial Features of Acute Radiation Injury
All that is known quantitatively about the immediate effects of various radiations on humans comes from analysis of experience with radiation therapy of patients, from studies of accidental radiation exposures, and from the study of Japanese exposed to atomic bomb radiation.
Classification of Radiation Injury
The following is a description of some effects that could be expected as a result of an acute whole-body exposure from fallout radiation, i.e., that received over a period of up to two to four days.
Asymptomatic Radiation Injury
This class of injury, not apparent to the victim and undetectable by the physician, occurs after brief exposure of less than 50R. The effects of an exposure of less than 50R on blood cells can be detected only in retrospect by statistical analysis of the blood cell counts or chromosomes of cells obtained from a large group of exposed people. Clinically, some normal persons irradiated in this dose range will show mils signs and symptoms of gastrointestinal distress, such as loss of appetite and nausea, easily confused with the effects of anxiety and fear.
Acute Radiation Syndrome
This class of radiation injury may be caused by radiation of the whole body or major portions of the torso or head. Clinical manifestations of the acute radiation syndrome include general 11 toxic 11 symptoms,. such as weakness, nausea,
vomiting, and easy fatigue, and specific symptoms and signs caused by damage to the gastrointestinal tract, the blood-forming organs and the central nervous system. The signs of systemic radiation damage include loss of hair (epilation)
and a tendency to bleed easily.
Five clinical levels of severity of acute radiation effects are distinguished and correlated with the size of the exposure:
Level I: Whole-body exposures in the range of 50-200R. Less than half the persons exposed experience nausea and vomit within 24 hours. There are either no subsequent symptoms or, at most, only increased fatigability. [Fewer than 5 percent (1 out of 20) require medical care for their gastric distress.]
2-15
All can perform tasks, even when sick. Any deaths that occur subsequently are due to complications such as intercurrent infections, debilitating diseases, and traumatic injuries such as those from blast and thermal burns.
•
Leve I II: Whole-body exposures in the range of 200-450R • More than ha If
of this group experience nausea and vomit soon after the onset of exposure and are ill for a few days. This acute illness if followed by a period of 1-3 weeks when there are few if any symptoms. At the end of this latent period, epilation (loss of hair) is seen in more than half; a moderately severe illness develops, due primarily to infection often characterized by sore throat and to loss of defensive white blood cells resulting from damage to the blood-forming organs. Most of the people in this group require medica I care. More than ha If will survive without therapy, and the chances of survival are better for those who received the smaller doses and improved for those receiving medical care.
Level Ill: Whole-body exposures in excess of 450R (450R to 900R). This is a more serious degree of the ill ness described for Leve I II. The initio I period of acute gastric distress is more severe and prolonged. The latent period is shortened to one or two weeks. The main episode of illness is characterized by extensive oraI1 pharyngea I, and derma I hemorrhages. Infect ions such as sore throat, pneumonia and enteritis, are commonplace. People in this group need intensive medical care and hospitalization to survive. Fewer than half will survive in spite of the best care, with the chances of survival being poorest for those who received the largest exposures.
Level IV: Whole-body exposures in excess of 600R (600R to l,OOOR). ·This is an accelerated version of the illness described for Level Ill. All in this group begin to vomit soon after the onset of exposure. Without medication this gastric distress can continue for several days or until death. Damage to the gastrointestinal tract is the predominant lesion. 1t is manifested by intense cramps and an intract~ able diarrhea, which usually becomes bloody. Death can occur anytime during the second week without the appearance of hemorrhage or epilation. All persons in this group require care for or relief of the gastrointestinal symptoms, but it is unlikely even with extensive medical care that many can survive. During a protracted exposure to this amount of gamma radiation, it is unlikely that this type of gastrointestinal distress would be the first evidence of injury. What I ittle clinical evidence exists indicates that any clinical problems resulting from this exposure at a low rate would be related to failure of the bone marrow.
Level V: Whole-body exposures in excess of several thousand R. This level is an extremely severe illness in which hypotensive shock secondary to vascular damage predominates. Symptoms and signs of rapidly progressing shock come on almost as soon as the dose has been received. Death occurs within a few days.
2-16
2-8.6 Recovery From Radiation Effects
If, over a period of a few days, a person is exposed to a dose of less than about 200 roentgens, he should not become incapacitated nor should his ability to work be seriously affected. If the dose exceeds about 200 roentgens, persons so exposed will suffer increasing radiation sickness with increasing dosage and the probabiIi ty of death is extremely high if the dose absorbed exceeds 600 roentgens.
The human body has the capability of repairing a major portion of radiation
injury, except in cases where the dose is so great that death occurs within a
period of up to several weeks. On this account, individuals can survive large
amounts of radiation if the exposure is spread over a period of time long enough
to allow the recuperative processes to take place.
In determining the probable biological effect of exposure to radiation, it may be assumed that about 10% of the exposure causes irreparable damage or is, in a sense, irrecoverable. About one-half of the remainder can be assumed to be recoverable in about a month and the other ha If after about three additional months. The equivalent residual dose (ERO) at any time is then equal to 10% of the accumulated dose plus the balance of the accumulated dose that has not yet been recovered or repaired.
If it is assumed that the recovery begins about four days after the onset of exposure and that repairoccursat the rate of 2.5% of the recoverable portion per day, the ERO can be expressed mathematically as follows:
t-4
ERO = 0.10 + 0.90(0.975)
In the above expression, 0 is a single day dose and t is the number of days from the onset of exposure to the time at which the ERO is to be computed. Table 2-2 gives powers of 0.975 as an aid in the solution of the above equation.
As an example of the use of the above expression, let it be assumed that a group of civil defense workers have been exposed to doses of 40, 25, and 15 roentgens each on three consecutive days. About 15 days after the first exposure this group is needed to carry out another emergency mission in a fallout area. What additional dose can the group tolerate on mission if their total ERO is not to exceed 100 roentgens?
2-17
Solution: (data from Table 2-2)
ERD = O.lD + 0.9D(O.975)t-4
ERD(l) = 0.1(40) + 0.9(40) (0.975)11 = 4.0 + 27.4 = 31.4 10
ERD(2) = 0. 1(25) + 0.9(25) (0.975) = 2.5 + 17.6 20.1 9
ERD(3) = 0.1(15) + 0.9(15) (0.975)= 1.5 + 10.8 = 12.3
The total ERD at the beginning of the mission is thus about 64 roentgens and the team can be exposed to an additional 36 roentgens on the mission. It is noted that, of the 80 roentgen dose accumulated prior to the mission, 8 roentgens are irrecoverable and, of the remaining 72 roentgens, about 16 roentgens have been recovered prior to the mission.
2-8.7 Late Effects
Some consequences of exposure to relatively large doses of nuclear radiation
may not become apparent except after severo I years from exposure. These effects might include some malformations in the offspring of those exposed, the formation of cataracts, shortening of the life span, leukemia and other forms of malignancy
and the retarded development of children in the uterus at the time of exposure. Although many theories have been advanced for the causes of these late effects, the entire matter is largely in the realm of the unknown.
2-18
TABLE 2-2
POWERS OF 0.975
Power Value Power Value Power Value
1 o. 98 15 o. 68 38 0.38
2 0.95 16 0.67 40 0.36 3 o. 93 17 0.65 45 0.32 4 o. 90 18 0.63 50 0.28
5 0.88 19 o. 62 55 0.25
6 0.86 20 0.60 60 0.22
7 0.84 22 0.57 65 0.19 8 o. 82 24 0.54 70 0.17
•
9 0.80 26 o. 52 80 0.13 10 o. 78 28 0.49 90 0.10
11 0. 76 30 o. 47 100 0.08
12 0.74 32 0.44 110 0.06
13 o. 72 34 o. 42 120 0.05 14 o. 70 36 0.40
2-19
208-401 0-76-4
2-9 Study Questions and Problems
1. In the fission process, what is the predominant feature of the fission fragments that are formed?
•
2.
How is radioactivity, associated with fission fragments, usually mani
fested?
3.
What is meant by 11 decay product 11 ?
4.
Apart from beta particles and gamma rays, what other forms of radioactivity are associated with nuclear explosions, and what are their sources?
5.
What is an alpha particle?
6.
Why are alpha particles not a consideration in shielding?
7.
What is the major danger associated with alpha particles?
8.
What is the difference between a beta particle and an electron?
9.
What is the major hazard associated with beta particles, and why are
they not a consideration in shielding?
10.
Of what do gamma rays consist?
11.
Compare gamma rays to X-rays.
12.
What is the importance of gamma radiation in shielding considerations?
13.
Why are neutrons not a consideration in fallout shelters?
14.
Distinguish between initial and residual radiation.
15.
What is the significance of the one-minute time as the dividing line between initial and residual radiation?
16.
Under what conditions of analysis and design is initial radiation important?
17.
Why is initial radiation not normally considered in fallout shelters?
18.
From what does the primary hazard from residual radiations stem?
2-20 •
19.
Tell how fallout is formed.
20.
Describe nuclear fallout.
21.
How much fission product (approximately) is formed for each kiloton of fission yield?
22.
Since fusion reactions do not produce radioactive fragments, why is there a fallout problem associated with such weapons? ·
23.
Distinguish between early and delayed fallout.
24.
What are the considerations that minimize the hazard associated with delayed fallout?
25.
Describe the manner in which early fallout is distributed and the factors that influence its distribution.
26.
Why is it impossible to accurately predict the deposition of fallout?
27.
Many uninformed people consider that fallout causes the air, even in a shelter, to be unfit to breath. Comment on this.
28.
On an areawide basis, comment on the relative hazards from thermal, blast and radiation effects.
29.
What is the significance of the roentgen as a unit ofmeasure in the radiation hazard? (Note: the instructor may wish to introduce other units of measure used for the same purpose • )
30.
Define dose rate •
31.
What is meant by the term 11 reference dose rate 11 ?
32.
Distinguish between dose and dose rate.
33.
What initial dose rates may be expected in areas of heavy, medium, and I ight fallout deposition?
34.
What is meant by half-life of a radioactive isotope?
35.
Explain the Seven-Ten Rule for describing the approximate rate of decay of fallout radiation.
•
2-21
36.
In terms of initial dose rate, what is the approximate accumulated dose to infinite time?
37.
At a point some distance from an explosion, fallout begins to arrive at H + 6 hours and continues to fall for 10 hours. After it has ceased to fall, an observation indicates a dose rate of 25R/hr. What will the dose ratebe at this location at H + 4 days?
38.
Forty-eight hours after a detonation, the observed dose rate is 80R/hr. A rescue team is sent on a mission 4 days after detonation and remains for 8 hours. What total dose will the team accumulate during the 8-hour mission!
39.
It has been determined that the H + 1 hour reference dose rate in an area is 500R/hr. A rescue team enters the area 4 days after detonation. How long
may it remain in the area if the accumulated dose over the stay time is not to exceed 40R?
40.
The reference dose rate in a disaster area is 1000R/hr and in an emergency
operating center in the area it is 10R/hr. A rescue team has spent 48 hours in the shelter and is to be sent on a mission in the area. How long can it remain if the total accumulated dose, including that accumulated in the shelter, is not to exceed 20R?
41.
What effect does ionizing radiation have on I iving organisms?
42.
Distinguish between the biological effects from acute and chronic doses of radiation.
43.
Briefly discuss the pathology of radiation injury.
44.
What effects may be expected as the result of whole body exposure to acute doses of 50R? 150R? 250R? 450R? BOOR? 5000R?
45.
What is meant by the term 11 equivalent residual dose 11 ?
46.
Why can the human body survive large amounts of radiation if such doses are spread over a long period of time?
47.
A civil defense rescue team has been exposed to doses of 30, 20, 10 and 15 roentgens each on four consecutive days. About twelve days after the first exposure, this group is needed on another emergency mission in a fallout area. What additional dose can be tolerated ifthe total ERD is not to exceed 100R?
2-22
48. Comment on the myth that radiation sickness is communicable.
49. What precautions should be observed with regard to the intake of food and
water that has been subjected to nuclear fallout?
2-23
CHAPTER Ill
BASIC CONCEPTS IN FALLOUT RADIATION SHIELDING
3-1 Introduction
The radioactivity associated with the fission products included in the early fallout from a nuclear surface burst manifests itself in the form of alpha and beta particles and gamma rays. Alpha and beta particles, although biologically dangerous if ingested or inhaled, or if they impinge upon exposed portions of the body, are almost completely attenuated by relatively light weight shields such as clothing. As a consequence, alpha and beta particles are not considered in fallout shielding problems. Gamma radiation, on the other hand, is not readily attenuat~d cind is biologically destructive. It
constitutes the sole consideration involved in shielding problems associated with fallout shelters.
Exposure to large acute doses of gamma radiation can result in serious illness or death to humans. The level of radiation that could be absorbed by unprotected individuals in areas of relatively light fallout contamination could also be lethal. It is the purpose of fallout shelters to minimize, to the extent practical, the biologically hazardous effects of gamma radiation from nuclear fallout. Fallout shelter analysis involves the calculation of the degree of radiation protection afforded by a she Iter to its occupants. To make the fallout shielding methodology and calculations more meaningful, certain basic concepts of radiation shielding are discussed in simplified terms. A clear understanding of these basic concepts is essential to a fallout shelter analyst.
The shielding procedure described in this text is officially designated as the "DCPA Standard Method for Fallout Gamma Radiation Shielding Analysis," and throughout the text is simply designated as the "Standard Method."
Basic data and primary calculations underlying the Standard Method were developed by L. V. Spencer and published in Structure Shielding Against Fallout Radiation From Nuclear Weapons, NBS Monograph 42, June 1962 (U.S. Government Printing Office, Washington, D.C.). The standard method was developed, from the work of Spencer, by Charles Eisenhauer of the National Bureau of Standards and Neal FitzSimons of the Defense Civil Preparedness Agency and was first published as Design
3-1
and Review of Structures for Protection from Fallout Gamma Radiation. An Engineering Method for Calculating Protection Afforded by Structures Against Fallout Radiation, NBS Monograph 76, July 2, 1964 (U.S. Government Printing Office, Washington, D.C.) by Charles Eisenhauer
•
discusses the assumptions and the reasoning by which the calculations
were derived from the basic data of NBS Monograph 42. Although the work of others has resulted in continuing refinement to the Standard Method, these three references serve as the basic foundation for this text, and occasional reference will be made to the material of this and following chapters.
3-2 Radiation Emergent From a Barrier
In Figure 3-1, a point source of radiation emits gamma radiation in all directions. Gamma radiation consists of continuous streams of photons, packets of energy without mass, that travel in straight lines from their source, the nuclei of radioactive isotopes, until they interact with electrons of obstructing atoms.
Any one of several things might happen to a photon that is incident upon a barrier, as illustrated in Figure 3-1. It may pass through the barrier without an interaction taking place, in which case it is termed direct radiation. It may interact with an orbital electron of an atom in the barrier and lose all of its energy to that electron through photoelectric absorption, in which case it is termed absorbed radiation. As a third case, a photon may interact with
•
an orbital electron without losing all of its energy, and a new photon with lower energy will depart in a different direction. This is the Compton Scattering. The departing photon is termed scattered radiation. Scattering can take place in the air or in the barrier as indicated in the figure. As the result of a scattering interaction, the new photon may emerge from the same face of the barrier upon which the original photon was incident. This is termed backscattered radiation.
There is a correlation between the energy loss and the angle of deflection that accompanies a scattering interaction. Gamma radiation that has undergone large changes in direction is apt to be much lower in energy than unscattered gamma rays. This is particularly true when the direction change is the result of several interactions. As energy is lost with each successive scattering, the chance of absorption becomes increasingly greater, since
photoelectric absorption is more prevalent at lower gamma ray energy levels.
3-2
• BARRIER ·:·:·:·:·:·:·:·:·:·:·:·:·:·:·: air-s catt e r
,.... ------.........................~:~ --------
I
I
I
I
GAMMA EMITTER \ f 1 I 1 J , ..... ... - -
' ... ' I I,, ,, / ~ / r __..,........ .... ----- direct
::::.~..--__:--,., ........~......."--
.... //,,, ............... --__ ~/~1 I \ ','' -.... __
~ \ '
back-scatter
FIGURE 3-1 RADIATION EMERGENT FROM A BARRIER
3-3 Barrier Effectiveness vs. Photon Energy
Photons having high energy have a higher probability of penetrating a barrier than those having lesser energy. Therefore, a given barrier will be more effective against radiation of low energy than it will be against that of higher
energy.
It has been pointed out that there are many different ways in which the nucleus of fissioned material may be split. Consequently many different fission fragments are possible, most of which are radioactive and undergo decay as a function of time. On the average, two to three decays are required in order for a radioactive fragment to reach a stable state. At any one time, something over two hundred different radioactive products may exist in the fission products from a nuclear explosion. These have half-1 ives ranging from fractions of a second to millions of years, and emit gamma radiation with energies primarily in the 0.2 to 3.0 million electron volts (MeV) range.
3-3
Figure 3-2 shows the distribution of gamma radiation energy from the fission products of a nuclear explosion for severo I different times after fission. The height of each bar is proportional to the fraction of energy content of gamma rays in the energy interval. It is noted that at about one hour after
•
fissioning the gamma rays have energies ranging between 0.5 and 2.5 MeV.
After about a day, most of the energy comes from photons with energies be low about 1 . 0 MeV. After about 10 days the higher energies become dominant. Note that the sum of the ordinates for each case adds to unity, so that the ordinates merely indicate the fraction of the total energy. The actual total energy will be decaying with time.
Since the effectiveness of a barrier depends on the gamma energy level, it is expedient to choose a single spectrum to serve as a basis for all spectra dependent data used in the development of a method for analysis. Primary data used in the development of the "Standard Method" were derived from consideration of the spectrum that exists 1. 12 hours after fissioning. This choice resulted from consideration that; this spectrum is fairly representative of other early times in terms of penetrating power, and that the greatest part of exposure to the radiation from nuclear fallout is apt to occur during the first few hours. The assumption of the 1.12 hour spectrum is on the conservative side and .is not sufficiently great to warrant complications in the procedure through admission of data based on a time dependent energy distribution.
3-4 Mass Thickness
In addition to its dependence on photon energy, barrier effectiveness depends, among other things, on the type of barrier material {chemical composition) and the total mass involved. As indicated previously, barrier effectiveness depends on interactions between photons and orb ita I electrons. Because nearly all important construction materials have relatively low atomic numbers, attenuation in those materials is due primarily to scattering interactions which are independent of the energy state occupied by the electrons in the barrier material. Attenuation produced by a barrier is, thus, almost completely dependent on how many electrons are put in the path of the gamma rays. This is simply the product of the number of electrons per unit volume and the thickness of the barrier.
Recalling the~( ) notation for atomic structure (Appendix A), Z is the
number of protons in the nucleus. In a neutra I atom there is one electron for each proton, thus Z is also the number of electrons. In this notation A is the number of protons plus neutrons in the nucleus and since almost all of the mass
3-4
----,-------------
----~---
11. 12 HOURS I
o.z---------------
-· :--------+---r-----· ~---~--~------------~----------:-----___:_ ___ i___ _
.0.4~----
~
:>< '
~ 0.3;-------.
--123.8 HOURS 1--;--
~
z
~ ~ 0.2;--------..
c::t:' '
~
E-4 0.1 ' ------:-------------;,__ __
~
~
H
E-4
u
<!l L ' , ,
ll:: 0.4r-----i-------;
~I l . • [ I
r'----------~
'
0.3\---------------1 9. 82 DAYS
~ . '
0.1 ;-------------------------"------- -~---;··-----:
0.1 2 5 7 1.0 2 3
ENERGY OF GAMMA RADIATION (MeV)
FIGURE 3-2
GAMMA ENERGY SPECTRUM AT DIFFERENT TIMES AFTER FISSION
3-5
(weight) of an atom is due to its protons and neutrons, A is closely related to the mass of the atom. The ratio Z/A is thus a measure of the number of electrons per unit weight. The number of electrons per unit volume is obtained by multiplying Z/A by the weight density (weight per unit volume) of the barrier.
The symbol X is defined as a parameter by which the effectiveness of a barrier can be measured. X is proportional to barrier thickness, t, barrier density, p, and the ratio of atomic charge to atomic mass, Z/A, a II averaged over the constituent elements of the barriers.
X a: (Z/A)pt.
But since Z/A is nearly 0.5 for practically all important construction materials, the parameter X is simply the product of density times thickness or, for all practical purposes in structure shielding, simply the weight per unit of area of barrier. This is termed mass thickness.
To determine the mass thickness of a barrier, one has merely to determine its weight per unit of area, generally pounds per square foot (psf). If the barrier is composed of more than one materia I, its mass thickness is the sum of the weights per unit of area of all constituents of the barrier.
Examples:
a. What is the mass thickness of an 8-inch thick (standard weight)
concrete slab? The d~nsity of standard weight concrete can
be taken as 150 lbs/ft •
8 2
MASS THICKNESS: X =12 150 = 100 lbs/ft (psf)
b. What is the mass thickness of 18 inches of soil which has a
density of 100 lbs/ft3?
18
MASS THICKNESS: X = T2 100 = 150 psf
A table of mass thicknesses of common construction materials is given in Appendix B.
3-6
3-5 The Standard
The protection furnished by a building is evaluated by comparing the amount of radiation received at some location within the building to that which would have been received in a completely unprotected location. To give meaning to such comparisons, it is desirable to assume some reference standard location against which protection furnished at other locations is compared. This is analogous to the situation-that exists in differential leveling where the elevations of all points are referred to mean sea level.
The standard unprotected reference position used by Spencer in generation of primary data is a detector located three feet above a smooth plane infinite in extent. Fallout particles having the average energy of the mixed fission product at 1.12 hours after weapon detonation are uniformly distributed on this plane. The plane (and detector) are embedded in an infinite homogeneous medium consisting of dry air at 76 em Hg pressure and 20 degrees centigrade temperature (standard laboratory air). In essence, the reference configuration is an infinite plane source in an infinite homogeneous medium.
Several reasons prompted this choice of the standard. The location of the detector 3 feet above the plane considers an average point at about mid-body height and/or a radiation detecting instrument carried at about that height in monitoring operations. Also for the reference conditions, the standard reference dose rate can be calculated accurately to within 2 or 3 percent.
Figure 3-3 depicts the standard unprotected location. The detector responds to photons arriving from any and all spherical directions. The photons received at the detector come directly from point sources on the plan (direct radiation) or as air-scattered radiation from points in the air.
It should be noted that, from below its plane, the detector is exposed to both direct and air-scattered radiation. From above its plane, it is exposed only to air-scattered radiation. Air-scattered radiation arriving at the detector from above its plane is termed skysh ine radiation. An analogy can be drawn between it and the glare that exists over a lighted city at night. As will be seen later, of the total amount of radiation reaching the standard detector from below its plane, the direct component is overwhelmingly dominant. It thus becomes convenient to discuss the radiation from below simply as direct radiation and that from above as skyshine radiation. In this context it should always be recalled that direct radiation includes an air-scattered component.
3-7
I I I I I
I
\
I
\ ' ' '
I
'
Smooth, infinite, uniformly contaminated plane
FIGURE 3-3 STANDARD UNPROTECTED LOCATION
3-6 Standard Detector Response Evaluated Qualitatively
Figure 3-4 considers a coli imated detector located at the standard unprotected location, and pivoted so that it may be revolved in a vertical plane about its horizontal axis. When this collimated detector is pointed in a particular direction defined by the angle 8 (theta), measured from the vertical axis, it will respond to the gamma photons that approach and reach the detector from that direction. It should be obvious that, since the standard radiation field has azimuthal symmetry, it is immaterial in which ,azimuthal direction the detector points, the important angular quantity is the polar angle 8 . If the incremental exposure dose rate is determined for a given value of 8 covering a .small increment of azimuthal angle, the total exposure dose rate for that polar angle is obtainable simply through a multiplication of the incremental exposure dose rate by the sum (integral) of bll increments of azimuthal angle in the 360 degrees of azimuth about the vertical axis. The qual itiative dose rate angular distribution, i.e., the detector response as it points in different directions, is plotted in Figure 3-4.
3-8
~ 10.0
1-1
E-4
p
Ill
1-1
~
E-4
CZl
1-1
Q
~
< 1. 0 1-----------t--~-------1 ...:I
5
z
<
~
E-4
<
~
~
CZl
0 0.1~----~~--~--------~
Q
> ~
1-1
E-4 SKYSHINE
<
E-4 RADIATION
1-1
...:I
<
§
DIRECT RADIATION
0.01~--------~----------
o0
e = 1so0 e = 90° e =
FIGURE 3-4
QUALITATIVE DOSE RATE ANGULAR DISTRIBUTION (UNPROTECTED DETECTOR)
3-9
Figure 3-5 serves as a simplified basis for certain characteristics of the curve that are of fundamental interest. In the figure, the field of view of the source plane is a minimum number of sources, as the detector is pointed straight down. As it is rotated from the downward position (0=0°), to values of 8 up to 90°, the field of view at the detector, projected onto the source plane, becomes increasingly greater. Obviously, these increases are proportional to the secant 8 . For these increasing angles of rotation, there is indicated a possibility of response to at least direct radiation from an increasing number of sources. For 8 just below 90°, the field of view would occupy an infinite area on the source plane. In the absence of some blunting effect, it might be assumed that the response in this limiting direction just below the horizon would be infinite. This would indeed be the case were the surrounding medium
a complete void. Since the medium is air, a lessening of response will occur as photons started in the direction of the detector are either absorbed or diverted through scattering interactions. The response thus peaks at some finite value when8 =90° as indicated in Figure 3-4. Radiation reaching the detector from
detector plane
3 I
*
FIGURE 3-5 COLLIMATED DETECTOR -SECANT EFFECT
3-10
below the horizon (8 between 0° and 90°) is labeled "Direct Radiation 11 in Figure 3-4 (although this includes an insignificant air scatter component).
When the detector is pointed above the horizon, it will respond solely to air-scattered photons. Air-scattered radiation which reaches the detector from above its plane is referred to as skyshine and the left-hand portion of the qualitiative plot in Figure 3-4 is so designated. The shape of the curve in Figure 3-4 is based on the standard height of 3 feet.· Different shapes would be obtained for higher detector locations.
The curve represents detector response to radiation from particular polar directions. The sum of such responses over all polar angles represents the total amount of radiation received at the standard unprotected location. Thus the area under the curve gives the total dose (or dose rate) received at the standard unprotected location. The area to the right of6 = 90° would be the response from direct radiation from below the detector plane, and the area to the left would yield the response to skyshine from above. Recognizing that the ordinates of the qualitiative response are logarithmic, it is seen that direct radiation represents about 90% of the total dose, and skyshine represents the remaining 10%.
3-7 Protected Detector Response Evaluated Qualitatively
Figure 3-6 shows a coli imated detector mounted at the standard 3-foot height in a building. The protection afforded by the building is the essential difference between Figures 3-6 and 3-4.
The building is assumed to be cylindrical and is azimuthally symmetrical. It consists of a roof and walls of some mass. The wall contains a continuous aperture. The detector of Figure 3-6 as in Figure 3-4 is rotated through successive increments of polar angle 9, and values of dose rate angular distribution are plotted against values of a. In the qualitative plot, detector responses are superimposed on those that would accrue to the standard detector of Figure 3-4. The dashed curve segments are a reproduction of corresponding parts of the plot in Figure 3-4. The solid curve segments represent qualitative responses at the protected detector.
As the detector is pointed vertically down,it responds to no radiation since the area within the structure is clear of fallout particles. Sources which normally would have occupied this area now occupy the equivalent area of the roof. Air-scattering within the structure is assumed to be negligible.
3-11
206-401 0 -76 -5
a
e = e = oo
FIGURE 3-6
QUALITATIVE DOSE RATE ANGULAR DISTRIBUTION (PROTECTED DETECTOR)
3-12
•
No radiation will be detected until ais such that the coli imated line of the detector intercepts the first source on the plane immediately outside the wall. The area marked "a" in the figure represents the lack of response due to the cleared area within the structure.
When the first source outside the wall is intercepted, the detector will respond. In the absence of mass in the wall, the response at this point would be exactly the same as the unprotected case. However due to attenuation in the wall the response will be less and will remain less through all angles of rotation up to that point where the I ine of sight of the detector intercepts the aperture. The area marked "b" in the figure represents the loss in response {compared to the standard) as the result of the effectiveness of the wall barrier. The vertically shaded area below indicates the response that has not been lost by virtue of the barrier. It includes direct radiation and radiation that has been scattered from points in the wa II.
As the aperture is first intercepted in the process of rotation, the detector will respond in exactly the same as the unprotected detector while the detector is pointing through the window.
Through that next increment of rotation involving the limits of the upper wall segment, the qualitative response of the detector will be as discussed above for the lower wall portion. The area marked "c" represents the loss resulting from the effectiveness of the wall as a barrier. This response is due to skyshine and wall-scatter radiation.
As the detector is rotated further, its line of sight will intercept the roof surface and it will respond to radiation of several origins. These include; direct radiation from sources on the roof, skyshine from above, scatter radiation from points within the roof barrier, and ceiling shine. Ceiling shine consists simply of backscatter radiation from the ceiling to the detector as the result of direct radiation from ground sources passing through the aperture and impinging on the ceiling. In the case of the unprotected detector, the response was only to skyshine. The response in the protected case for angles of rotation intercepting the roof can be greater or lesser than the unprotected response. This depends on how effective the roof barrier is in attenuating the radiation. In the plot it has been assumed that the response is greater. It is significant to note that the loss represented by area "a" in the figure has now been at least partially recovered ..
The qualitative plot of Figure 3-6 helps to explain the meaning of the "Protection Factor," PF. If the plot were to a linear scale, the area under the curve for the protected detector would give a relative indication of the total radiation received. The ratio of this area to the area under the curve
3-13
for the standard unprotected location yields a decimal fraction termed a
11 Reduction Factor, 11 RF. It indicates how effective various features of the shelter are in reducing radiation reaching the protected detector as compared
to the standard. A reduction factor of 0.01 would indicate, for example,
that the protected location receives only 1% of the radiation that would be
received at the standard unprotected location A.
The•'Protection Factor, 11 PF is simply the reciprocal of the reduction factor. A PF of 100, corresponding to an RF of 0.01, indicates a protected location 100 times better than the standard unprotected location in terms of exposure.
3-8 Protection Factor
It has been shown that a protection factor indicates the degree of protection furnished by a building at a specific point location within as compared to the standard unprotected location. In article 3-5 the standard detector and its location were defined. It is significant that the standard as defined does not consider the intensity of radiation associated with the uniformly contaminated field. Therefore the protection factor does not give a direct indication of the fallout radiation hazard. Such hazard is a function of the degree of contamination as well as the protection factor. It follows that a protection factor provides merely a means for comparison of structure against structure. An estimate can be made of the degree of contamination that might be expected in a given area, a design protection factor can be selected that will give reasonable assurance trot a certain biological hazard will not occur. .
3-9 The Essence of Shelter Analysis
Referring to Figure 3-6, the total area under the shaded curve can be considered as a reduction factor expressed as a decimal fraction. The total area under the response curve in the figure has been divided into several subareas. These sub-areas represent portions of the reduction factor corresponding to contributions to the detector of radiation emerging through the solid parts of the walls, through the apertures, and through the roof. In the application of the standard method, one makes separate calculations for contributions through walls, apertures and roofs. The sum of these contributions yields the total reduction factor, the reciprocal of which is the protection factor.
3-14
In Figure 3-6 the difference between the protected response and the unprotected response for any of the sub-areas is due to barrier effects and geometry effects. The height to the curve is almost purely a function of the effectiveness of the barrier in attenuating the radiation. The greater this effect, the lower the response values. The width of any sub-area is purely a function of the total angle of rotation involved and is consequently a geometry effect controlled by the physical dimensions of the structure. Thus, a contribution (C) may be considered as the product of a barrier factor (B) and a geometry factor (G). In application of the standard method for finding contributions, one is required to calculate certain geometric quantities from the physical dimensions of the building and to determine the mass thickness of the various barriers. With the aid of curves and charts, barrier effects and geometry effects are evaluated, all contributions are calculated, and the protection factor is determined.
3-10 Solid Angle Fraction
The effect of building geometry on detector response can be evaluated by considering the volume inside the building through which the radiation must pass in order to arrive at the detector. Figure 3-7 considers a contaminated plane above a centrally located detector. Rays drawn from the edges of the contaminated plane to the centrally located detector below, form an inverted pyramid with the detector at its apex and the contaminated plane its base. All radiation which reaches the detector from this contaminated plane does so on straight lines lying wholly within this pyramid volume. Three dimensions, W, Land Z, shown on the figure, have an effect on this volume and, consequently, determine the effect of geometry on detector response.
A solid angle n, shown at the apex of the pyramid, is used as a single parameter to characterize the effect of building geometry. A change in any of the three dimensions, W, Lor Z, will produce a change in n. As W or L or both increase or decrease (Z remaining constant)~ increases or decreases. As Z changes (Wand L remaining constant), n will change, increasing with decreasing values of Z and decreasing with increasing values. Thus, n, dependent on all three dimensions, is a single geometric parameter that can be used to relate detector response to physical dimensions. ·
Just as plane angles are measured in radians, solid angles are measured in 11 steradians. 11 In plane geometry, radian measure is related to the length of arc which an angle intercepts on a circle of unit radius. Analogous to this, a solid angle is measured in terms of the surface area it subtends on a sphere of unit radius. -
3-15
•
w
•
z
I
I
I
I
I
FIGURE 3-7 SOLID. ANGLE SUBTENDING RADIATION SOURCE
Figure 3-8 shows, in (a), a detector subtending a circular area and, in (b), a detector subtending a rectangular area. The solid angle at the detector is the area, A, subtended on the surface of a sphere of unit radius. In fallout shelter analysis it is more convenient to work with "solid angle fractions" than solid angles. The solid angle fraction w (omega} is defined as the area A (which the solid angle subtends on a sphere of unit radius} divided by the area of a hemisphere of unit radius.
A plane area of infinite extent would subtend an entire hemisphere .and thus would have a solid angle fraction of 1.0. Solid angle fractions for plane areas obviously cannot exceed unity in value. The hemispherical concept also explains the fact that a solid angle fraction is a solid angle divided by 2TI since the total solid angle at the center of a hemisphere is 2TI steradians.
3-16
An expression for the solid angle fraction for a circular area is given in Figure 3-S(a). In order to develop a similar expression for rectangular areas, the area A in Figure 3-S(b) must be evaluated. The resulting expression for the solid angle fraction wsubtending a rectangular area W by L at a distance Z is:
2 -1 W/L
w = -tan 'IT 2(Z/L) ( 4(Z/L)2 + (W/L)2 +
In every fallout shelter analysis problem one or more solid angle fractions have to be evaluated. To avoid having to use the time-consuming equation, a chart has been developed for the determination of w. Figure 3-9 gives w in terms of the dimensionless ratios:
e = W/L =eccentricity ratio (width to length)
a = Z/L =altitude ratio (altitude to length)
where Wand Lare, respectively, the width and length of the base of the pyramid with w at its apex; and Z is the altitude of the pyramid.
To use the chart, one normally calculates values of W/L and Z/L from known physical dimensions and determines w from the curves. I For example, if W =50, L = 100, and Z =20, W/L =50/100 =0.50 and Z/L = 20/100 =0.20. To get w, one draws a vertical line through W/L = 0.5, a horizontal line through Z/L =0.2, and reads w at the point of intersection of these lines. This example is shown in Figure 3-9 and the value of w is estimated to be 0.51.
For convenience, Figure 3-9, together with other charts used in making fallout calculations, are reproduced in Appendix Cat the end of the manual. Figure 3-9 appears as Chart 1A. Once the charts have appeared in the text· and have been discussed, reference to them in subsequent calculations will be in terms of chart numbers in Appendix C.
3-17
•
w = 1 -cos 8
where tan 8 = R
z
L
(a) CIRCULAR AREA (b) RECTANGULAR AREA
FIGURE 3-8
SOLID ANGLE FRACTIONS
3-18
.7 .5 .4 .3 .2 0.1 .07 .05 .04 .03 .02
,-,-,-,-=, . ...,.,., 10.
7.
5.
3.
...J
._
N
:I:
1
(!)
z
w
...J 0
1w
c
::J
1
i=
...J <(
1.0
0.1
.07 .05
FIGURE 3-9
SOLID ANGLE FRACTION, W(W/L,Z/L)
(CHART 1-A APPENDIX C)
3-19
Study Questions and Problems for Chapter 3
1 . What type of nuclear radiation from fallout is the sole consideration in
fallout shelters?
2.
What is the purpose of fallout shelter analysis?
3.
Define direct radiation, scatter radiation, and skyshine radiation.
4.
Qualitatively, what is the relationship between barrier effectiveness and
photon energy?
5.
Why is it necessary, in the development of the analysis method, to choose
a single spectrum for gamma radiation energy distribution, and what
spectrum has been chosen?
6.
Define mass thickness, its units, and comment on the relative effectiveness as barrier material of common construction materials.
7.
Describe the standard unprotected (detector} location and explain the
purpose of this standard in fallout shelter analysis.
8.
To what kinds of radiation is the standard detector subjected, and what is
the source of 'each kind?
9.
Sketch, the standard detector response to radiation from all directions.
10.
By means of a sketch, show how the angular distribution curve for a protected location differs from that for the same detector unprotected.
11.
Define; contribution, reduction factor, barrier factor, and geometry factor and protect ion factor.
12.
What is the significance of a protection factor of 100?
13.
Explain why a protection factor, in itself, does not give a direct indication of the fallout radiation, biological hazard.
3-20
CHAPTER IV
FALLOUT SHELTER ANALYSIS OF SIMPLE BUILDINGS
4-1 IntroduCtion
In this chapter, the DCPA Standard Method for Fallout Gamma Radiation Shielding Analysis will be developed and applied to a wide variety of simple buildings.
The discussion of Chapter Ill was presented to .anable a fallout shelter analyst to make a qualitative evaluation of the effect of variations in pertinent parameters on the protection provided by a structure. The abi I ity to make such qualitative evaluations is one of the most valuable tools in the mental equipment of a shelter analyst or designer. Its importance cannot be overemphasized.
The approach to be used in the development of the Standard Method
will be to begin with a simple one-story 11 blockhouse, 11 devoid of complicating features. Progressively more and more real building parameters will be added such as: interior partitions, basements, windows, multi-stories, irregular shape, and adjacent buildings, until all basic considerations in fallout shelter analysis rove been developed. Complex shielding applications and design
techniques will be presented in the next chapter.
The format for the deveI opme nt of the methodology will be to discuss each shielding parameter qualitatively before presenting the data for making quantiative calculations of contributions, reduction factors, and protection factors.
Various aspects of geometry and barrier that are significant in shielding problems are discussed from a qualitative point of view with explanations of how variations in certain parameters would probably affect the calculated protection factor.
In the development of the standard method of analysis frequent ref
erence will be made to the work of L. V. Spencer reported in Structure Shielding Against Fallout Radiation from Nuclear Weapons, National Bureau of Standards Mongraph 42, June 1, 1962 and to that of C.M. Eisenhauer
reported in An Engineering Method for Calculating Protection Afforded by Structures Against Fallout Radiation, National Bureau of Standards Monograph 76, July 2, 1964. Basic data used in the standard method were generated by
Spencer. Conversion of that data to compilations and plots most convenient• 4-1
for use in engineering applications was accomplished by Eisenhauer. These two documents form the foundation for the standard method of analysis.
The importance of a full understanding of this chapter cannot be overemphasized. It will later be seen that the analysis of complex buildings involves only simple extensions of the concepts developed in this chapter. If it is clearly understood, no difficulty should later be experienced in the analysis of the most complex of buildings.
4-2 Functional Notation and Charts
In the standard method relationships are developed and expressed in mathematical form utilizing functional notation. When two variables are so related that the value of the first is determined when the value of the second is given, then the first variable is said to be a function of the length of a side, L. The second variable, L, to which values may be assigned at will (within limits depending on the problem) is called the independent variable or argument. The first variable, whose value is determined when the value of the independent variable is given, is called the dependent variable or function. Frequently, when two related variables are considered, either may be fixed as the independent variable; but, the choice once made cannot be changed without certain precautions and transformation. Again, for example, the area of a square is a function of the length of its side. Conversely, the length of the side of a square is a function of its area.
The general symbol f(x) is a functional notation. The letter f represents the dependent variable or function and x represents the independent variable. In terms of the example above, functional notation could be written as A(L) or L(A) depending on what is chosen as the independent variable. Considering A(L), the expression indicates that a given value for L determines the value of A. Parentheses do not indicat~ multiplication. They are used simply to set the independent variable.
The value of a function is often determined by more than one independent variable. For example, relative to solid angle fractions, w(e,a) indicates that the function,w, is determined when unique values are assigned to each of the independent variables, e and a. Stated in another way,w cannot be determined until values of e and a are determined. Independent variables may, themselves, be functions of other independent variables; i.e., e(W, L) and a (Z, L). Thus when unique values of W, Land Z are assigned, the functions of e and a are determined. Such determined values of the functions e and a lead to the deter
mination of the function w. Since functional notation is extensively used in
this manual, it is important for the user to recognize it when it is used and,
further, to recognize the relationships that such notation indicates.
The approach to fallout shelter problems using the standard method is to first write the functional expression representing the solution. In some cases the functional expression will be quite simple, but in most cases lengthy, complex expressions will be obtained. After the functional expressions have been written, numerical values are obtained using a series of charts. One of these charts, namely Chart 1A (Solid Angle Fraction) has already been discussed. Chart 1A merely represents the solution of a fairly simple closed form equation. Most of the other charts, however, are based on lengthy (computer) calculation for which simple closed form equations do not exist. Throughout this chapter the basis for, and the use of, each chart will be discussed. The complete set of Standard Method charts is contained in Appendix C.
4-3 Basic Structure
4-3. 1 Basic Blockhouse Description
The key to full understanding of fallout shelter shielding ana lysis is a simple one-story blockhouse. This building is assumed to be isolated on a horizontal, plane field extending infinitely in all directions. It is rectangular or circular in plan with its floor at grade. The walls are assumed to contain no apertures (openings) and are of uniform mass thickness. Radioactive fallout particles are assumed to be uniformly distributed over the entire plane surface outside the building and over the entire roof surface.
The end result of an analysis of the radiation shielding properties, of the building described above, is the determination of a protection factor. Protection factors can be calculated only for a point location. The focal point of the calculations becomes a fictitious detector located at some specific point location within the building. For the immediate purpose, it is assumed that the detector is located centrally in plan and at some height H above the floor. It responds to radiation received from all directions.
The basic building with a centrally located detector is shown in Figure 4-1. Certain symbols are noted. Throughout this text, symbols will be defined as they first appear. A complete list of symbols is given in the front of the manual.
H = the vertical distance from a contaminated ground plane to the detector.
4-3
Section
w Plan
FIGURE 4-1 THE BASIC RECTANGULAR BUILDING
4-4
L = the length or greater plan dimension of a rectangular building.
W = the width or lesser plan dimension of a rectangular building.
R = the radius, in plan, of a circular building.
X = e the mass thickness (weight in pounds per square foot of surfac~ of the solid portions of an exterior wall.
X= the mass thickness of all horizontal barriers between the
0 detector and the contaminated roof plane or, simply, the
overhead mass thickness.
Z = -the vertical distance from a contaminated overhead plane to the detector.
It should be noted that the shaded wall and roof outlines are not intended to represent physical dimensions. Relative to the horizontal dimensions and story heights of a building, the actual thickness of vertical (wall) and horizontal (roof and floor) barriers are usually of second order importance and can be neglected. In the calculations, the building can be represented as a line drawing, using outside dimensions.
4-3. 2 Detector Response
The sources of radiation reaching the detector in the basic building are the radiating fallout particles on the contaminated plane below the plane of !he detector (the ground plane) and those on the contaminated plane above the plane of the detector (the roof plane). Ultimately, the detector receives radiation from the ground and from overhead.
c = a contribution at the detector due to radiation that
g
has first emerged from the exterior walls of a building;
referred to as a wall (or ground) contribution.
C = a contribution at the detector due to radiation that 0 has first emerged from the roof of a building; referred to as roof (or overhead) contribution.
Although the detector responds to radiation that originates on the ground or on the roof, it does so only as the radiation emerges from the inner surfaces of the wall and roof barriers. From the strict point of view of the detector,
4-5
the walls and the roof are the radiating surfaces and one may speak interchangeably of ground or wall contributions and of overhead or roof contributions. • Figure 4-2 shows the radiation paths to the detector. This is an extension of the
•
FIGURE 4-2 RADIATION PATHS TO Tlill DETECTOR
4-6
concepts presented in article 3-2 concerning the character of radiation emerging from the inner surface of a barrier from a single radiating particle. The effect of the planar distribution of the many particles considered here is largely one of magnitude. The character of emergent radiation is the same. It is either direct, barrier-scattered or air-scattered. To get the protection factor of the basic building, the overhead contribution C ·, and
0
the ground contribution C must be eva Iuated.
g
4-3.3 The Overhead Contribution, Co
Attention is first focused on radiation which emerges from the underside of roof barrier in Figure 4-2, and reaches the detector as overhead contribution Co. Overhead contribution has three basic components: direct (overhead) radiation which travels in straight lines from fallout particles on the roof to the detector, scatter (overhead) radiation which as a result of scattering interactions in the roof barrier is 11 aimed 11 at the detector, and skyshine which originates from sources on the ground or on other planes such as the roofs of adjacent buildings and the roof of the subject building, and arrives at the detector after passing through the roof barrier. Ceiling shine contributions, i.e., radiation which comes through the wall and scatters in the ceiling (overhead barrier), will be handled as part of the ground contribution C .
g
In NBS Monograph 42, Dr. l.V. Spencer developed a solution for aerector response to a circular source of radiation with a barrier mass concentrated at the source. Spencer•s consideration of a barrier mass concentrated at the source plane corresponds basically to the practical case of the detector in the basic one story building. In such cases, the detector is separated from the overhead plane of contamination by one intervening horizontal barrier, the roof mass itself which is concentrated at the source plane.
One major difference between the Spencer model and practical cases, is apparent from a consideration of geometry. In most buildings roof geometry is rectangular while the Spencer model considers circular disc planes. Figure 4-3 is a schematic representation of actual and model configurations. In (a) the detector is located centrally below a rectangular source plane with a barrier of mass thickness, X , concentrated at the source plane. A solid
0
angle fraction,w , subtendsthe source plane, the base of a pyramid defined
by rays extending from the boundary of the base to the centrally located
detector point below. The Spencer model in (b) considers a detector point
centrally located below a circular source plane, a mass thickness of X
concentrated at the source plane and a solid angle fraction, w , subten~ling
the base of a cone.
4-7
208-401 0 -76 -6
The circular roof model can be used to approximate overhead contri
butions from rectangular roofs within certain practical I imits. Studies involving
the fairly extreme case of a rectangular source having a length five times its width and involving a detector first very close and then very far from the source, indicate errors of at most 20% in the approximation. Most practical cases will have much smaller differences because rectangular roofs are usually less eccentric than these extremes, and angular distributions, dependent on
the detector position relative to the source plane, will thus be less severe.
It is important to note that errors are generally on the conservative side if the circular disc approximation of a rectangle is used.
(a) (b)
X0
ACTUAL MODEL
FIGURE 4-3 ACTUAL vs. MODEL OVERHEAD CONTRIBUTION
4-8
A second major difference between Spencer's model as shown in Figure 4-3 and practical cases arises out of the fact that, in an actual situation, several discrete horizontal barriers may I ie between the source plane and the detector position. Such is the case if the detector is located in other than the uppermost story of a multi-story building. Such cases could be approximated by another of Spencer's models which considered a detector separated from the source plane by a homogeneous mass uniformly distributed between the source plane and the detector. In fact, earlier versions of the standard method of analysis utilized Spencer's data for this model in solutions for such cases. However, experimenta I studies have revealed better (but still conservative) agreement with predictions from the model of Figure 4-3 even when several separate barriers are present between the source plane and the detector. In the present version of the standard method, the model of Figure 4-3, serves as the basis for determining overhead contributions for a II cases .
Summarizing the standard method utilizes data derived by Spencer for the model shown in Figure 4-3 in calculating overhead contributions. These data are plotted in Figure 4-4 (Chart 9 in Appendix C.) If the detector is separated from the overhead source plane by more than one horizontal barrier, the total intervening mass is considerea concentrated at the source plane.
becomes the sum of the separate mass thicknesses of all the intervening
X0 horizontal barriers. Although .usual cases involve rectangular source geometry, the standard method assumes that data for circular source geometry are applicable, if the solid angle fraction,w , subtending the rectangular plane is equal to that subtending the circular plane.
4-3.3 Calculation of Overhead Contribution, Co
Figure 4-4 (Chart 9, Appendix C) shows that the overhead Contrib!Jtion Co depends on two basic parameters. Geometry effects are accounted for by the solid angle fraction, w , and barrier effects are accounted for by the overhead mass thickness Xo. In functional notation this is written Co(Xo,w). In order to get Co from Figure 4-4, both Xo and w are needed. As an example of the use of Figure 4-4 consider the case in which Xo = 150 psf and w = 0.40. Enter Figure 4-4 with 0.4 on the wscale and proceed vertically until the curve representing a mass thickness of 150 psf is reached, and then proceed horizontally to the scale on the left to read Co= .0035. In real life problems and Xo are not given and must be calculated from the buildi~g properties. Problem 4-1 shows the calculations for getting overhead contribution Co from basic building properties.
4-9
.3 .2 0.1 .08 .06 .05 .04 .03 .02
.05~ctm~-~~~~~~-~~~tT+~~~,~~+.M~<~~h+~h~~~~,, .04~H:';~~~~;~~~i~'N~=,~~~~~~,A~+.8'~*~~r;~~~c~~~'i~~-~~~
%~~;;:$:~~~~~·~~~~-i:~~~~~~~~,~~-~~~~~~~:ch~~~~"~~~~:ct~~~:4~~~--~~~
7
:ooa F..,,·,""·~S-'4
.007 ::::::'; ::··
0
X
0
(.)
0.001
.0009 ~-""::;2"~.o.;.;,•-+'T'-+"""''f~~.i-'i-t-+7-"'ioot-:-· :.--i'~~" -h~i;4.-:~·7'~or.f·•:""+~~-·i'IIO.'~·~''""
.0008 [::ii'iifc:+'t'T'-'f;~~~;.;poo;c.;.;-~~-:-.,..;--"'!,;i.0007 r.:+:~OI;;::_O.:~:r.-::;~1+.-'-:~ ~""'=-'-'--~~'~
.0006 ~!O<E'-+:'~""!i;;~F ""'..::t:-:-:-f""":-t~~ ....,._--+"''.l:c:-:~..t
.0005
f:i·C:tiC:~~'S.i,;;-:ti'
.0004
.6 .5 .02 0.01
SOLID ANGLE FRACTION, (A)
FIGURE 4-4
OVERHEAD CONTRIBUTION, Co(X0 , (J.)) (CHART 9-APPENDIX C) 4-10
PROBLEM 4-1
Consider a simple, one-story, aboveground building having a width, W, of 40 feet and a length, L, of 60 feet. A centrally located detector lies at a distance, H, of 3 feet above the contaminated fround plane and at a distance, Z, of 10 feet from the contaminated roof plane. The roof construction is a one foot thick standard weight concrete slab.
It is assumed that the building is isolated in a contaminated field of infinite extent and that radioactive particles are uniformly distributed on the roof. Find the overhead contribution C .
0
L 1
,~
= 40'
I = 60' =
I
12" thick
w ---·@-- concrete
slah
I
a) Find the solid angle fraction, w (W/L,Z/L)
u
w 40 z 10
= 0.167
I.:= 60 = 0.67 I.: = 60
~(W/L,Z/L) = wu(0.67, 0.167) = 0.64 (Chart 1A)
b) Find the overhead mass thickness, X
0
Standard weight concrete has a weigh-density of 150 lbs. per cubic foot. Therefore a one-foot thick slab would have a mass thickness of 150 psf.
c) Overhead contribution:
C (w ,X ) = C (0.64, 150) = 0.0043 (Chart 9)
0 u 0 0
4-11
A detector located beneath a contaminated roof plane wi II respond not only to radiation originating with the fallout partiCles on the roof but also to a certain amount of skyshine. As explained earlier, skyshine is radiation resulting from scattering interactions of photons in the air and passes directly
•
through the barrier to the detector without further interaction. Chart 9
(Figure 4-4) includes the effect of skyshine through the solid angle fraction
subtending the roof and no additional consideration need be given for the
usual cases. For the special case, involvinga roof that may have been
cleared of contamination by some effective means, the only contribution
through the roof would be skyshine. This matter is considered as a special case
later.
A further study of Figure 4-4 (Chart 9) reveals that it is not necessary to compute wto a fine degree of precision. Generally, two places after the decimal point, are sufficient. It may be further observed, from a study of the figure, that, particularly for relatively high mass thicknesses, overhead contributions are relatively insensitive to changes in values of the solid angle fraction in the range 0.6 to 1.0. This indicates that beyond a certain limit, increases in area will have very little effect on overhead contribution. Stated in another way, the major portion of the overhead contribution stems from sources in the centrally located region of the area. There is no reason to be extremely precise in establishing the dimensions Wand L, particularly if they are large.
4-3.5 The Ground Contribution Cg
Consider in Figure 4-2 the radiation emerging from the inner surface of the exterior wall barriers. The centrally located detector responds to this radiation as it arrives from all angular directions. All of the radiation reaching the detector through the walls originates from the fallout particles on the contaminated ground plane and the aggregate is the ground contribution, Cg.
As indicated in Figure 4-2, it comes either directly from the source through the wall without an interaction, or as radiation that has scattered in the wall or ceiling barrier, or as radiation that has undergone a scattering interaction in the air and then passes directly to the detector through the Wa II barrier without further interaction.
Several very important shielding considerations become apparent through a study of Figure 4-2.
1. Since direct radiation travels in a straight line from sources on the contaminated plane, through the wall, to the detector, direct radiation can come through only that portion of the wall below the plane of the detector.
4-12
2. Each photon incident upon the wall may enter into a scattering interaction within the wall barrier; and, hence, every point
on the interior of the wall is a potentia I contributor of scatter radiation to the detector. Scatter radiation may thus reach the
detector from those portions of the wall both above and below
the plane of the detector.
3. A scattering interaction may take place at any point in the air
above the contaminated ground plane and departing air-scattered radiation may pass directly to the detector through either the portion of the wall above or below the detector. As explained
in Chapter Ill, air-scatter which arrives at the detector from above its plane is called skyshine. Air-scatter which arrives from below the detector plane is included as a component of what is termed direct radiation. Any air-scatter which under
goes a further scattering in a barrier and then is intercepted by the detector con be considered as a component of the wa11scattered radiation referred to simply as scatter.
4.
Although Figure 4-2 does not indicate absorbed radiation; of the infinite number of rays incident on the exterior wa II barrier, some will be absorbed and will not emerge from the inner wa II surface. Also much of the radiation, whether direct, scatter, or skyshine, emerging from the inner wall surface will travel on I ines that will not be intercepted by the detector.
5.
A large amount of radiation emerging from the inner wall surface
would ordinarily miss the detector but could scatter in the air within the structure, scatter off the ceiling, or back-scatter from the opposite wall. Conceivably, such secondary interactions within the structure could result in an additional contribution to the detector above and beyond that of a primary nature considered in items 1, 2, and 3 above. With one exce ption, these secondary effects are minor in nature and are not considered in standard method calculations. The exception is ceiling shine. If the exterior walls contain large amounts of apertures, direct radiation from ground sources will pass through these apertures and impinge on the ceiling above the detector. Photons back-scattered from the ceiling (ceiling shine) can, in some cases, represent a significant portion of the total detector response. The standard method permits one to calculate ceiling shine contributions for such cases.
4-13
4-3.6 Calculation of Ground Contribution, Cg
Calculations for the ground contribution, through the walls of a structure are more complex than those for the overhead contribution.
•
Before proceeding with the calculations for the ground contribution to the
detector in the basic blockhouse (Figure 4-1), it is necessary to consider more extensively some basic concepts, and to develop a fundamental understanding of several charts that will be used in .a determination of Cg. These will be treated with considerable detail. They require extensive study and full understanding, without which, the meaning of the calculations cannot be clear.
Figure 4-5 shows, in section, a single-story, cylindrical structure with its floor at grade and with the detector centrally located 3 feet above the contaminated ground plane. It is assumed, that around the structure the radiating field is infinite in extent in all directions. In this discussion, only the contribution, Cg, through the walls will be considered. The walls of this
structure are of a special character. They have a mass thickness approaching 0 psf. The structure is referred to as "thi n-wa II ed." The fact that the wa lis have no mass is of particular significance. In the absence of mass, any radiation incident upon the outside surface of the wall will pass directly through without absorption or scatter. Any radiation reaching the detector arrives on a direct line from the source either as direct radiation or skyshine radiation.
thin walls
h
Xe = 0
FIGURE 4-5
THE THIN-WALLED STRUCTURE
4-14
Of interest in Figure 4-5 is the radiation which emerges from the inside of the
exterior walls and reaches the detector from directions indicated by the shaded
zones. These are complementary to the unshaded zones defined geometrically
by the upper and lower solid angle fractions,wu and wl. In the solution for
overhead contribution, solid angles were used to define the zone through which
radiation passes; but in the case of ground contribution w u and wLare used to
define zones through which wall emergent radiation does not pass in arriving at
the detector. Regardless of this fact they may still be used as a parameter to interpret the effect of geometry on response to the detector through the shaded zones. Also, since there are more than one zone of interest, subscripts (U for upper and L for lower) are used to further define the solid angle fractions. As previously discussed, it is important to note that direct radiation, approaching the detector only through the shaded zone below the detector plane, includes an air-scattered component (skyshine) in addition to the major component that
comes directly from the ground sources. It is termed direct purely for conveni
ence. Through the shaded zone above the detector plane, only skysh ine radi
ation approaches the detector.
As both the upper and lower solid angle fractions approach zero in Figure 4-5 the situation becomes identical with that of the standard unprotected location described in Chapter 3. As these solid angle fractions increase from zero, contributions through the wall decrease because the photons that would approach from the directions defined by the solid angle fractions, wu and wLt are el iminated from consideration. The reductions are, in both cases, purely functions of geometry since no barrier exists (other than air).
Spencer derived separate expressions for the response of a detector in the standard position to skyshine radiation from above and direct radiation from below. He expressed these as functions of solid angle fractions subtending discs free of contributing sources but surrounded by contributing sources extending infinitely in all directions. The cylindrical structure of Figure 4-5 would correspond to Spencer's solution for given values of upper and lower solid angle fractions.
The reduction in skyshine (air scattered) radiation response as wu gets larger and larger may be thought of as a "geometry reduction factor for skyshine radiation, or (for short) the "skyshine geometry factor," Ga •
G = Geometry Factor for skyshine radiation through that portion of
a a wall of a building lying above the detector plane, a function of upper solid angle fractions, Ga(w).
4-15
The lower curve of Figure 4-6 gives the Skyshine Geometry Factor as
a function of solid angle fraction w, i.e., G ( w). Figure 4-6 is Chart 2 in Appendix C. Note that the scale for w (the agsissa) is an inverted logarithmic scale. This is due to the fact that although wis used as a parameter to characterize the geometry effect, the actual skyshine contribution comes through the zone outside of w, or the zone (1-w) .
To get the skyshine geometry factor G (w), enter the curve with the
a
value of the solid angle fraction wand proceed vertically to the skyshine curve. Go horizontally to read the Skyshine Geometry Factor G ( w) on the left hand
a scale. Example w= 0.6,G (0.6) = .068.
a
Unlike skyshine radiation which varies only negligibly with height, the
angular distribution (section 3-6) of direct radiation is markedly affected by the height of the detector above the contaminated plane. Consequently, the Direct (Radiation) Geometry (Reduction) Factor Gd depends on both the solid angle fraction w, and the detector height H.
Gd = Geometry Factor for direct radiation through that portion of a wall of a building lying below the detector plane, a function of lower solid angle fraction and the height of the detector above the contaminated ground plane, GiH, w).
Figure 4-7 gives Geometry Factors for Direct Radiation in terms of solid angle fraction wand detector height H. For the case of the basic block house
being considered, the detector height H is 3 feet and Gd(3•, w,) is read along the bottom of the chart, which represents H = 3 ft. When the detector height is more than 3 ft., such as in upper story location, the chart has a more genera I use. Take as an example the case in which w = 0.6 and H = 10ft. Enter the chart with w = 0.6 along the bottom scale and proceed vertically until the horizontal line through H =10ft. (on the left hand scale) is intersected. Estimate the value of Gd at the intersection, i.e., Gd(10,0.6) = 0.64. If the detector height H is 3 feet and wremains at 0.6, the Geometry Factor for Direct Radiation is estimated to be: Gd(3,0.6) = 0.72 (read along the bottom scale at w = 0.6 which is between Gd = 0.70 and Gd = 0.75. In Appendix C Figure 4-7 is divided into two charts at w= 0.9 and becomes
Charts 3A and 3B. From Figures 4-6 and 4-7, it is noted that, for the extreme case in which, for a cyI i ndricaI, th i n-wa II ed structure, both the upper and lower solid angle fractions approach zero, the sum Gd + Ga = 0.90 + 0.10 =
1.00. This indicates that the normalized value of unity for the standard
detector has been reached -that 100% of the radiation to which the standard
detector responds has been accounted for.
4-16
.98 .99
0.003 '+UU'~"-"'-'-'"
0 .1 .2 .3 .4 .5 ® .98 .99
SOLID ANGLE FRACTION, W
FIGURE 4-6 GEOMETRY FACTORS-SCATTER, G5 ( W) AND SKYSHINE, Ga (W)(CHART 2-APPENDIX C)
4-17
~
'
.....
co
.1 .2 .3 .4 .5 .6 .7 .8 .85 .90 .92 .93 .94 .95 .96 .97 .98
00 litiHI \-::It t:,lA.ii\::J\ct:-t Jt: XL::x!L:q \ ~: ,1\\\ \ '..;..\[~T\1-.---r\1 I H I t ! .:k:
90
80
70
60
50
40
~
30
-£
...:
:I:
<.:lw
:I:
20
10
9
8
7
6
5
4
.2 .3 .4 .5 .6 .90 .92 .93 .97
SOLID ANGLE FRACTION, W FIGURE 4· 7 GEOMETRY FACTOR -DIRECT, Gd(H,(LI)
(CHART 3A and 3B Appendix C)
Although the geometry factors, Gd and Ga, of Figures 4-6 and 4-7 were
derived from a consideration of cylindrical structures, they may also be used
for rectangular structures. It is assumed that, if the solid angle fraction of
interest in a rectangular structure is the same as that for a cylindrical structure,
the geometry factors, Ga and/or Gd, will be equal. The basic concepts of the
wall contribution through a thin-walled structure are illustrated in problem 4-2.
The solution to problem 4-2 gives a reduction factor of 0.52, indicating
that geometry and barrier effects associated with the protecting building have
reduced the contribution to 51% of that of the standard unprotected location
The protection factor of 2.0 indicates that the standard detector receives 1/2
the radiation. received at the protected location. Attention is also called to
the relative magnitudes of the direct and skyshine contributions. The protec
tion could be materially increased if the direct contribution could be elirrfi
nated, such as by depressing the building 3 feet into the ground. Complete
burial, would eliminate all contributions except the overhead, and result in
a PF of a bout 180 .
Here we have considered a very simple situation, but it points out how the results of the calculations can be analyzed from the viewpoint of taking possible design measures to increase protection. This is of great importance in the process of "slanting" building design to enhance protection against fallout radiation.
The thin-walled structure represents one extreme in the concept of wall or ground contributions. The thick-walled structure is at the other extreme. Figure 4-8 represents, schematically, a section through a single-story, cylindrical structure having very thick walls. Again, only the exterior wall contribution will be considered in this discussion. The only interest at this time is in geometry effects. In the case of a thick-walled structure, it is impossible to completely separate geometry and barrier effects. If the walls of a structure are extremely thick, the chance that photons can pass directly through them to the detector without interaction is remote. It follows that the contribution to the detector consists entirely of wall scattered radiation from both the upper and lower wall segments. This is shown in Figure 4-8 where w uand w L are used to define the complementary zones through which scatter photons approach the detector. These complementary zones, shown shaded, indicate the scatter contribution that is left out of the total potential that would exist if both the upper and lower solid angle fractions were zero. As previously discussed in the thin-wall case, contributions approaching the detector through the directions defined directly byWu and W L are eliminated from consideration. Although only
geometry reduction is of immediate interest in the discussion, it should be observed that very large exterior wall mass thicknesses would eliminate virtually all of the wall contribution through barrier reduction alone.
4-19
1---------·-------------------------------,
PROBLEM 4-2
The building of Problem 4-1 is selected and it is assumed
that X ~o psf. The building is thus a thin-walled building.
The de~ector responds to an overhead contribution (calcu
lated in Problem 4-1), and to a wall contribution consis
ting of skyshine from the upper portions, and direct from
the lower. The calculations below should be self-explana
tory except to note, once again, no barrier effect for the
wall.
,,
II
Xe == 0 psf ~I
-1+-
1 I
Lower solid ~ngle fraction, ,, = 3r,
I
w 40 I
= = 0.67
w = 40'
L 60
L = 60'
H 3'
3 =
= = 0.05 (Z = altitude of pyramid)
60 Xo = 150 psf
:;::
Xe 0 psf
0.885 (Chart A) Upper solid angle fraction, w = 0.64 (Problem 4-1)
u
Wall (ground) contribution, C
g
G (w ) = Ga(0.64) = 0.064
a u cg = o.45 + o.064 = 0.514 Overhead contribution, C = .0043 (Problem 4-1)
0
H.eduction f~cto_:r, RF
RF = C + C = 0.514 + 0.004 = 0.52 (rounded off)
g 0 Protection factor, PF PF = 1/RF = 1/0.52 = 2.0 (approximately)
4-20
In the standard method, the geometry (reduction) factor for (wall) scatteredradiation, G is defined as; ·
s
Gs = geometry factor .for scatter radiation through the walls of abuilding lying either above or below the detector plane, afunction of either the upper or lower solid angle fraction,
G (w).
s
Values for G (w)
s are plotted in Figure 4-6. This curve was derived by assumingthat angular distributions for th ick-wa II scattered radiation is simi lor to that forskyshine (which is also a scatter phenomenon). Thus, the shape of the angulardistribution curve of thick-wall scattered radiation would correspond to that forskyshine as shown in Figure 3-4 (e between 90° and 180°).
It was further assumedthat angular distributions fore between 0° and 90° (below detector plane) would
h thick walls
FIGURE 4-8THE THICK-WALLED STRUCTURE
4-21
plot as the mirror image of those fore ranging between 90° and 180°. Now, if the total integrated dose angular distribution for the thick-wall case is to be the standard reference dose of unity, 0.50 must arrive at the detector from all directions above its plane and 0.50 from all directions below its plane. This immediately fixes the scale of Gs values as precisely five times those for Ga since the integrated skyshine dose from above the detector plane is 0. 1,
i.e. Ga(w = 0) in Figure 4-6.
Referring to the Ga and Gs curves in Figure 4-6, it is observed, that, for a any value of w, Gs = 5Ga. In a previous example it was determined that Ga( w= 0.6) from Figure 4-6 (Chart 2, Appendix C) is found to be 0.34 which is exactly five times 0.068. It is further observed that, forw= 0.0, Gs = 0.50. Since both upper and lower solid angle fractions are involved, when both are zero, the unit reference dose is preserved. The inset figure adjacent to the curve denotes the necessity for considering Gs as a function of both upper and lower solid angle fractions, and shading of the walls is used to differentiate thick-wall from thinwa II geometry factors.
In the case of the thin-wall building it was assumed that geometry factors Gd and Ga derived on the basis of circu Jar geometry are applicable to cases of rectangular geometry for equal values of solid angle fractions. Such is not the case for thick-wall geometry factors, Gs. As discussed above, Gs values plotted in Figure 4-6 (Chart 2 Appendix C) have been derived through representation of the thick-wall scatter response to the thin-wall skyshine response. Such representation implies that, for a given value ofe (Figure 3-4), scatter will be of the same intensity at every degree of azimuth just as in the case of skyshine. However, when a scatter interaction takes place in a wall, the most likely path for the departing photon to follow in emerging from the wall is the shortest path from the point of interaction to the point of emergence. This will be the normal direction, and thus there is the tendency for radiation to emerge from a thick wall in the direction normal to the wall. If the wall is circular, the normal directions of emergence are azimuthally symmetrical and representation of scatter response by skyshine has azimuthal correlation. Such will not be the case when scattering walls are not circular and emergence tends to be in directions perpendicular to the wall.
To correct for this effect in scatter geometry factors, Gs, an adjustment,
the shape factor is applied as a multiplier to the scatter geometry factor, Gs.
This factor is given by
1 + e
E(e) = .V/l
+ e2
where e = W/L is the eccentricity ratio of the building.
4 -22
E = a shape factor always applied as a multiplier toGs (and only Gs) to correct for the shape of the building; E(e).
The shape factor is normalized to unity for the case of a very long narrow building, since barrier factor data, which will be discussed later corresponds to· such a case. For a square building (e = 1 . 00), E =V2 and for a cyl i ndrica I case it is 11'/2. Values of E(e) are plotted in Figure 4-9 which appears as Chart 4 in Appendix C. For a building 60ft. by 40 ft. in plan, E = W = 0.67 and E(0.67) = 1.39. L
The basic concepts of the wall contribution through a thick-walled structure are illustrated in problem 4-3.
The discussion, so far, has been limited to geometry factors for thin-walled and with thick-walled structures. Practically all real buildings have exterior walls that are intermediate in mass thickness between thin walls and thick walls. Figures 4-6, 4-7 and 4-9 (Charts 2, 3 and 4 in appendix C) are applicable to
the direct determination of geometry factors for only thin and thick-wall structures. Spencer's work does not give similar data for walls of intermediate mass thicknesses.· In view of this the method of analysis is based on taking
a weighted average of thin-wall and thick-wall geometry factors for real cases. The weighing factor is termed the scatter fraction and is designated by Sw. It estimates the fraction of radiation reachi-ng the detector that has been scattered at least once in the walls.
Sw = scatter fraction, that portion of the total radiation reaching the detector that has been scattered in the walls, a function of exterior wall mass thickness, Sw(Xe).
Figure 4-10, Chart 5 in Appendix C, gives Sw as a function of exterior
wall mass thickness. The figureSw is entered with the value of the wall mass thickness Xe to obtain the scatter fraction Sw(Xe). For example, if Xe is 100 psf, Sw(lOO) = 0.775 from Figure 4-10. The weighting factor Sw is applied as follows:
Thick-walled geometry factors, Gs terms with shape factor correction
(E), are multiplied by Sw(Xe)· Thin-walled geometry factors, Ga
and Gd terms are multiplied by 1 -Sw(Xe).
The results are added to get the total geometry factor for ground contribution to the detector through the walls of a building of finite mass thickness. The rationale for the construction of the complete functional equation for the geometry (reduction) factor for ground contribution Gg is discussed next.
4-23
208-401 0 -76 -7
0 0.1 0.2 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1.0
1,50 r----r··--.---.----,·r·c-·-r-·-r---,.--·-:,----·,-----,--·----··-,--,-c--·4 ·-,----,,-----,-:--:-c--·
-
~
w
.
a:
0
1
(.)
<( LL
w
Q.
<(
J:
(I)
0.1 ~2 ~3 ~4 ~5 Q6 OJ 0.8 0.9 1.0
ECCENTRICITY, e is W/L
8
E (e) FOR CIRCULAR STRUCTURES IS ~ = 1.571
FIGURE 4-9 SHAPE FACTOR, E (e) (CHART 4, APPENDIX C)
4-24
PROBLEM 4-3
The building of Problem 4-1 (and 4-2) is again considered but in this case the wall mass thickness X is assumed to be very large, i.e., a thick-walled building.e Only the geometry effect of reduction in wall-scattered radiation are considered in this example.
w= 40'
L = 60'
wa!lls
H = 3'
X 0 =(C0 will not be considered)
X e = Very Large
Values of w
WL = 0.885 (Problem 4-2)
wu = 0.64 (Problem 4-2)
Values G
s G (u; ) = G (o.885) = 0.135 (Chart 2)
s L s G (u: ) = G (0.64) = 0.325 (chart 2)
s u s Value of the shape factor, E e = W/L = 40/60 = 0.67 E(e) = E(0.67) = 1.39 (Chart 4)
Scatter geom~try reduction {G (wL) + G (w )} E(e) = {0.135 + 0.325} 1.39 = 0.639
s s u
• 4-25
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
1.0
0.9
Q0.8
0
-Q)
X
-
3:
en
.
2 0 1
u
<(
a:
u.
a:
w
I
I
<(
~
40 60 80 240 260 280 300
EXTERIOR WALL MASS THICKNESS, Xe psf
FIGURE 4-10 SCATTER FRACTION, Sw (Xe) CHART 5 APPENDIX C 4-26
The geometry factor for the thin-walled structure is [Gd(H,wl)+Ga(wu)]. For the thick-walled structure, the geometry factor is [Gs(Wu)+Gs(w L)]E(e). For the structure of intermediate wa II mass thickness, the geometry factor is the weighted average of those for the thin and thick-walled structures where the
weighting factor is a function of the mass thickness of the exterior wall, Xe. Thick-wall geometry is multiplied by Sw(Xe), thin-walled geometry by [1-Sw(Xe)] and the results are added. The resulting complete functiona I equation for the
geometry factor for ground contribution GQ for the simple blockhouse (Figure 4-1) is:
Gg = total geometry factor for ground contribution.
It should be noted that, if the mass thicknesses of the upper and lower portions of the wall were different, upper and lower wall geometry would have to be separated because of the two different values of Sw involved. The analyst should study very carefully the functional expression for the geometry factor of intermediate wall mass thickness buildings. Strict attention should be given to the concepts involved rather than to a memorization of the symbols or the order in which they appear. This functional expression will be used consistently· in practically all calculations involving the determination of protection factors in aboveground locations, and will be modified as other shielding parameters are taken into account. In learnirg fallout shelter analysis, emphasis shouiu be placed on developing the ability to formularize the appropriate functional expressions through consideration only of basic concepts. (Symbols are of secon~ary importance.) If the basic concepts are well understood, no difficulty should be experienced in writing the proper functional expression for even the most com pi ex cases.
So far, only geometry effects have been evaluated; in order to complete the determination of the blockhouse ground contribution C9, barrier effects must also be considered. The geometry factor for ground contribution indicates to what extent geometry has reduced the contribution relative to the standard detector location. This is now modified by a barrier reduction factor which accounts for the effect of the exterior wall mass thickness in reducing radiation incident on the wall.
A barrier factor1 B, can be defined as the fraction of radiation, incident at a point on one side of a barrier, that penetrates through to the other side. For example, a barrier factor of 0.10 would indicate that, of the radiation incident at a particular point on the barrier, only 10% will penetrate to the opposite face. In the case of the blockhouse, under consideration, the
4-27
detector is 3 feet above the contaminated plane (the standard height) and the barrier factor depends only on the mass thickness Xe of the exterior wall. When upper story detector locations are discussed, it will be seen that the exterior wall barrier factor will in addition depend on the height of the detector above the contaminated plane, due to (a) the mass of the intervening air, (b) the change in the dose rate angular distribution of direct radiation with height, and (c) reduction of intensity with distance from the source. These effects will be elaborated upon when upper story locations are considered, but to generalize the discussion of exterior wall barrier factors, the dependence on height will be included in the functional expression at this time. Therefore, the barrier factor for the exterior wall must be a function not only of the mass thickness of the wall but also of the height of the point of interest on the wall above the contaminated plane.
B = exterior wall barrier factor, a function of mass thickness
e and height, Be(Xe, H).
Since a particular wall segment would show different barrier factors because of different heights of points on the wall above the contaminated plane, it is necessary to select some point on the wall as an average point and consider the barrier factor associated with that point as constant for the entire wall. As indicated in the definition for Be given above, the point selected should Iie opposite the detector and hence the height of the wall point corresponds to the height, H, of the detector above the contaminated plane.
Using data generated by Spencer, Eisenhauer calculated exterior wall barrier factors as the ratio of; exposure at a point sandwiched between two vertical slabs of infinite height and length on an infinite-plane standard source to exposure at the standard unprotected location. The results giving barrier factors for exterior walls as a function of height and mass thickness are shown in Figure 4-11 (Chart 6 in Appendix C). It should be noted that the minimum value of H considered is 3 feet. If H is less than 3 feet, the value at 3 feet should be used. It is further noted that, for a mass thickness of exterior wall of 0 psf, the barrier factor for H =3 feet is 1 . 00. A detector height of 7 ft. and an exterior wall mass thickness of 90 psf gives a barrier factor Be(7, 90) =
0. 1.
It is now possible to complete the functional equation for the ground contribution for a simple one-story blockhouse. The ground contribution is the product of the geometry factor for ground contribution [Gg] and the exterior wall barrier factor Be(H,Xe)·
C = [G ]·B (H,X)
g g e e
4-28
3 4 5 6 8 10 20 30 50 70 100 200 400 700 1000
1.0 ,8
-
J:
xa,-
t!JOJ
rr.·
0
1
~
u.
a:
w
rr.
a:
<(
t!J
_,
..J
~
a:
0
a:
w
I
X
w
30 50 100
HEIGHT, H, ft
FIGURE 4-11
EXTERIOR WALL BARRIER FACTORS (Be(Xe,H)
(CHART 6 APPENDIX C)
4-29
4-3.7 Calculation of Blockhouse Protection Factor
The total blockhouse contribution consists of the Overhead Contribution
and the Ground Contribution Cg. Detailed calculation of Overhead Contri
C0 bution was given in Problem 4-1. Components of the ground contribution geometry factor were calculated in Problems 4-2 and 4-3. These calculations are brought together in Problem 4-4, which shows the steps involved in determining the protection factor of a typical blockhouse.
The analyst should follow each step carefully being sure that he comprehends the meaning of all values and how they were obtained. Any difficulties can be cleared up by reference to the preceding material where the concepts have been discussed in detail. The solution begins with the basic data required, which consist of the dimensions of the building and the mass thicknesses of walls and roof. This is followed by a compilation of data taken from the appropriate charts. Of particular advantage is the manner, suggested in the solution, in which solid angle fractious and geometry factors are presented in tabular form. Such an arrangement lends order to the computations and allows them to be readily followed. Following the data compilation, the functional expressions for C and C are set up and solved. The reduction factor and protection factors r8und
g out the sol uti on.
In the solution to Problem 4-4, note that the ground contribution C is larger than the overhead contribution by more than a fac.tor of ten; and t~erefore (in this case) C0 has only a small effect on the protection factor. To increase the protection, the exterior wall mass thickness Xe would have to be increased. This would be a trial-and-error procedure since both Sw(Xe) and Be(H,Xe) depend on the value of Xe. In other words, since Xe appears in both the geometry factor and the barrier factor, the ground contribution functional equation cannot be easily "inverted" for design purposes.
4-4 Blockhouse With Variation in Exterior Wall Mass Thickness
One conclusion that can be reached, in a qualitative interpretation of shielding parameters, is that an increase in the mass thickness of any barrier interposed between sources of radiation and a detector should result in a lesser contribution to the detector. In general, this conclusion is correct, but there are exceptions.
Consider the structure shown in Figure 4-12, and for the purpose of this discussion, let it be assumed that only the upper wall segment (that portion above the detector plane) contributes to the detector. In Figure 4-12(a) it is assumed that the upper wall segment has zero mass thickness. Normally, the
4-30
PROBLEM 4-4
w = 40 ft. L = 60 ft. X = 100 psf 3' X0 e = 150 psf
w L z W/L Z/L w Gd Gs Ga
wu 40 60 10 0.67 0.167 0.64 ----0.325 0.064
WL 40 60 3 0.67 0.05 0.88 0.45 0.135 -----
E (0.67) = 1.39 s (100) = 0.77, B (3,100) = 0.093
w e Gg = {G s (wu ) + Gs (wL)} E(e) Sw(Xe) + {Gd(H,wL) + G (w )} {1-S (X )}
a u w e Gg = {0.325 + 0.135} {1.39} {0.77} + {0.77 + 0.064}
{0.23} = 0.492 + 0.118 = 0.610 Cg = Gg Be (H,Xe ) = 0.610 x 0.093 = 0.0567 C (w X ' = 0.0043
o u' oJ RF = C0 + Cg = 0.0043 + 0.0567 = 0.061
PF = 1/RF = 1/0.061 = 16
4-31
upper wall segment would contribute both skyshine and scatter radiation to the detector. In the absence of mass thickness, no scatter can take place and the detector in Figure 4-12(a) receives only skyshine radiation from directions defined by the upper wa II segment.
In Figure 4-12(b), the upper wall segment is assumed to have mass thickness greater than zero. Increasing the mass thickness above zero creates a dual effect with opposing results. A certain amount of skyshine radiation, which would ordinarily reach the detector through the zero mass thickness wall, will now be absorbed, and less skyshine will reach the detector. On the other hand, since mass has been added, the upper wall segment will begin to scatter radiation towards the detector as an additive quantity. For a certain range of mass thicknesses above zero pounds per square foot, the amount of radiation scattered to the detector may exceed the amount of skyshi ne absorbed, and the net effect on the contribution may be an increase. This effect is shown numerically in Problem 4-5.
(a)
(b)
--........
--.,.(/
/
/
/
///
FIGURE 4-12EFFECT OF INCREASING MASS THICKNE$SON SKYSHINE VS. SCATTER RADIATION
4-32
Problem 4-5(a) considers the normal wall contribution for a building having 0 psf walls above the detector plane and 40 psf walls below. Since the mass thicknesses differ, it is necessary to calculate the contribution in two parts, that from above and that from below. It should be noted that the contribution from above consists only of skyshine radiation, since Sw =0; and the scatter terms drop out. The functional equation has been written to include scatter in order to keep the equation general.
In part (b) of the problem, the ground contribution has been calculated for a mass thickness of 40 psf for all parts of the wa II. The contribution from the lower wall portion is the same for parts (a) and (b), but it is noted that the contribution from the upper wall segment has increased from 0.068 to 0.107 when the wall mass thickness was increased from 0 to 40 psf. This is characteristic of low wall mass thicknesses. As the mass thickness is increased from 0 psf, the wa II begins to scatter rod iation into the detector . At first, the amount of radiation scattered in is greater tho n that absorbed by the barrier effect. This is true for mass thicknesses between 0 psf and about 35 to 40 psf. As the mass thickness is increased above 35 to 40 psf, the reduct ion due to the barrier effect begins to dominate, and the contribution begins to decrease. It continues to decrease with further increase in mass thickness. It should be noted that an attempt to increase protection by such measures as, for example, filling in apertures with material of low mass thickness may in some cases be to no avai I and may, in fact, have the opposite effect (i.e. reduce protection).
4-5 One-Story Blockhouse with Interior Partitions
4-5.1 Effect of Interior Partitions
The placement of interior partitions, between the exterior walls and the detector, results in a decrease in contribution from both the ground and overhead sources. Interior partitions furnish increased mass between the radiating sources and the detector. Hence, their influence on contribution is essentially an attenuation effect.
Figure 4-13 shows plan and section views of a single-story blockhouse with a centrally located detector completely surrounded by interior partitions. Figure 4-13(a) is a plan of the roof showing radiating particles uniformly distributed over its entire surface. The difference in shading is intended to indicate the position of the particles -some over the core area, defined by the boundaries of the interior partitions, and others over the peripheral area outside the partitions. Radiation coming from those particles over the core area and passing to the detector is not influenced by the partitions. That which originates over the peripheral area can reach the detector only after passing through a partition.
4-33
PROBLEM 4-5 w = 50 ft.L = 100 ft. X = 40 psf (below De
•
e
teeter) Part (a) X = 0 psf (above De
e
teeter) Part (b) X = 40 psf (above De
e
teeter)
Note: Ceiling shine neglected
w L z W/L Z/L w Gd Gs Ga
uu 50 100 15 0.50 0.15 0.61 -----0.340 0.068
WL 50 100 3 0.50 0.03 0.915 0.038 0.100 ----
E(0.50) = 1.34, S (40) = 0.55, S (0) = 0.0
w w
B (3,40) = 0.38, B (3,0) = 1.00
e e
Part "a"
Portion of wall above detector:
G = G (w ) E(e) S (X e ) + G (w u ){1-Sw(X e )}
g s u w a
= (0.340 X 1.34 X 0.0) + (.068 X 1.00)= 0.068
C~ = G B (H,X } = 0.068 x 1.00 = 0.068 (above)
c g e e
Portion of wall below detector:
G = G (wL)E(e)S (X ) + Gd(H,wL){1-S (X )}
g s w e w e
= (0.100 X 1.34 X 0.55) + (0.380 X 0.45) = 0.245
Cg = G B (H,X ) = 0.245 x 0.38 = 0.093 (below)
g e e
Total ground contribution = 0.093 + 0.068 = 0.161
Part '' .J"
Portion of wall above detector:
G = G (w )E(e)S (X ) + G (w ){1-S (X )}
~ s u w e a u w e
-(0.340 X 1.34 X 0.55) + (0.068 X 0.45) = 0.281
C = G B (H,X ) = 0.281 x 0.38 = 0.107
g g e e
Total ground contribution = 0.107 + 0.093 = 0.~00
4-34
FIGURE 4-13 EFFECT OF INTERIOR PARTITIONS ON DETECTOR RESPONSE
4-35
In so doing, it will be reduced in intensity by virtue of the attenuation effect of the mass thickness of the partition. Thus, one of the effects of interior partitions is to reduce the amount of radiation reaching the detector from
overhead sources. Figure 4-3(b) portrays this effect; the vertically hatched
•
shading indicates a nominally uniform intensity of radiation approaching
the detector from the underside of the overhead barrier. The broken line hatching indicates a reduction in intensity as a portion of the original rays are absorbed in the partition barrier.
Figures 4-13(c) and (d) show a similar effect with respect to ground
(or wall) contribution. Radiation emerging from the inside, exterior wall surface and traveling on a path to the detector is attenuated as it passes through the interior partition. This is indicated pictorially in the figure by a change from solid line to dashed line hatching.
The overall effect of interior partitions is one of reducing both ground and overhead contributions and, consequently, increasing protection.
4-5.2 Attenuation Factors vs. Barrier Factors
Attenuation factors are applied as corrections to roof and wall contributions to account for the presence of interior barriers such as partitions,
ceilings, and floors. An attenuation factor is defined generally as the ratio of a contribution at a point in a building with an interior barrier to the contribution for the same conditions but with no barrier. Attenuation factors are intended to account for both barrier and geometry effects, and are dif
ferentiated from barrier factors in which only barrier effects are accounted for. In the standard method of analysis, the term barrier factor applies only to the reduction of contributions through exterior wall barriers while the term
attenuation factor applies to reduction through interior barriers.
The effect of placing interior partitions in the standard one-story blockhouse is to reduce both roof and wall contributions from what they would be if there were not interior partitions. Separate attenuation factors are required to evaluate wall and roof contributions because the angular distribution of radiation incident
on the interior partition is different in each case. In the case of the wall con
tribution, emergence is from the roof perpendicular to the partition.
4-5.3 Partition Effect on Ground Contribution C g
In the standard method it is assumed that the angular distribution of radi
ation incident on the interior partition is not significantly different from that on
an exterior wall at a point 3 feet above the source plane. Further, interior ·
4-36
partition attenuation is assumed to be independent of the exact location of
an interior partition relative to the exterior wall and the detector. Stated
in another way, geometry is assumed to play an insignificant role for this
type of attenuation factor. Therefore the inteior partition attenuation
factor, Bi, applied to wall contributions is represented by the exterior wall
barrier factor Be at a height of 3 feet: Bi(Xi)=Be(Xe=Xi, H = 3.3).
Bi(Xi) is given in Figure 4-14 also reproduced as Chart 7 in Appendix C. Following the discussion above, it is noted that the values for Bi(Xi) coincide with those from Chart 6 for Be(H, Xe) when H = 3 feet.
It should be noted that H is not a factor in the evaluation of Bi. The effect of height is always taken into account only in the exterior wall barrier factor, Be(H, Xe), even though Xe may be zero. Since His involved only in Be, it is not permissible in the standard method to add pottition mass thickness to exterior wall mass thickness to obtain a single barrier factor, Be(H,Xe+ Xi). Figure 4-13(c) and (d) illustrates the effect of interior partitions in reducing wall contributions to the detector. In calculations, the functional expression for Cg becomes:
Bi = attenuation factor for interior partitions applied to wall contributions; Bi(Xi).
Xi = average mass thickness of interior partitions in pounds per square foot of surface area.
Partitions contain openings Vvh ich are ineffective in reducing the contribution. In the calculations, this is accounted for by taking Xi as the average 11 smeared11 weight in pounds per square foot. For example, if the weight of the solid parts of a partition is 50 psf, and the partition contains 20% openings, Xi is taken as 80% of 50 or 40 psf.
If more than one partition intervenes between the exterior wall and the detector, the 11 Smeared 11 mass thicknesses of these are added together to obtain a single value of Xi which then is used to determine a single partition attenuation factor applicable to cg.
In problem 4-4 the grOund contribution for a simple blockhouse without interior partitions was calculated as C = .0567. If interior partitions having a mass thickness Xi = 40 psf4Jnd compfetely surrounding the detector) are added to the building, the interior partition attenuation factor for ground contribution
4-37
•
B·=
I
I
B·=
I
(/,)
a:
0
1
(.)
<(
u.
2 0
1
<( :::> 2
w
II
<(
2 0
II
a:
<(
0..
a:
0
a:
w
1
2
25 50 75 100 125 150 175 200 225 250
INTERIOR PA RTITION MASS THICKN ESS, X i psf
I
FIGURE 4-14
I
INTERIOR PARTITION ATTENUATION FACTORS, Bi(Xi) AND Bi(Xi) (CHART 7 APPENDIX C)
4-38
Bi(40) is 0.38. The ground contribution then becomes Cg = 0.0567 x 0.38 = .0215.
It is emphasized again that, at this stage in the development of the standard method, only rectangular (or circular) buildings, with a centrally located detector and with symmetry about the detector axes in plan, can be analyzed. Complex structures lacking symmetry or with other irregularities will be considered later.
4-5.4 Effect of Partitions on Overhead Contribution, C0
Figure 4-15 shows plan and section views of a single-story structure with a centrally located detector completely surrounded by partitions. Consideration is given to those sources lying on the core area and on the peripheral area of the roof shown in plan. The area included within the partitions is the core area and that outside the partitions is the peripheral area.
Referring to the section, it is observed that radiation, originating with fallout particles on the core area and passing to the detector through the zone defined by w , is unaffected by the existence of the partitions. That origi
o
nating with fallout on the peripheral area can arrive at the detector only by passing through the partitions where attenuation will occur.
Considering the entire roof and ignoring, for the time being, the partitions, the contribution for all roof sources, both core and peripheral, would be C0(w~, X0). Considering only the core area and ignoring, for the time being, the presence of partitions, the contribution would be C0( w0, X0). It follows that the contribution originating from periphera I sources is evidently the difference between the whole roof and core contributions, or, C0(w 0 I ,X0)C0(w , X ). This peripheral contribution is affected by the partitions. A partition gtten~at.ion factor must be applied rendering [C0(w~, X0 )-c0 (w0 ,Xo)]B1i(Xi) for the peripheral contribution to the detector. In this expression
I
B i = P9rtition attenuation factor applied to overhead contributions; Bi(Xi),
and all other symbols are as previously defined with Xi being taken as the average or 11smeared11 mass thickness of a partition with openings.
The total overhead contribution to the detector is evidently that from the core area plus that from the peripheral area, or,
I I
C0(W0,X0) + [C0(w 0, X0)-C0(w0, X0)]Bi(Xi).
4-39
208-401 0 -76 -8
L
I~
w
11110111
FIGURE 4-15 EFFECT OF PARTITIONS ON C
0
4-40
The partition attenuation factor, Bi(Xi),to be applied to C0 is discussed below.
Eisenhauer's work gives only one case of a barrier perpendicular to a horizontal plane of contamination. This is the case of the exterior wall barrier factor, Be(H,Xe), of Figure 4-11 and Chart 6. This is illustrated in Figure 4-16(a). In Figure 4-16(b), there is shown a vertical barrier adjacent to a horizontal plane of contamination but with a horizontal barrier of mass thickness Xinterposed between the source and the vertical barrier. With
0
the exception of the X0 barrier, the two figures are similar. Furthermore,
Figure 4-16(b) is similar to a roof-partition barrier situation (turned upside down). Since the only barrier factor chart that is available and applicable pertains to the situation of Figure 4-16(a), some scheme must be devised to convert the case of Figure 4-16(b) to 4 -16(a) in order that Figure 4-11 (Chart 6) may be used to describe attenuation effects of interest.
In Figure 4-16(b), the radiation originating from the covered sources is reduced in penetrating the mass thickness, X0 • The material of which the barrier is composed is of no consequence. It could be air or it could be any solid material. If it were air, its physical thickness would be 13 .3X0 , since
13.3 feet of air weighs one pound per square foot (approximately). Clearly, then, the amount of radiation emerging from the horizontal barrier of mass thickness, X0 , would be the same as though it were emerging from a fictitious height, Hf, of air equal to 13.3X0 • Attenuation effects including both the fictitious air and the partition mass thickness, could be expressed as Be(Hf, Xi) where Hf = 13.3X0 , and Chart 6 (Figure 4-11) could be used to determine values. However, this total barrier effect cannot be applied directly to the case of an overhead contribution through a partition, since C0 has, in itself, already considered a reduction in passing through the horizontal barrier, X0 • It follows that Be(Hf, Xi) must be divided by some factor to eliminate an otherwise dual reduction involving the mass thickness X0 • This factor can again be considered as a reduction through 13.3X0 feet of air and can be expressed as Be(Hf, 0 psf) giving, as the total attenuation factor.
Be(Hf, Xi) Be(Hf, 0 psf)
Stated in another way, a barrier factor is simply the ratio of emergent to incident radiation. In the case of the interior partition intercepting a roof contribution, it is the ratio of the amount of radiation emerging from the inside of the partition to that incident to the outside. Emerging radiation has been reduced by the horizontal barrier, X0 , replaced by a fictitious height of air, Hf = 13.3X0 , and by the interior partition mass thickness Xi. The emerging quantity is the
4-41
0
X
(V)
.
(V)
iT
.....
I
(a) (b)
FIGURE 4-16
PARTITION BARRIER EFFECT ON C
0
numerator of the factor given above. The radiation inCident upon the outside of the partition is that which has penetrated the roof and has been reduced by attenuation in the mass thickness X0 . The replacement of Xo with H f gives this quantity appearing in the denominator of the expression. Chart 6 can be used to determine both. For example, considera roof contribution passing through
an interior partition. Let X0 =50 psf and Xi = 40 psf. Hf = 13.3x50 = 665 and Be(Hf,Xi)=Be(665,40)=0.021. Also, Be(Hf,O)=Be(665, 0)=0.075. The ratio 0.21/0.075 = 0.28, which would be applied as the attenuation factor for that portion of an overhead contribution passing through an interior partition.
It turns out, and the analyst may verify, that as X0 becomes greater than about 50 psf, increases beyond 50 psf do not significantly affect the ratio for all values of Xi· Most of the change in the ratio occurs for values of X0 between 0 and 15 psf. As a result, it is possible to plot one curve based on X0 =50 psf
4-42
for varying values of Xi· This single curve will give results very close to what would be obtained if the ratio were used. This curve has been plotted on Figure 4-14 (Chart 7 in Appendix C) and may be used in I ieu of the ratip expression.
In the example cited above, it is found that Figure 4-14 yields Bi(40)=0.27, which compares favorably with the ratio calculated from Chart 6 values.
Problem 4-6 shows the detailed calculation of the roof contribution if 40 psf partitions are added to the one-story blockhouse of Problem 4-4.
Problem 4-7 involves all the basic concepts considered to this point.
Interior partitions are assumed to surround the centrally located detector forming a core that is 20 feet wide and 25 feet long. The interior partitions weigh, in their solid parts, 80 psf, but contain 25% openings. Their effec,tive mass thickness is, thus, 60 psf. This value is used in determining Bi and Bi from the charts.
The solid angle fraction, w 0 , defines the core contribution from overhead. Data for determiningware recorded in the set of tabular values. Geometry
0
factors ( G d, Gs and Ga) for w0 are not needed in the probI em and have not been recorded.
4-6 Buried Structures
4-6. 1 Partially Buried and Completely Buried Structures
Figure 4-17 depicts several stages of burial of a single-story structure. In (a), of the figure, the structure is completely exposed and passes full wall and overhead contributions to the centrally located detector. In (b), the floor is indicated below grade with the plane of the detector still being located above the contaminated ground plane. Essentially, only the portion of the wall below
the detector plane is affected by this partial burial. The total contribution to
the detector has obviously been reduced as indicated by the increase in the
lower solid angle. Only a portion of the lower wall segment contributes direct
radiation to the detector.
In (c) of the figure, the detector plane is at the same elevation as the contaminated ground plane, and no part of the wall below this plane contributes
to the detector. All of the direct contribution and scatter has now been elimi
nated from the lower wall segment. Contribution from the upper wall segment
and overhead remain unaffected.
In (d), the structure has been further depressed with a resultant decrease in skyshine and scatter contributions from the upper wall segment. The overhead contribution is unaffected.
4-43
PROBLEM 4-6
(whole roof)
w = 40 ft.
L = 60 ft.
z = 10 ft.
(core) ~·~ ~'D'D'~
w = 15 ft.
L = 30 ft.
" -· 10 ft. 30'
r I....: 60'
X ~~ = 150 psf I 0
I
X = 100 psf
:~r·.........·:··$=·~···:·····;·;·;·;\;
X. e l. = 40 psf -----fo;<4-15 40I
:::. .=:=.:
_j_
'
~=~·-····················· ·.·.·.·.·.·.·.···········:: ---
I
Ground Contribution:
C = .0215 (Article 4-5.3)
g
Overhead Contribution:
Whole roof contribution
C (w' X ) = 0.0043
o o' o
Core contribution
w 15
= = 0.50
L 30
z 10
= 0.33
L 30
w~
w <r z)= (0.50, o.33) = o.33 (Chart 1)
0 0
J
C (w , X ) = C (0.33, 150) = 0.0032 (Chart 9)
0 0 0 0
Partition barrier factor
B~(X.) = B~(40) = 0.27 (Chart 7)
l. J. l.
Total overhead contribution
C (w, X)+ {C (w', X)-C (w , X )}B~(X.) =
0 0 0 0 ' 0 0 0 0 0 1 l.
0.0032 + (0.0043 -0.0032) 0.27 = 0.0035
RF = c + c = 0.0215 + 0.0035 = 0.025
g 0
PF = 1/RF = 1/0.025 = 40
4-44
PROBLEM 4-7
Building: w = 50 feet L = 100 feet Core: w = 20 feet L = 25 feet
X = 100 psf
0
X = 120 psf
e
X. = 80 psf
1
(25% open)
w L z W/L Z/L w Gd G s G a w 50 100 15 0.50 0.15 0.61 ----0.340 p.068
u
,... ____
WL 50 100 3 0.50 0.03 o. 915, 0.380 0.100
w 0 20 25 15 0.80 0.60 0.24 ----
E(0.50) = 1.34, S w(120) = 0.80, B e (3,120) = 0.060 B.(60) = 0.24, B~(60) = 0.16 (60 = 75% of 80)
1 1
Gg = {G(wu) + G(wL)}E(e)Sw(Xe) + {Gd(H,wL) +
8 8
Ga(wu)}{1-Sw(Xe)} = (0.440 X 1.34 X 0.80) + (0.448 X 0.20) = 0,561
cg = G B (H,x )B.(X.) = o.561 x o.o6o x o.24 = o.oo81
g e e 1 1 C 0 (w0 ,X)+ {C (w ,X) -C (w ,X )}B~(X.) =
0 0 u 0 0 0 0 1 1 0.0075 + (0.014 -0.0075)0.16 = 0.0085
RF = cg + c = o.oo81 + o.oo85 = o.0166
0
PF = 1/RF = 1/0.0166 = about 60
4-45
FIGURE 4-17
~FFFrT OF STRUCTURE BURIAL ON
DETECTOR RESPONSE
4-46
It could logically be asked whether or not the particles on the ground
contribute radiation to the detector on direct paths through earth and buried
wall to the detector. Theoretically, there is such a contribution, particularly
from those sources immediately adjacent to the structure. Such contributions
are, in practical cases, small compared to other contributions and can reasonably
be neglected. In calculating wall contributions, a belowground detector is
assumed to receive no contribution in the form of direct radiation (or scatter)
through the buried wall segment from ground sources. Only the exposed portions
of the wall contribute.
In (e), the entire wall is buried and the only contribution is that from
overhead sources. As the structure is further depressed, as in (f), the effect
is essentially one of adding overhead mass thickness by virtue of increased
earth cover. As indicated in the figure, the area of contamination contributing
to the overhead contribution is also increased but the increased barrier effect
and consequent decrease in contribution far outweighs the increased area effect
and increase in contribution.
A qualitative interpretation of the effect of burial, all other parameters remaining constant, leads to the general observation that increasing depths of burial are accompanied by decreases in contribution to the detector and increased
protection.
4-6.2 Completely Buried Simple Rectangular Structure
A completely buried rectangular structure, with a centrally located detector requires no new concepts of analysis beyond those previously discussed. A belowground detector is assumed to receive no radiation through those portions of walls
lying below the contaminated ground plane. The only contribution that must be considered in the analysis of a completely buried shelter is that which comes from overhead; i.e., C0 • With this assumption in mind, the calculations of
Problem 4-B(a) should require no explanation. The structure is rectangular
with a centrally located detector. In the (b) part of the problem, the protection factor is known. The reciprocal of the protection factor is the required reduction factor which, in turn, is the overhead contribution, C0 , since there are no other
contributions to be considered.
Since wis also known, the required mass thickness is determined by entering Chart 9 withw, proceeding vertically to the required C0 and hence interpolating to read X0 •
Problem 4-9 is presented not as the representation of a practical shelter,
but to illustrate a technique of analysis. The roof of the core over the centrally located detector has a reduced mass thickness. In the first step, the entire roof is assumed to have a mass thickness of 200 psf, the same as the periphera I area,
4-47
PROBLEM 4-8
w = 30 feet L = 80 feetRoof = 8" concrete= 100 psf
••••• •••• •• • ................. 'J' ......... ~· •
(a) Find the PF if the roof is at grade.
(b) What amount of earth cover would be required to give a PF of 1000 if earth is assumed to weigh 120 pcf and Z is held at 12 feet?
w ~o = 12
(a) e = -L = so= 0.375, a = Lz 80 = 0.15
wz
w(L'L) = w(0.375,0.15) = 0.55
C (w,X ) = C (0.55,100) = 0.013
0 0 0
PF = 1/0.013 = 77
(b) For PF = 1000, RF = C0 = 1/1000 = 0.001
c (w,x ) = c (0.55,X ) = 0.001
0 0 0 0
From Chart 9, if w = 0.55 and C= 0.001, X0
0 required is 210 psf. Approximately one foot
of earth cover would be required to give a
total X0 = 210 psf.
4-48
PROBLEM 4-9
= 150 psf (core) = 200 psf (periphery) = 40, L = 80 (whole) = 20, L = 20 (core)
1. whole roof at 200 psf z 10
w = 40 -0 50
y; 80 -. ' L = 80 = 0.125
,<w z) = w'(0.50, 0.125) = 0.67
w L'L
C (w',X) = c (0.67,200) = 0.0014
0 0 0
2. core at 200 psf z 10
w 2200 = 1.00
L = y; = 20 = 0.50
w'(~.~) = w(1,00,0.50) = 0.33
C (w,X ) = C (0.33,200) = 0.00097 say 0.0010
0 0 0
3. periphery at 200 psf
0.0014 -0.0010 = 0.0004
4. core at 150 psf c (w~x ) = c (0.33,150) = 0.0032
0 0 0
5.
Total contribution = 0.0032 + 0.0004 = 0.0036
6.
PF = 1/0.0036 = about 280
4-49
and the contribution is determined to be 0.0014. In the second step, the
contribution from the core area is determined to be 0.0010 with an assumed
mass thickness of 200 psf. It should be evident that the difference between these two values, 0.004, represents the actual contribution from the peripheral area which has an actual mass thickness of 200 psf. In step 4, the core contribution is calculated as 0.0032, using its actual mass thickness of 150 psf.
The sum of the actual core and peripheral contributions, 0.0036, represents the total overhead contribution yielding a protection factor of about 280.
The technique employed in Problem 4-9 is termed differencing of over
head c~ntributions. This is a technique that will be found extremely useful
in handling certain complex situations. In differencing overhead contributions,
three rules are observed. First, the detector must be centrally located with
respect to the overhead plan areas. Second, the vertical distances from the plane of the detector to the overhead contaminated planes must be the same. Third, the mass thicknesses utilized in expressions for C0 that are to be differenced, must be the same.
A study of the calculations for Problem 4-9 leads to some interesting observations. It is noted that of the total contribution of 0.0014 from an area of 3200 square feet at 200 psf, 0. 0010 originates from a central area of 400 square feet at 200 psf. About 70% of the tota I comes from about 12% of the area centrally located with respect to the detector. It is further noted that decreasing the core mass thickness 25%, from 200 to 150 psf, increases the core contribution by a factor of about 3.20.
4-6.3 Single-Story, Semiburied Structures
The effect of partial burial of a single-story structure has been discussed
qualitatively, now the analysis method will be applied to several cases involving
varying degrees of buria I from zero to full depth. The depth of buria I has no
effect on overhead contributions so the illustrative examples that follow will
be restricted to a consideration of ground contribution.
Figure 4-18 shows the structural configurations for Problem 4-10 which
will be worked in five parts corresponding to the depths of burial shown in "a",
"b", "c", "d", and "e". Part "a" of the problem involves no burial. The
solution is identical with that for any single-story blockhouse. For purposes
that will become clear as the remaining parts to the problem are solved, the
ground contribution has been calculated in two parts, that from the portion of
the wall above the detector plane and that from below the plane of the detector.
The solid angle fractions and geometry factors (Gd, Ga, Gs) for all parts to
the problem have been recorded in one table. The solid angle fraction, w ,
u
4-50
w= 30ft. L = 50 ft. Xe = 100 psf
(a)
(b)
(e)
FIGURE 4-18 STRUCTURES FOR PROBLEM 4-10
4-51
PROBLEM 4-10
w L z W/L Z/L w Gd Gs Ga
w 30 50 10 0.60 0.20 0.56 -----0.360 0.072
WL u 30 50 3 0.60 0.06 0.85 0.500 0.175 ----
w'L 30 50 1.5 0.60 0.03 0.925 0.360 lo .088 ----
w'
u 30 50 5 0.60 0.10 0.76 -----p.255 0.051
E(0.60) = 1.37; Sw(100) = 0.775; Be (3,100) = 0.093
Part "a"
~ortion of Wall Above Detector:
Cga = {G 8 (wu)E(e)Sw(Xe) + Ga(wu)[1-Sw(Xe)]}Be(H,Xe) = [(0.360) X 1.37 X 0.775) + (0.072 X 0.225)] 0.093 = 0.0370 Portion of Wall Below Detector: Cgb = {G 8 (wL)E(e)Sw(X8 ) + Gd~'~)[1-Sw(Xe)]}Be(H,Xe) = [(0.175 X 1.37 X 0.775) + (0.500 X 0.225)]0.093 = 0.0278 Total Ground Contribution: = 0.0370 + 0.0278 = 0.0648
Part ''b"
(wL)E(e)Sw(Xe) + Gd(H,wL)[1-Sw(Xe)]}Be(H,Xe)
cgb = {G 8 = ((0.088 X 1.37 X 0.775) + (0.360 X 0.225)]0.093 = 0.0162 c = 0.0370 + 0.0162 = 0.0532
g
Part "c"
= 0.0370
4-52
PROBLEM 4-10, (cont.)
Part "d" = [G (w ) -G (w' )]E(e)S (X ) + [G (w )
s u s u w e a u G (w' )] [1-S (X )]
a u w e= (0.105 X 1.37 X 0.775) + (0.021 X 0.225)= 0.1162 = Gg Be (H,Xe ) = 0.1162 x 0.093 = 0.0108 Part "e" c = 0.0
g
4-53
is common to all parts and appears only once in the table. The total ground is ega (from above) and cgb (from below).
contribution, cg, for Part 11 a II
In Part 11 b11 , it was necessary to calculate only the contribution from below the plane of the detector, since that from above has already been computed in Part 11 a 11 Note that, even though the detector plane is less than 3 feet above
•
the contaminated plane, all values that are height dependent are determined for H =3 feet. Burial of half the depth of wall below the plane of the detector has, in this case, reduced the contribution from the portion of wall below the detector by about 40%.
· In Part 11 C 11 , all of the contribution from below the detector plane has been eliminated. It is well to point out, however, that contributions and protection factors are calculated for point locations. A 6-foot tall man, standing at the center of the structure in Part 11 C 11 , would still receive 0.0278 (Cgb from Part 11 a 11 solution) at about the level of his eyes. To take full advantage of the
elimination of this contribution, he would be required to maintain himself below the plane of the detector at all times.
In all of the problems that have been considered to this point, ground In Part 11 d 11 of Problem 4-10 a technjque
contributions have been additive.
is illustrated which involves the differencing of ground contributions. This
is a technique that has wide application in fallout shelter analysis. With ) account for radiation
reference to Figure 4-18(d), both Gs(w ) and Ga(w contributed through the entire 10 feet ofwall above t~e plane of the detector. Interest in ,the problem exists only in the top 5 feet of the wall above. Gs(wu)I and Ga( wu) account for radiation contributed through the bottom 5 feet of the wall above the detector. Obviously, the difference between the two Gs values and the two Ga values determines the scatter and skyshine geometry factors respectively for ground contribution from the top 5 feet of interest. It can readily be seen that this technique of differencing ground contributions can be used to isolate the contribution through any vertical section of any wall. Similar differencing of contributions can be applied to a portion of the lower part of the wall. Adding and differencing contributions are extremely important concepts in the writing of functional equations for ground contribution.
4-7 Basement Shelters
All else being equal, basement areas of buildings generally provide the highest degree of protection from gamma radiation. From the discussions previously given on buried and semi-buried structures, it is obvious that the elimination of all or part of the ground contribution, by depressing the detector below ground level 1 has significant effect on the protection factor. A basement 4-54
for the purpose of this discussion, is a story of a building buried to the extent
that a detector, located 3 feet above the floor, is below grade; i.e. below
the contami noted pia ne. Part of a basement wa II may be exposed, or the
entire wall may be beneath the ground surface.
Figure 4-19 shows a section through a rectangular bui Iding composed of
a basement and a story above. A portion of the basement wa II is exposed.
The total contribution to the detector can be considered in three parts -an
overhead contribution from roof sources, a ground contribution through the
walls of the story above that passes through the ceiling to reach the detector,
and a ground contribution through the exposed part of the basement wall.
Attention is first directed to the overhead contribution. The solid angle· fraction w• indicates the zone through which the overhead contribution arrives at the detector. In arriving there, it must pass through both the roof barrier and the ceiling barrier directly over the detector. Each of these barriers is effective in reducing the contribution to the detector. In calculating the overhead contribution, the total mass between the contaminated roof plane and the detector (roof and ceiling) is assumed to be concentrated at the
contaminated plane.
The overhead contribution is defined by the functional expression, C0 (w 11 , X0 ). In this expression, Xis taken as the combined overhead mass
0
thickness which is the sum of the mass thicknesses of the roof and the ceiling
above the detector, in this case.
The contribution through the exposed portion of the basement wa II consists only of skyshine and scatter radiation through the zone defined by w and w•. The ground contribution reaching the detector through the exposed portion of the basement wall is calculated in a manner identical with that used 11 d 11
in Problem 4-10 Part , using the differencing technique. The differencing technique, is also employed for the story above. It is noted that this latter contribution arrives at the detector only after passing through the ceiling mass
where it suffers a reduction. The functional expression for this contribution must contain an attenuation factor associated with the ceiling mass thickness and applied as a multiplier to cg.
The following formula is used to evaluate ceiling attenuation factors used in the standard method of analysis:
Bc(Xc, w) =(l-3.5e-2.3w)e-1.0 Xc + (3.5e-2.3w)e-0.04 Xc
4-55
208-401 0-76 -9
FIGURE 4-19BASEMENT DETECTOR LOCATION
Be = attenuation factor applied to ground contributions passing through a ceiling above the detector; Bc(Xc, w ) .
Xc = the total mass thickness in pounds per square foot of a horizontal barrier (ceiling) directly above the detector.
w = the solid angle fraction subtending the ceiling.
The formula above was developed from an evaluation of experimental data from various sources. It reproduces the experimentally observed attenuation in ceilings of the most significant test structures for which data were available. This approach to the so-called 11 in -and-down11 problem differs from earlier methodology in that it is based on experiment rather than calculation.
4-56
Figure 4-20 (Chart SA, Appendix C) gives the ceiling attenuation factor for ground contribution in terms of the ceiling mass thickness Xc and the solid angle fraction Wsubtending the ceiling. For a case in which Xc is 100 psf and w is 0.82, the ceiling attenuation factor is 0.0092.
Problem 4-11 is illustrative of the analysis of a simple structure with its basement completely beneath the contaminated ground plane. Attention is directed to the differencing technique in the calculations for ground contri
11 b11
bution, the lack of scatter for the 0 psf case (Part ) since Sw = 0, and the
application of the ceiling attenuation factor Bc(Xc, W) as a new multiplier in
Cg. Attention is also directed to the use of H=3 feet for the exterior wall
barrier factors even though the detector is be low grade.
Note the reduction in Cg and the increase in the protection factor as
Xe decreases from 40 psf to 0 psf. As has been previously explained, parti
cularly where the contribution is a combination of scatter and skyshine, low
mass thickness will scatter more radiation into the detector than it will absorb.
The net effect is that the ground contribution may increase as the exterior wall
mass thickness is increased above 0 psf to some low value below about 70 psf.
It should be emphasized that 11 usually 11 protection factors increase as mass thickness increases, and that the phenomena described above (in which the protection factor decreases with increasing wall mass thickness) is a special case. The mechanism is associated with wall scattered radiation and low mass thickness walls. In cases in which there is appreciable direct radiation, increasing the wall mass thickness wi II increase the protection factor.
Qualitative consideration might also be given to the additional ground contribution that would come to the detector from an additional story above. At least for the building of Problem 4-11, it appears that such contribution, passing through two ceiling barriers, would be on the order of only 0.0092 times as much as that from the first story. This reduction, coupled with other reductions, would render the additional contributions quite negligible. This is particularly so for ceiling mass thicknesses that are large. For very low mass thicknesses of horizontal barriers this may not be the case. However, once the contribution from the first story above is calculated, it becomes readily apparent whether or not that from an additional story would be negligible. As a general rule, one considers as significant only the contribution from one story above, but the analyst must be cautious in exercising judgment that such maynot always be the case for basement shelters.
4-57
25 50 75 100 125 150 175 200 225
-CJ
3
u -X CJ
co z '
0 1
<(
::::>
z
w
I
I
<(
(!)
z
..J
w
u
0.001
0 25 50 175 200 225
FIGURE 4-20 CEILING ATTENUATION FACTOR, Bc(Xc,U)c) 1 (CHART SA, APPENDIX C)
4-58
PROBLEM 4-11
w = 60 ft. L = 90 ft. (a)X = 40 psf
e (b)X = 0 psf
e X =150 psf (roof)
r X =100 psf (ceiling)
c
w L z W/L Z/L (Jj Gd G G
s a
(Jj 60 90-7 0.67 0.08 0.82 ----0.20 0.040
(Jj 60 90 20 0.67 0.22 0.55 ----0.37 0.074
E(0.67) = 1.37; s (40) = 0.55; s (0) = 0.00
w w
Be(3,40) = 0.38; Be(3,0) = 1.00; Bc(100,0.82) = 0.0092
1. Ground Contribution
Part "a"
G = [G (w') -G (w)]E(e)S (X ) + [G (w')
g s s w e a G (w)] [1-S (X )]
a w e = (0.17 X 1.37 X 0.55) + (0.034 X 0.45) 0.143
' C = G B (H,X )B (X ,w)
g g e e c c = 0.143 X 0.38 X 0.0092 = 0.00050
Part "b"
G = G (w') G (w) = 0.034
g a a
Cg = GgBe(H,O psf)Bc(Xc,w) = 0.034 X 1.00 X 0.0092 = 0.00031
2. Overhead Contribution
C (w' ,X) = C (0.55,250) = 0.00055
0 0 0
3. Protection Factors RF = 0.00105 PF = 958 (a); RF = 0.00086 PF = 11GO (b)
4-59
Problem 4-12 involves the analysis of a building with the detector centrally located in a basement. A portion of the basement walls is exposed. No new concepts are involved. Problems 4-10 and 4-11, with pertinent discussion, have developed the methodology assocated with the ground contributions through the exposed portions of the basement wall and through the walls of the story above. Partitions have been assumed to surround the detector forming a centrally located core area. These partitions affect the ground contribution and the overhead contribution through the introduction of attenuation factors.
Attention is directed to the effect of basement exposure on the protect
ion factor. Complete burial would eliminate any contribution from the basement walls. The result would be a total contribution of0.00292 and a protection factor of 345, about double. Elimination of exposed basement walls generally result in considerable increase in protection in basement shelters.
4-8 Simple Multi-story Buildings
Very often it is necessary to calculate the protection factor at some location in an upper story of a multistory building. In selecting the position of the detector, normal practice is to place it 3 feet above the floor in
question. Unless there is some definite reason for doing otherwise, the
detector is always assumed to lie 3 feet above the floor. In an upper story
location, the distance H between the detector and the ground contaminated
plane is greater than the standard 3 feet. Detector height H affects both
the geometry factor for ground direct radiation and the exterior wall barrier factor.
The effect of detector height on ground direct radiation is shown in Figure 4-21 .
In the figure, a single-story blockhouse, with a centrally located detector 3 feet above the floor, has been fictitiously elevated so that the floor is some distance above grade. For purposes of this discussion, it is
assumed that the only contribution of the detector is that through the walls
of the structure from floor to ceiling.
The most significant consideration, in Figure 4-21, is the effect of elevation on the direct contribution through the portion of the wall below the detector plane. If the floor were at grade, every radiating source from the outside boundary of the wall outward to the limit of the contaminated plane (infinity is assumed here) would be a potential contributor of direct radiation through the lower wall segment. Assuming no contribution through
4-60
PROBLEM 4-12
X = 75 psf (roof
r X = 75 psf (ceiling)
c X = 50 psf (above wall)
e X = 100 psf (basement wall)
e
X. = 40 psf (partition)
1
w L z W/L Z/L w Gd G G
s a w 20 30 20 0.67 0.67 0.17 -----------
0
w 50 100 20 0.50 0.20 0.51 ----0.380 0.076
w' 50 100 7 0.50 0.07 0.80 ----0.220 0.044 w" 50 100 4 0.50 0.04 0.89 ----0.130 0.026
E ( 0. 50) = 1. 34; s (50) = 0.61; s (100) = 0.775
w w B (3,50) = 0.30, B (3,100) = 0.093; B.(40) = 0.38
e e 1 B (75,0.80) = 0.029, B!(40) = 0.27
c l
1. Roof Contribution C (w ,X ) = C (0.17,150) = 0.0019
0 0 0 0
C (w,X ) = C (0.51, 150) = 0.0039
0 0 0
C ( w , X ) + [C ( w, X ) -C ( w , X ) ] B! (X-~·) •
0 00 0 0 0 0 0 1 1
0.0019 + (0.0039 -0.0019)0.21 = 0.00244
2. Ground contribution -Story Above
G = [G (w) -G (w' )]E(e)S (X ) + [G (w) -G (w' )]
g s s w e a a
4-61
PROBLEM 4-12 (cont.)
[1-S (X ) ]'
w e = (0.160 X 1.34 X 0.61) + (0.032 X 0.39) = 0.1435 C = G B (H,X )B.(X.)B (X ,w)
g g e e 1 1 c c
0.1435 X 0.30 X 0.38 X 0.029 = 0.00048
3. Ground contribution --Exposed Basement
G = [G (w') -G (w")]E(e)S (X ) +-[G (w')
g s s w e a
G (w")] [1-S (X )]
a w e
= (0.090 x 1.34xQ.775)+(0.018x0.225)=0.0975
C = G B (H,X )B.(X.)
g g e e 1 1
= 0,0975 X 0.093 X 0.38 = 0.00345
4.
RF = 0.00244 + 0.00048 + 0.00345 = 0.00637
5.
PF = 157
\
4-62
•
FIGURE 4-21
EFFECT OF DETECTOR HEIGHT ON DIRECT CONTRIBUTION
the floor of the structure, as is implied in the figure,elevating the structure eliminates a certain portion of the close-in sources as contributors of direct radiation through the wall to the detector. These are the particles lying between the boundary of the structure and the inner limit of particles on the ground that can be "seen" by the detector as it looks through the bottom of the lower wall segment. Obviously, the greater the reduction in direct radiation through the lower wall segment of interest, the greater the protection. This reduction in direct contribution is a very important factor and accounts for the fact that upper story locations in multi-story buildings often have good protection factors.
Figure 4-7 (Chart 3A and 3B in Appendix C) gives the geometry factor for direct radiation as a function of detector height and solid angle fraction Gd(H,w). There is a dual dependence on height in the chart. First, as discussed in Chapter Ill, the dose angular distribution for direct radiation is different at different detector heights. Therefore, for a given value of w, the geometry factor at different heights would be different. A more significant effect, however, is the fact thatfor a given value of wthe "cleared area 11 around the building increases sharply with increasing detector height H. In Figure 4-21 the area between the boundaries of the building and the closest (to the building) fallout particle that the detector can "see," may be thought of as a "cleared area" around the bui I ding. This is purely a geometric effect and is accounted for in Charts 3A and 3B of Appendix C.
4-63
The effect of detector height on ground contributions is accounted for in the value of the exterior wall barrier factor Be(H,Xe) Figure 4-11 (Chart 6, Appendix C). The influence of increased distance from the source, the mass of intervening air, and the variation of the angular distribution of radiation with height are accounted for in the exterior wall barrier factor. Since Be(H,Xe) is applied as a multiplier to the ground contribution geometry factor, skyshine, scatter and direct radiation are all reduced with height.
It should be obvious that overhead contribution is not a function of the height of the detector, H, above the contaminated ground plane. Skyshine through the roof is accounted for by an allowance in Chart 9.
For purposes of evaluating an upper story detector location, consider the three-story building with the detector centrally located in the middle story, shown in Figure 4-22.
Attention is first directed to the contribution through the walls of the story in which the detector is located, hereafter referred to as the detector story. The portions of the walls of the detector story lying above the plane of the detector contribute only skyshine and scatter. As discussed previously, elevating the detector has no effect on skyshine and scatter geometry factors and the exterior wall barrier factor takes into account height effects.
The portions of the wall of the detector story lying below the detector plane, contribute both direct and scatter radiation to the detector.
The functional equation for the ground contribution to the detector through the waIts of the detector story wi II be exactly the same as thatfor the single story blockhouse. The difference is that in the terms Gd(H,w L) and Be(H,Xe) the detector height H is no longer 3 feet.
Radiation reaching the detector through the walls of the story above the detector is similar to the ground contribution to a basement detector location, through the walls of the story above. The functional equation will be similar to that for a basement location and the effect of story height on the in-and-down radiation is accounted for in the exterior wall barrier factor,
Be(H,Xe).
Consideration is now given to the contribution arriving at the detector
from the walls of the story with the detector story or, simply, the story below. This consideration arrives through the zone included between the rays defining wLand wL' extended to intersect the contaminated ground plane. All of those sources lying beyond have contributed to the direct radiation through the walls
4-64
FIGURE 4-22
CENTRALLY LOCATED DETECTOR
4-65
of the detector story. As discussed previously, all particles regardless of their horizontal orientation, are potential contributors of scatter radiation at any point in any wall of the structure building. It should be noted that the floor immediately below the detector acts as a horizontal barrier to a II radiation coming from below. Direct and scatter radiation emerging from
the walls of the story below and traveling on paths toward the detector will
be reduced in quantity on passing through this floor barrier. This is indicated
in the figure by a change in hatching from solid diagonal lines to broken diagonal lines.
The differencing technique for geometry factors can be utilized to define geometry for each part of the direct radiation contribution. Gd, as a function of wLt for example, defines the direct geometry factor for the walls of the detector story. Gd, as a function of wl, minus Gd as a function · of WL defines the direct geometry factor for the walls of the story next below the detector story.
Scatter geometry through the wall below the story of the detector can be defined in the same way as for direct radiation, utilizing the differencing technique The geometry factor for the ground contribution to the detector through the walls of the story below the detector is:
G = {[Gd(wl~ H) -Gd( wl' H)][1-S (X )] + [G ( wl:•) -G (w L)]S (X )E(e)}
g we s s we
An attenuation factor is needed to account for reduction in radiation caused by the floor barrier.
Even though the ceiling above and the floor below may both have the same mass thickness, the barrier effects associated with each of them will differ. In Chapter Ill, it was noted that one of the parameters in determining the effectiveness of a barrier is the energy distribution of the photons incident on it. Since each scatter reaction results in departing photons of less energy than that of the original photons, the average energy of photons incident on the ceiling is less than that on the floor. The former are all either wallscattered or air-scattered while the latter contains a direct component.
Figure 4-23 (Chart 8B) gives the attenuation factor, Bf(Xf), applied to a contribution arriving at the detector through the floor below. It is applied as a multiplying function to the other factors involved in the functional expression for Cg. This curve has been derived by considering the reduction as a function of height a lone for X = 0 psf. For example 1 from Chart 6 with X= 0 psf, and H = 333 feet, the barrier reduction factor is 0.17. A height of air column of 333 feet weighs 25 psf. In Chart 8B, Bf(25 psf) is reasonably close to 0.17.
4-66
Although only 3 stories have been considered in this discussion, extension, without change in fundamental concepts, could be made to include more stories above and below the detector story.
Generally1 in the case of a detector located in an upper story of a building, it is necessary to consider wall contributions through the detector story and only one story above and one story below. It becomes readily apparent from these calculations whether or not additional stories must be considered. It is extremely rare that contributions from more than one story above and one below the detector story are significant. Considering 3 stories only, of the total ground contribution, approximately 900/o arrives through the walls of the detector story and the bulk of the remainder from the story below. Considering more stories would indicate precision in the method beyond ti-e range of reason.
Problem 4-13 considers an isolated 12-story building 90 feet wide by 300 feet long. All stories are assumed to be 10 feet high. A centrally located detector in the lOth story is surrounded on all sides by interior partitions having a mass thickness of 40 psf and extending through all stories. These partitions form a core 10 feet wide by 280 feet long. This corresponds to a central corridor in a multi-story building. All floors and the roof are assumed to have a mass thickness of 50 psf. The exterior walls, containing no apertures, are assumed to have a mass thickness of 60 psf. It is required to find the protection factor at the indicated detector location. This problem involw s the use of all basic concepts and charts that have been previously developed.
In step 11 the roof contribution is determined. The differencing technique for overhead contribution is used to calculate the peripheral contribution to which the partition attentuation factor has been applied. The solid angle fractions involved have been calculated in the table.
In step 2, the ground contribution through the walls of the detector story has been calculated. It is noted that the functiona I equations used are absolutely identical with those used for a single-story blockhouse. The difference lies in the chart values for Gd and Be, which are a function of H = 93 feet.
In step 3, the contribution from the walls of the story above have been calculated. It is again noted that the functional equations used are identical with those employed in determining the contribution through the walls of the story above a basement in which a detector is located. Here the differencing technique has been employed to determine the scatter and skyshine contributions.
4-67
FLOOR MASS THICKNESS, Xf,psf FIGURE 4-23 FLOOR ATTENUATION FACTOR Bt(Xf) (CHART 8-B APPENDIX C)
4-68
M 4-13
I:'
C'il
0 II
~
N
II
C"') (j) 0 rl
(§)
C'il
rl
~
C"') (j)
II
::t::
xr = xf =X c = 50 psf
X e = 60 psf, X. 1 = 40 psf
w = 90, L = 300, W' = 10, L' = 280
w L z W/L Z/L w Gd G s G a
w 10 2'80 27 0.036 .096 0.12 --- --- ---
0
w-' 0 90 300 27 0.300 .090 0.64 --- --- ---
w' 90 300 17 0.300 .056 0.76 --- --- ---
u
w u 90 300 7 0.300 ,023 0.90 --- .117 .023
WL 90 .300 3 0.300 .010 0.96 0.12 .0.48 ---
w'L 90 300 13 0.300 .043 0.82 .140 . 2.00 ---
E(0.30) = 1.24; Sw(60) = 0.66 B (93,60) = .082
8
B.(40) = 0.38; B!(40) = 0.27, B (50,0.90) = 0.063; Bf(50 = 0.078
1 ~ c
4-69
PROBLEM 4-13 (cont.)
1. Roof contribution C0(w~,X0 ) = C (0.64,150) = 0.0043
0
C (w ,X) C (0.12,150) = 0.0015
000 0
C 0 (w ,X0 ) +[C (w',X)-C (w ,X )]B~(X.)
0 0 0 0 0 0 0 1 1
= 0.0015 + (0.0043 -0.0015) X 0.27 = 0.00226
2. Detector stor~
G = ['G ( w ) + G (wL)]E(e)S (X ) + [Gd(H,wL) +
g s u s w e
G (w )] [1-S (X )]
a u w e G g = (0.165 X 1. 24 X 0. 66) + (0.035 X 0.34) = 0.147
c = G B (H, X )B. (X. )
g g e e 1 1 c = 0.147 X 0.082 X 0.38 = 0.00458
g
3. Stor~ above G = [G (w') -G (w )]E(e)S (X ) + [G (w')
g s u s u w e a u
G (w )] [1-S (X )]
a u w e G g = {0.133 X 1.24 X 0.66) + (0.027 X 0.34) = 0.1187
c = G B (H,X )B. (X. )B (X , w)
g g e e 1 1 c c
= 0.1187 X 0.082 X 0.38 X 0.063 = 0.000232
4. Story below C = [G ( wL' ) -G ( wL)] E(e)S (X ) + [ Gd ( H, wL' )
g s s w e
Gd (H, wL)1 [ 1-Sw( Xe )]
G g = (0.152 X 1. 24 X 0. 66) + (0.128 X 0.34) = 0.168
c = G B (H,X )B. (X. )Bf(Xf)
g g e e ::1.. 1 c = 0.168 X 0.082 X 0.38 X 0.078 = 0.000408
g
5. Protection factor RF = 0.00226 + 0.00458 + 0.000232 + 0.000408
RF = 0.0075 PF = 1/0.0075 = 133
4-70
The details of setting up the problem merit some attention. First of all, in the solution, the stories of interest were isolated. These included the detector story and one story above and below. Rays were drawn from the detector to embrace the wall segments of interest. These rays determine the solid angle fractions that are of interest for each wall segment. From the dimensions, the solid angle fractions can be determined, and the appropriate geometry factors can be recorded. The barrier and attenuation factors used in determining contributions are based on the sketch by noting through which barriers the radiation must pass in traveling through its zone on a path to the detector. If the analyst draws a sketch, such as was drawn in the problem solution, and mentally solves the problem in a qualitative sense, no difficulty should be experienced in the quantitative aspects. The figure itself leads to a determination of what chart values are necessary, and these should be recorded before any functional equations are written. The figure also leads to the proper functional equations if the analyst is sufficiently knowledgeable concerning the very few basic concepts and techniques involved.
4-9 Wa II Apertures
4-9. 1 Introduction
Apertures are openings in any wall or overhead barrier, such as windows, doors and skylights. The mass thickness of apertures is assumed to be zero even though, in reality, the material of which such things as windows and doors are composed may weight a very few pounds per square foot. Mass thickness of the order of that embodied in ordinary apertures is so low as to have a negligible influence on the reduction of radiation incident upon them. Obviously, there are forms of construction which result in considerable mass thickness in such things as windows, as for instance, glass block windows. Such construction cannot be properly classed as apertures in the shielding sense of the term. As a rough rule, mass thicknesses, in the order of 5 pounds per square foot or less, may be considered as aperture and the mass thickness neglected. The judgment of the analyst is an important consideration, and should be tempered by the mass thickness of material surrounding the aperture. For example, if a window weighing perhaps even 10 or more pounds per square foot is a part of a wall weighing 100 pounds per square foot, an analyst may be included to treat it as an aperture of zero pounds per square foot. On the other hand, if the surrounding wall is of low mass thickness, say 15 or 20 pounds per square foot, the analyst may choose to treat the window not as an aperture but as a section of wall of different mass thickness from that surrounding it. In this text, the term aperture is restricted to those situations where the mass thickness involved can be assumed to be zero with no undue loss of precision in the calculations.
4-71
208-401 0 -76 -10
' Figure 4-24 shows a section through a one-story blockhouse taken through a part of the wall containing an aperture. The dashed wall outline represents the aperture extending both above and below the detector plane. The shaded areas represent the flow of radiation from the walls to the detector.
The areas shaded with solid, diagonal lines, indicate radiation through the apertures and those shaded with diagonal, broken lines, indicate radiation through the solid parts of the wa fl .
FIGURE 4-24 EFF~CT OF APERTURES ON DETECTION RESPONSE
The portion of the wall lying above the plane of the detector would norm·ally contribute both skyshine and scatter radiation to the detector. That lying below the detector plane would normally contribute both direct and sce~tter. In Figure 4-24, this is true of those solid portions of the wall included within the solid angle rays between w and w , and betweenW Land
• ~ aandw a. In the figure, that part of the wall which is aperture and which lies above the detector plane will contribute only skyshine radiation while that part of the aperture-below the detector plane contributes only direct radiation. Zero mass thickness does not absorb nor scatter radiation. Obviously, the
effect of an aperture is generally to increase the contribution and to decrease the protection. This is particularly true, and the effect is significant, if
4-72
•
apertures exist below the detector plane, so that direct radiation may pass to the detector without benefit of barrier reduction. In Chapter Ill, it was determined that the standard detector, receiving only skyshine and direct radiation, received about 90% direct and 10% skyshine. Obviously, an aperture of a given size would have a more adverse effect on protection if it is located below the detector plane. An additional adverse effect of apertures is the matter of ceiling shine. In some cases ceiling shine can be a significant part of the
toto I detector response.
4-9.2 Calculations Involving Apertures
The development of the standard method of analysis to this point has generally been based on concepts that involve azimuthal symmetry. The presence of apertures (openings) in the exterior walls of real buildings represents a departure from azimuthal symmetry. From this point of view,
discussion relative to the handling of apertures in the standard method could properly be deferred to Chapter V which discusses complex problems. However, because apertures occur so frequently in real buildings, the manner in which they are handled in the standard method is developed in this chapter. A further consideration for their treatment in this chapter on simple buildings
arises out of the fact that ceiling shine may become an important component of the ground contribution when the exterior wa lis of the detector story contain apertures. Ceiling shine has been mentioned in previous articles but has not
been included in any of the illustrative problems solved nor has the manner in which it is calculated been discussed.
4-9.3 Normal Wall Contribution, Detector Story
Problem 4-14 represents the detector story of a building having a width, W, of 50 feet and a length, L, of 100 feet. The detector, centrally located 3 feet above the floor, is assumed to I ie 40 feet above the contaminated ground plane. It is assumed that a continuous aperture occupies the central 6 feet of wall section leaving 2 feet of solid wall both above and below the aperture strip. The mass thickness of the solid portions of the wall is assumed to be 75 psf. The mass thickness of the apertures is assumed to be very low and can be taken as 0 psf. The aperture extends continuously around the perimeter of the building. It is required to determine the ground contribution to the detector through the walls of the detector story. The determination of this contribution involves 4 solid angle fractions. The normal upper and lower solid angle fractions embracing the entire wall are of interest; and, since there is something significantly different about the aperture strip, the 2 additional solid angle fractions, w and w~, are drawn in the figure to
0
define the aperture strip. It should be evident that the total ground contri
4-73
2' PROBLEM 4-14
5'
w 50 ft.
L = 100 ft.
1' Xe = 75 psf
H = 40 ft.
2'
w L z W/L Z/L w Gd G G
s a w 50 100 7 0.50 0.07 0.81 -----0.210 0.042
u w 50 100 5 0.50 0.05 0.86 -----0.160 0.032
a w' 50 100 1 0.50 0.01 0.97 0.012 0.036 ----
a 50 100 3 0.50 0.03 0.92 0.070 0.095 -----
WL
E(0.50) = 1.34; Sw(75) 0.71,B (40,75) = 0.084; B (40,0) = 0.54
e c B (40,0) = 0.54
e
1. Solid Portion of Wall Above Aperture Strip
Gg = [G (w ) -G (w )]E(e)S. (X ) + [G (w ) -G (w )][1-Sw(Xe·~]
s u s a w e ·a u a a ·
G (0.050 X 1.34 X 0.71) + (0.010 X 0.29) = 0.0505
g
G -G B (H,X ) = 0.0505 x 0.084 = 0.0042
g g e e
2. Contribution through Aperture Strip
Gg Gd(H,wa) + Ga(wa) = 0.044 C = G B (H,O psf) = 0.044 x 0.54 = 0.02376
g g e
3. Solid Portion of Wall Below Aperture Strip Gg = [G(wL) -G8 (w~)]E(e)Sw(Xe) + [Gd(H,wL)
8
-Gd (H, w~)] [1-Sw(Xe)]
(0.059 X 1.34 X 0.71) + (0.058 X 0.29) = 0.0729
G B (H,X ) = 0.0729 x 0.084 = 0.0061
g e e
4. Total Contribution 0.0042 + 0.0237 + 0.0061 0.034
4-74
PROBLEM 4-14 (ALTERNATE SOLUTION)
1. Assume entire wall solid
G = [G (w ) + G (w )] E(e)S (X ) + [Gd(H,wL) +
g s u s L w e
G (w )J [1--S (X)]
a u w e G g = (0.305 X 1.34 X 0.71) + (0.112 X 0.29 =
C = G B (H,X ) = 0.3227 x 0.084 = 0.0271
g g e e
2. Assume aperture stri2 solid
G = [Gs(wa) + G (w' )] E(e)S (X ) + [Gd(H, w~)
g s a w e
G ( w ) ] [ 1-S ( X )]
a a w e G = 0.196 X 1.34 X 0.71) + (0.044 X 0.29) =
g c' = G B (H,X ) = 0.1992 X 0.084 = 0.0167
a g e e
3.
Aperture strip 0 £Sf C = fGd(H,w') + G (w )] B (H,O psf)
a -a a a e
= 0.044 X 0.540 = 0.0238
4.
Total contribution c + rc c 1]= 0.0211 + o.oo11 = o.o342
g ~ a a
0.3227
+
0.1992
4-75
bution may now be calculated in three parts --that through the solid part of the wall above the aperture strip, that through the aperture strip, and that through the solid portion of wall below the aperture strip. Data for determining these contributions are recorded in Problem 4-14.
In Step 1, the contribution through the solid portion of the wall above the aperture strip determined by differencing contributions through w and w as shown. u
a
The contribution through the aperture strip are next determined by combining contributions throughw and w'. It is noted that the mass thickness of the aperture strip is 0 psf, aand S a(X ) is also zero. Obviously, the scatter portion of the geometry factor wrfl beezero, and the only geometry factors that must be considered are Gd and Ga. Since Sw is zero, 1-Sw will be unity and Gg is merely Gd(H,w~) + Ga( wa).
In step 3 the contribution through the solid portion of wall below the aperture strip can be determined by differencing contributions through the two lower angle fractions as indicated in the calculations.
The total contribution is the sum of the three parts, or .034.
0. 0045 + 0.0237 + 0.0061 = 0.034
Although the above calculations are straightforward and involve no new concepts, the contribution would normally be calculated using a slightly different technique. This will now be explained and illustrated by means of an alternate. Solution to Problem 4-14.
In the first step, the entire wall is assumed to be completely solid, and the contributions is calculated. In the second step, the contribution is calculated assuming the aperture strip to be completely solid.
c' = ground contribution through a wall segment, containing
a apertures, calculated by assuming the apertures to have the same mass thickness as the solid parts of the wall.
In step three, the aperture strip is assumed to have zero mass thickness (as it has in this case), and Ca, the ground contribution, is calculated.
C = ground contribution through a wall segment, containing
a apertures, calculated by assuming the entire segments
to be of zero mass thickness.
4-76
It should be clear that, if C is the entire wall contribution, assuming the entire wall to be solid, and g C~ is the contribution through the aperture strip, assuming it to be entirely solid, then Cg-C~ is the contribution through
those portions of the wall above and below the aperture strip that are completely solid. If to this remainder the contribution, Ca, for the aperture strip at zero psf mass thickness is now added, the resultant sum is the total wall contribution for the story. This algebraic sum has been determined in step four of the calculations and is illustrated pictorially in Figure 4-25.
The sketch in (a) of the figure represents Cg computed, assuming the entire wall solid. The sketch in (b) represents C~ computed through the aperture strip, assuming it to be solid. Ca, is represented in (c) of the figure and assumes the entire aperture strip to be zero psf. The sketch in (d) shows the combined final contribution.
Suppose, now, that the aperture strip had not been composed of a continuous opening around the perimeter of the building but consisted, rather, of windows spaced uniformly around the perimeter. The strip would then consist of windows (apertures) with intermittent solid wall intervals. Let it be supposed that 6-foot high windows (the full depth of the aperture strip) were 6 feet
Cg
Ca' Ca
+
(b) (c)
(a) (d)
Total Contribution: Cg + (Ca -Ca'
FIGURE 4-25 CONTINUOUS APERTURE CONCEPT
4-77
wide and were uniformly spaced at 10-foot centers around the perimeter of the building.
Pa = fraction of the perimeter of an aperture strip that is occupied
•
by apertures; the total width of windows around the peri
meter of a building, divided by the perimeter of the building.
In the example, Pa would be 0.60, since 6-foot wide windows are spaced on 10-foot centers uniformly around the perimeter. Cg, C~ and Cwould be
0
calculated as before. The total contribution could then be found as Cg +
[Ca -C~] Pa. That this relationship is valid can be seen from Figure 4-26.
The sketch at (a) in the figure represents the contribution, Cg, for the entire
wall assumed solid. This should be reduced by a quantity representing the
contribution through those portions of the aperture strip which are assumed
to be filled with solid wall materials. Since C~ is the contribution through
(a) (d)
111111-
Cg
Total Contribution: cg + CCg-Ca')Pa
FIGURE 4-26 APERTURE CONTRIBUTIONS
the entire aperture strip (assumed solid) and Pa is the fraction of the total strip
that is occupied by fictitiously solid apertures, the reduction is clearly C~ x p .
then Cg -c~ X Pa represents the contribution through the parts of the wall thata
are solid. C~ x Pais represented in (b) of the figure. Next the contribution
through the aperture portions of the wall must be added to that through the solid .portions. Ca is the contribution for the entire aperture strip if it is zero psf.
Since Pais that fraction of the aperture strip area that is zero psf, obviously
Ca xPa is the contribution of interest and the entire 'contribution is C~ + [Ca
C~]Pa. In the Figure CaxPa is represented in (c) and the total contnbution in
(d).
4-78
•
The following calculations complete the determination of the contribution through the modified (intermittent windows) walls of the detector story in Problem 4-14, assuming 6-foot high by 6-foot wide windows at 10-foot centers.
SOLUTION TO PROBLEM 4-14 WITH INTERMITTENT WINDOWS
c = 0.0271
g
Cl = 0.0167
a
c = 0.0238
a
p = 0.60
a c + [c -c '] p = 0.0271 + (0.0071)0.60 = 0.0314
g a a: a
= 0.0316
4-9.4 Ceiling Shine Contribution, Detector Story
•
Where the exterior walls of a detector story contain large areas occupied by apertures, a ceiling shine contribution may be a significant portion of the total ground contribution, particularly if the direct radiation component is relatively small. Ceiling shine is radiation that back-scatters from the ceiling immediately above the detector. If apertures are large, significant amounts
of direct radiation will pass from ground sources through the apertures unreduced in intensity and will impinge on the ceiling. Some of this radiation will "back scatter" to the detector. This is illustrated in Figure 4-27 {on page 4-81) for a point on the ceiling directly above the detector.
Figure 4-27, w , geometrically defines the zone through which ceiling shine arrives at the dJltector. A point in the ceiling directly above the detector is taken as an "average" point representing all points on the ceiling. Direct radiation from ground sources between points 1 and 2 on the source plane pass through the aperture and impinge on this point in the ceiling. Solid angle fractions we andw~ can be used to geometrically define the zone through whk:h direct radiation travels to reach this point. Back-scatter from this point to the detector is •Jssumed to be representative of back-scatter from all points in the ceiling.
The geometry factor for determining the ceiling shine contribution at the detector is given by: 4-79
G (w w w') = 5 [G (We) -G (W'] [0. 10 -G (W )]
c u' c' c a a c a u
The first bracketed term represents radiation directed through the aperture to the point in the ceiIing. The second bracketed term represents that arrivj ng at the detector as scatter from the ceiling. The above expression represents an empirical approach to the ceiling shine problem. Although it employs skyshine geometry factors taken from Chart 2, it should not be implied that ceiling shine is air-scattered. Ga terms are used merely to approximate the poorly defined angular distribution of the radiation.
The ceiling shine contribution for Problem 4-14 is calculated to illustrate the procedure.
w L z W/L Z/L w Ga wu 50 100 7 0.50 0.07 0.81 0.042 w 50 100 8 0.50 0.08 0.77 0.049
c w' 50 100 2 0.50 0.02 0.94 0.014
c
Gc(wu,wc,w~) =s[Ga(wc) -Ga(w~)][ti.lO -Ga(wu)J
Gc = 5[0.035][0.058] = 0.0102 Cc = GcBe(H,O psf)Pa = ceiling shine contribution Cc = 0.0102 x 0.54 = 0.0055 for continuous apertures Cc = 0.0102 x 0.54 x 0.60 = 0.0033 for intermittent
aperture
The values for Cc would be added to the normal wall contributions previously calculated to complete the solution to Problem 4-14.
4-80
®
FIGURE 4-27 CEILING SHINE
4-9.5 Aperture Problems
Problems 4-15 through 4-17 should be studied as a group. They illustrate the difference in ground contribution for different positions of apertures in a wall. The buildings are identical except for the vertical position of the apertures. In Problem 4-15, the sills of the 6-foot high windows are 1 foot below the plane of detector. In Problem 4-16, they are at detector height. In Problem 4-17, the heads of the windows are at the top of the wall, placing the sills 2 feet above the plane of the detector. Only the ground contribution is calculated in each of the problems.
•
4-81
Attention is particularly directed to the difference in contributions for Problem 4-15 and the other two. Placing the sills of the window one foot below the detector plane allows a significant quantity of direct radiation to reach the detector without benefit of barrier reduction. This one foot results in more than a two-fold increase in the contribution above what would exist if the sills were at or above detector height. Be this as it may, it still must be stressed that contributions and protection factors are calculated at point locations. Personnel standing with portions of their bodies above the window sills would receive direct radiation without barrier reduction from the exterior walls regardless of the elevation of the sills. For that reason, shelter managers should be instructed to advise people sheltered to maintain themselves in positions where direct ground contributions through apertures are avoided insofar as possible.
In comparing Problems 4-16 and 4-17, it is noted that the position of the window, in elevation, has minor effect on the total contribution provided that it is completely above the detector plane.
4-82
PROBLEM 4-15
w = 50 ft.
L = 100 ft. xe = 75 psf Windows 6 ft. high X
6 ft. wide at 8 ft. centers
w L z W/L Z/ L w
Gd Gs Ga wu 50 100 8 0.50 0.08 0.78 ----0.235 0.047 wa 50 100 5 0.50 0.05 0.86 ----0. 160 0.032 WI
50 100 1 0.50 0.01 0.97 0. 19 0.036 ----
a WL 50 100 3 0.50 0.03 0.92 0.37 0.095 ----
E(0.50) = 1.34, Sw(75) = 0.71, Be(3,75) = 0. 17, Pa = 0.75
l. Entire wall solid = {[Gs(wu) + G5 (wl)]E(e)Sw(Xe) + [Gd(H,wl) +
c9 Ga(wu)][l-Sw(Xe)]}Be(H,Xe) Cg = {(0.330 X 1.34 X 0.71) + (0.417 X 0.29)}0. 17 c= o.o739
9
2. Aperture strip solid
c~
= {[Gs(wa) + G 5 (w~)]E(e)Sw(Xe) + [Gd(H,w~) +
a
Ga(wa)][l-Sw(Xe)]}Be(H,Xe)
c~
= {(0.196 X 1.34 X 0.71) + (0.222 X 0.29)}0. 17
a
= 0.0427
4-83
PROBLEM 4-15 (cont.)
3.
Aperture strip 0 psf
4.
Normal contribution C9 + [Ca -C~]Pa = 0.0739 + (0.222-0.0427)0.75 Total contribution = 0.2084
5.
Ceiling shine
w L z W/L Z/L w Ga
we 50 100 9 0.50 0.09 0.75 0.052
WI c 50 l 00 3 0.50 0.03 0.92 0.019
Gc(wu,wc,w~) = 5[Ga(wc) -Ga(wc)J[O. 10 -Ga(wu)J Gc = 5[0.033][0.048] = 0.0079 Cc = GcBe(H,O psf)Pa = 0.0079 x l .0 x 0.75 = 0.0060
6. Total Contribution
0.2084 + 0.0060 = 0.2144
PROBLEM 4-16
w= 50 ft.
L = 100 ft.
Xe = 75 psf
windows 6' high x
8 1
6' wide at centers w L z W/L Z/L w Gd Gs Ga wu 50 100 8 0.50 0.08 0.78 ----0.235 0.047 wa 50 100 6 0.50 0.06 0.83 ----0.190 0.038 WL 50 100 3 0.50 0.03 0.92 0.37 0.095 -----
E(0. 50) = 1 . 3 4 , Sw ( 7 5) = 0. 71 , Be ( 3 , 7 5) = 0 . 1 7 , Pa = 0.75
1.
Entire wall solid
C9 = 0 . 0 7 3 9 ( same as Pro b 1 em 4-15)
2.
Aperture strip solid
C~ = {[Gs(wa)E(e)Sw(Xe)J + Ga(wa)[l-Sw(Xe)]}Be(H,Xe)
= [(0.190 X 1.34 X 0.71) +(0.038 X 0.29)][0.17] = 0.0326
3.
Aperture strip 0 psf
4.
Normal contribution
+ [Ca -C~]Pa = 0.0739 + [0.038 -0.0326]0.75
c9
4-85
PROBLEM 4-16 (cont.) Normal = 0.0780
5. Ceiling shine
Z/L = 0.08, we= 0.78, Ga(wc) = 0.047 Z/L = 0.02, w~ = 0.94, Ga(w~) = 0.014 Gc = 5[Ga(wc) Ga(w~)][O.lO-Ga(wu)J
Gc = 5[0.033][0.053] = 0.0087 Cc = GcBe(H,O psf)Pa = 0.0087 x 1.0 x 0.75 = 0.0065
6. Total contribution
0.0780 + 0.0065 = 0.0845
PROBLEM 4-17
w = 50 ft. L = 100 ft. Xe = 75 psf
windows 6 ft high X 6 ft wide at 8 ft centers
w L z W/L Z/L w Gd Gs Ga wu 50 100 8 0.50 0.08 0.78 ----0.235 0.047 wa 50 100 2 0.50 0.02 0.94 ----0.070 0.014
50 100 3 0.50 0.03 0.92 0.37 0.095 -----
WL
E(0.50) = 1.34, Sw(75) = 0.71, Be{3,75) = 0. 17, Pa = 0.75
4-86
PROBLEM 4-17 (cont.)
1.
Entire wall solid
0.0739 ( s a me a s p r o b 1em 4-15 )
2.
Aperture strJ2 solid C~ = {[Gs(wu) -Gs(wa)]E(e)Sw(Xe) + [Ga(wu)
Ga(wa)] [1-Sw(Xe)]}Be(H,Xe)
C~ = [{0.165 X 1.34 X 0.71) + (0.033 X 0.29] 0.17
= 0.0283
=
4. Normal contribution C + [C -C']P = 0.0739 + [0.033-0.0283] 0.75
g a a a Normal = 0.0775
5. Ceiling shine Z/L = 0.06, we = 0.83, Ga(wc) = 0.038 Z/L = 0.00, 1. 00. Ga(w~) = 0.000
=
G = 5[0.038] [0.053] = 0.0101
c
= G B (H,O psf)P = 0.0101 x 1.0 x 0.75 = 0.0075
c e a
6. Total contribution
0.0775 + 0.0075 = 0.0850
4-87
208-401 0 -76 -11
4-9.4 Apertures, Stories Above and Below Detector
In the usual upper story location, the ground contribution from the story below the detector is of the order of 1/10 of the total ground contri"':' bution and the ground contribution from the story above is of the order of 1/20 to 1/50 of the total ground contribution. Also the position of the windows, in the walls of the stories above and below, has a relatively minor effect on the respective contributions. Positioning them at maximum or minimum elevation in the stories above and below might result in a change in contribution of perhaps about 10% at most in those contributions. A 10% change in the contributions from above and belowwould result, generally, in a change of 1% to 2% in the total contribution from all three floors. This suggests that an approximate determination of contributions from above and below would be in order.
In Problem 4-18 the detector is located in an upper story of a building and the detector height H is 50 feet. The sills of the 5-foot high windows are at detector Ieve I, 3 feet above the floor. It is assumed that a II stories are identical in all respects.
The 11 theoretically correct11 procedure for hand I ing the ground contributions from the stories above and below the detector would involve considering, in addition to the usual solid angle fractions, two solid angle fractions each for the story above and the story below. These are the solid angle fractions defining the aperture strip in adjacent stories. The contribution from stories above and below would then be evaluated, using the differencing technique for calculating Cg, c· I and c .
a a
Although the above procedure is more theoretically correct, due to the increased amount of calculations involved, and the fact that in the usual case the increase in accuracy is not warranted, this procedure is not recommended for multi-story buildings with apertures.
The method employed in Problem 4-18 to account for apertures i1 a multi-story bui !dings is an approximate method which results in reasonable precision. It is the recommended method that should be used in situations involving multi -story buildings.
The calculations for the contribution from the walls of the detector story is the usual procedure. In considering the contributions from the stories above and below, they are first assumed to be composed of completely solid walls, and C is calculated on that basis. Then, the entire wa II is assumed to be zero m9ss thickness, and Cis calculated on that basis. The total
0
4-88
•
contribution from either the story above or below is then determined as the sum of the products Cg[l-Ap] and CaAp.
A = ratio of total window area to total wall area.
p
In the problem, Ap is the ratio of 25 to 100 or 0.25 since 5 1 X 51 windows are uniformly spaced around the perimeter of a 10• high wall at 10-foot centers. Twenty-five percent of the wa II area is occupied by apertures.
The approximate procedure employed for the contributions from above and below cannot be used for that from the detector story. Problems 4-15, 4-16, and 4-17 have revealed that changes in the vertical position of the apertures in the detector story can have significant effect on the total contribution, particularly since direct radiation is involved and the contribution from the detector story is in the order of 90% of the total. The aperture strip in the detector story must be considered, through solid angle fractions that define it, in the exact manner in which it has been considered in all preceding problems.
4-89
PROBLEM 4-18
~~ = 50 ft. , L = 50 ft. Xe = 75 psf Xf = 50 psfEtl.OO) = 1.41Sw (7 5 ) = 0 . 71Be(50,75) = 0.075Be(50,0) = 0.50Bc(50,0.75) = 0.086Bf(50) = 0.080Pa5/l0 = 0.50Ap = 25/100 = 0.25
ceiling shine
Z/ L = 0. l 4we= 0.75Ga = 0.052
Z/L = 0.04 w~ = 0.93
Ga = 0.016
\\l:::::::::::::::::::::::::-:::::::::::::::::::::::::::::::::::::::::::::::·:·:·:·:{
w L z W/L Z/L w Gd Gs Ga
w' 50 50 l 7 l . 00 0.34 0.49 0.39 0.078
u wu 50 50 7 l. 00 0. 14 0.75 0.26 0.052
wa 50 50 5 l . 00 0. l 0 0.82 0.20 0.040
WL 50 50 3 l . 00 0.06 0.90 0.09 0. l 2 -----
WLI 50 50 l 3 l.00 0.26 0.58 0.51 0.35 -----
Detector stor~
cg = { [Gs (wu) + G5 (wl)]E{e)Sw(Xe) + [Gd{H,wL) +
4-90
PROBLEM 4-18 (Cont.)
Ga(wu)] [1-Sw(Xe)} [Be(H,Xe)
c = [(0.38 X 1.41 X 0.71) + (0.142 X 0.29~0.075 = 0.0316
g C' = {fG (w )E(e)S (X )l + G (w )[1-S (X )l} B (H,X)
a '--s a w e ~ a a w e 'J e e C' = ~0.20 X 1.41 X 0.71) + (0.040 X 0.29) 0.075]= 0.0159
a c = Ga(wa)Be(H,O psf) = 0.040 x 0.50 = 0.0200
a c + [ca -c) Pa = 0.0316 + [0.0200 -0.0159] 0.50
g
= 0.0337
Ceiling Shine
Gc(wu,wc,w~) = 5[Ga(wc) -Ga(w~)) [0.10 -Ga(wu)] G =[5 0. C36] [0. 048] = .0086
c C = G X P X B (50,0) = .0086 X .5x.5 = .0022
c c a e Detector Story Contribution
0.0337 + 0.0022 (ceiling shine) = 0.0359
Story above
C = { [G ( w ' ) -G ( w )l E ( e ) S (X ) + [ G ( w ' )
g s u s u-w e a u Ga(wu)] [1-Sw(Xe)]} Be(H,Xe)Bc(Xc,w) C = [(0.13 X 1.41 X 0.71) + (0.026 X 0.29)] 0.075 X 0.086
g c 0.00089
g
C = [G (w')-G (w )]B (H,O psf)B (X ,w)
a a u a u e c c C = 0.026 X 0.50 X 0.086 = 0.00112
a C [1-A J + C A = (0.00089 x 0.75) + (0.00112 X 0.25)
g P a P Contribution story above = 0.00095
Story below
C g = {[G s ( wr) -G s ( wL ) ] E ( e ) S w ( X e ) + [G d ( H , wr)
Gd(H,wL)]f1-S (X )]}B (H,X )Bf(Xf)
· w e e e
4-91
PROBLEM 4-18 (Cont.)
C g = [(0.23 X 1.41 X 0,71) + (0.42 X 0.29)] 0.075 X 0.080 c = 0.00211
g
Ca = [Gd(wi) -Gd(wL)]Be(H,O psf)Bf(Xf) C = 0.42 X 0.50 X 0.080 = 0.01680
a Contribution story below C [1-A 1 + C A = 0.00578
g p a p Total contribution all stories
0.0359 + 0.0009 + 0.0058 = 0.0426
4-92
4-10 Limited Fields -Mutual Shielding
4-10.1 Introduction
All of the situations discussed so far have assumed an isolated building subject to ground contributions from an infinite field of contamination extending horizontally in all directions.
In many cases of practical interest, buildings are not isolated on infinite horizontal fields. They are generally surrounded by adjacent buildings with
varying but limited ground area between them. Such adjacent buildings act,
mutually, to shield each other.
Mutual shielding involves consideration of limited fields of contamination. Considering for example, a building in the middle of a commerical city block sandwiched between other buildings on two sides, and facing other buildings across a street in front and an alley in back.
The contribution through the walls of the building under consideration
is essentially Iimited to radiation originating only from those particles lying
on the street and alley. Radiation originating from other ground sources is
effectively blocked off by other buildhgs. The building under consideration
is subject only to limited fields of radiation.
Although mutual shielding (or limited fields) is one of the most important factors in enhancing protection factors for practical structures, there has not yet been developed a simple and complete method by which reduction factors from limited fields may be calculated with the degree of precision associated with the calculation of reduction factors from infinite fields of contamination.
The problem is extremely complex. The procedure that will be explained in this section can be considered to yield only approximate results, particularly with regard to scatter radiation. In general, however, the results, of the standard method, are probably conservative. It should be always kept in mind that, if calculated protection factors do nothing else, they reveal the relative
degree of protection afforded by one structure compared to another. As long as the method of determination is consistent and the parameters associated with the structures are not widely divergent, consistency will be maintained
in the comparisons that are drawn from calculated protection factors.
In determining reduction factors from I imited fields, two approaches could be used. They could be determined by applying appropriate factors to infinite field results or by integrating results from point sources over a finite rectangular array. The latter approach, although it has distinct potential
4-93
advantages in many regards, cannot be used since barrier and geometry factors for radiation incident on a vertical barrier from point sources on a horizontal field have not yet been defined. The method that will be employed consists, then, of certain corrections applied to the infinite field results. The major advantage in this approach lies with the fact that the infinite field results, as exemplified in the preceding sections, are readily calculated.
Figure 4-28 shows a simplified mutual shielding situation in plan and section. The detector is located centrally in a square single-story structure surrounded, at a distance We, by a shield assumed effective in blocking off radiation from all ground sources lying beyond. Only those particles between the shield and the structure contribute or radiate against the walls of the structure. Since the shield has no influence on the particles lying on the roof, the overhead contribution is not affected by mutual shielding.
In the plan of Figure 4-28, the structure is shown surrounded by a limited field, indicated by dot hatching and bounded by a shield, so marked on all four sides. In the section, the shield is shown equal in height to the structure. There is, of course, no restriction on relative height of structure and shield.
Attention is now directed to the section view and the wall contribution to the detector. Both the upper and lower portions of the wall contribute scatter radiation to the detector. But the amount of scatter radiation reaching
the detector will be less then normal because of the limited field of contami
nation (or reduced number of radiating particles that are potential contributors).
Neglecting the very small amount of air scatter that can occur in the
space between the shield and the structure, it could be argued that skyshine
contribution is restricted to only the top part of the upper wall segment between the rays defining w and w' • But back scatter from the shield may
be of essentially the same inunature ~s skyshine,and so skyshine will conservatively be assumed to come through the entire upper portion of the wall.
Direct radiation is restricted to the bottom part of the lower wall segment and originates in those particles lying on the limited field between the shield and the structure. Direct radiation from the remainder of the lower wall segment has been eliminated by virtue of the shield.
Summarizing mutual shielding has been shown to be effective in reducing wall contributions (direct, scatter) and results in increased protection. Mutual shielding is an important parameter in shielding calculations and, in part,
4-94
FIGURE 4-28
MUTUAL SHIELDING AND LIMITED FIELD
4-95
accounts for the fact that large numbers of shelter spaces having acceptable protection factors are located in aboveground positions in many buildings.
4-10.2 Direct Radiation From Limited Fields
The method for calculating reduction factors associated with Iimited, rectangular fields of contamination requires separation of scatter contributions from direct and skyshine contributions. The reason for this will become evident as the discussion in this section proceeds.
Figure 4-28 depicts a square building completely surrounded by a shield effective in preventing any ground sources beyond it from directly contributing radiation to the walls of the building. (In this chapter consideration will be given only to structures completely surrounded by a shield. Cases where only one wall 1 or a part of one wall, is shielded will be taken up in Chapter V.) The field contributing to the detector is I imited to sources lying between the structure and the shield and has a constant width of We.
We "" width of a limited field of contamination measured from the wall of the structure to the edge of the field.
It is seen, from the section in the figure, that direct radiation is contributed to the detector only through that portion of the wall below the detector plane between the rays defined by wl and ·w i: The direct contribution involved can be obtained by differencing the airect geometry factors, Gd, that are a
function of those two solid angles. The problem is, in form, no different from
that associated with calculation of direct radiation from a story below a
detector story. The ge?metry factor for the direct contribution is thus Gg =
[Gd (H,wl)-Gd(H,wJHl-Sw(Xe)]. To obtain the direct contribution, Gg
is merely multipi ied by whatever barrier or attenuation factors are applicable.
These would normally include Be(H,Xe), Bi(Xi) and Bf(Xf). For rectangular
buildings surrounded by a finite field of rectangular proportions,wl should be
evaluated on the basis of width (W) and length (L) dimensions determined by
the outer boundaries of the field. Care must be exercised to insure that azi
muthal symmetry is preserved. For example, if the width of the contaminated field is different on opposite sides of the building shown in plan in Figure 4-28, the solid angle fraction,wL, at the detector would not be subtended by the base
of a regular pyramid and the use of field dimensions defined by outer boundaries
would yield erroneous results. Problems involving such nonsymmetrical cases
are considered in Chapter V~
It has been pointed out that G d va I ues based on the work of Spe ncer were derived from a consideration of cylindrical structures but were assumed appticable
4-96
to rectangular structures with equal values for w. The errors involved in this assumption are also inherent in calculating direct responses from limited fields.
4-10.3 Skyshine and Mutual Shielding
Figure 4-29 shows a section through the structure of Figure 4-28. Apparently, if the small amount of skyshine produced between the shield and the building (below the ray defining w;,) is negligible, the shield would be effective in restricting skyshine contribution to the segment of upper wall included between the rays defining w andw •. Through differencing, the skyshine geometry factor could be deter~ined. uThe standard method of analysis does not treat the skyshine contribution in this manner. In the method, skyshine contributions, irrespective of mutual shielding, are calculated in the normal way considering contribution through the entire segment of wall above the detector plane. This may be conservative but is justified by virtue of the fact that a vertical mutual shield will back-scatter radiation in the direction of the building of interest. Back-scatter, Iike ceiling shine, involves a reflection combined with penetration of a vertical wall. They may therefore be of the same order of magnitude. Calculating skyshine in the normal way tends to make up for a contribution that would otherwise be neglected.
FIGURE 4-29
LIMITED FIELDS -SKYSHINE RADIATION AND BACK-SCATTER
4-97
4-10.4 Shielding and Scatter Contribution
Direct and skyshine contributions in limited field situations are determined in a manner completely consistent with the procedure applicable to an infinite field. The calculations do not involve any new considerations. Such, however,
is not the case with that attributable to scatter radiation.
In the case of direct radiation, since most photons travel on a straight path from the sources to the detector, the geometry factor is a function of the solid angle fraction subtended by the source area at the normal detector position. The case with respect to the scatter contribution is considerably more complex. Geometry is dependent on two solid angle fractions, one at the detector subtended by the wall or walls which are the source of radiation as far as that detector is concerned, and one at a typical point on the wall subtended by the rectangular source area that contributes to that wall and, ultimately, to the
These are indicated in Figure 4-30 which shows one wall of a structure.
detector.
In the case of direct radiation, the geometry factor itself takes into account the variation in source geometry associated with a limited field. This geometry factor is a function of normal solid angle fractions at the detector position. Further, the normal wall barrier factor is used as a multiplier to Gg in obtaining Cg .. In the case of scatter radiation, the geometry factor, as a function of solid angle fractions at the detector position as it normally is calculated, has nothing to do with source geometry. Every point on the wa II contributes scatter radiation to the detector; hence, the geometry factor must be a function of structure dimensions which are, of course, independent of source geometry. The result is that, if the norma I geometry factor associated with scatter radiation is to be used, the correction to account for a limited field must be applied in some way other than geometry. It has been decided that the analysis method should take limited source geometry for scatter radiation into account by means of a modified barrier factor. For scatter radiation, the method consists of computing the usual geometry factor. This is then multiplied, in determining the contribution, by a modified barrier factor for the exterior wall. It is for this reason that direct and scatter contributions must be separated when limited fields are involved. For direct radiation (and skyshine}, the normal exterior wall barrier factor, Be (H,Xe), is used. Forscatterradiation, a new barrier factor, Bs, is used. Bs is a function of w s and Xe wherews is calculated from the dimensions of the
Iimited field. The solid angle fraction, ws, is shown in Figure 4-30 subten,ded
by the I imited field.
Bs = exterior wall barrier factor for scatter radiation from limited fields; Bs(2ws, Xe).
4-98
FIGURE 4-30 LIMITED FIELDS -SCATTER RADIATION
w = the solid angle fraction at a point in the wall of the structure
s opposite the detector subtended by a limited field of contami
nation.
It is noted that w is at the apex of half a regular pyramid. Solid angle fractions, as normally ~alculated with the aid of Chart 1, are at the apices of regular pyramids. This chart may still be used. Referring again to Figure
4-30, if e is calculated as 2Wc/Lc then (2Wc/Lc,H/Lc), taken from Chart 1, is actually 2Ws, and Ws is half the chart value.
4-99
Figure 4-31 gives values of Bs(2ws,Xe). It is based on unpublished work
of Spencer who calculated such factors considering radiation from semicircular finite sources adjacent to a wall. His semicircles were concentric about a point at the base of the wall directly below its center. These results,show.n in
Figure 4-31, are applied to rectangular source planes under the assumption that the effect is the same as for semicircular sources if the solid angle fractions are the same. Figure 4-31 appears also in Appendix C as Chart lOA. In the plot, 2 ws has been used instead of w simply to avoid the necessity for a division by 2 as would be required to defermine ws once 2ws is taken from Chart 1.
It should be noted that B , the limited field barrier factor applied to scatter
11 11
radiation calculations in the standard method, is not a pure barrier factor since it includes the geometry of the Iimited field.
Most limited fields lie adjacent or close to a wall of the building of
interest. As a consequence, the slight amount of air between the source and a point at height H in the wall will be negligibly effective in attenuating radiation. The plot of Figure 4-31 (Chart lOA) does not consider attenuation in air between the source and the wall point. As the size of the Iimited field becomes large, the effect of air attenuation of radiation from the far out sources becomes significant and, ultimately, the barrier factor approaches Be(H,Xe) for an infinite field. For this reason, Chart lOA does not plot results beyond values of 2ws =0.80. It is assumed that, for values of 2Ws less than 0.80, the attenuation effect of the air can be neglected. For values greater than 0.80, a 11 coupling 11 must be provided such that, when the limited field approaches that of an infinite field, Bs approaches Be(H,Xe). Figure 4-32 (Chart lOB Appendix C) provides the required coupling covering the cases of large limited
•fields. A limited field height factor, Fs(H,2 Ws) is taken from the chart and applied as a multiplier to the regular barrier factor, Be(H,Xe).
In summary, the exterior wall barrier factor to be used in calculating the scatter portion of the exterior wall contribution in limited field cases is given by:
Bs(2Ws,Xe) for 0.872Ws70.0 and
Bs(2Ws, Xe) "" Fs(H,2 ws) · Be(Xe, H) for 0. 80<2Ws<l. 0
In the first case, Chart lOA is used. In the second case, Chart lOB is used to evaluate Fs which is the multiplier applied to Be taken from Chart 6.
In most practical problems, the width of the contaminated field, We, can be defined with reasonable accuracy. Problems related to the definition of geometry parameters usually arise with respect to the length, L0 which usually is indeterminate. In the standard method of analysis, to provide con
sistency to those cases where the length of field is indeterminate, Lc is taken
as infinity.
4-100
.06 .04 .03 .02
-"'
"'3 N
a,
-X <II CQ
a:
0
1
(..)
<l:
u.
a:
w
-
a:
a:
<l:
CQ Cl
...J
w
u. 0
w
1
2:
...J
.004
0.1 .06 .04 .03 .02 0.01 .006 .004 .002
SOLID ANGLE FRACTION, 21.1) 5 FIGURE 4-31
LIMITED FIELD BARRIER FACTOR 8 (Xe,2 W5)
5
(CHART 10A APPENDIX C) 4-101
-.,
3C'l!.
J: LL.Cll
a:
0
1
(.)
<(
LL. 1-
J:(.!)
w
J: Cl
-l
w
LL. Cl
w
1
2 •
-l
HEIGHT, H, ft
FIGURE 4-32 LIMITED FIELD HEIGHT FACTOR, F5(H,2w 5) B5(Xe,2 W5) = F5(H,2 w5)•Be(Xe,H) (CHART lOB APPENDIX C)
4-102
For the case in which Lc approached infinity the procedure for calculating 2ws, is simplified. As Lc approaches infinity the ratios Wc/Lc and Z/Lc approach zero and the equation for the solid angle fraction 2ws becomes:
2ws = I. tan -1 We rr H in which H (previously the altitudes) is the height of the detector above the limited strip.
Figure 4-33 (Chart 1 B Appendix C) gives the solid angle fraction, 2 ws, versus the limited field width to height ratio, Wc/H. The functional expression for the limited field solid angle fraction is thus:
2ws = 2ws(Wc/H).
In the analysis of problems involving real buildings, it will generally be the case that different walls of a building will be subject to different widths of I imited fields Wc. This will necessitate a wall by wall analysis of the ground contribution. Problems of this sort are considered in Chapter V.
4-10.5 Simple Limited Field Problem
Problem 4-19 considers a simple, square, single-story blockhouse subject to a ground contribution from a limited field 75 feet wide on all sides. The protection factor is calculated at a centrally located detector.
A section through the structure shows the normal solid angle fraction
and wL. The additional solid angle fraction, wi_ at the detector is necessary to determine the direct contribution. The solid angle fractionWL is determined using a Z distance of 3 feet (H) and Wand L equal to the dimensions of the field (225 ft.)
Data for the three solid angle fractions of interest at the detector are included in the table of values together with the usual values (E(e), Sw(Xe), and Be(H,Xe). The normal exterior wall barrier factor, Be(H,Xe), taken from Chart 6, is used for determining the direct and skyshine contributions.
Step 1 of the calculations involves the determination of the exterior wall barrier factor applied to the scatter contribution. As indicated in the sketches, the walls are assumed subject to a limited field (We) 75 feet wide and infinitely long. The barrier factor is calculated at a point in the wall directly opposite the detector and applied, in Step 5, as a multiplier to the normal geometry factor for scatter radiation. It is noted that 2ws is determined using Chart lB. It is based on W c/H =75/3 =25.
4-103
208-401 0-76 -12
0.1 0.2 0.3 0.5 2 3 5 7 10 20 30 50 100 300 500 1000 0.997
0.996
0.995
0.994
0.993
0.992
0.991
0.990
3"' N z
0.98
0
1
u
<(
0.97
0:
LL
UJ
....1 0.96(!)
z<( 0.95
0 0.94 ....1
en0
0
....1
UJ
LL
0UJ
1
::2:
....1
0.7
0.6
LIMITED FIELD WIDTH TO HEIGHT, Wc/H
FIGURE 4-33
LIMITED FIELD SOLID ANGLE FRACTION, 2W 5
(CHART 18 APPENDIX C)
4-104
PROBLEM 4-19
w = 75 feet L = 75 feet X0 = 150 psf X = 100 psf
e
w L z W/L Z/L w Gd Gs Ga
wu 75 75 10 1. 00 0.133 0.76 ----0.26 0.05
WL 75 75 3 1.00 0.040 0.93 0.35 0.08 ---w'L ~25 225 3 1. 00 lo.013 b.975 0.16 -------
E(1.00) = 1.41, Sw(100) = 0.775, Be(3,100) = 0.093
1. Scatter barrier
1 ..
225'Wc /H = 75/3 = 25; 2w s (25) = 0.975,
F (0.975,3) = 0.73, B (2w ,X ) =
s s s e
F (2w
s s ,H)Be (H,Xe ) = 0.73 x 0.093 = 0.068
4-105
PROBLEM 4-19 (Cont.)
2. Overhead contribution C (w ,X ) = C (0.76,150) 0.0046
0 u 0 0
3. Ground contribution -direct Cg = [Gd(wL,H) -Gd(wi,H)] [1-Sw(Xe)lBe(H,Xe)
C = 0.19 X 0.225 X 0.093 = 0.0040
g
4. Ground contribution -skyshine
Cg = Ga(wu) [1-Sw(Xe)lBe(H,Xe)
C = 0.050 X 0.225 X 0.093 = 0.0010
g
5. Ground contribution -scatter
Cg = [G 8 (wu) + G8 (wL)lE(e)Sw(Xe)B8 (2w8 ,Xe)
= 0.34 X 1.41 X 0.775 X 0.068 = 0.0252
6. RF = 0.0046 + 0.0040 + 0.0010 + 0.0252 = 0.0348 PF = 1/0.1348 = 29
4-106
Step 2 is the calculation o( overhead contribution which is not affected by the Limited Field. In Step 3, the direct ground contribution is calculated by differencing the Gd factors through the two lower solid angle fractions. Step 4 gives the skyshine contribution (Note that the effect on the shield is neglected). Steps 3 and 4 could have been combined.
Step 5 gives the scatter contribution which is the product of the normal geometry factor for scatter radiation and the modified exterior wall barrier factor.
It should be of interest to the analyst to note the total effect of the shield on ground contribution. Skyshine is unaffected. The infinite field direct contribution would have been (0.35/0.19)x (0.0040) =0.0073, and the scatter contribution, (0 .093/0.068) X (0. 0252) = 0.034. The tota I cg would be, for an infinite field, 0.0413 as opposed to 0.0348. The effect of the shielding has been to reduce the ground contribution to about 85% of the infinite field value.
4-11 Summary
This Chapter has presented the standard method of analysis used in fallout shelter analysis. A number of problems have been solved to illustrate applications of the method. The fallout shelter analyst must comprehend fully all of the principles that have been used and the methods in which they have been considered in the calculations. There are few additional concepts to be learned for even the most complex of problems. The solution to complex problems is generally a matter of technique. It will be seen that a complex problem is reduced, in analysis, to the simple types of problems that have been considered in this chapter. If these simple problems are well understood, no difficulty should be experienced in extensions to the most complex problems that occur in practical situations.
4-107
Study Questions and Problems Chapter 4
1. What is the focal point for the calculation of a protection factor in a
simple, rectangular structure, and what is the location of this point?
What are the ultimate sources from which the detector in a structure receives radiation?
2.
What kinds of radiation reach the detector in a building?
3.
What types of radiation reach the detector from overhead; from the portions of the walls below the detector plane; from the portions of the walls above the detector plane?
4.
How is the skyshine, that occurs below the detector plane, accounted for?
5.
How is scattering, that takes place within a structure, accounted for?
6.
How do changes in W. L. and Z affect overhead response?
7.
Explain how variations in the geometric parameter, w, affect overhead
responses.
8.
Describe Spencer's model from which overhead contributions are calculated.
9.
What assumptions underlie the use of Spencer's model for determining overhead contributions of practical, rectangular structures?
10.
Do the differences between S~encer's model and practical cases result in conservative or unconservative values for overhead contributions?
11.
Given: =0.50 and X0 = 100 psf. Find C0 .
12.
Given: =0.20 and C0 = 0.00015. What is the overhead mass thickness?
13.
Given: a square plane of contamination located 10 feet above a centrally located detector. Plot a curve showing the variation of Cwith area for
0
a mass thickness of 50 psf.
14.
Describe the structure configuration used in determining G0 values on Figure 4-6 (Chart 2 Appendix C).
15.
Explain why Gand Gd values taken from Figures 4-6 and 4-7 (Charts 2 &
0
3) are not directly applicable as geometry factors for wall contributions except for a very specia I case.
4-108
16. Under what conditions are Gd and Gvalues from Figures 4-6 and 4-7
0
applicable directly to rectangular structures?
17.
Of the total contribution to the standard unprotected detector, what per
centages arrive as skyshine and direct?
18.
How were values determined for Gs in the plot of Figure A-6 for the
scatter response?
19.
Under what conditions are the Figure 4-6 Spencer•s values of scatter
geometry factors directly applicable to rectangular structures?
20.
For what reason are Gs values multiplied by the shape factor, E(e)?
21.
Explain the concept of the scatter fraction, Sw, as a means for interpolating between thin wall and thick wall structures to obtain a geometry factor for walls of intermediate mass thickness.
22.
What is the physical meaning of a barrier factor?
23.
How do increases and/or decreases in the upper and lower solid angle fractions affect detector response to wall emergent radiation, all else remaining equal.
24.
Explain under what circumstances low wall mass thicknesses may result in higher contributions than would zero mass thickness in the walls.
25.
Explain why it is necessary 'to consider the height, above the contaminated plane, of a point on an exterior wall in determining an exterior wall barrier factor.
26.
What point is normally selected for H in Be(H,Xe)?
27.
H0 w does increased story height, all else remaining equal, affect overhead contributions; ground contributions above and below the detector plane?
28.
Everything else remaining equal, what is the effect of an increase in building area on overhead and wall contributions?
29.
How do interior partitions affect overhead and wall contributions?
30.
Are apertures always adverse to protection? Why?
31.
Explain how depressing the floor of a one-story structure below grade will affect the protection factor.
4-109
32.
Show, by means of a sketch, how an increase in height of a detector above the contaminated plane affects the barrier factor for the exterior wall.
33.
Show how elevating a detector story (and floor) above grade reduces the direct contribution through the lower portion of the exterior walls.
34.
In considering contributions to a detector in an upper story, contributions from stories above and below pass through floor (and ceiling) barriers. If the barriers are the same mass thickness, will the reduction through them be the same for the above and below contributions? Why?
35.
In general, where is the best protection in an aboveground area? A belowground area?
36.
What is mutual shielding?
37.
Explain how the I imitation of fields affects protection.
38.
Explain why it is necessary, in limited field cases, to consider 2 solid angle fractions in colculating scatter contributions.
4-110
CHAPTER V
APPLICATION OF THE STANDARD METHOD
TO COMPLEX BUILD! NGS
5-l Introduction
All of the methodology required to determine contributions to a detector in any building, no matter how complex, has already been developed. The buildings, for which problem illustrations were made in Chapter IV, were all simple structures, rectangular in plan, with the detector in a centrally located position. Exterior walls had their solid parts of uniform mass thickness on all sides. The treatment of apertures considered openings of uniform size and spacing and at a constant elevation in the exterior walls. Partitions were, similarly, of uniform mass thickness completely surrounding the detector and forming a centrally located core in plan. The buildings were either isolated in an infinite, horizontal field uniformly contaminated, or they were symmetrically surrounded by a Iimited field. Clearly, these types of buildings are rarely, if ever, encountered in practice. From this point of view, the shielding conditions associated with such buildings were idealized and the buildings themselves could be termed idealized buildings.
It should further be recognized that the methodology, as developed, must be restricted, in its direct application, only to such idealized cases. The assumptions underlying the method preclude direct application to complex situations. The Standard Method Charts are used for idealized structures only. A non ideal structure must be dissected into parts which correspond to parts of ideal structures. Contributions are determined for the latter, and by proper weighting of those contributions. The contribution to the nonideal structure is approximated. In other words, contributions are calculated for the idealized (fictitious) buildings, and, by the application of a technique;'Jhey are reconverted to contributions to the detector in the actual (real) building.
This chapter is devoted largely to the solution of typical problems involving
complex situations. Certainly, it is not possible to anticipate every variation from an ideal situation that can be encountered. The techniques involved are, however, readily adaptable to a wide variety of cases other than those that will be considered. If these techniques are completely understood, the analyst should experience no difficulty in extending them to other situations .
• 5-1
5-2 Building Conversion·
As indicated in article 5-1, complex buildings are handled by first a conversion to one or more fictitious buildings. Contributions are calculated. for the fictitious buildings and are reconverted to represent contributions to the detector in the actual building. Variable complexities, that may be encountered, often require different conversions for determining overhead and ground (wall) contributions. In such cases, the techniques for reconversion of the contributions are different. For that reason, this chapter will consider conversion and reconversion for overhead and ground contributions separately.
5-3 Overhead Contributions
5-3. 1 Genera I
In Chapter IV, an introduction was made to the core concept for determining
overhead contributions. In several problems, which involved variations in overhead mass thickness and/or cores formed by interior partitions, the technique of differencing overhead contributions was used. This technique can be extended to permit the determination of the overhead contribution from any rectangular segment of any contaminated overhead plane regardless of its orientation with respect to the detector.
When used with the technique for calculating overhead contributions from peripheral and core areas, it permits the solution to an infinite variety of complex conditions of overhead contribution. Since actually no new concepts or principles are involved, the procedural techniques are, perhaps, best illustrated by direct application to a variety of problems.
5-3.2 Eccentric Detector Locations
Problem 5-l shows a detector eccentrically located in plan of a rectangular building. It is required that the overhead contribution to the detector be determined.
Overhead contributions can be calculated only for the idealized case involving
a detector centrally located with respect to the plan area of a rectangular (or circular) overhead plane of contamination. In the case of such an idealized rectangular plane, it can be reasoned that, one fourth of the total overhead contribution will be received at the detector from those sources lying on the quadrants defined by rectangular axes
through the geometric center of the plane. This provides the concept by which
Prob I em 5-1 may be solved.
5-2
PROBLEM 5-1
X = 100 psf
-
0
Z = 15 feet
L~~~
1~---=-5-=-0'-~""---"'2'-=-5___,'-+
----·----,--··---···----
fictf't~s w L z W/L co 0. 25C0 l
,___
bl ·
·-<=:=·
-··=-=
~~jk:
A 40 100 15 0.40 0. 5 0.0134 0.0034
i
-------------·--·-·-t-----~--------
B 60 100 15 0.60 0. 15 i0. 65 ·0.0150 0.0037
--·--·---·-t--·---·-··--··-·---------
40 50 15 0.80 0. 8 0.0123 0.0031 -·-------------·-· 50 60 15 0.83 5 0.0134 0.0034
D
0. ~lt~-Total Overhead Contribution
5-3
In the problem sketch, the detector is eccentrically located in plan. Rectangular axes through the detector and projected to the roof form four "quadrants, 11 A, B, C, and D, each of which contribute to the detector. It is clear that the entire roof contribution cannot be obtained directly, since
•
the detector is not centrally located. However, it should be obvious that the
detector in the actual structure will receive the same contribution from quadrant A, for example, as would be received at a detector in a fictitiou-s building, with its centrally located detector, from one of four quadrants oriented with respect to the detector in the actual building. In considering, then, the actual contributions from the four quadrants of interest, the actual building is converted to four fictitious buildings, A, B, C, and D, each having four identical quadrants with the same dimensions respectively of those in the actual building. These four fictitious buildings are shown in the problem solutions, each with one quadrant shaded to indicate its correspondence to a quadrant in the actual building. The overhead contributions for each of the fictitious buildings is computed. These are divided by four to obtain the part of the total contribution of interest, and the results are added to obtain the reconversion of overhead contribution to the actual bui I ding.
5-3.3 Complex Variations in Partition Arrangements
Problems 5-2 is a complex variation of the determination of overhead contributions from core and peripheral areas. In the problem, an interior partition exists only on one side of the detector, resulting in a nonsymmetrical situation which cannot be treated directly. The actual structure is shown in plan and section as the left-hand sketch in the problem solution. The actual bui I ding is converted to a fictitious building as shown in the right-hand sketch of the problem solution, by the insertion of a fictitious partition symmetrically placed. The fictitious building can now be analyzed as a core -periphery problem just
as similar problems were analyzed in Chapter IV. Using the differencing technique, C is calculated for the peripheral areas. Were the idealized structure the 8ctual structure, this contribution would be multiplied by the
partition barrier factor. In the actual structure, however, only half the contribution from the peripheral area is affected by the interior partition. It follows then, that only half the difference is multiplied by the partition barrier
factor. The other half is not reduced. The final overhead contribution to the actual detector is the sum of the core contribution, half the peripheral contri
bution modified by the partition barrier factor, and the half not so modified.
5-3.4 Irregularly Shaped Bui I dings
Problem 5-3 considers the overhead contribution to the detector in an irregularly shaped building which is assumed to be void of partitions. The plan
5-4
PROBLEM 5-2
I I
B. (X.)= B. (50) = 0. 20
1 1 1
w L z WfL Z/L w Co whole w/ 30 48 10 0.62 0.21 0.55 0.037
core w 18 30 10 0.60 0.33 0.39 o. 029
C (w, X ) = 0. 029
0 0 [ c (w',X)-c (w,X )] B!{X.)l/2 = 0.008x 0.20 X 0. 50
0 0 0 0 1 1
= 0.001 -C (w',X)-C (w,X .)]1/2 = 0.008x. 0. 50 = 0.004
0 0 0 0
L
Total C = 0. 029 + 0. 001 + 0. 004 = 0. 034
0
5-5
PROBLEM 5-3
X = 75 psf
0
Z = 25 feet
20'
r , ,..,
;:;::::::::: I -c 40I .....,
o CD
c':l -"
-f------0
en
-30' _,20'
.. -~
...
I~ 100'--------~~~
-...-~====""C"t"-----...... o I
il.••.••.••.'.••.••.••.••.••.•_•.i.'.L_
~ ·· d ~~-~-
····· ::::::::::::;::::::::::-.=:·::·:·:·=·= . -----+-~ ...... '!=V
0
_..._......______-+------J
c
Area w L z W/L Z/L w Actual
0
A 40 100 25 0.40 0.25 0.38 . 021 .0053
B 20 100 25 0.20 0.25 0. 21 . 012 .0030
20 80 25 0.25 0.31 0. 21 . 012
20 40 25 0.50 .. 0.62 0.15 . 009.
c Difference = .003 000075
E,F 40 60 25 0.67 0.42 0.32 . 018 .0090
-----1
20 _0. 62 . 009'
40 25 0.50 0.15
D Difference = .009 ,0023
•02035
Total =
5-6
view of the structure is divided into 6 sections, A, B, C, D, E, and F, for which
separate contributions are calculated. The fictitious bui !dings, from which the
respective contributions are determined, are shown in figures on the problem
solution sheet with that part of the area of interest shaded. The analyst should
recognize that the actual building could have been broken up into areas in
different ways, yielding a different set of fictitious buildings. The choice is
simply a matter of judgment. The final results, within the precision of the
calculations should be the same.
The fictitious buildings are analyzed in the table and the actual part of the contribution from the fictitious building that is of interest in the actual building is separated in the last column. Contributions A and Bare calculated in the normal way. They are simply one fourth the total overhead contribution for their respective fictitious buildings. Contributions C and Dare calculated using the core-periphery concept and differencing of overhead responses for the fictitious buildings. The contribution that they transmit to the detector in the. actual building is simply one fourth of the peripheral contribution determined for their respective fictitious buildings. Contributions E and Fare considered together, since the fictitious buildings are the same. The sum of the two is half the total for either fictitious building.
5-3.5 Contributions From Multi-level Roofs
Problem 5-4 considers the common occurrence of an overhead contribution to a detector from roofs of different elevations. Although the calculations should be relatively self-explanatory, some comment is required with respect to the contribution from low roof sources. The high roof contribution is without compl ication, and the actual building represents, in itself, a fictitious building for this contribution.
The fictitious building for the low roof contribution, although it is not shown, can be visualized from the sketch of the actual building. It is a onestory structure 40 x 120 feet in plan with a centrally located detector 12 feet below a roof having a constant mass thickness of 50 psf. The required portion of the total contribution from the fictitious building is that which originates from the peripheral area lying outside the interior partitions. This is determined by differencing the overhead responses through the whole roof and through the core area. The partition barrier factor is applied to this difference. Responses can be differenced only if the mass thicknesses involved are the same. Therefore, in the idealized structure, the core area was fictitiously taken to have an overhead mass thickness of 50 psf corresponding to that of the peripheral areas of interest.
5-7
PROBLEM 5-4
X = 60 psf (upper)
r
X = 50 psf (lower)
r
xf = 75 psf -. = 50 psf
en 50
.1
~ 40' 40' ~1.... 40' ,...,
B~(X.)1 1 = B~(50)1 = 0. 20
w L z w,L Z;L w xo Co
w 40 40 27 1. 00 0.67 0.23 135 0.0036
w' 40 40 12 1.00 0.30 o. 53 50 0.048 w" 40 120 12 0.33 0.10 0.63 50 0.052 . (a) High roof contribution C (w,X) = C (0.23, 135) = 0.0036
00 0
(b) Low roof contribution [c(w",X)-C (w',X)] Bi(Xi) =
0 000
(0. 052 -o. 048)0. 20 = o. 0008
(c) Total overhead contribution
0. 0036 + o. 0008 = 0. 0044
5-8
5-3.6 Sloping Roofs
The usually recommended idealization of a linearly pitched roof is a simple, horizontal roof uniformly contaminated and extending over an area equal to that of the horizontal projection of the actual roof. The elevation of the idealized horizontal roof could conservatively be taken as the eave elevation of the actual roof, or, perhaps more reasonably, it could be taken as the midpoint elevation of the sloped roof.
Since I ittle data are available on the retentive characteristics of roof coverings on fallout particles, it is recommended that all roofs be considered fully contaminated regardless of their smoothness and pitch. In cases of extreme pitch and smoothness, the analyst might exercise other judgment, but he should do so only with. extreme caution.
An arched roof can be idealized as a series of 11 steps11 of different elevation, as illustrated by Problem 5-5, using the differencing technique for determining the contribution from each step. The calculations should be self-explanatory, and no comment is deemed necessary.
Alternately, the overhead contribution could be determined as in Problem 5-6. In the problem, the arched roof is idealized by three equal segments which closely approximate the actual shape of the roof. More segments could have been used. The segments are so oriented geometrically that a line from their midpoint to the detector is perpendicular to the segment. In the case of the problem, it happens that the center of curvature of the circular arch is coincident with the detector so that the perpendicular distances are all equal as are the segment lengths. Extension to a more generalized case should introduce no difficulties. Each one of the segments is an idea I ized structure with a centrally Iocated detector. The contribution can be determined for each and the resu Its added to determine the tota I contribution.
The approach in Problem 5-6 is theoretically more correct than that of the step method. In the idea I ized step structure, the slant distance through the mass thickness of the roof in the far areas results in an effective mass thickness for those areas substantially more than th_e actual weight in pounds per square foot of surface. Consequently, the contribution from those far areas is considerably less than it should be. In the second method, the roof mass thickness is more correctly considered insofar as its orientation with respect to the detector is concerned, and the slant distances through which the radiation penetrates the mass thickness are, on the average, less than those for the first method. Obviously, in the case of the problem, 50 psf is the effectivemass thickness everywhere for each source in the actual structure. The more nearly the approximation
5-9
208-401 0-76 -13
PROBLEM 5-5
\
,::·
13' ·.·.
w L z wt z; w X 0 c c
0
L .
wa 16 50 21 0.32 6.42 Oa18 50 0.019 0. 019· w 30 50 19 0.60 0.38 Oa32 50 0.032
c wb 16 50 19 0.32 0.38 o. 20 50 o. 021. Difference = 0.011 0.011, w 36 50 13 0. 72 0.26 0.50 50 10, 045
e wd 30 50 13. 0.60 0.26 Oa 46 50 0.043
--.,
Difference = 0.002 0.002
Total contribution = 0. 032
5-10
PROBLEM 5-6
X = 50 psf
14' 0 L = 50 feet
:·.
w 14
= = 0. 28
L 50
:z 21.5
=-= 0.43
L 50
w(e,n) =w(0.28,0.43) = 0.15
C (w,X ) = C (0. 15, 50) = 0. 016
0 0 0
The distribution of particles per unit of area on the slopin idealized segments will be less than that on the horizontal segment. To account for this, the contribution from th sloping segments shQuld be multiplied by the cosine of th angle of inclination with respect to the horizontal. The tot contribution becomes
o. 016 + 2(0. 016)(11/14) = o. 041
THIS ADJUSTMENT SHOULD BE MADE FOR ALL CASE
WHERE OVERHEAD CONTRIBUTIONS ARE CALCULATE
FOR SLOPING SEGMENTS BY THE ALTERNATE METH
OD.
5-11
of the idea I ized structures to the actua I case (the more segments), the more precise the end result. Attention is also directed to the manner in which the solution in Problem 5-6 considers the wider distribution of particles on the
idealized sloping segments. The step method essentially accomplishes this by virtue of the slant distance effect.
It is emphasized that the analyst should reflect on the application of the method of Problem 5-6 to linearly sloping roofs and to the more generalized case of the arched roof, where the center of curvature and detector are not coincident, including the case of eccentric locations. The entire key to precision is conversion to idealized structures that closely approximate actual conditions. The techniques are simple. The analyst must use ingenuity reinforced by fundamental understanding and tempered by practical judgment particularly concerning precision.
5-3.7 Nonuniform Overhead Mass Thickness
In many instances the fallout shelter anlayst must exercise careful judgment in determining overhead contributions. This is particularly true in cases where a uniform slab is supported at intervals in one or two directions. When the slab is supported at large intervals the analyst generally neglects the increased mass thickness of the supporting members and bases his calculations on the mass thickness of the slab only. Such cases include one-and two-way slabs supported by steel or concrete beams spaced several feet apart. Neglecting the increased mass thickness of these supporting beams is conservative but not excessively conservative.
This procedure applied to other forms of construction can lead to overhead contributions that are extremely conservative. Forms of construction in this category include: "waffle" type two-way and flat slabs, one-way pan systems where the slabs are thin but supported at close intervals, and prestressed concrete tees. These type of rib-slabs should afford more radiation protection than similar slabs without ribs. Radiation protection wi II be even greater if the slab were completely covered with ribs; i.e. no space between ribs. This suggests that a mass thickness "in-between" the extremes, no ribs or all ribs, should give the same contribution as the actual mass thickness of the rib-slab configuration.
Any technique of smearing mass thickness cannot be justified on purely theoretical grounds; however, it can be justified as an empirical approach if it gives results comparable to experiments.
Studies have shown that the smeared mass thickness is an appropriate choice in certain situations for determinirag overhead contribution. On the other hand,
5-12
they show that it often gives non-conservative results; i.e. protection factors result which are higher than actual.
Accordingly it is recommended that in the application of the standard method area weighting and 100 percent mass thickness smearing not be used for computing overhead contributions through rib-slab configurations instead the ''adjusted smearing11 procedure is to be used. By this procedure, only a portion of the smeared-rib mass thickness, as determined from Figure 5-1 is to be added to the base slab mass thickness. The curve of Figure 5-l has evolved through extensive comparisons of experimental results and calculations with actual rib-slab configurations.
It is expected to serve as a satisfactory means for handling rib-slab roofs as well as intermediate floors. The curve is drawn through an envelope of curves extending + 5 percent. A slightly conservative approximation to the curve of Figure 5-1 is the following acceptable rule:
Use 700/o of Smeared Rib Mass Thickness if Spacing is >0.5 ft. but<1 ft; Use 60% if > 1 ft . but < 2 ft; Use 500/o if >2 ft. but < 4 ft; Use 400/o if >4 ft. but < 8 ft; Use 300/o if >a ft. but <16ft.
Figure 5-1 Rib/Slab Mass Thickness Curve for use with the adjusted smearing method can also be applied to two-way rib-slab (waffle) configurations. Although the number of experiments that have been conducted with these configurations is small, they do indicate that slightly conservative results are still obtainable by using the adjusted smearing technique. Typical calculations are shown in Problem 5-7.
5-4 Ground Contributions
5-4.1 General
The extension of the methodology for calculating the ground contribution to centrally located detectors in simple rectangular structures, such as were considered in Chapter IV, can be made through the concept, again, of fictitious buildings and the additional concepts of azimuthal sectors and/or perimeter ratios. This article considers a variety of such complex variations.
5-13
I
+J-Hlll :111!111 I Ul"lil • ' '
'' .mf
I ! ~
0
l-en
(I) en
enw
wz
2~
70
~(.)
u
_J: J:l
1-en
(/)en
en<:(
<:(~ ~co
CO<:(
-....~
a: en 0 w·
wen
a:<:(
<:(CO
wo
~1
eno
1-w
zo
wo
(.)<:(
a:
20
ww
a.. CO
I
! I
i
I
I I I
I
1-t+++-IH,+t+l+r!+li'!""''.Hit+HW,I
i I i 'I !I' iJ I II Iii I!!·;H.' ',;
l":~jll_ '' i I 1-H·+H-t+H-H-H+IH!iI I I
I !(1!11 i ill
I
I I 1 1
i
ttt-t-H-H+H+H+H-H-It--!-+-i-++-H-t+h+HtH-+~t+tt+Ht+H-Hi-ri+--~H-~t-it-i~~+Y-~~f+fH~
: !
I ''I ,!1 I I
I i i '
!
I I I
· i I I I I I I H~! I 1 liill1'i : l__j-'-I
,
! i
' II
.6 .8 1.0 2 3 4 6 8 10
RIB/BEAM SPACING (CENTER-TO-CENTER) IN FEET
FIGURE 5-1 RIB/SLAB MASS THICKNESS CURVE
' -'
1-1~·:
• Ll:!,
I I I!
'
:
'
I I : i ~ (.)
i j ..... i' <:(J: ....."'1 -, co 1iiI II I I ' I t-L J
l I !
... ~) .. ... ·. . . . .."( .. ·. ,.J..·.. :-..... :1Jd. a~
I • • • •• • • • In : •. ,.,.·__,_,
~·..:,_.'-'ljl
,.. ~~·., .·: ~:~
1
I• ·.. I~·~···
~pl L:~
[RIB/BEAM SPACING 1 ';s';i 1.,: 11
j 'I I I i LL ' ' I LL' .. ' 'I
FOR USE WITH THE "ADJUSTED SMEARING PROCEDURE"
5-14
i '
8
H
[~
[~
C
_;'irS
J. I I iiI -'· ' : : ;
-~ ~ i__;J_ i UlifF++i~
Ll ! I I
I : '
20
PROBLEM 5-7
Find the "adjusted sneared" mass thickness of the concr3te joist system shown below. 'The concrete density is 150 lbsjft which is equivalent to a mass thickness of 12.5 psf per inch of thickness.
24" 24''
Avg. ThicknessJ•w·•c-CDNCREI'E JOIST SYSTEM
'rhe recommended procedure for determining the effective weight of any slab system with ribs, joists, beams or other dropped sections is to add to the base slab mass thickness an adjusted mass thickness value for the joists or beams. This adjusted value is obtained fran Figure 5.1.
1. BASE SLAB MASS THICKNESS
t}~(;~;))}))~;)t~;)))}}:;:::::;:::::;:::::;:::::;:::::;:;:::::::::::;:;:;:;:::::;:::::::::;::::::::f~
BASE SLAB
(Slab thickness) x (density/inch thickness) 3 in. x 12% psf/inch thickness= 37% ps
2. SMEARED JOIST MASS THICKNESS
(D) X (Avg. W) 12 5 f/' h = 10" X 4Ya" 12 5 = 25 4 psf
Joist Spacing x · ps lnc 24" x r · · Since the center-to-center joist spacing is 2ft., enter Figure 5.1 to determine that only 60% of the smeared joist weight is used.
3. 'IUI'AL MASS THICKNESS 6Cf;b x 25.4 psf = 15.2 psf
Base slab mass thickness
Percent smeared joist mass thickness = 15.2 psf TOTAL MASS THICKNESS 52.7 psf Use
5-15
5-4.2 Justification of Idealized Structures
In Figure 5-2(a), an irregularly shaped building is shown in plan. Consideration is given to the ground (wall) contribution from one section of the exterior walls of that structure which arrives at the detector through the shaded zone. The sketch of Figure 5-2(b) shows another building, square in shape, in which consideration is given to the ground contribution through one of the exterior walls to a centrally located detector. Let it now be assumed that the wall in building "a" lies in the same relative position to the detector in "a" as the wall in "b" lies relative to the detector in "b". Let it be further assumed that the walls under consideration are identical in all respects and that each is subjected to the same field of radiation it can be reasoned that, irrespective of the remaining walls, the contribution through the wall in "a" to the detector in "a" should be the same as that through the wall in "b" to the detector in "b".
I 20· 20' zo· 20·
~ .,..,..,1 ..,
40'
~0'
Building Building ";J"
(a) (b)
FIGURE 5-2
WALL BY WALL IDEALIZATION
5-16
The methodology developed in Chapter IV can be applied directly to building "b" if its walls are the same all around its perimeter and if all other conditions of symmetry exist. The methodology for determining ground contributions developed in Chapter IV cannot be applied to building "a". However, with respect to the wall of "a" under consideration, building "b" becomes the fictitious building, and there remains only to develop a technique for determining what portion of the total ground contribution in bui I ding "b" arrives through the wall of interest. If this can be determined, ground contribution can be proportioned to the wall of interest. The proportioned contribution becomes that through the corresponding wall of the actual structure.
The actual structure can be completely analyzed wall by wall by formulating fictitious buildings for each wall, analyzing the fictitious buildings and extracting the portion of the contribution that is of interest.
5-4.3 Azimuthal Sectors and Perimeter Ratios
There are two methods, which can be used to determine what portion the total ground contribution, (of a fictitious building) is attributable to a particular wall, (of interest). These are termed the azimuthal sector method and the perimeter ratio method.
In the azimuthal sector method, it is assumed that equal contributions
arrive at the detector through each of the 360 degrees of azimuth around the
detector. Referring to Figure 5-2 (b) that part of the ground contribution arriving at the detector of building "b", the fictitious building, through the wall of interest is simply the total ground contribution multiplied by the ratio of angle A in degrees to 360. The ratio of A (degrees) to 360 is termed the az imutha I sector.
A = azimuthal sector, the ratio of the plane central angle
z (degrees) at the detector, subtended by a wall segment of interest in a fictitious building, to 360°.
In the perimeter ratio method, it is assumed that, in an idealized structure,
ground contributions arrive at the detector equally from each increment of (wall) length in the perimeter of the structure. Stated in another way, equa I lengths of wall in a fictitious building contribute equally to the detector ..Referring
again to Figure 5-2 (b), the wall contribution to the detector through the wall of interest may be determined by multiplying the total ground contribution by the ratio of the length of wall of interest to total perimeter or 40/320 =0.125. This ratio is termed the perimeter ratio.
5-17
P = perimeter ratio, the ratio of the length of wall of interest
r
in an idealized structure to the total perimeter of the idea Iized structure.
It should be noted that azimutha I sectors and perimeter ratios are based on the geometry of the idealized structures and are applied to contributions determined out of consideration only of idealized structures (i.e. fictitious buildings).
5-4.4 Choice of Method
The perimeter ratio and azimuthal sector methods are equally acceptable in the method of analysis. The choice is generally one of convenience for the analyst. Usually, in application to complex buildings, the two methods will yield substantially the same results if the fictitious buildings are judiciously selected.
The azimuthal sector method is more "theoretically correct" than the perimeter ratio method. Figure 5-3 shows a long, narrow idealized structure. Two wall segments of equal length are situated so that one is directly opposite the detector and one far removed. Application of the perimeter ratio method would yield equal contributions through these two segments. The azimuthal sector method would indicate a greater contribution from the near segment. The latter is evidently a more precise determination. As an analogy, if the wall segments of interest were windows, a light meter in the position of the detector would register substantially more response from the close source than from the far source.
5-4.5 Conversion to Fictitious Buildings
In determining the total ground contribution to a detector in a complex building, it is first necessary to incorporate each exterior wall of the actual building into a fictitious building. Initially, the only consideration is the geometry and construction of the exterior walls. In developing the fictitious buildings, interior partitions are temporarily ignored.
Figure 5-4 shows a complex structure. For convenience, the exterior walls are numbered as separate segments changing in number assignment upon crossing the detector axes or turning a corner. The walls in the actual structure of the figure are consecutively numbered 1 and 12. The process of incorporating these walls into fictitious buildings is simply one of geometry. There are two simple rules. The fictitious building must be square or rectangular with the detector centrally located (sometimes cylindrical structures are advantageous), and the wall of interest must have the exact same· dimensional relationship to
5-18
the detector in the fictitious building as it has to the detector in the actual building.
Four fictitious buildings are used in Figure 5-4 to incorporate all of the walls. It should be carefully noted that they are dimensionally located with respect to the detector of the idealized structure exactly as they are in the actua I structure. The central angles that they subtend in the actua I structures are the same as those subtended in the idealized structure.
X
y
/
0
0..
·.·.: :··:··: . :•. ~·-.::· :'.i: ........... ~ :·::: . . ·. ~•. ·. -::.··: : :. :.·•... ·... ··.:...·. :·.:_.-'::·:.
·: .. ~·:·: ...~:=-.·:· .........{.;::. :·.':..:~· ~-:'::'···:·;.·~ :·: i :.= •....: :·. •.
FIGURE 5-3
AZIMUTHAL SECTORS vs. PERIMETER RATIOS
Most frequently, it may be possible to incorporate a wall into more than one of the fictitious buildings. For example, walls 4 and 9 were incorporated in a structure together with walls 5, 6, 7, and 8. They could have been incorporated
into the structure containing walls 3 and 10. The choice is generally one of Unless there is some reason for doing otherwise, the
convenience to the analyst.
choice should be the structure that is more nearly square. The justification for this is the fact that directional responses, Gd' G , and G , were based on cyl in
s a drica I structures as discussed in Chapter IV. The more nearly a structure is square, the more nearly true is the assumption that it can be considered equivalent to a cylindrical structure. Incorporation into a more nearly square structure, given a choice, introduces a larger value of the shape factor, E(e), into the calculations and, for that reason alone, the computed contribution will be larger.
The fact that G , G , and G responses, as taken from Charts 2 and 3,
d a s are derived from a consideration of cylindrical structures and are directly applied
5-19
FICTITIOUS ACTUAL BUILDING 4 BLDG. "A"
~
-r
ll
~ 3 . :::.
1 I
6 Q I
1 "" .... !?.>
I
, I
~::::: . ::
. . . . ..
12 "
.............
. . . . . . . . . . . . .
. . . . . . . . . . . . I
I
11
::;:· .: 7 ~
I I
.. ,,:,:,: ,. I
L_
60' 3~· I~ 70'
--! .. J
FICTITIOUS BLDG. "D" FICTITIOUS
.. .. -. -r--------~ BLDG. "E"
". --~-
. : : . . . . . . . . . . . . . . I
. ':: ' : ':: > . .. : I I 3 .[:, El
"
" : : " : . . " . : ::::::::,
I I I ":'
I I
L---------~--------J
FICTITIOUS BLDG. "C"
------------------,
I~ 160'
FIGURE 5-4
COMPLEX STRUCTURE IDEALIZED FOR Cg
5-20
to rectangular structures also suggests that neither the azimuthal sector method
nor the perimeter ratio method is strictly correct. Either would be exact
only for cylindrical fictitious buildings. The only reason that can> therefore,
be advaneed for preference of the azimutha I sector method is that, to some
degree, it considers the location of the wall segment relative to the detector.
The perimeter ratio method does not, although it is still an acceptable method .
. The ground contributions for the fictitious buildings are calculated, and, through the application of either the azimutha I sector or perimeter ratio methods, the contributions of interest are extracted.
An idealized structure is not so by virtue of geometry alone. To be ideal, the structure must conform to all other conditions of uniformity and symmetry that are appropriate. In Figure 5-4, it could well be that walls 4, 5, 6, 7, 8, and 9 were all different. Were such the case, it would be necessary to determine the ground contribution six times, assuming the idealized structure to have uniform walls the same around its perimeter corresponding in turn to each of the variations. From each such case, the contribution would be extracted for the wall of interest by either of the two methods. Variations could exist in a single wall necessitating additional calculations and extraction of smaller contributions of interest.
With the exception of the labor of the calculations, the entire matter of idealization is exceedingly simple. It involves only the necessity for determining the different variations in wall section. Fictitious buildings are analyzed for each variation assumed to exist in entirety in the perimeter of the actual building. An appropriate portion of the total contribution of interest is extracted by either the azimuthal sector or perimeter ratio method.
5-4.6 Complex Partition Arrangements
The buildings of the problems in Chapter IV had partitions of uniform mass thickness completely surrounding the detector. Their only effect on the calculations for the ground contribution was a partition barrier factor applied as a multiplier to the other terms of the functional equation. Apart from the fact that complex partition arrangements affect, to some degree, the amount of labor involved in computing azimuthal sectors or perimeter ratios, they do not further complicate the determination of the ground contribution beyond the introduction of a partition barrier factor into the calculations.
Problem 5-8 considers a complex partition arrangement in a rectangular building with a centrally located detector. The building is a 3-story structure with all stories 12 feet high from floor to floor. Windows are 6 feet high with
5-21
PROBLEM 5-8
~--~.
:!.·:
"\):
-
0
N
0
N
5-22
their sills 3 feet above the floor. Their widths are dimensioned on the plan, and they are indicated unshaded in the exterior walls. The opening, indicated at one end of the 13-foot wide corridor, is a full height glass light. The solid port ions of the exterior wa lis, shown shaded in the figure, are 80 psf. The corridor partitions weigh 40 psf but contain 25% openings so that their effective mass thickness is 0.75 x 40 = 30 psf. All other partitions weigh 25 psf and contain 20% openings so that their effective mass thickness is 0.80 x 25 =20 psf. It is assumed that all floors have the same window and partition arrangements. The roof and all floors are assumed to have a mass thickness of 75 psf. The protection factor is to be determined for the centrally located detector in the second story 3 feet above the floor.
The problem will be solved first using the complete concept of fictitious buildings as discussed in article 5..,.4 .5. The number of fictitious buildings that must be analyzed is dependent upon the number of different wall sections that exist in the exterior walls. Since the detector is already centrally located in a rectangular structure, no consideration need be given to exterior wall geometry. Partitions are temporarily ignored.
There are three, different types of wall section in the building. If a section is passed anywhere through the exterior walls, it will show either all solid wall or 3 feet of solid wall above and below a 6-foot high aperture or, at one end of the corridor, complete aperture. These three types of wall sections define the exterior walls of three fictitious buildings that must be analyzed. One fictitious building will have all solid walls in its perimeter, one a continuous aperture 6 feet high with 3-foot solid wall segments above and below, and one will have exterior walls completely aperture. All fictitious buildings, in this problem, have the same dimensions. Schematic sections and plans are shown and, (in the order listed above) are labeled Buildings A, B, and C. Solid angle fractions of interest in each case are shown on the figures. The table below the sketches contains all of the data that are required for insertion into the appropriate functional equations for ground contributions and overhead contributions. They are taken from the charts in appendix C.
Total ground contributions are computed for each of the three idealized structures. The calculations for Bui Iding A are performed in a manner identical with that of Problem 4-13. The ground contribution for Building B is determined in the same manner as that in Problem 4-18 except that ceiling shine contribution is neglected. A =0.5 since half the total wall area is aperture in fictitious
p building B (note that P = 1.0 since apertures are continuous).
. a
5-23
PROBLEM 5-8
FICTITIOUS BUILDINGS
* *. ...* * * .* . * -*. .* * ~ *.. * * * * * .:1< * *·. *...
·l~ ~=~-~· ~:~=i 1\=~~=11
~Vi~,,~·~·
!---i-/~·-~:~~: ~ ~
~'~'~!~·~\
WL .·. , .. w 1
r
• . • • ·. L •
I
1
w L Z W/L Z/L w G s G a
I
w"
67 120 21 0.56 0.175 b.58 -----0.35 b.070
u
w u 67 120 9 0.56 0.075 p.81 -----0.21 b.041
w
a 67 120 6 0.56 0.05 p.87 -----0.15 b,030
w
L 67 120 3 0.56 .025 p.93 0.14 0.08 1-----.w/
L 67 120 15 0.56 0.125 p.70 0.53 0.29 ------
E(O. 56) = 1. 36, s (80) = 0. 72
w
B (15, 80) = Oo 10, B (15, 0) = 0. 74, Bf(75) = 0. 040
e e B.(30) = 0.48, B.(50) = Oo30, B (75, 0.81)=0.027
1 1 c B~(30) = 0.37, B~(50) = 0.20, A = Oo 50
1 1 p
5-24
PROBLEM.5-8 cont.
FICTITIOUS BUILDING GROUND CONTRIBUTIONS BUilDING A
Detector story
G = [G (w ) + G (w )] E(e)S (X ) +
g sL su we
[G (H,wL) + G (w )] [1-S (X )) =
d a u w e
G = (0.29 X 1.36 X 0.72) + (0.181 X 0.28) = 0.335
g
c = G B (H,X ) = 0.335 X .10 = 0.0335
g e e
l g !J Story above
I I [ I
jGg = Gs(wu)-Gs(wu)J E(e) Sw(Xe) + t
1
I [Ga(w -Ga(w )l [ 1-S (X ) ] =
u u
w e
I
!G = (0.14 X 1.36 X 0.72) + (0.029 X 0.28) = 0.145
! g
i
cg = G B (H,X )B (X ,w) = 0.145 X 0.10 X 0.027
g e e c e
= 0.0004
IStory belc:m
I
I
!G = [Gs(wL) -Gs(wL)] E(e) Sw(Xe) +
i g
[Gd(H,w') -Gd(w )l (1-S (X )] =
L L w e Gg = (0.21 X 1.36 X 0.72) + (0.39 X 0.28) = .315 Cg GgBe(H,Xe)Bf(Xf) = 0.315 x 0.10 X 0.04 = 0.0013
Total ground contribution Building A = 0.0352 Building B Detector story all solid
Cg = 0.0335 (same as Building A)
aperture strip solid
----"-·~--~--~~--·"'·-·--
5-25
208-401 0-76 -14
PROBLEM 5-8 cont.
G g = G (w ) E(e) S (X ) + G (w ) [1-S (X )]
s a w ~ a a w e Gg = (0.15 X 1.36 X 0.72) + (0.03 X 0.28) = 0.155 C' = G B (H,X ) = 0.155 x 0.10 = 0.0155
a g e e
aperture strip all aperture Ca = Ga(wa) Be(H,O psf) = 0.030 x 0.74 = 0.022 Total contribution
C + C -C' = 0.0402
g a a Story above all solid
Cg = 0. 0004 (same as Building A)
all aperture
C = [G (w 1 )-G (w )] B (H, 0 psf) B (X, w)
a au au e cc
C = 0.029 X 0.74 X 0.027 = 0.0006
a contribution Cg [1-~] + CaAp = .0005 Story below all solid Cg = 0.0013 (same as Building A) all aperture Ca = [Gd(H, ut) -GiH, ~)] Be(H, 0 psf) Bf(Xf) C = 0.39 X 0.74 X 0.040 = 0.0115
a contribution Cg [1-A ] + C (A ) = .0064
P a P
Total ground contribution Building B .0471
(Ceiling shine contribution neglected)
5-26
PROBLEM 5-8 cont.
Building c
1. Detector story
Ca = Gd(H,~) + Ga(wu) Be(H,O psf)
Ca = 0.181 X 0.74 = .1339
2. Story above
C = 0.0004 (same as Building B)
a
3. Story below
C = 0.0115 (same as Building B)
a
4. Total contribution Building C = 0.1458
Note: Ceiling shine contribution neglected Perimeter Ratios
Sect. Feet Pr B.
c 1 c
AO 13 0.0347 0.0352 1.00 0.00122 0.2645
•
Al 99 0.0352 0.48 0.00445 A2 149 0.3983 0.0352 0.30 0.00422 B1 40 0.1067 0.0471 0.48 0.00241 B2 60 0.1601 0.0471 0.30 0.00226
CD 13 0.0347 0.1458 1.00 0.00506 Total 0.01962 Azimuthal Sectors
A C B c
Sect. Angle
z i
AO 12A 0.0344 0.0352 1.00 0.00120 Al 119.9 0.3333 0.0352 0.48 0.00560 A2 112.6 0.3130 0.0352 0. 30
0.00329 B1 61.7 0.1712 0.0471 0.48 0. 00387 B2 41.2 0.1142 0.0471 0.30 0.00161 CD 12.4 0.0344 0.1458 1.00 0.00502
Total 0.02059
5-27
PROBLEM 5-8 (continued)
~------------·-------------------------------------------------~
3. Overhead Contribution
Since the .total overhead contribution will be small compared to the
ground contribution, it is reasonable to neglect the 20 psf room partitious in calculation C0 . Corridor Roof W/L = 13/120 = 0.108, Z/L = 21/120 = 0.175
w(0.108,0.175) = 0.17
C (w,X ) = C (0.17,150) = 0.0019
0 0 0
Roof Over Roc::ms
Whole Roof
WuI = 0.58 (from Table)
C (w,X) = C (.58,150) = .0041
0 0 0
Contribution of Interest:
(.0041-.0019) B' (30)
(.0022) (.35) = .0007
Total Overhead Contribution
Corridor = .0019
Roans = .0007
Total .0026
Rf = 0.02059 + 0.0026 = 0.0232
pf = 1/0.0232 = 43
5-28
The total ground contribution is calculated for Building C in a straight
forward manner. Since the walls are entirely aperture, there is no scatter
contribution from any story. Thus, the calculations are quite simple.
In analyzing each of the three fictitious buildings, no attention has yet
been paid to the presence of interior partitions. In each case, the total
contribution has been computed considering only the geometry and barrier
effects associated with the exterior wa lis. Barrier effects associated with
interior partitions can be incorporated at the appropriate time by the appl i
cation of a single multiplier to the contributions calculated.
Attention is now directed more to the plan of the actual structure for the general purpose of determining those parts of the actual structure that conform to the various corresponding parts of the points in the exterior walls where the wall section changes. Additional rays are drawn from the detector through points of intersection of interior partitions, and these rays are extended to the exterior wall. The sectors, so formed between adjacent rays, separate the total exterior walls into parts corresponding to the three different wall sections and define the number of partitions through which the contribution through that sector must pass in order to arrive at the detector. Recorded for convenience, in the various angular sectors on the sketch, are combinations of capital letters and numerals. The capital letters A, B, and C designate the fictitious buildings for which the sectors correspond. The numerals indicate the number of partitions through which the exterior wall emergent radiation must pass in reaching the detector. For example, the contribution throtgh any of the sectors marked A2 in the actual structure is assumed identical to that through the same sector in fictitious Building A, and must pass through two partitions. Because of symmetry, only half of the total sectors have been marked.
Shown also on the plan of the actual structure are the angles between adjacent rays and the lengths of the exterior wall segments between rays. These are used in applying the azimuthal sector and perimeter ratio methods to complete the determination of the ground contribution to the actual structure. Both methods are employed to illustrate their application and also for comparative purposes. The dimensions and angles could be computed or scaled from a drawing, whichever is most convenient. Precision in this regard is not critical, and small discrepancies are entirely inconsequential. In the calculations, the accuracy implied by four significant figures in the table of values is fictitious. Slide rule accuracy is entirely adequate.
The perimeter ratio method is applied first, and the calculations are recorded in tabular form. The first column I ists the sector designation. The
5-29
second column lists the total length of wall of that designation. The third column gives the perimeter ratio determined by dividing each value in the second column by 374, the perimeter of the idea Iized structure. The fourth column gives the total ground contribution calculated for the idealized structure of interest. The fifth column gives the partition barrier factor taken from the chart data on the second page of the computations. In the case of a contribution passing through one partition (corridor), the barrier factor is
B.(30) =0.48. Those passing through two (corridor plus room) are modified
I
by B.(50) =0.30. The final column gives the sector contribution in the
I
actual structure. It is the product of the total idealized structure contribution, the perimeter ratio and the partition barrier factor.
Azimuthal sectors are used in following tabular computations. The method of calculation is similar to that described above for perimeter ratios. The second column gives the total central angle for each sector designation. These are divided by 360 to obtain the azimutha·l sector. The remaining calculations are identical with those for the perimeter ratio method substituting, of course, A furP. z
r
The 4% difference between the results is insignificant and does not necessarily indicate preference for one method over the other. As indicated previously, judgment or convenience will usually dictate the choice of method.
If the plan sketch of the actual structure is drawn to scale, as it ordinarily
should be to accurately define the different sectors, it is generally just as
convenient to scale off angles as it is to scale Iinear dimensions. If the plan
is not drawn to scale and azimuthal angle increments or increments of length
must be calculated, sometimes the angle would have to be computed in order
to compute the segment length. It thus appears that, considering the probable
higher precision of the azimuthal sector method, it should very often prove
the judicious choice of method. It is emphasized, however, that either is
acceptable.
In Problem 5-8, it was assumed that the partitions were identically arranged in all three stories considered. If those in the stories above and below were differently arranged, an additional element of complexity would be involved if one sought the most precise determination of ground contribution attainable using this method of analysis. One needs only to reflect on the additional number of solid angle fractions that might be required to define all variations in the contributions from the stories above and below.
Usually, in multistory buildings, partition arrangements are fairly uniform, often identical in adjacent stories. It is recalled also that the contribution from the stories above and below is in the order of 10% of the total
5-30
ground contribution, so that even a significant error in them would result
in a rather minor error in the total. There appears to be no justification for
seeking refinements to the above and below contributions. If the partitions
do not line up but are of about the same number and mass thickness in adjacent
stories, they can be assumed to Iine up with only very minor error. The same
azimuthal sectors and perimeter ratios applied to detector story contributions
can then be applied to those from above and below. This was the case in the
solution to Problem 5-8. No additional solid angle fractions are required.
If the partitions above and below were heavier and more numerous assuming
them the same would be conservative. If they did not exist at all, a very
unlikely circumstance, the error would still not be large to assume that they
were the same as those in the detector story. As a rather firm rule, it is
acceptable to assume that partitions in adjacent stories of interest are identical
in orientation and mass thickness, thus circumventing complexities in the
co Icu lot ions.
It must be emphasized, however, that no rule or collection of rules has ever been formulated as a suitable replacement for engineering judgment. The shielding methodology used is probably as well advanced as methodologies in most other areas of structural engineering, but, as in all areas of engineering practice, there is always the strong necessity for the application of sound
engineering judgment to supplement factual knowledge as well as that based
on idealized assumptions.
Overhead contributions are required to complete calculations for the protection factor. Since the overhead contribution is small compared to the total contribution an approximation is made in which the 20 psf partitions between the rooms are neglected. This greatly simplifies the calculations and would have an insignificant effect of the protection factor.
5-4.7 Complex Structures with Limited Fields
Article 5-4.4 has discussed, in a general way, the analysis of irregularly shaped buildings on a wall by wall basis using azimuthal sectors and/or perimeter ratios for determining the contributions through those parts of the idea Iized structure that correspond with parts of the actua I structure. Problem 5-8 illustrated the manner by which complex partition arrangements could be treated using both azimuthal sectors and/or perimeter ratios as the basic techniques. The structure of Problem 5-8 was assumed surrounded by an infinite field of contamination.
Most often, there are irregularities in buildings apart from complex partition arrangements. These irregularities may extend not only to the physical
5-31
dimensions of the structure itself, or the location of the detector in an eccentric position, but also, to irregularities in the field of contamination surrounding the structure. The latter, although they may add to the labor of analysis do not prove unduly complicated if the concept of idealization is adequately
comprehended. Chapter IV has discussed the method of analysis once a I imited field has been defined. It is the purpose of this present article to extend that discussion to include the technique of limited field idealization.
Since the matter is simply one of technique in which the judgment of the analyst plays an important role, it is best considered by means of an illustrative example.
Problem 5-9 considers an irregularly shaped building completely enclosed on the north, south, and west, and sufficiently shielded on the east, so that judgment would indicate complete enclosure. It is noted that the shields to the north and south extend some indefinite distance beyond the partial shield on the east, so that rays which might be drawn from the detector through the corners of the east shield would still strike the shields to the north and south.
The detector is centrally located in a room assumed to have been designated as shelter area. Partition arrangements are obviously complicated and have been purposely arranged in that way to add realism to the problem, although primary
emphasis is directed to the shielding problem. In this way, the problem serves
as an excellent comprehensive example of practically all shielding concepts that are generally encountered. It is, therefore, suggested that the student follow the various steps in the solution with meticulous care.
The plan of the actual building together with structural data are given on
the first sheet of the calculations. Partition mass thicknesses are given as net. This indicates that the mass thicknesses are adjusted to account for any openings that exist in the partitions. The rays emanating from the detector in the plan
view indicate the various sectors of the actual building that will be treated by consideration of separate fictitious Buildings R, S, T, U, and V.
Sheet 2 of the calculations shows the fictitious buildings in plan together
with the idealized limited fields. The shaded sectors of the fictitious buildings are in exact correspondence with sectors in the actual building. The idealization .of the structure follows the procedures discussed in article 5-4.5. All fictitious buildings must have their exterior wall geometry and idealized I imited fields symmetrical with respect to rectangular axes through the detector. First consideration is given to idealized structure R. The West wall is subjected to radiation from a Iimited field that extends 400 feet to the west. A question arises relative to the other dimension of the limited field in idealized form.
5-32
PROBLEM 5-9 (SHEET 1)
continuous shield
' r
1.{)
C\J
' 0
'¢
continuous shield
4 stories of 15' -detector in 2nd story. Corridor partitions 30 psf net, others 15 psf net.
xr == 60 psf' xf == '75 psf
W == 400 feet for West wall
c North and South Walls: X == 75 psf, windows 9' high x 6~wide at 9' centers. East and West Walls: X == 60 psf, windows 9' high x e 6' wide at 12' centers.
All sills at detector height.
5-33
PROBLEM 5-9 (SHEET 2)
FICTITIOUS BUILDINGS AND LIMITED FIELDS
R
1'4 110 I ~
1--160' .. ,
5-34
PROBLEM 5-9 (SHEET 3)
~ FICTITIOUS BUILDING R (Schematic Elevations)
We = 400'
a o' West Wall
Xe = 60 psf 400 We = 400' , H = 18' , WcjH = = 22
18 2w(Wc/H) = 2w8 (22) = 0.972, (18,0.972) = 0.88
8
Be(60,18') = 0.15 Be(Xe,H) · F8 (H,2w8 ) =
0.15 X 0.88 = 0.132
Xe. = 75 psf Wc = 55' , H = 18' Wc/H = 55/18 = 3 2liB(3) = 0.80
B8 (Xe, 2w ) =
8
B (75, 0.8) .03
8
50 1
55'
North Wall
5-35
PROBLEM 5-9 (Sheet 4) Fictitious Building R (One quarter pl.an)
-
13 1 171 10 1 20 1 20/
~r ·r.. , I • ·~~
r 1
.... "-.... \.
f ..... g ,,, h '\ I j
\
0
"\
- \
Q.)
" " '\
\
" "
I-, \.
...... " " \
........ "\
...... " "
'\ \
........ I'"
" I
........ '\
'I() ...... ....... " \
........
"'0 " '"\
-........ \
...... "
........
" \ \
........
~"-.... .......... " ", \
........
-r
"'
........
\
-~-----
.... -...._ ·--.. --.. ........ ....... " '"\ \ I
(]) ...._ ------ '~''
...0 ---.. ........ ........ "" " \ \
---------...._ " " '\ \
........ ........
r-::::.. -::::_ c:::c -' <':'~\
---- ---. -...................._-....... ........... ' "" \
'
I()
0 -----~...._ '-"-"'"\ \ I
-
--- ......... ':::::::......_ ............ ="'-'-\.
-----">:::::. ..,._ ~::::..."" ' I
--""""'~ '
_--~©
w L z W/L Z/L w Gd G G
s a
w
a 100 160 27 0.63 0.169 0.63 -----0.33 0.065 w
100 160 12 0.63 0.075 0.82 -----0.20 0.039
b w 100 160 9 0.63 0.056 0.87 -----0.15 0.029.
c
w d 100 160 3 0.63 .019 0.95 0.07 0.06 ----960 18 0.32 .019 0.92 0.15 0.09 ----
w e 310
0.27 ----
wf 100 160 18 0.63 0.112 0.73 0.46
E(0.63) = 1.37 Bi(30) = 0.50 Sec. deg. L part. a
Sw(75) = 0.70 Bi(45) = 0.33 ~T -15 130
b 6 -g 160
Sw(60) = 0.65 Bi(60) = 0.24 c 1 1 45 d 9 15 75
B (18,75) = 0.12 Bi(75) = 0.17
e e 5 10 90
Be(18,60) = 0.16 Bi(90) = 0.12 f 6 13 90 Bf(75) = 0.04 g,i 23 37 75
Be(18,0) = 0.70
n,J ~~ ::su lbU Bc(75,0.82) = 0.025
5-36
PROBLEM 5-9 (SHEET 5)
FICTITIOUS BUILDING S (Schematic Elevations)
East Wall
Xe = 60 psf We = 35' H = 18' Wc/H = 35/18 = 1.94 2w (1.94) = 0. 7
s B8 (60,0.7) = 0.035
North Wall
Xe = 75 psf
We = 25'
H = 18'
WcjH = 25 = 1.4
18
2w (1.4) = 0.62
s B (75,0.62) = 0.016
s
5-37
PROBLEM 5-9 (SHEET 6)
FICTITIOUS BUILDING s (one half plan)
7/ 1 .. 301 5' 5'
33
r~ -rOlf
e \ \ f h I
' \
\ I
\ I
....
\
If') I
\
C\J I
c \
\ \ \ \
.......
\
.......
-
....... \
-
.......
....... \
-
.......
....... \
....... \
-
\
... -
\
0
-
C\1 a -\
-\
s' s' 20J
. I I I
k I m
•
I
J I I
I I
I I
I
I I
I
I I
,I I I
I
I
5-38
PROBLEM 5-9 (ShPPt: 7)
w L z W/L Z/L w Gd G G
s a !
wa 110 160 27 0.69 0.169 0 .-6~ ---0.32 .065 w
b 110 160 12 0.69 .075 0. 84 ---0.18 .035
wc 110 160 9 0.69 .056 o. 8E ---0.14 .028 l
wd 110 160 3 0.69., .019 0 .9!: 0.07 0.06 --
we 160 180 18 0.88 0.100 0. 81 0.38 0.20 --
wf 110 160 18 0.69 0.112 0. 75 0.43 0.26 ---
E(O. 69) = 1. 38 Bi (30) = 0. 50 Sec. deg. L part.s (75) = 0.70 Bi (60) = 0. 24 a 14 20 75sw(60) = 0.65 Bi (75) = 0. 17 b 7 10. 105Bw (18, 75)= 0. 12 Bi (90) = 0. 12 c 13 25 120Be (18, 60)= 0.16 Bi(105) = 0. 09 d 3 7 120Be(18,0) = Oo70 Bi(120) = 0. 06 e .1 25 43 75
e
Bf (75) = 0. 04 k f. g. j 54 60 60Bc(75, 0.84) = 0.024 h. i 10 10 30m 9 15 90
FICTITIOUS BUILDING T (Schematic Elevation)
'I~-~ Xe = 75 psf
I
WQ I We = 30'
I 'l{')
-H = 18'
I
wb Wc/H = 30 = 1.66
I 18
c f'(')
w-~·~ 2w (1.66) = 0.66
8
I ,
I I 0'> B8 (75,0.66) = 0.018
---1\I ~
Wd~')
we '
1 ;::~
wf ~'---JI .~ ', -!:
~~~~'
s s' 301
5-39
PROBLEM 5-9 (Sheet 8)
Fictitious Building T (one quarter plan)
--o---
®
' '-
I \ ' ".
I.I'',, "
I I,, "
I \ ' '
I \ \
'
\ \
I '
"
\ \
I I \
\
\
I I \ \ '\
I \ I \ \
I I ' I \
'
I \ I I \
'
/ I a \
'~
20" 20' w L z W/L ZIL
w
a 110 110 27 1.00 .245
12 1.00 .110
wb 110 110 w c 110 110 9 1.00 .082
~d 110 110 3 1.00 .027
w
e 170 170 18 1.00 .106
wf 110 110 18 1.00 .164
E(l.OO) = 1.41 Bi(15) = Sw(75) = 0.70 Bi(45) = Bi(75) =
Be(18,75) = 0.12 Bi(75) =
Be(18,0) = 0.70 Bc(75,0.81) = 0.026
'
"
'
'
'
'
'
"
\ \
\ \
\
\
b \
10' w Gd
p.60 ----) . 81 ----
0.86 ----
p.95 0.07
p.81 0.37
0.71 0.47
0.72
0.33
0.17
0.04 Sec. a
b
c
"
'
'
"
"
"
c
25" G
s
0.34
0.21
0.16
0.06
0.21
0.28
deg. L . 40 40 9 10 16 25
" ' ' "
G
a
0.069
0.042
0.032
part.
15
45
75
~--------------------------------------
5-40
PROBLEM 5-9 (SHEET 9) FICTITIOUS BUILDING U
wa-1 1 Xe = 75 psf E(Q.36) = 1. 28
We = 460', H = 18'
I (, Sw(60) = 0.65 I I ~ WcfH = 460/18 = 25.5
I I I Be(18,60)= 0.16 I
I -2w (25.5) = 0.976
8 Be(18,0) = 0.70 Wb ----__,~F8 (18,0.976) = 0.88' Bi(15) = 0.72
we IJ ~ Be(75,18) = 0.11 : /fi , B8 (Xe,2w8 ) = (0.88_) Bf(75) = 0.04 1 I <n '(0.11) 1
I ' B (75,0.63)
c
= 0.04
40/
F, 15~ • I .. -J
\ ..........
\
..... ......
I 1"--.
\
.....
.....
\
.....
..... ' 0
\
.....
(\J
.....
\
.....
.....
\
.......
.....
\
.....
......
\ a ............ _ w L z W/L Z/L w Gd G G
s a w a 40 110 2.7 0.36 0.245 0. 36 -----0.42 0.085 w 40 110 12 0.36 0.109 0.63 . -----0.33 0.065
b
w
40 110 9 0.36 0.082 0.72 -----0.28 0.056
c
.017 0.97 0.03 0.04
w 960b..030 18 0.93 ----
d w 40 110 3.0 0.36 0.027 0.90 0.18 0.12 ----
e wf 40 110 18 .c 0.36 0.164 0.50 0.65 0. 38· -----
Segment a -33° -40 FEET· 15 psf partitions
5-41
208-401 0-76 -15
PROBLEM 5-9 (SHEET 10 )' FICTITIOUS BUILDING V
•
X = 75 psf
W = 70' H = 18'
[]:~ c e '
w
l{)
Wc/H = 70/18 = 3.88
a I
2w (3.88) = 0.84
8
Fs(18, Oo84) == Oo44 B;(75, 18) =0. 1_1' ~ . B~(XeI 2 w~) :=: (Oo 11 )(0. 44) :=: Oo 048
B. (15) = 0. 72
1
= 0.50
3 o' ·-+------------
-
-~--/
-~--------/
~----------/
------.--...---//
-
a b
"""----------
w L z e n w Gd Gs Ga
w a 30 160 27 0. 19 0.34 0.'30 ----0.44 0. 092 wh 30 160 12 0.19 0.15 0.57 ----0.35 0.082 w_e 30 160 9 0.19 0. 11 0.66 ----0.31 0.075
: ..
wd 30 160 3 0.19 0.04 0. 8'7 . 0. 25 0.15 ----we 30 160 18 0.19 0.23 0.44 0.68 0.39 -----
I
E(O. 19) = 1. 17; s (75) ~ 0. 70
Seg. deg. L part.
B (18, 75)= 0. 12; Bw (18, 0)= 0. 70 e a 6 30 '30
B:(75) = 0. 04; B (75,0.57)=0.046c b 21 30 15
5-42
PROBLEM 5-9 (Sheet 11)
Ground Contribution -Fictitious Building R
A. North Wall
1. Detector Story direct radiation: (No direct because of shield) skyshine radiation:
c = Ga(~) [1-Sw(Xe)] Be(H,Xe)
g
cg = 0.039 X 0.30 X 0.12 = 0.00140
c'a = Ga<wc) [1-Sw(Xe)l Be(H,Xe)
Cl = 0.029 X 0.30 X 0.12 = 0.00104
a
c = G (w ) B (H,O psf)
a a c e
Ca = 0.029 X 0.70 = 0.0203
Cg + [Ca -Calr Pa; Pa = 6/9 = 0.67
0.00140 + [0.0203 -0.00104] 0.67 = 0.0143
scatter radiation:
cg = [ Gs(~) + Gs(wd)] E(e)Sw(Xe )Bs (ws,Xe) [1-AJ
~ .-(6 X 9)/(9 X 15) = 0.40
cg = 0.26 X 1.37 X 0.70 X 0.030 X 0.60 = 0.00494
Total detector story = 0.01924
2. Story belc:w direct radiation:
cg = [G (H,wf) -Gd(H,w )] [1-S (Xe)J B (H,Xe)B~(Xf)
d e w e ~
cg = 0.31 X 0.30 X 0.12 X 0.04 = 0.00044
5-43
PROBLEM 5-9 (Sheet 12)
Ca = [Gd(H,wf) -Gd(H,we)] Be(H,O psf) Bf(Xf)
Ca = 0.31 X 0.70 X 0.04 = 0.00868
Ap = (6.4 X 6)/(9.4 X 9) = 0.45
Cg [1-A ] + C A = 0.00415
P ap
scatter radiation:
Cg = [Gs(wf) -Gs(wd)] E(e)Sw(Xe)Bs(ws,Xe)Bf(Xf)
[1-AJ
~ = (6 X 9)/(9 X 15) = 0.40 Cg = 0.21 X 1.37 X 0.70 X 0.030 X 0.04 X 0.60 = 0.00014 Total story below = 0.00429
3. Story above skyshine radiation: C· = [G (w ) -G (w. )] [1-S (X )] B (H,X )B (X )
g aa ao wee ecc
Cg = 0.026 X 0.30 X 0.12 X 0.024 = 0.00002
Ca = [Ga(wa) -Ga(~)l Be(H,O psf) Bc(Xc,w)
ca = 0.026 x 0.70 x 0.025 = 0.0004
Ap (6 X 9)/(9 X 15) = 0.40
C = [1-A ] + C A = 0. 00017
g P a P scatter radiation: Cg = [Gs(wa) -Gs(~~ E(e)Sw(Xe)Bs(ws,Xe) Bc(Xc,w) [1-A]
p
C = 0.13 X 1.37 X 0.70 X 0.030 X 0.025 X 0.60 = 0.00006
g
Total story above = 0.00023
4. Total -R -North Wall
0.01924 + 0.00429 + 0.00023 = 0.02583
•
PROBLEM 5-9 (Sheet 13)
B. West Wall (of Fictitious Building R) The West Wall of Fictitious Building R has exterior mass thickness of 60 psf. The previous calculation was for a mass thickness of 75 psf. Similar calculations have to be made for an .exterior wall
mass thickness of 60 psf. rrhe resulting total ground contribution
for West Wall of Fictitious Building R is:
Total Ground Contribution -R -West Wall = 0.03504.
Ground Contribution for Fictitious Buildings
Fictitious Building S:
East Wall Cg = 0.02056
North Wall Cg = 0.02127
Fictitious Building T: c = 0.02453
g
Fictitious Building U: c = 0.06077
g
Fictitious Building V: Cg = 0.05070
5-45
PROBLEM 5-9 (Sheet 14)
-~"
GROUND CONTRIBUTION -ACTUAL STRUCTURE
p
Bi cg Az
Seg.ldeg. L r
Fictitious Building R
2a 22 30 0.50 0.03504 0.38544 0.52560
b 6 9 0.24 0.03504 0.05045 0.07568
I
c 1 1 0.33 0.03504 0.01156 0.01156
d 9 15 0.17 0.03504 0.05361 0.08935 e 5 10 0.12 0.03504 0.02102 0.04204 f 6 13 0.12 0.02583 0.01859 0.04029
g,i 23 37 0.17 0.02583 0.10099 0.16247 h_l_j 29 30 0.24 0.02583 0.17977 0.18597 I f Summation 0.82143 1.13296 I r Az/360 , p /520
r 0.00228 0.00218
i
Fictitious Building S
I I
a 14 20 0.17 0.02127 0.05062 0.07232
I
b 7 10 0.09 0.02127 0.01341 0.01917 c 13 25 0.06 0.02127 0.01659 0.03191 d 3 7 0.06 0.02056 0.00370 0.00864 e,l 25 43 0.17 0.02056 0.08738 0.15029 f,g, j,k 54 60 0~24 0.02056 0.26646 0.29606 h,i 10 10 0.50 0.02056 0.10280 0.10280 m 9 15 0.12 0.02056 0.02220 0.03701 Summation a·. 56316 0.71820
Az/360 , Prf440
0.00156 0.00133
Fictitious Building T a 40 40 0.72 0.02453 0.70646 0.70646 b 9 10 0.33 0.02453 0.07285 0.08094 c 16 25 0.17 0.02453 0.06672 0.10425
Summation 0.84603 0.89165 A /360 ' , p j440
z r 0.00235 0.00202
,. .......... ---
·'*·*=~ .. . -· ~
PROBLEM 5-9 (SHEET 15)
Seg. deg. FICTITIOUS \ L B.·1 BUILDING U cg I Az pr
a 33 40 0. 72 0.06077 Az/360 ' Pr/300 FICTITIOUS BUILDING v 1. 44389 0.00401 1. 75018 0.00583
a b 6 21 30 30 0.50 0. 72 0.05070 o~ o5o7o ,0.15210-0.85277 0.76050 1. 10512
Summation Az/360 . pr/380' 1. 00487 0.00279 1. 86562 0.00491
GROUND CONTRIBUTION 0.01299 0.01627.
OVERHEAD CD.N'IRIBuriON
1. Roof of Shelter Area
W/L 30 = --= 40 0 75 . ' Z/L 42 = --= 40 1 05 w = . ' 0 09 .
c (0.09,210)0 = 0.00028
2. Roof over room to South
W/L 40 = 110 = 420.36,Z/L =110 = 0.381 w = 0.20
1/2 [c (0.20,210)-c {0.09,21o)1 = 1/20 0 [0.00052-0.0002~ = 0.00024 0.00024 B~(15)=0.00024x0.6=0.00014 l
3. Roof over room to West 30 42W/L = 110 = 0.30, Z/L=100 = 0.42,w = 0.17 1/2 [ C (0.17,210)-C {0.09 ,210)]0 0 = 1/2 [0.00048-0.00028}= 0.00020 O.J0020B~(15) = 0.00020 X 0.6 = 0.00012
5-47
PROBLEM 5-9 (Sheet 16)
4. Corridor to North
•
40 42
W/L = = 0 80 Z/L = = 0.84 w = 0.14
50 . ' 50
[C(0.14,210) -C (0.09,210)] 0.50 B~(30) =
0 l
0
[ 0. 00040 0. 00028] 0. 50 X 0. 35 . = 0.00002 Total Overhead Say = 0.001
Total Rf = 0.001 + 0.013 = 0.014, Pf = 71 Azimuthal sector method or 0.001 + 0.016 = 0.017, Pf =59 Perimeter ratio method
5-48
The rule is that it must be symmetrical with, in this case, the X-X axis through the detector. In the actual building, 105 feet of field lies north of the axis and 85 feet south. Since Sector R encompasses mostly the north side, it is chosen to idealize it at 105 feet on either side of the X-X axis of the fictitious building. In the actual building, that portion of the North wall, corresponding to fictitious Building R in order to produce the required symmetry with respect to the Y-Y axis.
On the sketches the limited fields of contamination are not shown all around the fictitious buildings, but it is understood that if the sector or interest encompasses two walls with unequal widths of contamination, the widths of contamination on the opposite walls are symetrically equal. If a sector encompassed only one wall, the width of contamination is assumed to be equal on all four walls of the fictitious building.
A limited field having a width of 35 feet lies to the east of the building. This field acts against the East wall of fictitious BuildingS and, again, to maintain symmetry with the X-X axis it is assumed to extend 25 feet beyond on either end, giving a total dimension of 210 feet as opposed to 190 feet actual. In the actual building, that part of the North wall corresponding to fictitious Building S is subject to a 25 feet wide field. This is maintained in fictitious BuildingS.
Simi lor discussions apply to fictitious Buildings T and V. It should be clt::ar that the ground contribution through the triangular shaded segment of fictitious BuildingS could have been included in T. As a general rule, it should have been, since, given a choice, one should usually include a wall segment in the idealized structure more nearly square. This was not done in this case, since such inclusion would have required T to be analyzed twice. Judgment was exercised contrary to the rule to save the additional labor and in cognizance of the fact that the difference would be rather small.
The West wall of the actual structure, in correspondence with fictitious Building U, presents a much more complicated situation than any of the others. Radiation from the full 460 feet of field can impinge on it, and, conservatively, it has been so assumed. In this actual situation, more than any of the others, this is probably very conservative, not so much out of consideration of scatter radiation, but particularly in consideration of direct'radiation. In all of the previous cases, with the exception of V, direct radiation was I imited to that from the ideal width of field selected. Such is not the case here. In U, a direct ray can arrive at the detector through the shaded sector from a source no further away than 93 feet (against the south shield) not 460 feet. In V, a direct ray could come from as far away as the west shield (400 feet) not 70. Perhaps the two discrepancies tend to cancel each other, but, in any event,
5-49
the methodology as it has been developed to this point, restricts the methods
of analysis and procedure to those used so that no other recourse is available
for handling such situations. In general, the overall treatment of limited
fields is conservative.
The third sheet of the calculations shows schematic sections pertaining to fictitious Building R with dimensions and solid angle fractions of interest. The calculations, for the exterior wall barrier factor applied to scatter radiation, are normal and should require no comment.
The fourth sheet shows a quarter plan of fictitious Building R. Partitions are shown in correspondence with those of the actual building. Different wall segments are lettered to indicate such variations as partition mass thicknesses. The table in the lower right corner gives the scaled lengths of wall and central angle for each segment and the total mass thicknesses of partitions. The remaining data are the usual data necessary for determining solid angle fractions, and other shielding parameters taken from the charts. Sheets 5, 6, and 7 give similar information for fictitious BuildingS, sheets 7 and 8 for T, sheet 9 for U, and sheet 10 for V.
The remaining sheets contain, first, the calculations for the ground contribution for the several structures through the exterior walls only. Partitions are considered later. Fictitious Bui I dings Rand S are analyzed twice, since two situations exist with respect to exterior walls. Scatter, skyshine, and direct contributions are determined separately for each of the three stories involved. This is necessary because of the different exterior wall barrier factors for scatter radiation.
Following the determination of the total ground contribution for each fictitious building the portions of interest in the actual building are extracted from each. Calculations are given in tabular form and are made using both azimuthal sectors and perimeter ratios for comparative purposes. It should be particularly noted that, except for fictitious Buildings U and V, there is good agreement between the two methods. Structures, R, S, and T are square or nearly so. Structures U and V are relatively long and narrow, and the segments of interest in them are relatively far from the detector. This recalls the discussion in article 5-4.4 and Figure 5-3 which suggests that the aziumuthal sector results may be the more precise.
The calculations from overhead are straightforward. They begin with the area giving the greatest contribution, that directly over the detector, and progress to adjacent areas until there is an indication that additional contributions would have a relatively minor effect on the protection factor. Of the
5-50
two protection factors computed, 71 using azimuthal sectors and 59 using perimeter ratios, the larger is probably more precise, i.e., more in agreement with the basic assumptions underlying the methodology. The discrepancy points out the preferential consideration that one should give to the azimuthal sector method, particularly when dealing with idealized structures that are long and narrow. For square or nearly square idealized structures, the results
will be in good agreement. The choice, in such cases, could be one of convenience. It should be mentioned that to mix the two in a single problem
is acceptable. The perimeter ratio method can be used, if convenient, for the square or nearly square idealized structures, the results will be in good agreement.
It may be meaningful to study the calculations in an effort to find means be which the protection factor could readily be increased to some required value over 71.
A comparison of the roof contribution with the ground contribution indicates
that it would be futile to attempt to increase the protection factor by increasing
the overhead mass thickness. ·If, for example, a protection factor of 100 were
desired, it could not possibly be obtained without reducing the ground contri
bution. It should also be mentioned·that increasing roof mass thickness in an existing building might often require major structural changes making the effort
less economical than other means. In a structure that is in the design stage,
it may be possible to increase overhead mass thickness without substantial cost
1n
increases. For example, increasing the thickness of a concrete slab resu Its
lower weight of reinforcement. The savings in reinforcing steel in the slab
could partially or totally defray the cost of providing increased strength in
supporting members.
A study of the tabular values for ground contribution indicates that about half the total comes from wall segments considered in fictitious Buildings U and
V. An obvious solution is to provide additional mass thickness in either the room partition to the west or the south of the detector or both.
If a protection factor of 100 is required, the total ground contribution must
be reduced from 0.013 to 0.009. Increasing the mass thickness of the south partition to 75 psf would reduce the ground contribution from fictitious Building U from 0.00401 (azimuthal sector method) to 0.00095. This would result in a
reduction of toto I ground contribution from 0.01254 to 0.00942. Increasing
its mass thickness to 80 psf would reduce the total ground contribution to about
0.009 and would result in a protection factor of about 100.
5-51
It may well be, of course, that the above solution is not the most economical.
Although economy is an extremely important consideration in shelter analysis, it
is beyond the scope of this present discussion. The analyst should reflect on other
means for obtaining the same result and compare relative merits.
The primary purpose of the problem solutions that are presented in this manual is to aid the analyst in his development of basic understanding of shielding methodology. Once proficiency is developed in analysis, the analyst is properly prepared to derive further benefits from a restudy of all problems from the point of view of increasing protection. A critical analysis of the various contributions can suggest, to the analyst, certain corrective measures that could be taken to reduce contributions and increase protection. If, at the same time, attention is paid to, at least, a qualitative evaluation of costs, the analyst can develop facility for 11 slanting 11
design to increase protection.
5-5 Miscellaneous Compi ex Conditions
5-5. 1 Partial Limited Fie Ids
In all the problems that have been solved to this point, where mutual shielding
was a consideration, buildings were completely surrounded by shielding elements such that each wall could be considered as being completely affected. A common occurrence in practical shielding problems presents a wall that may be partially
shielded by an adjacent structure and partially exposed to a field of vast extent. Such a situation is exemplified by Figure 5-5.
In the plan of the figure, it is assumed that the building, if irregular in shape,
has been idealized. Of interest is the East (right) wall. A line drawn from the detector through the midpoint of the shielded wall to intersect the face of the shield, actual or extended, defines the idealized width of contamination, We. Rays drawn from the detector to the near corners of the shield confine a segment of the wa II that is assumed to' be affected by the shield. In the figure, this is the segment subtending angle A in plan. Skyshine, direct, and scatter ground contributions are computed in the normal way as separate quantities, and the application to these quantities of the appropriate azimutha I sector, A/360, or perimeter ratio determines the contribution through the shielded portion of the wall.
Figures 5-6 through 5-8 show several arrangements of building and shield
with the idealized limited field shaded. The angle A is, in each of the six cases shown, the sector affected by shield. The figures should be self-explanatory. Note, that in those cases where the shield extends beyond the limits of the idealized
5-52
•
........... · ............... ·.. ·:···· .·.....•..·······
w
c
.......... · ... ···· .. ·.·:· .. ··.· ....•...·.······· ...
FIGURE 5-5 PARTIALLY SHIELDED WALL
5-53
structure (Figures 5-6b, 5-7a, and 5-8b), there should obviously be an effect not only on the wall directly opposite the shield but also on the wall perpendicular thereto. This effect is ignored. A shield is assumed to be effective only against a wall that lies directly opposite it.
The idealization of limited fields, as shown in the figures, is a drastic simplification of an extremely complicated situation. The effect on scatter radiation is particularly complicated. Any shield, regardless of how small, which eliminates radiation sources that ordinarily would impinge on a wall, must necessarily have an affect on every point in the wall, since every point is a potential scatterer of rays from every source. In the idealization, both scatter and direct affects are assumed limited to that segment of the wall defined by the sectors determined as shown in the figures. This is reasonable for direct radiation but not so precise for scatter. In any event, the procedure is most often conservative.
5-5.2 Effectiveness of Shields
All of the preceding discussion concerning limited fields has assumed the shield, providing field limitation, to be completely effective in attenuating the radiation originating from those part ides lying beyond the shield. The true effectiveness of a shield is obviously a function of its mass thickness. Theoretically, it could never be completely effective. In the analysis of structures, the analyst exercises judgment in determining whether to assume a shield fully effective or to ignore it completely. As a rough rule, a shield that provides in the order of 100 psf of mass thickness can be considered completely effective. The reduction factor for a 100 psf vertical barrier is 0.10 at a height of 3 feet. This means that the barrier is at least 90% effective in attenuating radiation, and probably more than that, since the emerging rays, containing a generous portion of scattered photons, are "softer" on the average.
Most structures of masonry construction offer at least 100 psf of mass thickness even if they are simply brick veneer. As a guiding rule, if the shielding structure is masonry, it can be assumed fully effective in field Iimitation. If it is wood frame or thin metal with a minimum of partitions, it can be conservatively ignored. The effectiveness of low walls and foundations that protrude reasonably above the ground should not be ov~rlooked.
5-54
1'""~'"~'='""'"'"'"'''11"\ '':'?'' .'.,,,,:,:'ll"'nn"''11'1 8
u
.....:l
1:='""''"'"''''="'""~"""'""";4' :,·, II
(a)
FIGURE 5-6
IDEALIZED LIMITED FIELDS
PARTIALLY SHIELDED WALLS
5-55
8
II
C)
.....:!
FIGURE 5-7 IDEALIZED LIMITED FIELDS PARTIALLY SHIELDED WALLS
5-56
8
II
8
II
C)
....::1
FIGURE 5-8
IDEALIZED LIMITED FIELDS
PARTIALLY SHIELDED WALLS
5-57
208-401 0 -76 -16
5-5.3 Externa I Cleared Areas
The procedures and techniques for handling contributions from limited fields can be extended to cover situations involving cleared areas adjacent to a structure. A building at or near the shore line of a pond or lake or on the bank of a river is illustrative of such a situation. However, caution should be observed in considering areas clear when the possibility exists that, at some critical time, they may not be. For example, if a building is located on the shore of a pond, say at least 2 feet deep (125 psf), particles falling into the water and settling to the bottom would be quite ineffective in radiating against the bui I ding. The pond, under such circumstances, could be considered as a cleared area. In northern climates, there is always the probability that a pond would be· frozen over during the winter months. It would, therefore, be unwise to consider a pond a cleared area in determining a protection factor for an adjacent structure in northern climates.
Problem 5-10 illustrates the extension of I imited field techniques to
a cleared area situation. The rectangular area, 50 feet by 110 feet, to the east of the structure is assumed c I eared. The computation relative to the ground contribution through sector Band relative to the overhead contribution are normal. Perimeter ratios are used in the ground contribution computation.
The east wall of the building, sector A, is subject to direct radiation only from the field of contamination beyond the cleared area. This is defined by GiH,wL)' and the computations for direct radiation alone is the reverse
of that exercised in limited field problems.
The scatter contribution, like direct, is computed by applying limited field techniques in reverse. The barrier factor1 B is computed assuming the
s cleared area to be a limited field. B (H,X ) is the barrier factor associated
e e with an infinite field. Bs, as computed fictitiously for the cleared area, is that part of the infinite f1eld barrier factor attributable to particles that would I ie on the cleared area. The difference between B and B is the barrier factor
e s for the infinite field less the cleared area, and it is this difference that is applied in the computations for the scatter contribution.
5-5.4 Adjacent Low Roofs
A combination of limited field and cleared area techniques can be employed to determine the 11 ground 11 contribution, to a detector in an upper story, originating from particles on a roof of an adjacent building with an
5-58
PROBLEM 5-10
X = 100 psf
e X = 150 psf
0
w L z W/L Z/L w Gd G s G a
wu 50 80 12 0.62 0.15 0.66 --- 0.31 0.063
IWL 50 80 1.3 0.62 0.016 0.96 0.24 0.05 -----
WL 50 80 3. 0' 0.62 0.037 0.91 0.40 0.11 ____...,..
E(O. 62) = 1. 37 s (100)w = 0. 76
B (3, 100) = 0. 094 p (B) =210/260 =0. 81;
5-59
cont.)
P (A) = 0. 19
r
1. Sector B
G = LGs(wu) + Gs(wLDE(e)Sw(Xe)+[Gd(H,wL) + Ga(wu~
g
-1-S (X )-~
Lw e_ G = (0.42xl.37x0.76)+ (0.463 x 0.24) = 0.548
g c = G B (H,X ) P
g g e e r c = 0.548 X 0.094 X 0.81 o;o417
g
2. Sector A W =50' ,H=3',W /H=16.66,2w =0.962,F (3,0.962)=0-68
c c s s B (100,3')=0.094 B =0.68 x 0.094 = 0.064
e s
B (H,X ) -B (w ,X ) = 0.094 -0.06~ = 0.030
e e s s e
scatter contribution:
C = [G (w ) + G (wL) l E(e) S (X ) B P
g _su s ~ we r C = 0.42 X 1.37 X 0.76 X 0.030 X 0.19 = 0:0025
g
direct and skyshine: C =~-Gd(H,w~) + G (w >l [1-S (X >l B \H,X ) P
g a u_ w e_ e e r
C =. 0.303 X 0.24 X 0.094 X 0.19 = 0.0013
g
Total Sector A = 0. 0038
TotalC = 0.0417 + 0.0038 = 0.0:455
g
3. Overhead Contribution C (w ,X ) = C (0. 66, 150) = 0. 0044
0 u 0 0
lL Reduction and Protection Factors
Rf = 0.0455 + 0.0044 = 0.6499, Pf = 20
5-60
elevation less than that of the detector. This is illustrated in,Problem 5-11.
In the problem, only scatter and direct ground contributions are computed for those sectors of the east wall that are affected by the abnormalities.
The adjacent low building acts both as a shield and as a second plane
of contribution. In part I of the calculations, contributions are calculated considering only the limited field of contamination between the two buildings at ground level. From this field, direct radiation is I imited to the lower part of the walls of the story below. Scatter is contributed, of course, through the entire walls of the detector story and the story below. No special comment on these computations is deemed necessary.
In part II of the computations, consideration is given to the contribution from the infinite field beyond the adjacent building. These far particles contribute direct radiation through the entire 3 feet of detector story wall beneath the plane of the detector. The ray of wb extended (the norma I lower
solid angle fraction) passes directly through the back side of the low building. The wall of the story below contributes, therefore, no direct radiation from the far ground.
Both the detector story and the story below contribute scatter radiation originating from the far sources. Actually, the detector story wall is subject to radiation from more sources than is the wa II of the story below. Only one
barrier factor for scatter radiation will be computed (recommended procedure), and this will be computed for the detector story. It will be applied to both the detector story and below story scatter contributions. This is conservative with respect to the story below.
The ray drawn from the normal point in the detector story wall opposite the detector and defining w•, passes over the backside of the low bui I ding to intersect the ground surfacesat a point 183 feet from the face of the building
A. The effect, then, of the low building, is to produce a cleared area with a width w of 183 feet. The first step in the calculations of part II is a determination 5f the barrier factor for scatter radiation from the far sources.
Part Ill of the computations deals with the direct and scatter ground contributions from the sources on the low roof. The low roof forms a definite limited field of contamination separated from the actual building by a cleared area at a distance H = 18 feet below the detector plane. The direct contribution is limited to that from the upper portion of the walls of the story below and is determined through a differencing of the directional responses for w wb' both a function of H = 18 feet.
5-61
PROBLEM 5-11
-
0
N
~-+--1
w
w a 40 wb
40 w c 40 wd
40 w e 40
L 40 40 40 40 40
/
/
Z! 12
!
3
I i
6 11
I
18.
W/L
1. 00
1.00
1. 00
1. 00
1. 00
X =
e xf =
All stories
60'
~"H = 18'
Z/L w l...;id
-~-...
0.30 0.52 ----
0.075 0.87 0.27
0.15 0.74 0.47
0.28 0.56 ---
0.45 0.37 ---
75 psf 60 psf
are 15
·H=33'' Gd
0.18
0.40
0.57
0.70
feet
-
0
co
Gs
-
0.38
0.15
0.27
0.36
0.42
+-------------·-------------~----------~~--~~~~
5-A?
PROBLEM 5-11 (cont'd) .
E(1.00) = 1.41, Sw(75) = 0.70, Be(33,75) = 0.09 Be( 18, 75) = 0.11, Bt(60) = 0.06 Pr(A) = 0.083 Pr(B) = 0.167
I. Limited Field Between Buildings
1. scatter barrier factor Xe = 75 psf, We= 40', H = 33', Wc/H = 1.21
2ws = 0.58
Bs (75, 0.58) = 0.013
2. scatter -detector story
c= Gs(wa)+Gs(wb) E(e)Sw(Xe) Bs(ws,Xe) Pr(B)
9
Cg = 0.53 X 1.41 X 0. 70 X 0.013 X 0.167 = 0.00113
3. scatter -story below
c= Gs(we)-Gs(wb) E(e)Sw(Xe)Bs(ws.Xe)BtPr(B)
9
Cg = 0.27 X 1.41 X 0.70 X 0.013 X 0.06 X .167 = 0.0003
4. direct-story below
C9 = [Gd(H,we)-Gd(H,wd)] [1-Sw(Xe)l Be(H,Xe) Bt(Xf) Pr(B)
Cg = 0.13 X 0.30 X 0.09 X 0.06 X 0.167 = 0.00004
5-63
PROBLEM 5-11 (continued).
I I. Infinite Field Beyond Low Structure
1. Barrier Factor for Scatter Radiation
Xe = 75 psf, We= 183', H = 33', Wc/H = 5.5 2ws = 0.89, F s (33, 0.89) = 0.69, Be(75,33) = 0.09 Bs = 0.69 x 0.09 = 0.062 B = Be(H,Xe)-Bs(w~,Xe) = 0.090-0.0621 = 0.029
2. Scatter Contribution
detector story:
= Gs(wa)+Gs(wb) E(e)Sw(Xe) B Pr (A)
c9 Cg = 0.53 X 1.41 X 0.70 X 0.029 X 0.083 = 0.00126
story below:
C9 = G5 (wa)+G 5 (wb) E(e) Sw(Xe) B Bf(Xf) Pr(A)
Cg = 0.27 X 1.41 X 0.70 X 0.029 X 0.06 X 0.0831 = 0.00004
3. Direct Contribution
detector story:
c9 = Gd(H,wb) 1-Sw(Xe) Be(H,Xe) Pr(A) Cg = 0.18 X 0.30 X 0.090 X 0.083 = 0.00040
5-64
PROBLEM 5-11 (continued)
I I I. Contribution From Low Roof Sources
1. Scatter barrier factor
(a) Out to the far side of the low roof.
Xe = 75 psf, We= 100, H = 18', Wc/H = 5.55, 2ws = 0.89 Fs( 18, 0.89)=0.60, Be(75, 18)=0.11, Bs = 0.60 x 0.11 = 0.066
(b) Fictitious plane between the building and the near
edge of the low roof.
Xe = 75 psf, We= 40', H = 18', Wc/H = 2.22, 2ws = 0.73
Bs = (75, 0. 73) = 0.025
(c) Scatter barrier factor for the low roof.
B = 0.066 -0.025 = 0.041
2. Scatter contribution
detector story:
Cg = [Gs(wa) + Gs(wb)] E(e) Sw(Xe) B Pr (A)
= 0.53 X 1.41 X 0. 70 X 0.041 X 0.083 = 0.00178
story below:
.cg = [Gs(we)-Gs(wb)] E(e) Sw(Xe) B Bf(Xf) P r(A) Cg = 0.27 X 0.41 X 0.70 X 0.041 X 0.06 X 0.083 = 0.00005
3. Direct Contribution
Cg = [Gd(H,wc)-Gd(H,wb)] [1-Sw(Xell Be(H,Xe) Bf(Xf) Pr(A)
Cg = 0.20 X 0.30 X 0.11 X 0.06 X 0.083 = 0.00003
5-65
Scatter radiation from the low roof sources is contributed to the detector through both the walls of the detector story and the story below. As is always the case, the contribution is computed by application of a modified scatter barrier factor to regular scatter geometry.
The field of contamination is definitely limited, being the roof area of the low structure. In step 1 of the computations of part Ill, the modified barrier factor is calculated. Bs is determined assuming the limited field to be 100 feet wide. This includes a fictitious area of contamination at H =18 feet between the buildings. A different Bs is calculated for the fictitious field 40ft. wide and the difference between the two is the barrier factor for scatter radiation.
5-5.5 Sloping Ground
In all previous examples, the ground surface surrounding the buildings was assumed to be horizontal. Where a building is located adjacent to a relatively steep upward slope, the effect of the slope may be pronounced in increasing the ground contribution to the detector, since direct radiation will be contributed from port ions of the wa II above the pIane of the detector.
Figure 5-9 shows a building, one wall of which is subjected to radiation originating from sources lying on an upward slope. The ground surface makes an angle of ewith the horizontal. The skyshine contribution to the detector is probably little affected by the sloping ground and may be computed in the normal way. The direct contribution is obviously increased. Figure 5-9 suggests a method by which it can be computed. An axis drawn through the detector parallel to the slope, defines the section of exterior wall that contributes direct radiation to the detector. If this I ine is taken as the detector axis and the sloping contaminated plane as the standard plane of contamination, a fictitious building for the direct contribution can be formed. This is shown in the figure by the dashed lines indicating a section through the exterior walls of the fictitious building below the idealized detector plane. The mass thickness of the exterior walls of the idealized structure should be based on the thickness of the actual walls measured parallel to be slope. It is the actual mass thickness divided by the cosine of e. The direct contribution is a function of w, as shown in the figure. The dimensional parameters involved in the determination of are Z, w•, and the length of the actual building perpendicular to the plane of the paper. These can be determined from the geometry of the actual building and that of the slope. GiH,w) would be taken for H= 3 feet. To use any other
value of H would introduce a shadowing effect from a horizontal barrier 3 feet below the detector which effect is non-existent. All sources contribute and none is shadowed out, as is the case in an upper story location. The density of particles on the sloping surface is less than that on a normal horizontal surface.
5-66
w
,... ..,
..
~~:,:.::::-:-·•.:,'.'/:'.:.:.:'::::: ·,.,: ;;,;_:·..:'i: :,:
FIGURE 5-9 UPWARD SLOPING GROUND
5-67
For consistency of results, an adjustment should be made to Gd as determined from considerations discussed above. This can be accomplished by multiplying the results by the cosine of e.
The scatter contribution is affected by the slope in a manner that cannot be determined as readily as in the case of the direct contribution. Each point on the exterior wall is a potential contributor of scatter radiation to the detector, and each such point receives radiation from all ground sources whether horizontally oriented or on a slope. The total number of particles involved is the same in either case. However, a given point on the wall is closer to a given partie le on the slope than it would be to that same particle were it deposited on a horizontal surface at a point beneath its position on the slope. It would thus appear that the number of photons, reaching a point on a wall from a slope source, would be increased above that received from the effective slant distance through the barrier, and hence the chance of scatter is greater for a particle on a horizontal surface than for one on the sloping surface directly above. This is an offsetting influence, and the net effect of slope on the scatter contribution is somewhat elusive. These two effects are portrayed schematically on Figure 5-9. Since the total effect is elusive and, in order to avoid compi icating the ana lysis out of reason with respect to precision, it is recommended that the scatter contribution be computed in the normal way, assuming a horizontal idealization of the sloping source plane. Only the direct contribution is considered to be modified by the slope.
It should be obvious that the two sides of the building perpendicular to the toe of the slope are also affected. At a point in the wall in plan at the toe of the slope, the direct contribution would be the same as that for the wall lying along the toe of the slope. At a point opposite the detector, assuming a horizontal surface of contamination as shown in Figure 5-9, the c;Jirect contribution would be normal. The average direct contribution between these two points can be used for the sector involved.
In Problem 5-12, one wall of the building is subjected to radiation from a finite slope. The section of the fictitious building, used to determine the direct contribution from slope sources, is shown superimposed on the section of the actual building. The dimensions are computed from the actual geometry.
The detector is 9. 1 feet above the idealized source plane. The idealized
9. 1 feet of wa II contributing direct radiation to the detector includes a 3.3-foot solid section, a 4. 1-foot aperture strip section, and a 1. 7-foot section above through which no direct contribution comes. The computed dimension of the idealized structure parallel to the idealized source plane is 27 feet.
5-68
PROBLEM 5-12
windows: 6' wide at 9' ctrs.
Xe = 64 psf
cos e = 9/9. 85 = o. 91
x Icos e = 70 psf Be(3, 64) =· 0. 22 Be(3, 70) = 0. 19 Se(64) = 0.67 sw(70) = 0. 69
w w L z W/L Z/L w PJ3,w)
w a 24 27 1.7 0.89 0.063 0.88 0.46
wb 24 27 5.8 0.89 0.215 0.62 0.71
we 24 27 9.1 0.89 0.337 0.47 0.77
1. Direct Contribution -Sector C
W/L = 24/32 = 0.75, Z/L = 3j3:2' = 0.093, w = 0.80 c Gd(H,w) 1-S (X ) B (H,X ) p
g w e e e r c = 0.56 X 0.33 X 0.22 X 0.50 = • 0203
£;
5-69
PROBLEM 5-12 (cont.)
2. Direct Contribution -Sector A
(a) through 3. 31 solid wall_ -idealized structure
•
Cg = [Gd(H,wc)-Gd(H,wb5][1-Sw(XeU Be(H,Xe) Pr c = 0.06 X 0.31 X 0.19 X 0.235 =
0.00083
g
(b) through 4. 11 windows strip -idealized structure all solid:
c~ a = [Gd(H,wb) -Gd(H,wa)J[1-Sw(Xe)J Be(H,Xe) p r c~ = 0. 2 5 X 0. 31 X 0. 19 X 0. 235 = 0.0035
a all aperture: c = [ G d (H, wb) -G d (H, wa)_] B (H, 0) p
a e r c = 0. 2 5 X 1. 00 X 0. 2 3 5 = 0.0587
a p
= 6/9 = 0. 67' 1-P = 0.33
a a
(0. 0035 X 0. 33) + (0. 0587 X • 67) = 0,. 0404
Total contribution = 0. 0404 cos e = 0. 0404 X 0. 91 = 0. 0368
3. Direct Contribution -Sector B From 1.-C = 0.0203/0.50 = 0.0406
g From 2. -C = 0. 0368/0. 235 = 0.1565
P'
0.0406 (32/112) = 0.0116 0.1565 (32/112) = o. 0445 0.0561 X 0.5 = 0.0280
4. -Total direct contribution
0.0203 + 0.0368 + 0.0280 = 0.0851
5-70
The actual exterior wall mass thickness is 64 psf. The fictitious building involved in the slope contribution has an adjusted wall mass thickness of 70 psf determined by dividing the actual wall mass thickness by the cosine of e , where 6 is the angle of inc I ination of the slope with the horizontal. Exterior wall barrier factors are given for both the actual and adjusted mass thicknesses as are scatter fractions, Sw. A 3-foot height was used for the wall barrier factors. Normally, H =9. 1 feet would be used, and such use would be entirely acceptable. It was not used here simply because of a conservative judgment exercised by the analyst.
The table contains only that data relative to the slope contribution. Note that Gd has been calculated for H = 3 feet. As previously explained, there is no 11 shadowing 11 of close-in particles by virtue of an intervening horizontal barrier. Chart 3 values include this shadowing effect. Since it does not exist, the 3-foot height is used.
In step 1, the contribution of direct radiation is computed for sector C. A horizontal plane is the source here, and the calculations are normal. The Gd value was computed separately, since it was not included in the table.
Step 2 deals with the slope contribution. The contributions through the lower solid portion and through the aperture strip of the fictitious bui I ding are computed separately. Note that the final result involves cosine 8 as a multiplier to account for the difference in density of particle distribution on the sloping surface.
In step 3, the direct contribution for sector B is computed. The contributions previously calculated for sectors C and A are converted first to total fictitious building contributions by eliminating the previously applied perimeter ratio multiplying factors. These are, in turn, multiplied by the perimeter ratio factor for sector B. The average is taken as the fino I contribution for sector B.
A similar technique can be employed in cases where the ground slopes downward away from a structure. In such cases, the direct contribution may be materially reduced, particularly if the slope is relatively steep. The analyst should reflect on the idealization involved in such cases. As a further element of study, he should reflect on cases where there may be an intervening horizontal plane of contamination between a structure and a slope. Where slopes are very steep, it is possible to receive direct ground contribution through the roof of a structure. All such cases are treated in a manner identical with that suggested in this article and should not present complications beyond those already considered.
_5-71
5-5.6 Roof Contributions Through Partitions of Different Mass Thicknesses
Figure 5-10 considers the overhead contribution to a detector from a rectangular section of roof shown divided into areas S and T. By the technique of differencing overhead responses, the potentia I contribution from the entire area in question can be readily obtained. The difficulty arises in the application of the partition barrier factor if those parts from S and T pass through partitions of different mass thicknesses as is indicated by the solid and dashed partition I ines in the figure. In the figure, areas SandT are, in one case, equal. However, their c01tributions to the detector, even if partitions did not exist or were equal in mass thickness, would not be equal. Area T has more particles closer to the detector than does area S, and, hence, it is potentially a greater contributor.
If it is assumed that overhead contributions vary directly as the area and inversely as the square of the distance from the detector to the center of gravity of the area, the following expression can be developed giving the fraction of the total contribution, C0 , that can be considered as arriving from the sources on one of the two areas in question.
90'
.:-:~·.\<·.....·..:·::·:·~.:·:: •... : ..·. ·.·: .. ·.:· :·.:· .•.::.·...
. . ··.· .. ·······s
•
:;':
.......
FIGURE 5-10
OVERHEAD CONTRIBUTIONS THROUGH
PARTITIONS OF DIFFERENT MASS THICKNESS
5-72
c c + c (sum of contributions equals total)
0 s t
2
c A s (contributions vary directly as area t t and inversely as square of distance)
-=
t2
c A
s s
from which the contribution from S is derived as
co
c
s 2
s
+
A
s
In Figure 5-10, A = A = 2700 sq. ft. and Z = 20 feet.
s t
From the expression above, Cs = 0.41(and Ct =0.59(0 • C0 is determined
0
by the differencing technique, and the appropriate paratition barrier factor is applied to the portions Cs and Ct. This technique gives quite precise results and can be extended to include more than two areas, although such cases are
rare.
Other approximate solutions can be obtained by the exercising of judgment. . For example, SandT could be idealized as rectangular areas with the analyst 'using judgment in selecting dimensions. In the area shown in the lower right hand corner of the figure, the analyst might assume the entire contribution to
pass through the solid line partition. The error would be small, since Sis small.
He might a I so assume area S to be idea Iized as a resultant contribution through the dashed I i ne partition.
Whatever the situation, the areas giving the greatest contributions should be treated as precisely as possible. Areas contributing minor amounts may be treated in approximate ways that are, in the judgment of the analyst, reasonably precise.
5-5.7 Set-backs
Although direct reference was not made to set-backs in considering limited fields (article 5-5. 1), cleared areas (article 5-5.3), and adjacent low roofs (article 5-5.4), all of the techniques discussed are directly applicable to the treatment of set-backs. It is, therefore, not necessary to discuss computation methods in this article except in a general way.
5-73
208·401 0-76-17
Figure 5-11 shows a multistory building with a set-back. If the detector
lies in a story immediately below the set-back roof, the contamination on the roof has a dual effect on the contribution. It results in an overhead contribution that can be computed in a manner identical with that of Problem 5-4. As a·
•
second effort, it results in a scatter contribution reaching the detector through
the ceiling from the walls of the story above. This can be computed using the techniques employed in Problem 5-11.
If the detector lies in a story adjacent to the set-back, it will receive direct radiation, as well as scatte:r, from the set-back roof contamination through the exterior walls of the detector story. In additon, it will receive
scatter radiation through the ceiling from the walls of the story above. This scatter originates from the set-back roof contamination •. These may all be computed in a manner identical with that of Problem 5-11.
FIGURE 5-11 SET-BACKS
5-74
•
Located an additional story above, a detector would receive direct contributions from the set-back sources through the floor and, depending on the dimensions, also through the detector story walls. These same sources would give scatter contributions through the walls of the detector story, the story below and a story above (if it existed), all of this may also be computed by employing the techniques used in Problem 5-11.
The analyst should not overlook the fact that detectors located above the set-back roof may still receive direct and scatter contributions from sources on the ground. These may be more significant than those from the set-back sources. Problem 5-4 has considered such computations.
5-5.8 Ground Roughness
It will be recalled that the standard unprotected locationagainst which
protection factors are evaluated, consists of a detector located above a smooth plane uniformly contaminated (article 3-5). Particles deposited on rough planes represent a departure from standard conditions, and consequently some idealization may be in order to reduce a rough plane to a smooth plane.
A very I imited amount of data are available concerning the influence of ground roughness on contributions. The effect of roughness is similar to a barrier effect, and it appears reasonable to consider it as such. Data as are available, coupled with judgment, indicate that the effect of ground roughness can be included in the exterior wall barrier factor, Be(H,Xe), by adding an equivalent height, from Table 5-1, to the normal value of H.
The use of such modifications can be justified only with positive assurance that the condition assumed will be positively and perpetually maintained at least as rough as that assumed. Caution is therefore expressed over the reduction of contributions to account for ground roughness, since there are few situations where the possibility does not exist that conditons may change. The use of modifications should, in general, be restricted to attempts to improve protection in a critical time. Under ordinary circumstances, ground roughness should be ignored and considered as bonus protection not accounted for in the usual determination of a protector factor.
5-5.9 Passageways and Shafts
Figure 5-12, Chart 11 in appendix C, may be used to calculate the reduction factor at some point in a passageway or shaft. Two cases are considered on the chart. Case 1 considers a detector located below a circular horizontal aperture such as a skylight which has zero mass thickness and is uniformly contam
5-75
Condition of Plane Equivalent Height
Smooth 0
Paved 0-5
Lawn 5-10
Gravelled 10-20
Plowed, ordinary 20-40
Plowed, deep 40-60
TABLE 5-l
EQUIVALENT HEIGHTS FOR GROUND ROUGHNESS CONDITIONS
5-76
.6 .4 .3 .2 0.1 .08 .06 .04 .02 0.01 .006 .003 .002
3 u 2
0
1:::::>
cc
a:
1
2 0
u
SOLID ANGLE FRACTION,W
FIGURE 5 · 12 PASSAGEWAYS AND SHAFTS, C{u.)) CHART II APPENDIX C
5-77
inated with radioactive material. Such a detector would receive direct radiation from the overhead sources as well as skyshine. For w= 1.00, the reduction factor is unity. This corresponds to the case of a detector separated
from the source by 3 feet of air and corresponds to the standard detector location. Problem 5-13 illustrates the manner in which this chart may be used to determine the contribution through, say, a covered mine shaft to a detector
located opposite the opening to the shaft in the mine tunnel below. It is assumed that the mass thickness of the shaft covering is so low that it can be considered zero. Both the shaft and mine tunnel are assumed to have square cross-sections 10 feet on the side.
The contribution from overhead is first calculated for a point in the shaft midway in depth of the tunnel opening and centrally located in the shaft. It is assumed here, as in other overhead contribution computations, that rectangular
areas and circular areas subtending equal solid angle fractions will produce the same contributions. Cs(w s) is taken directly from Chart 11 (Figure 5-12). The contribution at point T is found by multiplying the contribution at S by 0.2wt· This is a11 empirical multiplier, substantiated by experimental data, which indicates that the amount of radiation diffused around the first right angle bend is 0 .2w times the contribution at the end of the first leg. For subsequent bends, the empirical multiplier is 0.5w which is applied to the contribution last found.
Case 2 of ·Figure 5-12 (Chart 11) gives the contribution at some point in a horizontal passageway leading from a vertical circular aperture receiving radiation from a-semi-infinite plane. Forw = 1.00, the reduction factor or contribution is 0.50, corresponding to the detector located directly in the
aperture and, therefore, subject to the semi-infinite field. Again, although
the chart is derived especially for circular apertures, its use is extended to
rectangular apertures subtending equal solid angle fractions. Problem 5-14
illustrates its use in determining the contribution to the detector at R. The
contribution Cp at Pis determined as a function of :.up from Chart 11. c0 is
found, as discussed above, by multiplying Cp by 0.2 wq, and CR by multi
plying Co by 0.5w .
r
5-6 Decontaminated Roofs
Studies have been made to evaluate the effectiveness of certain remotely operated systems which may be employed for roof decontamination, particularly for such facilities which have an extremely important emergency function.
5-78
PROBLEM 5-13
* * * -* -' _21<_
*
..
. . .
·,. : :: .. ·, .II . , : , I f .
. ::
I
: . :: I
I
:::
I
I
. . . . . I
.· •.·· .· .• .•· .· .•. {EC'!'t(JN .: i• • .. ::• : ... : • • :• : i:• \ -~s_ ! I . .
: •.·. ::· ~--~
...
. . . ::.:
·. · · · · ·. · ' ' . . ·. I I
:
::. ..
. .... . .. . :: . :: . I I
. .
:. :: .
. :: . :: . :
..... . . . : . . I I
. . .
: ..
::.: ..
. . :
I I I
. . . . :
I I
. :: :. :. : .. :
I
..
. . . I I
-
. ..
I I . :..
\I
s ~
::.
--
. . : . . ..
:: .
. : :: ..,.,.,.;.,.,:,.. : . . .
Shaft and Tunnel openings are 10 feet by 10 feet.
W/L = 10/10 = 1.00, Z/L = 40/10 = 4.0, w= 0.01
8
C8 (w8 ) = 0.0026 (Chart 11)
W/L = 10/10 = 1.00, Z/L = 20/10 = 2.0, wt = O.J4
CT = Cx 0.2wt = 0.0026 x 0.2 x 0.04 = 0.000021
8
pf = 1/.000021 = 47,000
5-79
PROBLEM 5-14
All passages 8 feet high R
~
Ill
PLAN
10' w L z W/L Z/L w
w p 5 8 12 0.62 1.5 0.040 wq
4 8 10 0.50 1. 25 0.045
w r 4 8 15 0.50 1.87 0.020
Cp(wp) = Cp(0.04 = 0.053 = cP x 0. 2W = 0.053 X 0.2 X 0.045 = 0.000477
CQ q
X 0.02 = 0.000005
0. 5W = 0.000477 X 0.5
CR = CQ X r = 1/0.000005 = 200,000
pf
5-80
Decontamination of roofs requires reliance on a complex, generally expensive system to achieve a result that is yet not completely predictable. Principle means are roof washdown systems, employing a rapidly moving film of water to loosen, dissolve, or suspend the fallout, roof blowdown systems using jets of air to prevent deposition of fallout, and disposable coverings which can be removed by some means after fa II out has collected.
Although, at the present time, complete reliance cannot be placed on such systems, later developments may prove otherwise for, at least, some special installations. From the viewpoint of analysis, the removal of contamination from the roof surface, if it is completely effective, restricts the overhead contribution to skyshine alone.
As previously discussed in Chapter IV, overhead contributions taken from Chart 9 include both the effect of radiation from the contaminating particles and from skyshine. Table 5-2 may be used to determine the overhead contribution from skyshine alone C (X ,w). The procedure for handling (partially)
OQ 0 decontaminated roofs is to obtain the overhead skyshine contribution from Table 5-2 and add to it any residual 11 direct11 overhead contribution from roof sources remaining after decontamination. This latter value is determined from the Chart 9 contribution value adjusted for the inefficiency of decontamination.
5-7 Detector Locations Adjacent to an Exterior Wall
A problem frequently encountered, in determining the range of protection factors within a shelter, involves the location of the detector as a probe located immediately adjacent to an exterior wall. As in all cases of eccentric detector locations, such problems are solved by considering fictitious buildings.
Figure 5-13(a) shows a detector located immediately adjacent to a wall at its midpoint in length. Two fictitious buildings are required to determine the total reduction factor. These are shown in (b) and (c) of the figure. The fictitious building shown at (b) involves nothing unusual. It would be analyzed in the normal way, and ha If the total ground contribution from the fictitious building in (b) represents the contribution through the North, East, and West walls of the actual structure. Half the overhead contribution from the fictitious building in (b) is the total overhead contribution to the detector in the actua I
structure.
A fictitious building shown in (c) of the figure involves no cleared area and consists simply of a detector centrally sandwiched between two walls. This is precisely the case considered by Spencer in developing Chart 6 for exterior wall barrier factors. Since this is so, the total ground contribution for the fictitious building in (c) is simply the barrier effect taken from Chart 6. There
5-81
TABLE 5-2
OVERHEAD CONTRIBUTION FROM SKYSHINE C0 a(X0 , U})
X~ 1.00 0.90 0.80 0. 70 0.60 0.50 0.40 0.30 0.20 0.10
0 0.1000 0. 0770 0.0570 0.0424 0.0324 0.0255 0.0190 0.0138 0.00880 0.00430
10 0.0474 0.0386 0.0306 0.0246 0.0205 0.0179 0.0150 0.0124 0.00880 0.00430
20 0.0246 0. 0211 0.0177 0.0151 0.0133 0.0123 0.0109 0.00947 0.00730 0.00430
30 0.0138 0.0124 0.0108 0.00958 0.00878 0.00837 0.00761 0.00678 0.00533 0.00322
40 0.00827 0.00765 0.00686 0.00623 0.00583 0.00566 0.00521 0.00470 0.00373 0.00227
50 0. 0051·9 0.00489 0.00446 0.00407 0.00389 0.00381 0.00354 0.00321 0.00256 0.00157
60 0.00334 0.00319 0.00294 0.00272 0.00260 0.00256 0.00239 0. 00217 0.00174 0.00107
U'l' 701 0.00219 0. 00211 0.00195 0.00181 0.00174 0.00172 0.00161 0.00146 0.00117 0.00072
'
~I 80 0.00145 0.00140 0. 00130 0. 00121 0. 00116 0.00115 0.00108 0.000984 0.000789 0.000485
90 0.000967 0.000934 0.000869 0.000814 0.000781 0,000772 0.000723 0.000661 0.000530 0.000326
100 0.000646 0.000625 0.000582 0.000542 0.000522 0.000518 0.000485 0.000443 0.000356 0.000219
110 0.000432 0.000418 0.000389 0.000364 0.000350 0.000347 0.000325 0.000297 0.000239 0.,000147
120 0.000289 0.000280 0.000261 0.000244 0.000235 0.000233 0.000218 0.000199 0.000160 0.000098
130 0.000194 0.000188 0.000175 0.000164 0.000157 0.000156 0.000146 0.000134 0.000107
140 0. 000130 0.000126 0.000117 0. 000110 0.000106 0.000104 0.000098 0.000090 0.000072
150 0.000087 0.000084 0.000079 0.000073 0.000071 0.000070
I
r=;:=· ;.::·..;.:..:~·.= :::t: ·=:::: ==.. ;:~==·:·.:=\~
·:·. .·:
.";~·. :;:
..
::
·:·;;
·:: ~.} :..:..~'-------t--_ ___a.;.:·.=~
I
I I
1 : 1 I I I I I I 1 1 1 I
I L ___ =-L-___I I
L ___ --~-____I
I
I
(c) (b)
FIGURE 5-13
DETECTOR AT MIDPOINT OF A WAL~
is no geometry reduction. Obviously, half of this contribution is that contributed
to the detector through the South wall of the actua I structure.
In summary, the total ground contribution to the detector consists of half that found from consideration of the idealized structure in (b) and computed in the normal way, plus half that from idealized structure (c) which is simply half the normal barrier factor from Chart 6.
Figure 5-14(a) shows a detector located in the corner of a building. Four fictitious buildings must be analyzed to determine the contribution to the detector. These are shown in (b), (c), (d), and (e) of the figure.
The total overhead contribution to the detector in the actual structure can be found from the fictitious building in (b). It is one-fourth the overhead contribution found for that fictitious building.
The ground contribution to the detector in the actua I structure through the North and West walls is determined from consideration of the fictitious building in (b). In magnitude, it is one-fourth the total ground contribution for the fictitious building computed in the normal way and includes both geometry and barrier reductions.
5-83
: :;:,..
(e)
(a)
I I
--------~------
I I
I
1 I I I I
I : I
I
I I I I I I
: L___ ------~--________ j
~---------l-------~-
(b)
,-----------I~ ---------,
-i~~~~~~=-~:;:;:;:~e;=:::-~ =---=--a 1
r•: . "·: :·· ::._..:,.'[ ~ --------•
(c)
FIGURE 5-14 DETECTOR IN CORNER LOCATION
5-84
ll!
[1 ·t
~; . . .
1>..
I [ I r:.
1 1:;
I
I til:· .
I
II I I II I I II I (d) I II I I Ill I
: I;
: ill :
L~-'
Ground contributions through the East and South walls of the actual structure are determined from an analysis of the fictitious buildings in (c) and
(d) respectively. One-fourth of the total ground contribution from each of these fictitious buildings is that reaching the detector from the East and South walls. As discussed in relation to Figure 5-13, the total ground contribution for fictitious buildings of (c) and (d) is simply the barrier factor taken from Chart 6, since they are essentially two-walled structures with the detector sandwiched between.
At first observation, it would appear that no further ground contributions are of interest, since all four walls of the actual structure have been considered. That this is not so should become readily apparent from consideration of the fields that contribute to the radiation received at the detector through the East and South walls. Contributions to the detector in the fictitious buildings of (c) and
(d) have resulted from consideration of an infinite field surrounding the twowall structures. Quartering the total contribution, to arrive at that part of the total attributable to the wall of interest in each case, implies that only one quarter of the infinite field, as shown shaded in (c) and (d) of the figure, has been taken into account. In (e) of the figure, the fourth fictitious building is shown as simply a square structure of no area (consequently no geometry reduction) with the detector sandwiched between four walls (actually pOints) of which two, the East and South, are of interest. Shown also on the figure are shaded areas representing the fields of contamination that have been considered in East and South wall contributions as discussed above. There remains the corner field that has not yet been accounted for and which contributes to the corner detector directly through the corner. Obviously, it is also a quarter of the total infinite field completely surrounding the fictitious building in (e). Again, it should be obvious that the penetration of radiation through the corner in the actual structure is one-fourth of the total contribution for the fictitious building in (e) which, again, is simply the barrier factor from Chart 6.
In summary, then, if the East and South walls of the actual structure are the same mass thickness, the total ground contribution is one-fourth the total from fictitious building (b) plus three-fourths the barrier factor from Chart 6 (one-fourth for the East wall, one-fourth for the South, and one-fourth for the corner). If the East and South walls are of different mass thicknesses, the added quantities are three-eighths of the barrier factor for each the East and South walls.
5-85
5-8 Summary
All of the methodology necessary for computing reduction factors in simple ideal structures was developed in Chapter IV. Chapter V has considered the extension of the methodology io include conditions that embody changes from the standard ideal structures considered in development of the method. Such considerations of complexities in this chapter have revolved around the technique of idealization. Whatever the complication or deviation from the standard, it can be accounted for by conversion of the complex condition to an idealized one. Many such complications have been exemplified by the problems that have been solved. Others have been discussed in general terms. An analyst, who is properly grounded in a knowledge of the fundamentals of shielding and in the analysis of simple structures, should have no difficulty in solving even the most complex shielding problems. In some cases, there may not be a direct approach that can be used readily. In such cases, fundamental understanding must be complemented by the judgment of the analyst. A proper combination of the two makes the standard method of analysis a powerful tool applicable to all structure shielding problems with reasonably precise results.
Although approximate methods of analysis are available, the standard method is that which has been presented in Chapters IV and V. Approximate methods have their place, particularly in preliminary design and analysis, but final computations most often require application of the standard method. An understanding of approximate methods, and particularly of their limitations, presuppose a firm understanding of the standard method, and the analyst is urged to continue his review of all material to the point of complete mastery.
5-86
CHAPTER VI
SLANTING TECHNIQUES FOR FALLOUT SHELTER
6-1 Introduction
Every building inherently provides shielding against gamma radiation from nuclear fallout. In the National Fallout Shelter Survey, involving the analysis of existing bui I dings designed and constructed with no consideration for protection from gamma radiation, almost 90 million shelter spaces, with a protection factor of 100 or more, were located. More than 50 mi Ilion additional spaces were found to have protection factors between 40 and 100. Many other buildings would have provided reasonably good protection except for certain nullifying weak points. If these weak points could have been detected during the initial design stage by an analyst competent in the area of radiation shielding, design changes could have been incorporated to maximize protection without exceeding budget limitations or, in many instances, without additional cost.
"Slanting" for radiation protection is defined as the incorporation of certain architectural and engineering features into the design of new structures, or the modification of existing structures, to maximize protection of occupants against gamma radiation from fallout with little or no increase in cost and without adversely affecting function or appearance. "Slanting" features may provide immediate optimization of shielding, or they may be of such nature as to facilitate later conversion of the structure for purposes of protection. From this point of view, slanting simply adds radiation shielding to the program elements normally considered in the design of a bui I ding.
There is nothing mysterious or complicated about "slanting." Qua Iitatively, it involves only the competence of the designer in recognizing the various parameters that influence protection factors. The material presented in Chapter IV of this manual is a good base for establishing qualitative interpretations. Quantitatively, "slanting" requires an evaluation of the contributions involved in the total reduction factor in order that the designer may observe the extent to which each contribution influences the degree of protection and the forms of the building. A competent fallout shelter analyst is prepared to make the necessary computations for such quantiative analyses. Lastly, but most importantly, "slanting" involves the mature judgment that is normally the equipment of every competent architect or engineer. Generally, a desired degree of protection can be obtained through the employment of one or more alternatives in design. With proper judgment and a knowledge of costs, a competent architect or engineer, who is also a qualified fallout shelter analyst, can make a judicious choice of alternatives in
6-1
design to incorporate maximum protection at little cost, or even at no additional cost, while still maintaining the integrity of his basic functional design. Above all, it must be recognized that "slanting" does not involve the separation of the shelter areas in a structure from other functions. Emphasis in design should still be on the basic normal function of the building. "Slanting" for radiation protection simply adds an element of emergency usage.
In a strict sense, this chapter considers nothing new. It will merely point out some schemes that have been or may be successfully applied in design to enhance protection. Each building, with its site, is an individual structure, and what may be the most appropriate "slanting" techniques for one may not be so for others. From this point of view, then, it is difficult to be specific, and emphasis is placed on generalities in most instances. The ingenuity of the
designer of the building is the real key to success in reaching radiation protection
objectives.
6-2. "Slanting" -A Concept of Design
6-2.1 General Considerations
The parameters involved in "slanting" for increased levels of radiation
protection can be most simply stated in the broad concepts of MASS, DISTANCE, and LIMITATION OF FIELDS OF CONTAMINATION. These should be obvious to the analyst who is reasonably knowledgeable in the methodology of shelter analysis comprehensively discussed in Chapters IV and V from both a quantitative point of view, and a qualitative point of view. By following a few logical steps,
•the designer can quickly place himself in the position of making those value judgments that are necessary for the economical incorporation of desired levels of radiation protection.
6-2.2 Steps for "Slanting"
The first step in "slanting" for increased radiation protection is coincident with the first step generally associated with the design of any building. Given the charge to design a building for a particular major use function and a specific site, the architect usually programs the project and prepares schematic designs fitting the building to the site in the most advantageous way. At this point, consideration should be given to those natural features of site topography that
can be utilized not only to enhance the functional and aesthetic qualities of
the building but also to increase radiation shielding effectiveness with due
regard to the economics involved in site preparation, foundations, etc., all
of which are normal to all design.
6-2
Following the establishment of an acceptable schematic design, the architect proceeds with design development, establishing form, selecting materials, and arranging components of the building in a manner best meeting the prime function, with due regard again to the aesthetic and economic qualities of his work. In this stage, the shelter analyst can aid immeasurably in exercising his special skills to provide qualitative judgments relative to enhancing shielding properties along with the many other considerations of design. At the termination of this second step, a true preliminary design for the building has evolved. From every point of view, basic dec.isions have been made from qualitative judgments tempered, of course, by the broad experience of the architect or engineer and the analyst.
When design development is completed through the exercising of qual itative judgments, a building exists, at least on paper, about which enough is known to place quantiative interpretations on all features of the design including, among others,functional utility, aesthetics, versatility, cost, and protection. Up to this point, consideration of shelter has amounted to nothing more than another element involved in decision making. From this point of view, it will, in fact, in many instances, prove beneficial in the sense of providing an additional consideration upon which a decision can be based (everything else being equal).
•
During the construction document phase, refinements to the pre I imi nary design can be made resulting in a final design that meets all shelter objectives . This is the quantitative stage, and it is here that the analyst tests his qualitative contributions to the design through calculations, the results of which may indicate modifications that can be accomplished with little or no effect on cost
but with marked effect on protection rea Iized.
Although the above steps have been discussed separately, it is recognized that no fine dividing lines exist. All steps tend to merge into one smoothly flowing procedure. It is implied, however, from the step separation, and essential to the maximum success of enhancing protection, that "slanting" techniques must be considered and applied from the conceptual stage continuously through to the construction documents stage. In this way1 with the exception of analysis time in the third step, no burden is placed on design by virtue of shelter consideration, and even the ana lysis time in step 3 approaches inconsequential proportions relative to all other considerations.
6-3
208-401 0 -76 -18
6-3 Analysis and "Slanted" Design
6-3.1 Analysis in the Preliminary Design Stages
During the intial phases of design, from the preparation of schematic drawings through design development, it is sufficient for the analyst to use such approximate methods of analysis as will render a reasonably precise
evaluation of the effect of alternate schemes on protection. There is nothing to be gained from a more precise analysis during these stages, since evaluations will generally consist of an analysis of the effect of varying a single parameter.
It is only after all parameters have been established, in the form of a sufficiently developed design, .that a more careful analysis will be beneficial and necessary.
6-3.2 Analysis Following Preliminary Design
Once a preliminary design has been completed, with all pertinent parameters for protection established, the analyst is in a position to make a complete analysis of the dual-use shelter areas utilizing all of the necessary. refinements
of the detailed method of analysis. As should be apparent, the standard method of analysis, properly applied, will indicate precisely what portion of the total
reduction factor is attributable to each parameter. To be as useful as possible
to the analyst, who must evaluate the relative magnitudes of contributions, the computations should be broken down into as many "packages" of individual contributions as are necessary to clearly identify major sources of contribution. Depending again on the complexity of the situation, the analyst may find it desirable to calculate separately the ground contributions above and below the detector plane with further separation of direct, scatter and skysh\ne contributions. In addition, he may consider entranceways separately from other wall contributions, since these often have a marked adverse effect on protection.
Once the several contributions have been calculated, the analyst is in an
excellent position to make value judgments as to how major contributions could
be reduced. If such improvements, as may be apparent, are economically feasi
ble and do not impair the functional and aesthetic qualities of the plan, they
may at once be incorporated into the final design.
6-4 Items for Consideration in "Slanting"
Since each building with its site has individual characteristics with regard
to radiation shielding parameters, specific recommendations are not properly a
purpose in this manu<:~l. Instead, the items listed below are given in a general
way merely to point out to the designer some of the things that he should consider
during all phases of the design. The I ist is by no means complete, and all items
6-4
may not be applicable to all structures. The ingenuity of the designer and his judgment, together with his intimate knowledge of the building being designed, remain the most important items in his technical repertoire.
(1)
A building can often be located on a site so as to achieve maximum benefit of mutual shielding from adjacent buildings.
(2)
Topography of such a nature that the earth slopes down away from the building can materially reduce the direct contribution through the walls. This may be a natural feature of the site or a consider
ation in the grading plan.
(3)
In grading of the site, earth berms artifically produced and attractively designed can provide a very effective element of field I imitation and increased protection.
(4)
Walls, as low as 3 feet high for first story (floor at grade) shelter
areas, can serve effectively in limiting the contributing field of contamination. These could be screen walls, retaining walls or pia nter boxes.
(5) Basement shelters inherently offer good protection. In preliminary
design stages, consideration should be given to the provision of
basement areas to serve normal functions appropriate to such a
location. In some parts of the country, for example, multi-purpose
rooms and cafeterias in schools have been placed underground with
resultant complete satisfaction.
(6) Where it is not appropriate to depress a potential shelter area completely below ground, consideration may be given to a partial depression of the first floor. This eliminates the contribution
through the depressed portion of the wall while still allowing the norma I amount of I ight and ventilation.
(7)
Planters, immediately adjacent to the exterior walls, up to detector height in first story shelter locations could add enough mass thickness to reduce the contribution from below the detector plant to negligible quantities.
(8)
Raising of sill heights to at least detector level aids materially in reducing direct radiation contributions.
6-5
(9) Modern lighting systems are such as to eliminate the necessity for
wide expanses of glass as I ight sources. Consideration should be
given to reducing window areas as much as possible.
(10) The use of skylights introduces particularly adverse conditions with regard to overhead contributions.
(11) In aboveground shelter locations, interior corridors often offer good potential for shelter areas, but this potential is often nullified by entranceways permitting direct entry of ground radiation. In many instances, doorways can be positioned off corridor ends to eliminate direct entry, or baffles can be used to provide barriers at the corridor ends.
(12) Stairwells can be positioned to provide additional barrier shielding at corridor ends.
(13) Consideration should be given to the use of dense solid walls, both exterior and interior.
(14) In some sections of the country, tilt-up walls and partitions have proved to be economically competitive with other types of construction. Increasing the normal thickness of such walls can be very effective in increasing protection. The small additional cost of the extra concrete can be at least partially offset by a decrease in the amount of reinforcement.
(15) Where walls or partitions are constructed of hollow masonry units, increased mass thickness can be obtained by filling the voids with sand, gravel or grout at Iittle additiona I cost.
(16) Interior partitions can be judiciously placed to block direct entry of radiation into a shelter area.
(17) Openings in partitions and exterior walls should be studied from the
viewpoint of staggering them so as to avoid direct penetration of
radiation into a shelter area without benefit of barrier reduction.
(18) Doorways in partitions surrounding a shelter can be baffled. An
attractive baffle may even eliminate the necessity for a door.
(19) The arrangement of building elements can be such as to obtain maximum
advantage in forming a protected core area.
6-6 •
(20) Protection afforded by protective core areas can be materially enhanced by more massive construction in partitions, floors and roofs than that of other portions of the building.
(21) Due consideration should be given to the more massive types of structural systems for floors, walls and roofs. Cost differentia Is between such systems and Iighter forms of construction are often negligible, but the more massive system obviously provides greater protection.
(22) Where practical, concrete floors and roofs can be thickened with the cost of the additional concrete and other added costs being at least partially defrayed by decrease in the amount of reinforcement required. Frequently, such thickening will reduce labor costs by making it easier to pour around conduits, etc.
(23) In interior corridors of aboveground buildings, protection can be enhanced by using a more massive type of floor or roof construction directly overhead.
(24) Although more massive types of construction may result in small increases in first costs, the additiona I expense may be justified not from the viewpoint of protection alone, but also from the long-range viewpoint of versatility and lower operating and maintenanee costs.
(25) In warmer climates, the use of pools of water may serve to limit contaminated fields, since fallout particles settle to the bottom and the mass of water becomes a barrier. The possibility of freezing in colder climates eliminates this as a positive means of enhancing protection on a 365-days-a-year-basis.
(26) The location of a building on or near the shore of a natural body of water provides possibilities similar to those mentioned in item 25.
(27) Where parking facilities are proposed, consideration should be given to placing them underground where they could serve as excellent shelter areas. Possible increased construction costs may be justifiable from the standpoint of preservation of valuable space above for other construction, or for open space, giving rei ief to congested urban environment.
•
6-7
(28) Attention should be given to ventilation of the shelter area in accordance with DCPA criteria. In aboveground areas, natural ventilation is entirely adequate to maximize the number of spaces, since windows and doors in adjacent areas can be opened to provide circulation.
(29) In belowground areas, ventilation requirements, in order to minimize cost, should be based usually on normal usage requirements for the facility. Additional ventilation for maximizing capacity may be obtained naturally, in many instances, through the judicious employment of such construction features as baffled areaways or windows that can be opened to provide natural circulation. Obviously, such features may, at first glance, appear to be detrimental to protection. Consideration of spaces added may, however, offset reduced protection, provided that the final protection factor remains at a reasonable value.
(30) Consideration should be given to sources of water in a building and their positive availability to the shelter area. These might include water found in tanks, the piping system, and other similar sources.
(31) Often, toilet facilities may be located adjacent to or near the shelter area without adverse effect on the efficiency of the building in its norma I use.
In the event of an impending emergency, or one that occurs with little or no warning, it would be extremely beneficial to enhance the protective features of any potential or actual shelter area to the maximum extent possible. Hasty or temporary modifications are generally the most economical means for modifying an area to provide a higher level of protection.
Hasty modifications generally involve readily available and transportable heavy material with little structural strength. Such materials may be stored near the area and moved into place, according to preconceived plans, when and if they are required.
Types of hasty or temporary modifications are too numerous to allow a complete listing in this manual. Possible uses are I imited only by the imagination and ingenuity of the designer. The following paragraphs are intended only to illustrate sufficient varieties of such modifications to aid the analyst in visualizing appropriate modifications for the specific shelter under consideration.
6-8
Deep plowing of the area surrounding the bui I ding would have good effect,
similar to that of field limitation.
Bulldozing of earth berms to provide a mutual shielding situation would be beneficiaI •
The grading of earth to form an embankment next to the exposed parts of basement walls, or the lower portions of first story walls, would be effective in reducing penetration of radiation through the wa lis.
Earth or other materials spread over a floor, up to its structural capacity, would be very beneficial in reducing overhead contributions.
Sandbags could be used to fill window or door openings, to baffle openings of all sorts and to shield other leaks in the shelter area.
Sandbags or hollow masonry units could be used to construct temporary screen walls or to form structural suppports for a separate shelter roof.
All available and movable furnishings and other equipment could be moved into position on the floor over the shelter area. If loads become excessive, consideration should be given to shoring from below.
Areaways could be filled with earth.
Nonstructural walls in other parts of the building could, in an extreme emergency, be dismantled and their materials used to enhance protection in the shelter area.
6-9
CHAPTER VII
HABITABILITY REQUIREMENTS FOR FALLOUT SHELTERS
7-1 Introduction
An acceptable degree of protection against the potentially harmful penetration of gamma radiation is only one of the requirements for fallout shelters. Space with an adequate protection factor becomes a suitable fallout shelter only if adequate provisions are made to make it habitable for its rated number
of occupants throughout a reasonable period of time. Therefore, apart from shielding, requirements for habitability must include minimum standards for space, physical environment, health and sanitation, services, and life sustaining supplies of food and water.
There is nothing in the previous experience of mankind that can serve
as a complete comparison to the conditions which would probably exist in fallout shelters after a nuclear disaster. Although some useful information has been gained from a study of conditions in the air-raid shelters of World War II, their use was so markedly different from what would be expected in fallout shelters that no close parallels can be drawn. Air-raid shelters were occupied by large numbers of people crowded very closely together. However, they were occupied for only short periods of time (a few hours at most) and
required almost nothing in the way of provisions, facilities, and equipment.
Fallout shelters, on the other hand, would be occupied for prolonged periods
under crowded conditions. This necessitates careful consideration of all
elements of habitability ahd the provision of at least minimal facilities and
supplies.
Problems of habitability in closed ecological systems have been solved in the past with excellent results. Notable examples of such systems are submarines and space capsules. In these systems, however, no expense has been spared to create conditions necessary not only to sustain life but also to permit well conditioned and specially trained crews to operate at maximum efficiency in reasonable comfort. In contrast, fallout shelters would be occupied by a random cross section of the civilian population, without previous training or conditioning. The prime consideration in establishing habitability requirements is survival under emergency conditions. For obvious reasons of economy, fallout shelters must be austere, and operation must take place with essentially an
absolute minimum of facilities, equipment, and provisions to meet the survival
condition.
7-1
7-2 Environmental Considerations
7-2.1 General
Environmental considerations involve the determination of minimum facilities and equipment based on human tolerance limits for heat, cold, humidity, carbon dioxide and oxygen. Tolerance limits for oxygen and carbon dioxide are governing factors in the control of the chemical environment, and tolerance I imits for heat, cold and humidity govern control of the thermal environment.
Considerations of environmental control beardirectly on space requirements in
fallout shelters and, consequently, on occupant capacity.
A complete treatment of the subject is beyond the scope and purpose of text or a course devoted to fallout shelter analysis. Qualified fallout shelter analysts are encouraged to pursue the subject in depth through enrollment in Shelter Environment Engineering courses sponsored by DCPA.
7-2.2 Space and Ventilation Requirements
The capacity of a fallout shelter refers to the number of occupants that can be safely accommodated. Under DCPA requirements, the minimum net
floor area allowance per person in shelters for the genera I public is 10 square feet. Net floor area is that clear floor area that remains after deducting from the gross floor area those portions occupied by such items as columns, fixed equipment, etc.
In addition to a minimum of 10 square feet of net floor area per occupant,
at least 65 cubic feet of volume per person must be provided. This latter requirement is an acceptable minimum only if 3 cubic feet of fresh air per minute per occupant are made available either with natural ormechanical ventilation. The requirement of 3 cfm per occupant is based on control of the chemical environment and results from the necessity for maintaining the carbon dioxide con
centration at 0.5% or less by volume.
For thermal control, the ventilation rate in a shelter must be sufficient
to maintain a daily average effective temperature of not more than 82°F for at least 90% of the days of the year. The minimum recommended shelter temperature maintained during the occupancy period is 50°F. These matters are discussed more fully in the articles that follow.
The analyst is also referred to Technical Memorandum 72-1 November 1972, which gives technical standards for fallout shelters including, among others, ventilation requirements.
7-2
7-2.3 The Effective Temperature Index
There have been many attempts to devise a reliable index to express, as a single number, the effect of an environment on the human body. Because of the many variables involved in human factors and environmental conditions, there is probably no one index which can be considered reliable for all conditions. Under ordinary room conditions, with still air, the best index for warmth is sti II the dry-bulb temperature.
One of the most widely used indices (the one most commonly applied for shelter conditions) is the effective temperature (ET) index developed by a research team of the American Society of Heating and Ventilating Engineers (ASHVE, now ASHRAE). It is based on the subjective sensations of warmth and coolness of a group of test subjects who were exposed to atmospheres with different temperatures, humidities and air movements. The results are presented in the form of a nomogram in the ASHRAE Guide and Data Book. From this nomogram, the ET may be determined from given values of the dry-bulb andwet-bulb temperatures and the air velocity. Figure 7-1 shows I i nes of effective temperature as determined from the ASHRAE nomogram for still air (20 feet per minute) superimposed on a psychrometric chart. The effective temperature may also be approximated by the empirical equation:
ET = 0.4 (WBT + DBT) +. 15
where WBT is the wet-bulb temperature and DBT is the dry-bulb temperature.
7-2.4 Ventilation for Thermo I Environment Control
The minimum ventilation rate of 3 cfm per person is sufficient to control the chemical environment within the specified limits of tolerance. However, in most locations in the United States, the reliability of maintaining a tolerable thermal environment with this rate of ventilation is very low. The minimum ventilation rate required to meet the thermal environmental criteria will be greater than that required to control the chemical environment. The governing factor, then, in determining the required ventilation capacity for a shelter is the control of the thermal environment. It is true that there could be times during cold weather when the necessity for maintaining the chemical composition of the air will require ventilation rates greater than are necessary for thermal control. However, the capacity of the ventilating system will be determined by the higher values of shelter temperature and humidity during hot weather.
The temperature and humidity that will develop in a shelter are determined by the heat and moisture balance. The sources of heat which might be present are:
7-3
FIGURE 7-1
PSYCHROMETRIC CHARTWITH EFFECTIVE TEMPERATURE LINES
7-4
1.
Heat losses of the occupants,
2.
Heat in the ventilation air,
3.
Heat from I ights,
4.
Heat foom mechanical equipment,
5.
Heat transfer to or from the surrounding earth or air,
6.
Heat from combustion processes, such as open flames for cooking, I ighting or heating, or from absorption type refrigeration equipment.
Sources of moisture in the shelter might include:
1.
Moisture loss from occupants,
2.
Moisture in the ventilation air,
3.
Moisture from leaks in the structure,
4.
Evaporation from open containers of water, food, or from sanitation system,
5.
Moisture from combustion hydrogen fuels used in cooking, lighting or refrigeration,
6.
Moisture from bathing or showers.
In addition to the sources of heat and moisture, it is necessary to have additional information if an analysis of the thermal conditions in the shelter is to be made. Such data would include:
1.
Ambient temperature and humidity, wind velocity, latitude, and cloud cover,
2.
Ventilation rate,
3.
Number of occupants and their metabolic rates,
4.
Physical and thermal properties of tre shelter, adjacent structures, and surrounding soil,
5.
Heat and moisture absorbed by mechanical cooling equipment, if any,
6.
The previous thermal history of the shelter and adjacent structures in order to determine the initial temperature distribution of the soil, if the shelter is in contact with the soil.
Analytical models have been developed which will treat the many aspects of the transient heat and moisture flows. Predictions based on these models closely approximate the results of simulated occupancy tests of shelters.
A simplified method has been developed which is based on the fact that only a sma II percentage of the total metabolic heat generated in large shelters will be dissipated by heat transfer to the shelter walls during hot summer weather. This would be essentially true for above-ground shelters in the core areas of large buildings and in most below-ground shelters after the first week of occupancy.
7-5
The method neglects any heat loss or gain through the shelter surfaces and requires that all heat and moisture be removed by the ventilation air. The shelter is treated as an adiabatic system, and the need for detailed information concerning the thermal characteristics of the shelter and its surroundings is eliminated.
Charts for the 91 weather stations have been used to plot contour lines of equal ventilation rates over the country as shown in Figure 7-2. A further simplification was made by regarding the contour map as a zona I map so that the areas between the contour lines were considered to be zones of equal ventilation rate. The ventilation rate for the zone was taken as the highest value contour bounding the zone. For example, the entire area between the 15 cfm contour and the 20 cfm contour is taken as requiring a ventilation rate of 20 cfm per person.
Use of the zone system not only simplifies the determination of required ventilation rates but a I so protects the sma II number of she I ters where the adiabatic assumption would result in underestimating the ventilation requirement. Only those shelters near the high boundary would not be given excess ventilation. It is believed that the number of shelters for which the system would underestimate the ventilation rate and which, in addition, would be close to the high boundary of the zone, would be quite small. Furthermore, the occupants of such shelters would still have the alternative of moving into areas of the building peripheral to the shelter area or even to another shelter if the thermal environment became intolerable. This alternative would not be available if radiation levels were high enough to prohibit moving into areas with a lower protection factor. Thus, I ives of the occupants would be endangered only when this combination of unrelated conditions existed.
To use this map, it is necessary only to determine the number of occupants of a shelter and multiply this by the ventilation rate as read from the map in order to determine the total ventilation capacity required for the shelter. The method is based on the heat load of sedentary people. No other heat loads are considered. Therefore, if other heat loads are present, it is suggested that they be treated as additional occupants at the rate of one additional occupant for each 400 Btu per hour of additional heat load.
Appendix D provides a method for computing existing shelter spaces.
7-2.5 Natural Ventilation
Natural ventilation would be most applicable to shelter areas in existing buildings which have large openings and passage necessary for the movement of air with small pressure differentials. In high-rise buildings, windows can be opened in the top floors and near ground level to provide a chimney effect
7-6
•
Alaska 5
Hawaii 20
FIGURE 7-2
ZONES OF EQUAL VENTILATION RATES IN CFM PER PERSON
7-7
for venti lotion of shelter areas on the mid-floors. Advantage can also be taken of stair-wells and elevator shafts to provide a chimney effect. If shelter areas are in the inner parts of large buildings with interior partitions, windows at the shelter level can be opened to permit a cross-flow of air.
As a genera I rule, it can be said that volume of air flow depends on the size of the exhaust opening and direction of the flow depends on the inlet opening. It would thus be desirable to have as many and as large openings as possible near the top of a building in order to provide volume of flow. Windows or doors at shelter level would be opened or closed as necessary to provide the best directional effect and to take advantage of prevailing winds. Obviously, stair-wells and other vertical passages would have to be open to permit the movement of air.
Since window glass provides almost no attenuation of gamma radiation, whether the windows are open or closed has no appreciable effect on the protection factor. The only possible hazard from open windows would be possible infiltration of fallout particles into the building. Once the fallout has been deposited, this should be no problem except, perhaps, in the case of an open doorway at ground level on the windward side of a building. During the time that falloot is being deposited, there could be some infiltration through open windows. However, tests have suggested that the amount would be small and would not reduce the protection factor in an inner core to any great extent. If, however, there are no interior partitions between the windows and the shelter area, it would probably be best to keep the windows closed during the time the particles are falling and open only after all the fallout has been deposited.
7-2.6 Air Filtration Requirements
In any discussion of ventilation requirements for fallout shelters, a frequently occuring question concerns the need for filters to exclude fallout particles from ventilation air. Studies have shown that filtration for fallout particles is generally unnecessary.
7-3 Hazards
In some instances, space that might normally be excellent shelter space becomes useless or, at best, marginal because of inherent hazards. Hazards to watch for include the storage of explosives or highly combustible materials, such as paints, cleaning fluids, etc. If the amount of such storage is small and can readily be removed in time of emergency, or if the hazards can be safely isolated, the capacity of the shelter should not be affected.
7-8
•
To the extent practicable, hazardous utility lines, such as steam, gas, etc., or exposed high voltage equipment should not be located in or near the shelter area unless provision is made to control such hazards before the shelter is occupied. Of course, all shelters must be co!'lstructed to minimize the danger
of fire from both i nterna I and externaI sources.
7-4 Electrical Power
It is assumed that normal electrical power will not be available.
Lighting is not a critical factor in shelters and, although no special lighting levels are required in ordinary shelter areas, the following levels are deemed adequate for emergency occupancies:
(1)
Sleeping areas-2 foot candles at floor level
(2)
Activity areas -5 foot candles at floor level
(3)
Administrative and medical areas-20 foot candles at desk levels.
The best source of emergency electric power is an engine-generator set with seven days supply of fuel. The relative merits of gasoline, diesel, and I iquefied petroleum gas engines should be carefully considered. Initial cost is important, but so are local code requirements, ease of maintenance, dependability, safety of operation, and storage characteristics of fuels.
Emergency engine-generator sets should have separate vents and be heat-isolated from the main shelter chamber. Special consideration must be given to the manner of installation of engine-generator sets and fuel tanks to minimize hazards from exhaust gases and fires.
7-9
208-401 0-76 -19
APPENDIX A
BASIC NULCEAR PHYSICS
A-1 Introduction
It is not necessary to have broad understanding of nuclear physics to analyze or design structures for fallout protection. However, a basic knowledge of the concepts and terminology associated with the structure of matter, radioactivity, fission and fusion, and attenuation of radiation are desirable to understand the need for fallout protection and the background of the system of analysis. The information provided in this section is a general survey and is intended to supplement the material presented in Chapters I, II, and Ill of the text.
A-2 ·Structure of Matter
A-2. 1 Elements and Compounds
All matter is made up of elements and compounds. Compounds consist of two or more elements and may be broken down into sim,pler substances, or formed from simpler compounds or elements, by chemical reaction. The components do not exhibit the characteristics of the original compound. For example, sugar is a compound which can be broken down into the elements carbon, hydrogen, and oxygen. The smallest subdivision of a compound which still retains its properties is the molecule which is a group of two or more atoms tightly held together.
The distinction between an element and a compound is made on the basis of chemical reactions. Chemical reactions may be produced by heating applying pressure, using a substance which promotes reaction (catalyst}, electrolysis, and so forth. If large numbers of reproducible experiments on a pure isolated substance show that none of these means is capable of breaking that substance down into still other substances, then that substance is said to be an element. There are 92 naturally occuring elements. Ten more have been produced artificially by man in laboratories. From these 102 elements, it is possible to produce, by chemical reaction, all the compounds known (as well as many as yet unknown). For example, water is built up from the elements hydrogen and oxygen. An atom is the smallest particle of an element which is capable of entering into a chemical reaction.
A-1
When two atoms of hydrogen combine with one atom of oxygen, they form one molecule of the compound water. It is exceedingly difficult to visualize the fantastically small size of atoms. For example, in one grain of ordinary table salt, there are approximately 1,300,000,000,000,000,000,000
(1.3 x 1021) atoms, half of which are sodium atoms and half of which are chlorine atoms. Each atom has a diameter of about 0.00000001 centimeter.
Each element has a different name and is represented by a symbol which is simply a shorthand notation. For example, the element hydrogen is given
11 H11 11 He 11
the symbol The symbol for the element helium is In general,
••
these symbols are chosen as the first one or two letters of the name of the element. It is necessary to use other letters for some elements. Also, some of the symbols appear illogical, as they are based on the .old Latin names
11 Na 11 11 Au 11
for the elements, such as for sodium and for gold. The great advantage of the element symbols is that they enable one to represent chemical reactions and chemical compounds in an abbreviated fashion. A molecule of water composed of two atoms of hydrogen and one atom of oxygen can be
11 H0 11
2•represented by the notation
A-2 .2 Atomic Structure
Despite their extremely small size, atoms are composed of still smaller
particles. There are basically three such particles, the electron, the proton, and the neutron. The many different kinds of atoms are formed, essentially,
from these three particles present in different numbers.
Although atoms of one element differ from those of another, all atoms have
the same general type of structure and are often described by comparing them to the solar system. The nucleus is the center of the atom, just as the sun is the center of the solar system. The nucleus has a positive electrical charge and is composed of one or more protons and neutrons. Moving at great speed around the nucleus in orbits, much as planets move about the sun, are a number
of particles called electrons. The electrons have a negative charge. This structure is indicated in Figure A-1. It should noted that a:neutral atom contains an equal number of electrons and protons. This concept, or 11 model 11 of the atom, has been replaced by more sophisticated concepts based up~n wave mechanics and probability. However, this model is adequate to explain the nuclear pheno
mena of interest in radiation shielding analysis. ·
The nucleus contains almost all of the mass of the atom, yet the diameter
of the atom is roughly 10,000 times the diameter of the nucleus. The atom,
therefore, is mostly space. Each of three basic particles composing an atom
has a specific charge and mass. 11 Charge11 refers to the electrica I charge on
A-2
the particle, and although "mass" has a precise meaning in physics, for the purposes of this text, it may be considered synonymous with "weight" without a serious error in reasoning. For simplicity, in dealing with atomic phenomena, the magnitude of the electric charge on an electron has been chosen as one unit
of charge. Since atoms are so small, it is inconvenient to use pounds, ounces, or even grams to measure their mass. The mass is measured by the atomic mass unit (amu) system. On the seale of this system, the mass of the proton is approximately one mass unit, and the other particles may be compared with it as a standard. The physical amu is defined precisely as one-tw..f'fth the mass of the natural carbon twelve atom and is equal to 1.66 x 102 grams. A carbon twelve atom is shown in Figure A-2. Its nucleus consists of six protons and
six neutrons.
...-----ELECTRONS (in orbit)
ORBITS
Protons
__NUCLEUS
Neutrons
FIGURE A-1 STRUCTURE OF AN ATOM
A-2.3 Particles of an Atom
Electron The electron is a negatively charged particle with a mass of approximately l/1845 amu. It is by far the lightest of the three basic particles. By convention, the charge of the electron is negative (-)and is one electronic charge in magni!VSe. The electronic
charge, so defined, is equal to 4.8 x 10 electrostatic units and is the smallest discrete charge observed in nature.
A-3
HYDROGEN ~H HELIUM 2He ..
LITHIUM ~Li
•0 0
Electron
CARBON 12 C
6
Proton
Neutron
FIGURE A-2 EXAMPLES OF ATOMIC STRUCTURE
A-4
Proton The proton has a mass of approximately 1 atomic mass unit and has a charge of +1.
Neutron The neutron has a mass only slightly larger than that of a proton. It may be taken as having a mass of 1 mass unit for the purposes of this text (its mass may be stated as 1+ to indicate that it is slightly more than that of the proton). The neutron has no electric charge. As the nucleus of an atom contains protons and neutrons,
it has a positive electrical charge, and the magnitude of this charge is the same as the number of protons. The properties of these particles are summarized in Table A-1.
TABLE A-1 PROPERTIES OF ATOMIC PARTICLES
PARTICLE CHARGE MASS (amu} Exact Approximate LOCATION WITHIN THE ATOM
Electron -1 0.00055 1 1845 Outside the nucleus
!Proton +1 1. 00728 1 In the nucleus
!Neutron 0 1. 00867 1+ In the nucleus
Figure A-2 shows some examples of atomic structures to illustrate that the atoms of all elements are built up from different combinations of the same three basic particles.
A-2 .4 The A and Z Number System
A shorthand notation has been developed which quickly indicates the exact structure of any atom. The notation is as follows:
A
Z x , in which
X -is a general representation of any element symbol (in each case the appropriate element symbol would be used).
Z -the number of protons in the nuc Ieus.
A-5
A -the number of protons + neutrons in the nucleus.
The Z number is usually called the atomic number. Since the Z number is equal to the number of protons in the nucleus, it is also equal to the number of electrons outside the nucleus in the normal neutral atom. Therefore, each element will have its characteristic Z number. For example, the element sodium will always have a Z number of 11. Conversely, a Z number of 11 will always identify the element sodium.
The A number is often called the mass number. A nucleon is defined as any particle found in the nucleus. The term simply provides a convenient way of referring to both protons and neutrons. Since the Z number represents the sum of the protons and neutrons, it is equal to the number of nucleons. The A number is also called the nucleon number. As the mass of both the proton and the neutron
is approximately one, the sum of protons and neutrons gives the approximate mass of the nucleus (and of the atom since the masses of the electrons are nearly zero.)
The number of neutrons in the atom can be determined by finding the difference between the A and Z numbers. 35 Example: l7C 1
Number of protons in this atom: 17
Number of electrons in this atom: 17
•
Number of neutrons + protons in this atom: 35
Number of neutrons in this atom: 35 -17 =18
Element of which this is an atom: C1 (chlorine).
A-2.5 Isotopes and Nuclides
It is possible for different atoms of the same element to have somewl-at different nuclear structures. These differing atoms of the same element (same Z) are known as isotopes. The difference is in the number of neutrons. For example, there are three known forms (isotopes) of the element hydrogen, two of which are found in nature and one of which is man-made. The structures of these three atomic forms of hydrogen are shown in Figure A-3.
Since two different atomic forms of an element (isotopes) have the same number of protons, they have the same number of electrons, and therefore, they
A-6
will have the same chemica I behavior. Diffr,rences do occur in p~sical properties, however, for example, hydrogen 1 ( 1H ) and hydrogen 2 ( 1H ) are not radioactive, but hydrogen 3 (~H) is radioactive. ·
The three isotopes of hydrogen have become very important in nuclear work. As a result, each has been given a separate name for convenience in identification. These names are:
Hydrogen 1 hydrogen (common)
Hydrogen 2 deuterium
Hydrogen 3 tritium
Hydrogen is the only element for which a special nomenclature has been devised for the different isotopes. For all other elements, th3 different 2.otopes are referred to by the more basic nomenclature; for example, He and He
2 2
are referred to as helium 3 and helium 4, respectively.
The term "isotope" is used only for elements which have more than one atomic form, and when distinguishing the different forms of the same element. Thus, helium 3 and helium 4 may be referred to as isotopes of helium.
Number of protons Element
Hyclrogen Hyclrogen Hyclrogen
H H
Element symbol H
2
Number of neutrons 0 2 3
Number of nucleons 2
Complete symbol 1H
1H1
FIGURE A-3 THE ISOTOPES OF HYDROGEN A-7
The term 11 nuclide 11 should be used when referring to specific forms of different elements. Thus, a statement would read, 11 Two radioactive nuclides commonly used to calibrate radiation instruments are cobalt -60 and cesium 13711 and not 11 Two radioactive isotopes, etc. 11
Since all nuclides are composed of varying numbers of neutrons and protons, they can all be represented by the A and Z number notation. Only certain combinations are possible. Some are observed to be stable, and some are unstable. Generally, the low-Z elements, i.e. the light test elements, are stable when the numbers of protons and neutrons are approximately equal or in a 1 to 1 ratio. As the elements become heavier, more neutrons than protons are found in the stable combinations. Among the high-Z elements, a ratio of 1-l/2 neutrons to 1 proton is found.
A-3 Radioactivity
A-3. 1 Historical Background
Nuclear radiation was discovered in 1896 by a French scientist, Henri Becquerel. Becquerel experimented with fluorescent crystals which, when struck by ordinary white Iight, gave off Iight of some other color, such as pink or green. He thought that he had discovered that certain crystals, when struck by light, gave off some sort of very penetrating rays, different from light rays, which could penetrate thin sheets of paper or metal.
Further research by Becquerel and others demonstrated that the emission of the strange new penetrating rays by these substances (called radioactive substances) was unaffected in any manner by heat, Iight, pressure, chemicals, mechanical force, or any other means then known. Much experimental work has been done in the years following Becquerel's discovery in an attempt to understand these rays.
A-3 .2 Types of Radiation
It was believed initially that only one kind of ray was emitted by radioactive substances. The nature of this ray was unknown. In the experiment depicted in Figure A-4 (a), a sample of radium (one of the few radioactive substances known at the time) was placed at the base of a cylindrical hole drilled in a piece of lead (the figure shows a cross section of the lead block). Since lead has the ability to absorb radiation very effectively, Iittle of the radiation penetrated through the sides of the block. Therefore, there was essentially a straight beam of radiation coming out of the hole. A photographic plate was placed across the path of the radiation, and, upon development, one dark spot showed in the center of the plate.
A-8
In a later experiment, depicted in Figure A-4(b), the beam of radiation was subjected to a strong electrical field. This time there were three black spots on the plate, indicating that the electric field had separated the beam of radiation into three kinds of radiations, as illustrated in the figure. The three types of radiation were arbitrarily identified by the first three letters of the Greek alphabet: alpha (a.) for the radiation attracted to the negative side of the field, beta (S) for the radiation attracted to the positive side of the field, and gamma (y) for the radiation not attracted to either side.
Similar experiments using magnetic fields also produced a separation of the beam of radiation into three components.
Several conclusions can be reached as a result of the illustrated experi
ment. The experiment indicates that: (1) alpha radiation, which was attracted to the negative plate, has a positive electric charge; (2) beta radiation has a negative charge; and (3) gamma radiation, which was undeflected by the electric field, has no charge (is electrically neutral).
Beam of
radiation
+
(a) (b)
FIGURE A-4 PATH OF EMANATIONS FROM A RADIUM SOURCE
A-9
A-4 Properties of Nuclear Radiations A-4. 1 General Properties
•
Alpha Alpha radiation consists of high velocity particles, each with
a charge of +2. Each particle has a mass of 4 atomic mass units, and, thus, each particle is the same as the nucleus of the helium--4(He4) atom. The helium--4 atom has two
2
· protons and two neutrons in the nucleus and two electrons outside the nucleus to balance the charge. If the electrons were stripped away, the resulting nucleus would be identical with an alpha particle. The configuration of two protons and two neutrons is an extremely stable nuclear structure. This helps explain why this structure is emitted from a nucleus in preference to other combinations of nucleons.
Beta The experiment on the separation of radiations showed that beta radiation has a negative electrical charge. Beta radiation is a stream of electrons traveling at high speed. The mass of a beta particle is 1/1845 atomic mass unit and its charge is -1. It is identical with electrons which orbit about the nucleus of atoms except for its speed and origin. Beta particles originate in the nucleus of the atom.
Gamma Gamma radiation has no electrical charge, and appropriate experiments have proved that it has no mass. Gamma radiation is pure energy trove I ing through space at the speed of Iight. It is one example of a general type of radiation termed electromagnetic radiation, which includes radio waves, I ight waves, and X-rays. The type of radiation most similar to gamma radiation is X-rays, which has about the same or somewhat less energy as gamma radiation. The distinction between them is their origin.
X-rays originate in the region of the orbital atomic electrons whereas gamma rays come from within the nucleus.
A-4.2 Specific Characteristics of Electromagnetic Radiations
Electromagnetic radiations are identified by their characteristic wave length (:\)and frequency (v) and their energy (E). These properties are related by two simple formula·e:
A-10
c = A."ll
10
where c = the speed of Iight, 3 x 10 em/sec
A. = wave length, normally measured in centimeters 1
"11 = frequency, normally measured in reciprocal seconds (sec-).
Since c is a constant, frequency increases as wave length becomes shorter.
E = h"W
where E = energy of one photon or quanta of radiation (ev) -27
h = Plank's constant, equal to 6.625 x 10 erg-sec.
-1
"11 = frequency (sec )
Since h is a constant, it is evident that the higher the frequency, the greater the energy of the photon .
Energy of radiation is normally expressed in units of electron volts (eV) or million electron volts (MeV). An electron volt is the amount of energy acquired by one electron movin¥.2through a potential difference of one volt.
One eV is equal to 1 .602 x 10 ergs. The unit of MeV is convenient for the kinetic energy of alpha and beta particles, as these particles usually have energies in the millions of electron volts.
Table A-2 summarizes the properties of the three types of radiation.
A-5 Radioactive Decay
A-5.1 Definition
Certain nuclear structures have excess energy and are thus unstable. Such atoms attempt to reduce their energy content by releasing energy. They do this, in the case of most nuclei, by emitting one of the three types of radiation; alpha,
beta, or gamma.
By definition, radioactive decay is the spontaneous transformation of one nuclide into a different nuclide or a different energy state of the same nuclide. In many cases the 11 unstable nucleus11 does not 11 become stable. 11
A-ll
TYPE OF RADIATION
Alpha
particle
)> I
__.
....,
Beta
particle
Gamma
ray
SYMBOL
4
2a
or
4 He2
0 -1/3
or 0 -1e
00
0
TABLE A-2
PROPERTIES OF RADIATION
MASS CHARACTER-
CHARGE (amu) ISTIC
2 Protons
2 Neutrons
+2 4 (same as
nucleus of
He-4 atom)
-1 1 1845 High speed electron
Form of
0 0 electromag
netic energy
similar to
X rays
EFFECT OF EMMISSION ON PARENT NUCLEUS
Atomic No. Mass No.
Decreases Decreases
2 4
Increases No change
1
No change No change
A-5.2 Nuclear Forces
It may appear peculiar that the nucleus is held together at all. Since I ike charges repel, the electromagnetic (coulomb} forces between protons apparently should cause the nucleus to fly apart. However, the repulsive
coulomb forces between protons are overcome by other forces within the
nucleus. These forces are of very short range and act only between nucleons close to each other. A balance occurs between the attracting nuclear forces and the repelling coulomb forces, and, as a result, the nucleus stays together.
In unstable atoms, this balance is a delicate one. If the repelling coulomb forces should overcome the attracting nuclear forces, part of the nucleus may break off and escape. In other cases, rearrangements within the nucleus, which lead to more stable configurations, may take place without the loss of particles.
Nuclides whose nuclei undergo this process, are said to be unstable or radioactive.
A-5.3 Modes of Decay
The configuration of the helium nucleus is extremely stable. This leads to its ejection from a nucleus as a unit. The off-going alpha particle has kinetic energy. The energy of the nucleus which emits the alpha particles
is decreased by the amount of the kinetic energy imparted to th~ particle.
It is not so easy to visualize how a beta particle can be emitted from a
nucleus. The statement that beta radiation comes from the nucleus, but that there are no electrons in the nucleus, appears to be a contradiction. The accepted explanation for this results is that it is possible for a neutron to split
into a proton and electron. If this splitting occurs, the electron is then ejected
from the nucleus with speed (kinetic energy) with a corresponding reduction of energy of the nucleus. Nuclei may release gamma radiation as a means of decreasing their energy content. Since gamma radiation consists of pure energy,
its emission reduces the energy of the nucleus by the energy magnitude of the
emitted y-ray. This emission of gamma radiation accompanies a rearrangement
of nuclear particles. It does not involve a change in the number or kind of
nucleons in the nucleus. It often occurs concurrently with beta emission.
A-5 .4 Measurement of Activity
A particular radioactive nucleus may decay at any time, or it may never decay. When large quantities of these radioactive atoms are present, however, probability of decay can be expressed statistically in terms of the disintegrations
taking place per unit of time. Radioactivity, or activity, is the spontaneous decay or disintegratioll of an unstable atomic nucle~s. A unit of measurement of activity is the curie which is defined as 3. 7 x 10 °disintegrations per second.
A-13
Mathematically, activity is expressed by the equation:
A= aN
where A= activity in disintegrations/sec.
N = number of radioactive atoms present
a= decay constant, expressed in terms of reciprocal time.
A-5.5 Decay Formula
When the formula expressing activity is integrated as a function of time, the following relation, which can be verified experimentally, is obtained:
N = N e-at
0
where N = number of radioactive atoms present at any time, t
N = number of radioactive atoms present at time t=O
0
a = decay constant
t = time interval between times t and t = 0
e = the base of the natural logarithms, a constant
•
Examination of this expression shows that although the number of radioactive atoms present, and thus the activity, decreases with time, it never reaches zero. If intensity is plotted on the logarithmic axis of semi logarithmic paper, against time on the linear axis, then a straight line results.
A-5 .6 Half-Life
Half-life is defined as the elapsed time required for the activity to decrease to one-half its original value. As shown by the equation, A =aN, the activity is directly proportional to the number of radioactive atoms present. Thus, the
half-life can also be defined as the time required for the number of particular radioactive nuclides to decrease by half. For example, iodinet-128 has a half
life of 25 minutes. :
Half-lives vary for radioactive isotopes of a single eleme:nt and for rad~active nuclides of different elements. Some are extremely short, such as 10seconds for astatine -215, while others are quite long, as 7.1 x108 years for
A-14
uranium -235. The half-life of a radioactive isotope is constant and is independent of the amount of radioactive atoms present or the age of these isotopes.
A-6 Artificially Induced Nuclear Reactions
A few radioactive nuclides are found in nature. Many other radioactive nuclides are found in nature since the advent of the nuclear age and nuclear weapon testing. Normally, artificial reactions in atoms are induced by firing nuclear particles at a target containing that type of atoms. The nuclear particles used as projectiles are made to move at great speed (with great energy) by the use of machines called particle accelerators. The following are particles most commonly used as projectiles:
4
Alpha particle He
2
os
Beta particle
1 1
Proton H , nuc I eus of the hydrogen -1 atom.
1 Deuteron fH ,nucleus of the hydrogen -2 (deuterium)
atom.
Some typical examples are given below to indicate the general nature of artifically induced nuclear reactions.
A I pha -neutron type:
9 4 1n 12 0
Be + He ---+ + energy
4 20 6
Alpha-proton type:
14N + ~He -----1H + 170 + energy
7 1 8
Neutron-gamma (radiative capture) type:
lH + 1 -----2H + oo +energy
1 on 1 0
It should be understood that in each of the reactions-shown above, the particle or ray emitted, such as a neutron, proton, or gamma ray, is emitted almost instantaneously when the reaction takes place-Eor instance, in the last example above, the equation does not mean that fH ,in this case, is
stable. In other cases, the product may be radioactive. Thus, the product nuclei may continue to emit radiation. A-15
208-401 0-76 -20
A-7 Fission and Fusion
Two artifically induced nuclear reactions which are of great importance are the two used in nuclear weapons, fission and fusion.
A-7. 1 Fission
The process of fission involves the splitting of very large nuclei, such as those of uranium--235 or plutonium--239, into much smaller nuclei. This splitting releases a vast amount of energy, judged by ordinary standards of comparison, such as the burning of coal or gasoline. Fission could take place spontaneously, but it is initiated deliberately by directing a stream of neutrons into a mass of uranium or plutonium which is properly arranged and is of the proper size. If an atom of fissionable material captures a neutron, it may fission into two smaller pieces. The fission of just one nucleus releases only a tiny amount of energy--too little to be measured by conventional means. However, even a small amount of material contains a vast number of atoms. When the small energy release from one fission is multiplied by the number of fissioning atoms, the total energy release is enormous.
There are different reactions which can occur in fissioning. Not every atom which fissions forms the same product nuclei. A few examples of fission reactions known to occur are the following:
+ + energy
+ + energy
A generalized equation can be written to represent the fission process
11 FP 11
making use of the symbol to stand for any fission product. This equation is:
+ + energy.
The energy released in any nuclear reaction, such as the genera Iized fission reaction above, comes from the conversion of mass into energy. If one were to add up the measured masses of the materials on the right side of this equation and those on the left side, he would find that the total mass on the right is less than the total mass on the left. Some mass appears to have been 11 1ost. 11 This mass has been converted into energy. Einstein predicted, as early as 1905, that mass and energy could be interconverted and that the
2
relationship between them was given by the equation E =mc , wherein E = energy equivalent to mass m, m '= mass equivalent to energy E, and c =
A-16
the speed of light. Calculations with this equation show that a very small amount of mass is equivalent to a large mount of energy. This conversion of mass into energy provides the enormous energy release from nuclear weapons.
In the generalized fission reaction equation presented above, there are two neutrons released for every one that enters. This figure of two neutrons released is a rough average for the whole set of possible fission reactions. The release of additional neutrons in the fission reaction permits the development of the chain reaction which occurs in a fission Weapon or a nuclear
reactor. Each neutron released is potentially able to produce another fission. Since each neutron which produces a fission leads to the release of approximately two (2 .46) more neutrons, the number of fissions in each step (generation) of fissions is greater than the number in the preceding generation. Thus, the reaction builds up until the energy release is sufficient to destroy the casing of the weapon and detonation takes place.
A-7.2 Fusion
A process which is the exact opposite of fission is also capable of releasing
great quantities of energy. This process occurs at the lower end of the scale of elements and involves uniting two small atoms into one larger atom. This is the fusion process. Although numerous reactions are possible, the equation
which follows will illustrate the nature of the reaction:
2 4
+ H -----He + energy
1 2
On a basis of weight of fuel necessary, this reaction produces several times the energy release of fission and does not produce residual radioactive products.
A-8 Chain Reaction-Criticality
The release of two or more neutrons at each fission makes the chain reaction possible. In order to create a chain reaction, certain conditions must be satisfied. If one of the atoms in a piece of fissionable material (u235) is caused to fission by bombarding it with a neutron, the two neutrons produced by the fissioning could do one of three things:
(1)
Strike other uranium nuclei and cause them to fission.
(2)
Pass between the uranium atoms and completely escape from the piece of material without causing any further fission (Atoms are largely empty space.)
A-17
(3) Strike nuclei (uranium or impurities) and neither cause fission
nor be captured.
~scape
\ ®
FIGURE A-5 NONSUSTAINING CHAIN REACTION IN A SUBCRITICAL MASS
For a chain reaction to occur, at least one of the neutrons produced per fission must strike a uranium nucleus and cause another fission to occur. In order to make this happen, escape and nonfission capture must be minimized. Nonfission capture may be minimized by using very pure fissionable material, because impurities tend to capture the neutrons and prevent fission. Escape may be minimized by having sufficient fissionable material ~vailable.
To visualize this, one may imagine a small, one-inch, spherical piece of fissionable material in which a fission occurs. There are relatively few nuclei available within the fissionable material that the two neutrons produced by the fission may hit before they escape. Therefore, the prob~bility of their striking other fissionable nuclei is very slight. If one of the neutrons happens to strike a nucleus and causes it to fission, the probability of one of the second pair of neutrons striking a nucelus before escaping i~ very slight.
A-18
Therefore, the reaction will quickly die down. A reaction of this type is called nonsustaining. A piece of fissionable material such as this is called a subcritical mass (Figure A-5).
Escape
if n/
/
Fifth Fission
E;9
8
FIGURE A-6 SUSTAINING CHAIN REACTION IN A CRITICAL MASS
If more material is added around the sphere, the neutrons have more nuclei which they may hit before they escape, and the probability of their striking nuclei is much greater. If enough fissionable material is present so at least one neutron from every fission strikes another nucleus and causes it to fission, the reaction will continue in a steady manner and is called a sustaining chain reaction (Figure A-6). A piece of fissionable material in which a steady reaction occurs is called a critical mass. Energy is released in a steady controllable manner such as in a nuclear reactor used for producing power.
If still more material is added to the sphere, more than one neutron per fission may strike a nucleus to cause further fission. When this occurs, the chain reaction will increase very rapidly and is called a multiplying
A-19
chain reaction (Figure A-7). This is known as supercritfcal mass. The energy is released very quickly and cannot be controlled.
\
SURFACE
// ///////////////:8/////////
235u -
J!)"' ',
N
-®~--€)---9-@
I
0 '0
A __ ®-~~N
~ ~~'C\
" " u
", 0.
®, B
~
'N ~~
N -~@
FIGURE A-7 MULTIPLYING CHAIN REACTION IN A SUPERCRITICAL MASS
A-9. 1 Introduction
Nuclear radiations are attenuated by passage through any mass. The amount of attenuation is dependent on the types and thickness of the mass and the form and energy of the incident radiation. Further, there are several different ways in which radiation is attenuated, and there is a wide range of effectiveness of specific elements for stopping different types of radiation.
A-20
•
A principle attenuating action is absorption, or capture, of the particles alpha, beta, or neutrons. This process results in ionization which destroys living cells but also permits ready detection and measurement of the radiation. Alpha and beta particles are readily attenuated and are, consequently, of no concern in shelter analysis. As neutrons are not emitted by fa Ilout, fallout radiation attentuation is concerned only with gamma rays. The reaction of alpha and beta particles is important, however, for a full understanding of gamma ray attenuation.
A-9.2 Interaction Between Alpha Particles and Matter
An alpha particle moving through matter faces a vast number of atoms
along its path. Figure A-8 illus'r~tes an interaction between an alpha particle and an atom of carbon--12 ( 6 C) as might occur in wood. The normal, neutral carbon atom with the alpha particle approaching it is shown in A-8a. When a positively charged particle, such as an alpha particle, is in the vicinity
•
of a negatively charged particle (an orbital electron), there is a strong force of attraction between the two particles. As a result of the attractive force, an electron may be pulled out of its orbit (this does not happen with every atom near which the alpha particle passes) and be released as a free-moving electron traveling at a considerable speed. If this occurs, th~ carbon atom is no longer electrically neutral, since it has six protons in the nucleus and only five electrons outside the nucleus. The atom has a net charge of +1, and, thereby, is a positive ion . .A positive ion is an atom with a net positive charge as the result of the removal of electrons from the neutra I atom. Although, strictly speaking, the electron which was removed from the atom is not an ion,
it is customary to refer to it as an ion in this context, because it is a dnrged particle. Production of ions is termed ionization. The atom, which has become ionized, and the electron that was removed are referred to as an ion pair. The ionization process and the terms used are illustrated in Figure A-Sb. A-9 .3 Energy Considerations in Ionization There is an attractive force between the electrons and the nucleus of an atom. Therefore, if the alpha particle is to "pull" an ele.ctron away from the atom, it must exert sufficient force to overcome the attraction of the nucleus. The alpha particle expends some of its energy in doing the work of removing the electron. In addition, it imparts energy to the electron which appears as kinetic energy (energy due to motion) of the off-going electron. Each time an alpha particle causes an ionization, it loses a little of its kinetic energy. As a result, its speed decreases continuously until, finally, it reaches equilibrium with other atoms in the matter and picks up two stray electrons to form a neutral helium atom. The distance from the source at which the alpha
A-21
a (+2)
A 88~
\0 0 8
e
Positive Ion
1
1 2 C Atom before ionization 6 2C Atom after ionization
6
FIGURE A-8 INTERACTION OF ALPHA PARTICLE WITH ORBITAL ELECTRONS
particle ceases to produce ionization is called its range. The range differs
with different absorbing materials and with varying initial energies of the alpha particle.
In summary, the ultimate result of the passage of alpha particles through matter is ionization. The alpha particle is not usually absorbed but becomes a heIium atom after loss of its energy to electrons.
A-9 .4 Interaction Between Beta Particles and Matter
When a negatively charged beta particle passes close to a negatively charged electron in passing through matter, there is a force of repulsion between the two electrons. This force of repulsion may push the orbita I electron out of its position in the atom. If the electron is pushed out of the atom, an ion pair is formed. Each time an ionization occurs, the beta particle gives up energy in the form of~work, to remove the electron from its orbit,
and in the form of the kinetic energy of the displaced electron. As a result, the beta particle slows down until it reaches equilibrium with its environment.
A-22
The distance from the source at which this occurs is the range of the beta
particle. The range of the faster, smaller beta particle is much greater than that of an alpha particle of the same energy. Note that, although the mechanism is somewhat different from that for alpha radiation, the net effect of the interaction of beta radiation with matter is the same, transfer and loss of energy through ionization.
A-10 Interaction of Gamma Photons With Matter
A-10. 1 General
The mechanisms by which gamma radiation produces ionization differ appreciably from those of alpha or beta particles. Gamma radiation has neither charge nor mass. The results of some experiments with gamma radiation can best be explained by considering that it is a wave which transmits energy through space. However, the results of experiments, such as those involving interaction between gamma rays and atoms, can best be explained by considering gamma rays to consist of a stream of tiny bundles of energy. Each bundle has
zero mass but is able to produce effects as though it were a particle. Each of these little "bundles" of energy is termed a photon, or quantum, of radiation. This dual wave-particle nature of electromagnetic radiation has been found to be a satisfactory explanation for the various possible interacti01s of electromagnetic radiations with matter and with electric and magnetic fields. The principle gamma photon-matter interactions are: (1) photoelectric effect;
(2) Compton effect; and (3) pair production.
A-10 .2 Photoelectric Effect
In the photoelectric effect, a gamma photo is completely absorbed by an orbital electron. This electron has an increased kinetic energy and escapes the atom thereby creating an ion pair. This effect is illustrated in Figure A-9.
The electron behaves as a beta particle and can cause further ionizations by repelling electrons out of the orbits of other atoms. The original ionization produced by the gamma photon is called primary ionization. The ionizations produced by the freed electron are called secondary ionizations. (Similar statements apply to electrons released by alpha and beta particles.) The secondary ionizations are much more numerous than the primary ionizations when gamma interact with matter.
A-10.3 Compton Effect
Under some conditions, an incoming photon is not completely absorbed by the electron, but continues as a lower energy gamma photon. This effect,
A-23
8
FIGURE A-9
PHOTOELECTRIC EFFECT
8
FIGURE A-10
COMPTON EFFECT
8
FIGURE A-11
PAIR PRODUCTION
A-24
illustrated in Figure A-ll, is the Compton effect (after Dr. Arthur H. Compton). As in the photoelectric effect, the off-going electron may produce many further ionizations. The remaining lower energy photon may undergo further Compton effects, but the last interaction resulting from it (the one in which the lowenergy photon is completely absorbed) must be a photoelectric effect. Most of the "skyshine" and wall scatter components of radiation involved in fallout shelter analysis are a result of Compton scatterings. Two important characteristics of Compton scatter are: (1) the resultant photon and beta particle have a tendency to travel in the same direction as the origina I gamma photon, and
(2) the greater the angle of scatter, the greater the energy loss of the gamma photon.
A-10 .4 Pair Production
The principle third interaction of gamma photons with atoms differs considerably from the photoelectric and Compton effects. If a photon with energy greater than 1.02 MeV passes close to a large nucleus (such as that of lead), it can be converted into two particles, an electron and a positron (shown in Figure A-ll). The positron is a particle identical with the electron in mass but with a positive electrical charge. The photon is eliminated in the process, as all of its energy is converted into the mass of the 1'\yo particles and their kinetic energy. Previously, the equivalence between mass and energy and the conversion of mass into energy in processes of fission and fusion were discussed. In pair production, the reverse process takes place in that energy is converted into mass. The created electron and the positron are capable of producing ionizations in their paths. The electron behaves as a beta particles, and the positron behaves in a somewhat similar manner, but with a positive charge. The positron is not a stable particle. When it loses most of its kinetic energy, it combines with an electron to produce two 0.5l(MeV)photons annihilating both particles. These characteristic 0.51 MeV photons which travel in 180° opposite paths are called "annihilation radiation. 11
A-10 .5 Summary of Gamma Photon Interactions
Although ionization is not the immediate result of pair productions, it is the eventual result. Thus, the three principle effects, photoelectric, Compton, and pair production, cause ionization ofatoms in the material through which the gamma photons pass. The probability of occurence of any of these events is a function of photon energy and absorber density and atomic number. Photoelectric absorption is most prominent with low energy photons in absorbers of high atomic number. Compton scattering predominates with intermediate photon energies (about 0.5-1.5 MeV) in absorbers of low atomic numbers. Pair production is significant with high energy photons in absorbers of high atomic num
A-25
ber. Compton scattering is the pri~cipal mechanism of attenuation in fallout shelters, since photon energies are in the intermediate range and most construction materia Is are made up of I ight elements.
A-ll Attenuation of Neutrons
Neutrons, having no charge, do not cause ionization directly. Instead, ionization results indirectly from several processes, some of which are outlined below:
(1)
Neutrons are capable of striking the nuclei of small atoms, such as hydrogen, and knocking these nuclei free of the orbital electrons. For example, if the nucleus of a hydrogen atom (a proton) were knocked free with a great dea I of energy, it would cause ionization in the same manner as an alpha particle. This is the principal cause of biological damage from neutron radiation.
(2)
Neutrons may be captured by nuclei with the instantaneous emission of gamma photons as described in Article A-10. These photons can cause ionization in the same fashion as any other gamma photon.
(3)
Neutrons may be captured by nuclei, in an object bombarded by neutrons, to form new isotopes of the original elements. These new isotopes are generally unstable (radioactive) and give off beta and gamma radiation. These will cause ionization in the manner already described.
Since there are no neutrons in fallout radiation, they are not a factor in fa IIout shelter analysis. Neutron radiation must be considered, however, in design of shelters to protect against initial effects.
A-12 Attenuation of Gamma Photons
A-12. 1 Narrow Beam Attenuation
Attenuation Formula: Gamma photons are absorbed in "one shot" processes so that any single photon may be absorbed at any point or not be absorbed at all. Gamma ray attenuation is thus based on probabilities of photon interaction. The result is a mathematical expression similar to that used for radioactive decay.
If a narrow beam of parallel gamma rays of a single energy level (monoenergetic) are passed through an absorber, the beam intensity (I) can be expressed as a function of absorber thickness (X) in the following expression:
A-26
where I = intensity of the beam after passing through a thickness X of
absorber
I0 = original intensity
X = absorber thickness
e = base of the natural logarithms, a constant
J.1 (mu) = the linear absorption coefficient
A-12 .2 Linear Absorption Coefficient
The linear absorption coefficient, J.l, in the equation of article A-12. 1,determines the rate of reduction with absorber thickness of the intensity of thebeam. It can be obtained experimentally and is a function of both absorbermaterial and the energy of the incident radiation. It increases with increasingdensity and atomic number of absorbers and decreases with increasing gammaenergies. Tabulations and graphs of absorption coefficients may be found inreferences, such as the RADIOLOGICAL HEALTH HANDBOOK.
A-12.3 Graphical Representations
Use of the Iinear absorption equation is awkward due to its exponentialform. It is usually more convenient to plot the results for a particular absorberand radiation on a semi-logarithmic graph on which the function reduces to astraight line with a slope equal to].l . An example of such a plot is presentedin Figure A-12. Note that the ratio, 1/10 , is plotted so that results are readin terms of a fraction of the original intensity. Problems can be readily solvedfrom such a plot, while their algebraic solutions would present difficulty dueto the exponents and logarithms involved in the formula.
A-12 .4 Broad Beam Attenuation
The formula for absorption, 1/1 0 =e-J.l x, is valid only for narrow beamsof mono-energetic photons moving parallel. Any effect which scatters a photonfrom the beam removes it from consideration. In a more realistic situation, asin the experiment illustrated in Figure A-13A, scattering events add to theradiation received by the detector, thus increasing the intensity for a givenabsorber thickness over that W, ich would be expected in the narrow beam situation. To account for this increase, a buildup factor is added to the equation: A-27
., ,
r~-:_t-r-=-~
--~ I'-1---
--~ I~--l--
~~£~1 \....t-
.....___
Radiation Source ::::::::::·
'
J
Barrier
iRadiation Source Collimator Barrier Collimator Detector
(A)TEST ~GEMENT
(A) TEST ARRANGEMENT
MASS THICKNESS,X(psf)
1.0'
)>
I MASS THICKNESS,X(psf) Q.5 00
"" ISO 200 250 300 350
5.0 1001.0
..... ,~
~ I G.2
~+-.0 0.5
'~ ...~
i ~ 0.
~ 0.2
r.:l
... '0 Jl. =e].lt I i ~
~ 0. I \"\ ~"' -~< 0.05
r.:l . 1\. IComlt-60
~ 0.051 \ ""\ 1< 1.25 MevJ'..--+---+--+---+---4f-
<
1 0.02
0.02,·__1 ~~~--~~~~~~--r-+-~~-r-+~~
lo.67 Mev1 \ '\
0.0.0
' 18 1a 20 22 24 28 2a 2 4 8 8 10 12 14 18 II 20
I 2 8 a 10 14
0·0·o 4 12 THICKNESS OFCONCRETE,t(inches) THICKNESS OF CONCRETE, t(inches)
(B) TEST RESULTS (B) TEST RESULTS
FIGURE A-12 FIGURE A-13NARROW BEAM TEST
BROAD BEAM TEST
-l.lx
1/1 = Be
0
in which the symbols are the same as in the narrow beam equation with the
addition of the buildup factor, B. The buildup factor, a function of absorber material and gamma energy, can be determined experimentally or, in some cases, developed theoretically. Note that in the case presented in Figure A
13B, the curve departs slightly from a straight line.
A-12 .5 Effect of Distance
Consideration is given to a point source of radiation in a vacuum emitting So photons/sec in all directions. If there is an imaginary sphere of radius R1 about the point source (Figure A-14), S0 photons/sec will pass through the
surface of the sphere.
FIGURE A-14
EFFECT OF DISTANCE
A-29
If S1 photons/sec pass through a unit area of the sphere,
s
For a largersphere with radius R,
2
If S is eliminated by combining the above equations,
0
R 2
2 R 2
1
The last equation states that intensity is inversely proportional to the square of the distance. This is the inverse square law which applies to many physical situations.
A-12 .6 Combined Effects of Absorber and Distance
If a point source is in an infinite medium, rather than in a vacuum, the
•
intensity will vary with distance due to both absorption and inverse square law. The equations governing both effects can be combined in a general expression using r as the distance from the source:
I
T = 2
0 4n r
Contribution of point sources can be integrated to develop functions for plane sources in special situations of geometry. This has been done in developing the
curves for the system of analysis presented in this text.
A-30
APPENDIX B
TABLE OF MASS THICKNESSES*
The following table gives the weight, in pounds per square foot, for the more common types of building materials. These weights are based on the best available data. Variations in weight exist from one section of the country to another as they do from one manufacturer to another. Where plans and specifications show a particular manufacturEr's product, the manufacturer's weights should be obtained and used. For materials not shown in this table, weights from any standard structurai or architectural handbook will be acceptable.
t-LJ\TERIAL WEIGHT (P.S.F.) Acoustical Tile
Applied directly with mastic to ceiling
Attached to rock lath and furring channels
Attached to wood furring strips
Adobe
12" wall ll6
Asbestos
Board, 3/16" 2
Corrugated 4
Asphalt Bituminous Paving
"Black Top", 1 inch 12
Brick
4" Common 40 4" Pressed 47 4" Modular 37
611
SCR 53 811 Hodular Wall 78 10II Hodular Cavity Wall 74
1211
Hodular Solid Wall 120 16 II Modular Solid Wall 160 {f II
c'1odul ar Brick· with 411 structural clay tile back-up 68 with 6" structural clay tile back-up 73 with 811 structural clay tile back-up 76 with 12'' structural clay tile back-up 88
L;" ~\odul.ar Brick with 4" hollow cinder concrete block 65 ~.;i th 4" hollow lightweight concrete block 57-63
•-~------------------------------------------------------------------------~ *From TR-68, Mass Thickness Manual for Walls, Floors, and Roofs
B-1
20B-401 0-76-21
MATERIAL
Brick (cont.)
4" Modular Brick with 4'' hollow cinder concrete block with 4" hollow lightweight concrete block with 4" hollow medium weight concrete block with 4" hollow standard weight concret'e block
4" Modular Brick with 6" hollow cinder concrete block with 6'' hollow lightweight concrete block with 6" hollow medium weight concrete block
ave~age weight with cores fully grouted with 6" hollow standard weight concrete block average weight with cores fully grouted
4" Modular Brick
·with 8" hollow cinder concrete block with 8" hollow lightweight concrete block with 8" hollow medium weight concrete block
average weight with cores fully grouted with 811 hollow standard weight concrete block average weight with cores fully grouted
4
11
Modular Brick with 1211 hollow cinder concrete block with 1211 hollow lightweight concrete block with 12" hollow medium weight concrete block
average weight with cores fully grouted with 12" hollow standard weight concrete block average weight with cores fully grouted
Built-Up Roofing
3 Ply felt composition, no gravel
5 Ply felt composition, no gravel
3 Ply felt and gravel
5 Ply felt and gravel
Ceramic Tile
5/16" Glazed Wall Tile with 111 mortar bed with organic adhesive on ~~~ gypsum board with thin-set mortar on ~" gypsum board with epoxy setting mortar on ~~~ gypsum board
5/1611 Mosaic Floor Tile
with l" mortar bed
Paver Tile
3/8" thick
1/2" thick
WEIGHT (P.S.F.)
65 57-63 61-68 68-79
73 64-68 70-74 99 82-87 118
82 68-72 75-80 120 89-96 135
104 75-84 84-95 161 101-118 183
3
4
51:2
6~
3 12
5!,;
5~
6
21:2
ll~
4 6
B-2
~-------------------------------------------------------------------~
NATERIAL WEIGHT (P.S.F.) Ceramic Tile (cont.)
Quarry Tile 1/2" thick 6 3/4" thick 8~
Clay Tile
Hollow clay partition tile 3" thick 16 4" thick 18 6" thick 25 8" thick 30 10" thick 35
Structural facing tile, partitions 4" thick 30 6" thick 47 8" thick 60
Terra cotta wall tile 4" thick 25 6" thick 30 8" thick 33 10" thick 40 12" thick 45
Concrete
Cinder, reinforced, 1 in. 9 Slag, plain, 1 in. 11 Stone, plain, 1 in. 12 Stone, reinforced, 1 in. 12~
Concrete, Lightweight
Aerocrete , 1 in. 4-6~ Haydite , 1 in. 7-8~ Nailcode , 1 in. 6~ Perlite , 1 in. 3-4 Pumice , 1 in. 5-7~ Vermicul~te , 1 in. 2-5
Concrete Block (C.M.U.)
Cinder block 4" 22 6" 30 8" 39 12" 61
B-3
MATERIAL WEIGHT (P.S.F.) Concrete Block (cont.)
Hollow lightweight concrete block (754t/ c u • f t • ) 4" 14-20 6" 21-25 8" 25-29 12" 32-41
Hollow medium weight concrete block (954f/cu.ft.) 4" 18-25 6" 27-31 6" with cores fully grouted 56 8" 32-37 8" with cores fully grouted 77 12" 41-52 12" with cores fully grouted ll8
Hollow standard weight concrete block (135#/cu. ft.) 4" 25-36 6" 39-44 6" with cores fully grouted 68 8" 46-53 8" with cores fully grouted 92 12" 58-75 12" with cores fully grouted 140
Concrete and Hollow Clay Tile Floor System
(One-Way Concrete Joists)
16" wide tile and 4" wide concrete joists
4" deep with 2'' topping 52 5" deep with 2" topping 56 6" deep with 2" topping 62 7" deep with 2" topping 67 8" deep with 2" topping 7l 9" deep with 2" topping 75 10II deep with 2" topping 79
I Curtain Walls
I
l
I Insulated panels -aluminum 3 I Insulated panels -steel 3l:i-l2
i
l
, Fiber Board
~ l:i" thick l
!
L__
MATERIAL WEIGHT(P.S.F.) Fiber Sheathing .1:2" thick l
Glass
~" Plate 3.1:2 .1:2" Plate 6.1:2 Window l Block 18-20
Gypsum
Block2" Solid 11.1:2 3" Hollow 10-12 4" Hollow 13-15.1:2 6" Hollow 17-22 ·Gypsum, 1" plain, in mineral form 4
Poured gypsum on steel rails per inch of thickness 5
Roof planks2" thick 12
Wall bo~Td or sheathing (~" sk~etrock) 2
Insulation
Bats, blankets, 1 in.
Cork board, l in.
Fiber glass
Foam glass
Rigid insulation boards
Metals
Plate steel, lin. 41 Corrugated steel sheets, 20 ga. 2 Steel panels, 18 ga. 3 Leadl" 59 ~II 29 ~II 14 Movable steel office panels 5 Steel decks (without insulation or finish) 2-20~
B-5
~---------------------------------~~·------------------------------~
MATERIAL WEIGHT (P.S.F.) Mortar
1" thick 9
Plaster
plaster, portland cement, sand, 1" thick 8 plaster directly applied, 3/4" thi.ck 6 plaster on fiber lath, 1/2" thick 5 plaster on gypsum lath, 1/2" thick 6 plaster on metal lath, 3/4" thick 6 plaster on wood lath, 3/4" thick 5 plaster on suspended channels and metal lath, 1" thick 10 Stucco, 1 inch 11 7/8" stucco on metal lath 10 3/4" stucco on wood lath 9
Precast Concrete Planks Doxplank 4" thick 20 with 1-5/8" concrete topping 40 6" thick 35 with 1-5/8" concrete topping 55 8" thick 45 with 2" concrete topping 69 10" thick 55 with 2" concrete topping 79
Spancrete 4" thick 30 6" thick 45 8" thick 60
10" thick 75 12" thick 90
Flexicore
Standard weight
6" thick 45 with 2" concrete topping 70 8" thick 53 with 2" concrete topping 78 12" thick 68 with 2.1:1" concrete topping 100
Lightweight
6" thick 35 with 2" concrete topping 60 8" thick 43 with 2" concrete topping 68 12" thick 55 with 2.1:1" concrete topping 87
B-6
MATERIAL
Shingles Asbestos, 5/32" Asphalt strip shingles Tile, cement flat Tile, cement ribbed Tile, clay mission Tile, clay shingle type Wood
Slate 3/16" 1/4"
Soils Clay and gravel, 1 inch Earth, dry and loose, 1 inch Earth, dry and packed, 1 inch Sand or gravel, dry and loose, 1 inch
Stone Masonry Cast stone, 1 inch Granite ashler, limestone, marble, 1 inch Sandstone, 1 inch
Terrazzo 1" 1~" on 1" mortar bed 1" on 2" concrete bed
Wood
3
11
creosoted blocks on ~~~ mortar bed
2" creosoted blocks on ~~~ mortar base
3" creosoted blocks on 1/8" mastic bed
1/811
2" creosoted blocks on mastic bed 25/32" hardwood floor 3/4" sheathing, yellow pine 3/4" sheathing &. sub-flooring, spruce, hemlock, fir 7/8" sheathing, white pine siding
6" bevel
8" bevel
shingles
6~" to weather
plywood
5/16" finished
1/2" finished
3/8" sheathing
WEIGHT (P.S.F.)
2
3 13 16
13~
8-16
2~
7
9~
8~
6 8 7
12 13
11
13
28~-30
38
21
12 9 3
3~ 2~ 2~
1
1~
1
1
1~
1
'-----------------------·-------------------·------------------------------~
B-7
•
TR-20 (Vol. 1, App. C)
APPENDIX C Standard Method Charts
C-2 Chart 1B Limited Field Solid Angle Fraction Chart 1A Solid Angle Fraction
C-3 Chart 2 Geometry Factors, Scatter and Skyshine C-4 Chart 3A Geometry Factor, Direct ( W = 0 to 0.9) C-5 Chart 3B Geometry Factor, Direct (W = 0.9 to 0.99) C-6 Chart 4 Shape Factor C-7 Chart 5 Scatter Fraction C-8 Chart 6 Exterior Wall Barrier Factor
C-9 Chart 7 Interior Partition Attenuation Factors c-10 Chart SA Ceiling Attenuation Factor c-11 Chart 8B Floor Attenuation Factor c-12 Chart 9 Overhead Contribution c-13 Chart 10A Limited Field Barrier Factor (2 w s = 0.002 to 0.8) c-14 Chart 10B Limited Field Height Factor (2W s = 0.8 to 1.0) c-15 Chart 11 Passageways and Shafts c-16
1.0 .7 .5 .4 .3 .2 0.1 .07 .05 .04 .03 .02 0.01
10. 10 .
_l
~
~ 7.
J1"
'~
I
;:':
7.• i+ I f=
5. ' ' I I t::; 5.
' \I I I ~
' \ .I I I
~
'Q.~.y c:=
~
\~
3. ~ 3.
=
,=
I "'. ,, "+
f=l::~
2.
~>;
i=t=-! 2.
ii I· ll' · i'; ' lit,, I;
;q
,1 !"" ,,,, No;;.
H ~!l
j; i': !, '!I :--
i i
I•' I !j ~ I I, I;::
1.0 I .. ,,, . 1.0
• 11
.;T
~q
...J .7
.7
-... ··o-<~
N
' .
::t
.5 .5
1
(!) •
z ~--,,
w ~~~
~u
...J 0 ~
.3 .3
jj
1
rc;
w
0
:::> ~
1-.2 .2
' i: l' ... r";;."
j:::
I·'
...J 'J [ I
r
f···~
<{
;ll: :! I
..... I I: i I i i '· '
:t:' ii.
I I d1 ' '
iLU'I, L L i il .I~ l! if "
' 0.1
0.1
.07 .07
.. -.:1··
I
+N
.05 .05
.03 .03
'II
~ +t-·
::.:::;~
~P-...
I, I .02
.02 'i!. 'l;;;i\ \'\:
:"N
li_l .N. .•..
-~ il " f)s
i 111
'!
0.01 !' ' 0.01
""'
1.0 .7 .5 .4 .3 .2 0.1 .07 .05 .04 .03 .02 0.01
WIDTH TO LENGTH , W/l
CHART1 A
SOLID ANGLE FRACTION,w(W/L,Z/L)
c -2
0.1 0.2 0.3 0.5 2 3 5 7 10 20 30 50 100
0.997
0.996
0.995
0.994
0.993
0.992
0.991
0.990
"'
3
N
z
0.98
0
6
<(
a:
u.. 0.97 w
...J
(!)
0.96
z
<(
0.95
Cl
...J
0 0.94
(/)
0.93
Cl
...J
w 0.92 u.. 0.91 Cl 0.9
w
I
~
:J
0.8
0.7
0.6·-
0.5
0.4
0.3
0.2
0.1
0.0
0.1 0.2 0.3 0.5 2 3 5 7 10 20 30 50 100
LIMITED FIELD WIDTH TO HEIGHT, Wc/H
CHART 18 LIMITED FIELD SOLID ANGLE FRACTION, 2W5 C-3
300 500 1000
300 500 1000
0 . 1 .2 .3 .4 .5 .6 . 7 .8 .85 .90 .93 .95 .96 .97 .98 .99
1.0 .9 .8 .7 .6 .5
.4
.3
.2
(/) a: 0 1u <( LL >a: 1w :2 0 w (.!) 0.1 .09 .08 .07 .06 .05 .04 .03
.02
0.01 llill#!#l#t .009 .008 .007 .006 .005
.004
0.003 0 .1 .2 .3 .4 .5 .6 .7 .8 .85 .90 .93 .95 SOLID ANGLE FRACTION,w .96 .97 .98 .99
CHART 2 GEOMETRY FACTORS· SCATTER, G5( W) AND SKYSHINE, Ga( W) C-4
0 .1 .2 .3 .4 .5 .6 .7 .8 .85 .90 100
~ j;:;:
:
90
80
'
70 ''
' '
60 ~a
50
1.!
. I l::lft··t
40 !1.. ~ :
'"' i=
,,, tg.~
,, i 1..
....... li' ,, I I 30 Wt11 ,g ' 1-
I 1$ Ill II,.,
LU ,~
t:±_~
l? 20 ffim :c
I
'r.
1:
I( :_1''"'
; i I jl,
-~~.
! i I I 11
I, f1-' : '
.
i'
i-\:-~~~
! .j ..I 'I 1-
I I . .
II i
,, H
'j
ll I -~
'
II II 11 ' I '
10
I ±=
9
h+
,, WI
8 I,
7 ' :'
6
5 :
4
I II
I
_..., I!
3
0 .1 .2 .3 .4 .5 .6 .7 .8 .85 .90 SOLID ANGLE FRACTION, w
CHART 3A
GEOMETRY FACTOR · DIRECT, Gd(H,(U)
C-5
.99
-1-++++--:
.........
' .+N-+-
I 'I
I' I
:--+
SOLID ANGLE FRACTION, W
CHART 38
GEOMETRY FACTOR · DIRECT, Gd(H,O))
C-6
ECCENTRICITY, e is W/L
E(e) FOR CIRCULAR STRUCTURES IS ~ = 1.571
CHART 4
SHAPE FACTOR, E(e)
C-7
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
0.9
0.8
Q.,
X
~
en
z
0
i=
u <( a: 0.5 .
u.
a:
w
~
<( u 0.4
en
0.2
0.1
0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
EXTERIOR WALL MASS THICKNESS, Xe ,psf
CHART 5
s;ATIER FRACTION, S w (Xe)
C-8
3 4 5 6 8 10 20 30 50 70 100 200 400 700 1000
1.0 .8 ~~~
.6 .5
.4
.3
.2
:::c Q) X -Q) co a: 0 1(.) <( LL. a: w a: a: <( co ...J ...J <(s: a: 0 a: w 1-X w 0.1 .08 .06 .05 .04 .03 .02 0.01 .008 .006 .005
.004
.003
.002
0.001 ~ 4 5 6 8 10 20 30 50 70 100 200 400 700 1000
HEIGHT, H, ft
CHART 6
EXTERIOR WALL BARRIER FACTOR, Be(Xe ,H) C-9
208-401 0 -76 -22
0 25 50 75 100 125 150 175 200 225 250
1.0
.9
.8 ~1
.7
.6
1!J r~~;
.5
.4 :;;_,~£:\
,:<~ ~;
.3
--~? F::: ....
-,;:7' . ·,. [·..,
.2 ·:z 777-'//////'-"/,'////////.'/////////.
I. .. . .. , . .. ...._-, .
C/)
a:
0 0.1 t; .09 ~ .08
LL .07 ~ .06
z .04
w
I=
~ .03 z
0 i= .02
i=
a:
a:
~
0
a: 0.01 ~ .009
z ,008 .007 .006 .005
~
.004;;
.003
0.001 0
25 50 75 100 125 150 175 200 225 250
INTERIOR PARTITION MASS THICKNESS, Xi ,psf
CHART 7
INTERIOR PARTITION ATTENUATION FACTORS, Bi(Xi) and Bj'(Xi)
C-10
0 25 50 75 100
1:8 ~:X
.8
.7
.6
.5
•4
i·':l::
.3
,_, ·-. r-,
.2
'" 1\
tJ H--~1+-~1~~~~~~~~~~1~,-~~~~~
1 1
s
3
xu tJ al cr.· .08 .07 .06 ,, \ ... ! . . ..L f:)_,~L.:
0 ~ .05 \
(.)
<( L.l.. .04 ill :L:
z 0 i= .03 ~...-<:::)
<( ::::> z w .02 :~ ; -~ "~
(.!)
z
:J ~~~~~~·~~H~~~·~~~~~~~~,~~~~~+~~MH
0.01 -~
w
(.)
.008 .007 .006 .005 .004
.003
.002
1\ '
1\
0.001 LL.LL.LL.LL.LL.LL.I-:......1-:......I-:......I-:......L.....l-.L.....l-.L.....l-.L.....l-J......L.l.l...U.U:....:l-l-JL.a..~L.U-.L.....l-J....J 0 25 50 75 100 125 150 175 200 225
CEILING MASS THICKNESS, Xc, psf
CHART SA CEILING ATTENUATION FACTOR, Bc(Xc ,We)
C-11
125 150 175 200 225
qjc;c;cfijcj!cf!:'/c;cJ;;C;!i;!i;!c;cJ~
..
~~~:
.lrt~ ¥8
N.Q'/:T/';:i• ·~::" .. ·>:·:'i.::~
rw ~;,}dl;/ w
rfr-~--~
b
CD
-
a:
0
I
(.) <( LL
z
0
i=
<( ::I
z
w
~
<(
a:
0
0
...J
LL
FLOOR MASS THICKNESS, Xf, psf
CHART 8B
FLOOR ATTENUATION FACTOR, Bt(Xf)
C-12
1.0 .8 .6 .5 .4 .3 .2 0.1 .08 .06 .05 .04 .03 .02
.07 .06 :: ~~~~~""~"O''l--X--l-.f : i=$-.:0 " ~ 6 :.5 ,A •-' I-.._
.03
.02 :. It . i+: I~
.! I
~ ;) 0 X 0.01 .009 .008 .007 I : IX: ; . : 1 I I I ' __;_ I-
z 0 i= ::J Cll a: 1z 0 u 0 <( w :I: a: w >0 .005 .004 . 003 . -·~ r_, ,. ~:; ;-!:"'~ !' I~' ~~"'i.,_ \ ~
~:c:f' I 1'S. ~; I [{ ,__ , .'lti Ni lil-IX__, ...::"';:.: f';.--7' ~t~
;~~n:l' ~- X ._J'f ::1·· ~0= r--"'~-'
' ' I ' I : I I ~- I
SOLID ANGLE FRACTION, W
CHART 9
OVERHEAD CONTRIBUTION. C0 (X0 C-13 • W)
1.0 .8 .6 .3 .2 0.1. .06 .04 .03 .02 0.01 .006 .004 .002
.4
1 .0
.8 .6 .5
.3
.2
.4-~
0.1
-.,
.08
~
N. .06
Q) .05
X
-.,
co .04
a: .03
0
1
u
.02 u..
<(
a:
w
a:
a:
0.01
<(
co .008 Cl
...J .006
w .005
u:::
.004
Cl
w
1-.003 :2 ::J
.002
0.001
.0008
.0006
.0005
.0003
.0004·--
.0002 1.0 .8 .6 .3 .2 0.1 .06 .04 .03 .02 0.01 .006 .004 .002
.4
SOLID ANGLE FRACTION, 2 w 5
CHART lOA
LIMITED FIELD BARRIER FACTOR, B5(Xe ,2w5)
C-14
CHART'lOB
LIMITED FIELD HEIGHT FACTOR, F5 (H, 2({)5)
C-15
•
1.0 .8 .6 .4 .3 .2 0.1 .08 .06 .04 .02 0.01 .006 .003 .002
1.0
.8
.6
.4
;3
.2
0.1 .08 ~\\~\\\\\-3 .06 w __ ...->
u. -~r--
z .04 ~\_\.~~~~'\'\'\0 PASSAGEWAY
i= .03
::::>
IXl
a: .02
1
z
0u
0.01
.008
.006
.004
.003
.002
0.001 LiW''~W-4L-"-""lU=w.I.UWW.J.U'-W.ll-'-'-'-'-L-L--!..J_J.---""""J.1WlJ-.!.l.lU.4.u=J.U~~~.l..l---J-.I-.W-l~""'
1.0 .8 .6 .4 .3 .2 0.1.08 .06 .04 .02 0.01 .006 003 .002
SOLID ANGLE FRACTION, w
CHART 11
PASSAGEWAYS AND SHAFTS, C( w1
C-16
APPENDIX D
Venti lotion Analysis
Method for Computing Existing Shelter Space
This method for computing the existing number of shelter spaces is used
by the Corps of Engineers and NAVFAC for shelter survey purposes. The ventilation requirements in cubic feet per minute (cfm} vary slightly with TM 72-1 11 Technical Standards for Fallout Shelter Design11 in that the cfm in
the northern part of the United States is 8 cfm in lieu of 7 l/2 cfm and county borders are followed in lieu of a curved line through the States. This will result in minor variations with TM 72-1.
1. Table D-1 is a listing of counties by States indicating two sets of data.
a.
One set of data consists of the zonal ventilation requirement in CFM of fresh air available to the shelter.
b.
The other set of data portrays correction factors, which are to be
used with the minimum zonal CFM figures in determining the existing spaces when sufficient ventilation does not exist for the maximum capacity based on 10 sq. ft. per person.
Note: It may be assumed that abovegrade areas have sufficient natural ventilation to meet the new venti lotion requirements except where the space is windowless or has a minimum of openings. If the aboveground shelter area does not have suitable openings to permit natural ventilation, the county
ventilation rates should be used to determine shelter capacity.
2. Procedure for computing the existing shelter spaces in areas without air conditioning:
a. Compute the maximum number of spaces assuming that adequate ventilation exists:
max. capacity= gross shelter area x usability factor*
10
*See Table D-2 for usability factors
or = net she Iter area
10
b. Compute the required ventilation: required ventilation=max. capacity (para a above} x zonal requirement.
D-1
c.
Measure, compute or estimate the existing ventilation in CFM, either natural and/or mechanical. If the existing ventilation equals or exceeds the required ventilation, para b above, record the existing spaces as determined by para a above.
d.
If existing ventilation is less than the required ventilation, then proceed with the following computations:
(1)
First determination
spaces =total existing ventilation =
zonal cfm requirement
(2)
Second determination:
(a)
spaces calculated in (1) immediately above =
correction factor*
*correction factor obtained from the appropriate
State and county (Table D-1)
(b)
Wall area in contact with the ground (sq. ft.) x 0.005 =
(c)
Floor area in contact with the ground (sq. ft.) x 0.01 =
(d)
Sum of (a), (b) and (c) =
(3)
Selected determination (use the greater of either (1) or
(2) (d)
Note: Since the.basement floor, in the case of a facility with a sub-basement
is not in contact with the ground, item (c) immediately above will be omitted for the basement story. If a portion of such a basement floor has ground contact, compute item (c) immediately above for that portion only.
D-2
TABLED-1 ZONAL VENTILATION REQUIREMENTS AND CORRECTION FACTORS
ALABAMA
COUNTY CFM FACTOR COUNTY CFM FACTOR
Autaug a Baldwin 20 25 1.25 1.20 Henry Houston 20 20 1.25 1.50
Barbour 20 1.25. .Jackson 15 1.33
Bibb 20 1.25 Jefferson 20 1.00
Blount 20 1.00 Lamar 20 1. 25
Bullock 20 1.25 Lauderdale 20 1.25
Butler 20 1.50 Lawrence 20 1.00
Calhoun 20 1.00 Lee 20 1.00
Chambers 20 1.00 Limestone 20 1.00
Cherokee 15 1.33 Lowndes 20 1.25
Chilton 20 1.25 Macon 20 1.25
Choctaw 20 1.50 Madison 15 1. 33
Clarke 20 1.50 Marengo 20 1.25
Clay Cleburne 20 20 1.00 1.00 Marion Marshall 20 15 1.25 1.33
Coffee 20 1.50 Mobile 25 1.20
Colbert 20 1.25 Monroe 20 1.50
Conecuh 20 1.50 Montgomety 20 1.25
Coosa 20 1.00 Morgan 20 1.00
Covington Crenshaw 20 20 1.50 1.50 Perry Pickens 20 20 1.25 1.25
Cullman 20 1.00 Pike 20 1.25
Dale 20 1.25 Randolph 20 1.00
Dallas 20 1.25 Russell 20 1.25
De Kalb 15 1.33 St Clair 20 1.00
Elmore 20 1.25 Shelby 20 1.00
Escambia 20 1.50 Sumter 20 1.25
Etowah 15 1.33 Talladega 20 l. 00
Fayette Franklin 20 20 1.25 1.25 Tallapoosa Tuscaloosa 20 20 1.00 1.25
Geneva 20 1.50 Walker 20 1.00
Greene 20 1.25 Washingtot! 20 1.25
Hale 20 1.25 Wilcox 20 1.25
Winston 20 1.00
ARIZONA
Apache Cochise 10 15 1.50 1.00 Mohava Navajo 15 10 1.00 1.50
Coconino 10 1.50 Pima 15 4.00
Gila 15 1.00 Pinal 15 4.00
Graham 15 1.00 Santa Cruz 15 4.00
Greenlee 10 1.50 Yavapai 15 1.00
Maricopa 20 3.00 Yuma 20 3.00
D-3
ARKANSAS
COUNTY Cfll FACTOR COUNTY CFM FACTOR
Arkansas 20 1.50 Lee 20 1.50
Ashley Baxter 25 15 1.20 1.67 Lincoln Little River 20 20 1.50 2.00
Benton 15 1.67 Logan 20 1.50
Boone 15 1.67 Lonake 20 1.50
Bradley 25 1.20 Madison 20 1.25
Calhoun 25 1.20 Marion 15 1.67
Carroll 15 1.67 Miller 20 2.00
Chicot 25 1.20 Mississippi 20 1.25
Clark 20 2.00 Monroe 20 1.50
Clay Cleburne 20 20 1.25 1.25 Montgomery Nevada 20 20 2.00 2.00
Cleveland 25 1.20 Newton 20 1.25
Columbia 25 1.60 Ouachita 25 1.60
Conway 20 1.25 Perry 20 1.50
Craighead 20 1.25 Phillips 20 1.50
Crawford 20 1.25 Pike 20 2.00
Crittenden 20 1.25 Poinsett 20 1.25
Cross 20 1.25 Polk 20 2.00
Dallas 20 1.50 Pope 20 1.25
Desha 20 1.50 Prairie 20 1.50
Drew 25 1.20 Pulaski 20 1.50
Faulkner 20 1.25 Randolph 20 1.25
Franklin 20 1.25 St Francis 20 1.25
Fulton 15 1.67 Saline 20 1.50
Garland 20 1.50 Scott 20 1.50
Grant 20 1.50 Searcy 20 1.25
Greene 20 1.25 Sebastian 20 1.50
Hempstead Hot Spring Howard 20 20 20 2.00 1.50 2.00 Sevier Sharp Stone 20 20 20 2.00 1.25 1.25
Independence Izard 20 20 1.25 1.25 Union Van Buren 25 20 1.60 1.25
Jackson 20 1.25 Washington 20 1.25
Jefferson 20 1.50 White 20 1.25
Johnson 20 1.25 Woodruff 20 1.25
Lafayette 20 2.00 Yell 20 1.50
Lawrence 20 1.25
D-4
CALIFORNIA
COUNTY CFM FACTOR COUNTY CFM FACTOR
Alameda Alpine Amador Butte Calaveras Colusa Contra Costa Del Norte El Dorado Fresno Glenn Humboldt Imperial Inyo Kern Kings Lake Lassen Los Angeles Madera Marin Mariposa Mendocino Merced Modoc Mono 8 8 8 8 8 8 8 8 8 10 8 8 15 10 10 10 8 8 10 10 8 10 8 10 8 8 1.00 1.33 1.33 1.00 1.33 1.00 1.00 1.00 1.33 1.00 1.00 1.00 1.00 1. 00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.33 Orange 10 Pacer 8 Plumas 8 Riverside 15 Sacramento 8 San Benito 8 San Bernardino 15 San Diego 10 San Francisco 8 San Joaquin 8 San Luis Obispo 8 San Mateo 8 Santa Barbara 8 Santa Clara 8 Santa Cruz 8 Shasta 8 Sierra 8 Siskiyou 8 Solano 8 Sonoma 8 Stanislaus 8 Sutter 8 Tehama 8 Trinty 8 Tulare 10 Tuolumne 8 1.00 1. 33 1.00 1.00 1.33 1. 33 1.00 1.00 1.00 1.33 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1. 33 1. 33 1.00 1.00 1.00 1.33
Monterey Napa Nevada 8 8 8 1.00 1.00 1.33 Ventura Yolo Yuba 8 8 8 1.33 1.00 1.33
COLORADO
Baca 1() 1.00 Logan 8 1.33
Bent 10 1.00 Otero 8 1.33
Cheyenne Crowley Kiowa 10 8 10 1.00 1.33 1. 00 Phillips Prowers Sedgwick 10 10 8 1.00 1.00 1.33
Kit Carson 10 1.00 Washington 8 1.33
Las Animas Lincoln 10 8 1.00 1.33 Yuma All Others 10 8 1.00 1.00
CONNECTICUT
Fairfield 10 1.50 All Others 10 1.00
D-5
208-401 0 -76 -23
DELAWARE
COUNTY CFM FACTOR COUNTY CFM FACTOR
All Counties 15 1.00
FLORIDA
Alachua 25 1.20 Lake 25 1.20
Baker 25 1.20 Levy 25 1.20
Bay 20 1.50 Manatee 2: 1.60
Brevard 25 1.60 Marion 25 1.60
Broward 30 1.33 Martin 30 1. 33
Charlotte 30 1.33 Monroe 30 1.67
Citrus 25 1.60 Nassau 25 1. 20
Clay 25 1.20 Okeechobee 30 1. 33
Collier 30 1.33 Orange 25 1.60
Columbia 25 1.20 Osceola 25 1..60
Dade 30 1.67 Palm Beach 30 1.33
De Soto 30 1. 33 Pasco 25 1.60
Dixie 25 1.20 Pinellas 25 1.60
Duval 25 1.20 Polk 25 1.60
Flagler 25 1.60 Putnam 25 1.20
Gilchrist 25 1.20 St Johns 25 1.20
Glades 30 1.33 St Lucie 30 1. 33
Hardee 25 1.60 Sarasota 25 1.60
Hendry 30 1.33 Seminole 25 1.60
Hernando 25 1.60 Sumter 25 1.60
Highlands 30 1. 33 Suwannee 25 1.20
Hillsborough 25 1.60 Taylor 20 1.50
Indian River 30 1.33 Union 25 1.20
Lafayette 25 1.20 Volusia 25 1.60
All Others 20 1.50
GEORGIA
Appling 20 1.25 Burke 20 1.25
Atkinson 20 1.25 Butts 20 1.25
Bacon 20 1.25 Calhoun 20 1.25
Baker 20 1.25 Camden 20 1.50
Baldwin 20 1.00 Candler 20 1.25
Ben Hill 20 1.25 Charlton 20 1.50
Berrien 20 1.25 Chatham 20 1.50
Bibb 20 1.00 Chattahoochee 20 1.25
Bleckley 20 1.25 Clay 20 1.25
Brantleu 20 1.50 Clinch 20 1.50
Brooks 20 1.50 Coffee 20 1.25
Bryan 20 1.25 Colquitt 20 1.25
Bullock 20 1.25 Columbia 20 1.00
D-6
GEORGIA
COUNTY CFM FACTOR COUNTY CFM FACTOR
Cook 20 1.25 Pulaski 20 1.25
Coweta 20 1. 00 Putnam 20 1.00
Crawford 20 1.00 Quitman 20 1.25
Crisp 20 1.25 Randolph 20 1.25
Decatur 20 1.50 Richmond 20 1.25
Dodge 20 1.25 Schley 20 1.25
Dooly 20 1.25 Sreven 20 1. 25
Dougherty 20 1.25 Seminole 20 1.50
Early 20 1.25 Spaulding 20 1.00
Echols 20 1.50 Stewart 20 1.25
Effingham 20 1.25 Sumter 20 1.25
Emanuel 15 1.25 Talbot 20 1.00
Evans 20 1.25 Taliaferro 20 1.00
Glascock 20 1.25 Tattnall 20 1.25
Glynn 20 1.50 Taylor 20 1.00
Grady 20 1.50 Telfair 20 1.25
Hancock 20 1.00 Terrell 20 1. 25
Harris 20 1.00 Thomas 20 1.50
Heard 20 1.00 Tift 20 1. 25
Houston 20 1.25 Toombs 20 1.25
Irwin 20 1.25 Treutlen 20 1.25
Jasper 20 1.00 Troup 20 1.00
Jeff Davis 20 1.25 Turner 20 1. 25
Jefferson 20 1.25 Twiggs 20 1.25
Jenkins 20 1. 25 Upson 20 1.00
Johnson 20 1.25 Ware 20 1.50
Jones 20 1.00 Warren 20 1.00
Lamar 20 1.00 Washington 20 1.25
Lanier 20 1.50 Wayne 20 1. 25
Laurens 20 1.25 Webster 20 1.25
Lee 20 1.25 Wheeler 20 1. 25
Liberty 20 1. 25 Wilcox 20 1. 25
Long 20 1.25 wilkinson 20 1.25
Lowndes 20 1.50 Worth 20 1. 25
McDuffie 20 1.00
Mcintosh 20 1.25 All Others 15 1. 33
Macon 20 1.25
Marion 20 1.25
Meriwether 20 1.00
Miller 20 1.25
Mitchell 20 1.25
Monroe 20 1.00
Montgomery 20 1.25
Muscogee 20 1.00
Peach 20 1.25
Pierce 20 1.25
Pike 20 1.00
D-7
IDAHO
COUNTY .9!!1 FACTOR COUNTY CFM FACTOR
All Counties 8 1.00
ILLINOIS
Alexander 15 1.33 La Salle 10 1.50 Bond 15 1.33 Lee 10 1.50 Boone 10 1.50 McHenry 10 1.50 Bureau 10 1.50 Madison 15 1.33 Calhoun 15 1.33 Marion 15 1.33 Carroll 10 1.50 Marshall 10 1.50 Clinton 15 1.33 Mercer 10 1.50 Coles 15 1.33 Monroe 15 1.33 Cook 10 1.50 Ogle 10 1.50 De Kalb 10 1.50 Peoria 10 1.50 Du Page 10 1.50 Perry 15 1.33 Edwards 15 1.33 Pope 15 1.33
Ford 10 1.50 Pulaski 15 1.33 Franklin 15 1.33 Putnam
10 1.50 Gallatin 15 1.33 Randolph 15 1.33 Grun~y 10 1.50 Rock Island 10 1.50 Hamilton 15 1.33 St Clair 15 1.33
Hardin 15 1.33 Saline 15 1.33 Henry 10 1.50 Stark
10 1.50 Iroquois 10 1.50 Stephenson 10 1.50 Jackson 15 1.33 Union 15 1.33
Jefferson 15 1.33 Wabash 15 1.33 Jersey 15 1.33 Washington 15 1.33
•
Jo Daviess 10 1.50 Wayne 15 1.33 Johnson 15 1.33 White 15 1.33 Kane 10 1.50 Whiteside 10 1.50 Kankakee 10 1.50 Will 10 1.50 Kendall 10 1.50 Williamson 15 1.33 Knox 10 1.50 Winnebago 10 1.50 Lake 10 1.50 Woodford 10 1.50 All Others 15 1.00
INDIANA
Bartholomew 15 1.00
Decatur 15 1.00 Boone 15 1.00
Dubois 15 1.33 Brown 15 1.00 Floyd 15 1.00 Clark 15 1.00
Fountain 15 1.00 Clay 15 1.00
Franklin 15 1.00 Clinton 10 1.50
Gibson 15 1.33
Crawford 15 1.00
Greene 15 1.00 Daviess 15 1.00
Hancock 15 1.00
Dearborn 15 1.00
Harrison 15 1.00
D-8
INDIANA
COUNTY :GFM FACTOR COUNTY CFM FACTOR
Hendricks Jackson Jefferson Jennings Johnson Knox Lawrence Marion Martin Monroe Montgomery Morgan Ohio Orange Owen Parke Perry 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.33 Pike Posey Putnam Ripley Rush Scott Shelby Spencer Sullivan Switzerland Vanderburgh Vermillion Vigo Warren Warrick Washington All Others 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 10 1.33 1.33 1.00 1.00 1.00 1.00 1.00 1. 33 1,00 1.00 1.33 1.00 1.00 1.00 1.33 1.00 1.50
IOWA
Adair Adams Appanoose Adubon Cass Clarke Davis Decatur Des Moines Fremont Harrison Henry Madison Mills Monroe 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 1.00 1.00 1.00 1.00 1.00 1.00 1. 00 1. 00 1.00 1.00 1.00 1.00 1. 00 1.00 1.00 Jefferson Lee Lucas Montgomery Page Pottawattamie Ringgold Shelby Taylor Union Van Buren Wapello Warren Wayne All Others 15 15 15 15 15 15 15 15 15 15 15 15 15 15 10 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.50
KANSAS
Barton Brown Cheyenne Clark Clay Cloud Decatur Doniphan 15 15 10 15 15 15 10 15 1.00 1.00 1.00 1.00 1.00 1.00 1.50 1.00 Edwards Ellis Ellsworth Finney Ford Gove Graham Grant 15 15 15 10 15 10 10 10 1.00 1.00 1.00 1.50 1.00 1.50 1.50 1.50
D-9
KANSAS
COUNTY CFM FACTOR COUNTY Q]:! FACTOR
Gray 10 1.50 Phillips 10 1.50
Greeley 10 1.00 Pottawatomie 15 1.00
Hamilton 10 1.00 Rawlins 15 1.00
Haskell 10 1.50 Republic 15 1.00
Hodgeman 10 1.50 Riley 15 1.00
Jewell 15 1.00 Rooks 15 1.00
Kearny 10 1.50 Rush 15 1.00
Lane 10 1.50 Russell 15 1.00
Lincoln 15 1.00 Scott 10 1.50
Logan 10 1.50 Seward 10 1.50
Marshall 15 1.00 Sheridan 10 1.50
Meade 15 1.00 Sherman 10 1.00
Mitchell 15 1.00 Smith 15 1.00
Morton 10 1.50 Stanton 10 1.50
Nemaha 15 1.00 Stevens 10 1.50
Ness 10 1.50 Thomas 10 1.50
Norton 10 1.50 Trego 10 1.50
Osborne 15 1.00 Wallace 10 1.00
Ottawa 15 1.00 Washington 15 1.00
Pawnee 15 1.00 Wichita 10 1.50
All Others 15 1.33
KENTUCKY
COUNTY CFM FACTOR COUNTY CFM FACTOR
Adair Allen Ballard Barren Boyd Breckinridge Butler Caldwell Carlisle Carter Christian Clinton Crittenden Cumberland Davies Edmonson Elliott Fulton Graves Grayson Green Greenup Hancock 15 15 15 15 10 15 15 15 15 10 15 15 15 15 15 15 10 20 20 15 15 10 15 1.33 1.33 1.33 1.33 1.50 1.33 1.33 1.33 1.33 1.50 1.33 1.33 1.33 1.33 1.33 1.33 1.50 1.00 1.00 1.33 1.33 1.50 1.33 D-10 Hardin Hart Hickman Hopkins Johnson Larue Lawrence Lewis Livingston Logan Lyon McCracken McLean Marshall Martin Meade Metcalfe Monroe Muhlenberg Ohio Pike Russell Simpson 15 15 20 15 10 15 10 10 15 15 15 15 15 15 10 15 15 15 15 15 10 15 15 1.33 1.33 1.00 1.33 1.50 1.33 1.50 1.50 1.33 1.33 1.33 1.33 1.33 1.33 1.50 1.33 1.33 1.33 1.33 1.33 1.50 1.33 1.33
KENTUCKY
COUNTY CFM FACTOR COUNTY CFM FACTOR
Taylor 15 1.33 Warren 15 1. 33
Todd 15 1.33 Wayne 15 1. 33
Trigg 15 1.33 Webster 15 1.33
Union 15 1.33 All others 15 1.00
LOUISIANA
COUNTY CFM FACTOR COUNTY CFM FACTOR
Acadia 30 2.00 Madison 25 1.20
Allen 30 2.00 Morehouse 25 1.20
Ascension 30 1.67 Natchitoches 25 2.00
Assumption 30 1.67 Orleans 30 1.67
Avoyelles 25 2.00 Ouachita 25 1.60
Beauregard 40 1.50 Plaquemines 30 1.67
Bienville 25 2.00 Pointe Coupee 25 2.00
Bossier 25 2.00 Rapides 25 2.00
Caddo 25 2.40 Red River 25 2.00
Calcasieu 40 1.50 Richland 25 1.20
Caldwell 25 1.60 Sabine ' 30 2.00
Cameron 40 1.50 St Bernard 30 1.67
Catahoula 25 1.60 St Charles 30 1.67
Claiborne 25 1.60 St Helena 25 1.20
Concordia 25 1.60 St James 30 1.67
De Soto 25 2.40 St John the
East Baton Rouge25 East Carrol 25 1.60 1.20 Baptist St Landry 30 30 1.67 2.00
East Feliciana 25 1.60 !·:t Martin 30 2.00
Evangeline 30 2.00 St Tammany 25 1.20
Franklin 25 1.20 Tammany 25 1.20
Grant 25 2.00 Tensas 25 1.20
Iberia 30 2.00 Terrebonne 30 2.00
Iberville 30 1.67 Union 25 1.60
Jackson 25 1.67 Vermilion 30 2.00
Jefferson 30 1.67 Vernon 30 2.00
Jefferson Davis30 2.00 Washington 25 1.20
Lafayette 30 2.00 Webster 25 2.00
La Sale Lincoln 25 25 1.60 1.60 West Baton Rouge 25 West Carrol 25 2.00 1.20
Livingston 25 1.60 West Feliciana 25 1.60
Winn 25 2.00
D-11
MAINE
COUNTY CFM FACTOR COUNTY Q1!
All Counties 8 1.00
MARYLAND
Independent
City 15 1.00 Harford 15 Allegany 10 1.50 Howard 15 Anne Arundel 15 1.00 Kent 15
Baltimore 15 1.00 Montgomery 15 Calvert 15 1.00 Prince Georges 15 Caroline 15 1.00 Queen Annes 15 Carroll 15 1.00 St Marys 15
Cecil 15 1.00 Somerset 15 Charles 15 1.00 Talbot 15 Dorchester 15 1.00 Washington 10 Frederick 15 1.00 Worcester 15 Garret 10 1.00
MASSACHUSETTS
All Counties 10 1.00
MICHIGAN
Alcona 8 1.33 Berrien 10 Alger 8 1.00 Branch 10 Allegan 10 1.00 Calhoun 10 Alpena 8 1.33 Cass 10
Antrim 8 1.33 Charlevoix 8 Arenac 8 1.33 Cheboygan 8 Baraga 8 1.33 Chippewa 8 Barry 10 1.00 Clare 8
Bay 10 1.00 Clinton 8
Benzie 8 i.33 Crawford 8
D-12
FACTOR
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.50
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.33
MICHIGAN
COONTY CFM FACTOR COUNTY CFM FAC'IDR
Delta 8 1.00 Mecosta 8 1.33
Dickinson 8 1.00 Menominee 8 1.00
Emmet 8 1.00 Midland 8 1.33
Gladwin 8 1.33 Missaukee 8 1.33
Gogebic 8 1.00 Montcalm 8 1.33
Grand Traverse 8 Houghton 8 Huron 8 Iosco 8 1.33 1.00 1.33 1.33 Montmorency Muskegon Newaygo Oceana 8 8 8 8 1.33 1.33 1.33 1.33
Iron 8 1.00 Ogemaw 8 1.33
Isabella Kalkaska 8 8 1.33 1.33 Ontonagon Osceola 8 8 1.00 1.33
Kent 8 1.33 Oscoda 8 1.33
Keweenaw Lake 8 8 1.00 1.33 Otsego Ottawa 8 8 1.33 1.33
Leelanau 8 1.33 Presque Isle 8 1.00
Luce 8 1.00 Roscommon 8 1.33
Mackinac 8 1.00 Schoolcraft 8 1.00
Manistee 8 1.33 Wexford 8 1.33
Marquette 8 1.00
Mason 8 1.33 All Others 10 1.00
MINNESOTA
Aitkin 8 1.00 Itasca 8 1.00
Anoka 8 1.33 Kanabec 8 1.33
Becker 8 1.00 Kittson 8 1.00
Beltrami 8 1.00 Koochiching 8 1.00
Benton 8 1.33 Lake 8 1.00
Big Stone Carlton 8 8 1.33 1.00 Lake of the Woods 8 1.00
Cass 8 1.00 Mahnomen 8 1.00
Chisago 8 1.33 Marshall 8 1.00
Clay 8 1.00 Mille Lacs 8 1.33
Clearwater 8 1.00 Morrison 8 1.33
Cook 8 1.00 Norman 8 1.00
Crow Wing 8 1.00 Otter Tail 8 1.33
Douglas Grant 8 8 1.33 1.33 Pennington Pine 8 8 1.00 1.33
Hubbard 8 1.00 Polk 8 1.00
Isanti 8 1.33 Pope 8 1.33
D-13
MINNESOTA
COUNTY CFM FACTOR COUNTY CFM FACTOR
Red Lake 8 1.00 Todd 8 1.33
Roseau 8 1.00 Traverse 8 1.33
St. Louis 8 1.00 Wadena 8 1.00
Sherburne 8 1.33 Wilkin 8 1.33
Stearns 8 1.33
Stevens 8 1.33 All Others 10 1.00
Swift 8 1.33
MISSISSIPPI
Adams 25 1.20 Monroe 20 1.25
Alcorn 20 1.25 Montogomery 20 -1.25
Amite 25 1.20 Neshoba 20 1.25
Attala 20 1.25 Noxubee 20 1.25
Benton 20 1.25 Oktibbeha 20 1.25
Calhoun 20 1.25 Panola 20 1.25
Carroll 20 1.25 Pearl River 25 1.20
Chickasaw 20 1.25 Pike 25 1.20
Choctaw 20 1.25 Pontotoc 20 1.25
Clay 20 1.25 Prentiss 20 1.25
De Soto 20 1.25 Quitman 20 1.25
Franklin 25 1.20 Stone 25 1.20
George 25 1.20 Tallahatchie 20 1.25
Grenada 20 1.25 Tate 20 1.25
Hancock 25 1.20 Tippah 20 1.25
Harrison 25 1.20 Tishomingo 20 1.25
Itawamba 20 1.25 Tunica 20 1.25
Jackson· 25 1.20 Union 20 1.25
Jefferson 25 1.20 Walthall 25 1.20
Kemper Lafayette Lee 20 20 20 1.25 1.25 1.25 Webster Wilkinson Winston 20 25 20 1..25 1.60 1.25
Lowndes 20 1.25 Yalobusha 20 1.25
Marshall 20 1.25 All Others 20 1.50
MISSOURI
Adair 15 1.00 Caldwell 15 1.00
Andrew 15 1.00 Christian 15 1.67
Atchison 15 1.00 Clark 15 1.00
Barry 15 1.67 Clinton 15 1.00
Buchanan 15 1.00 Daviess 15 1.00
Butler 15 1.67 De Kalb 15 1.00
D-14
MISSOURI
COUNTY CFM FAC'roR COUNTY CFM FACTOR
Douglas Dunklin 15 20 1.67 1.25 Newton Nodaway 15 15 1.67 1.00
Gentry Grundy Harrison 15 15 15 1.00 1.00 1.00 Oregon Ozark Pemiscot 15 15 20 1.67 1.67 1.25
Holt 15 1.00 Pike 15 1.00
Howell 15 1.67 Putnam 15 1.00
Knox 15 1.00 Ralls 15 1.00
Lewis 15 1.00 Ripley 15 1.67
Linn 15 1.00 Schuyler 15 1.00
Livingston McDonald 15 15 1.00 1.67 Scotland Shelby 15 15 1.00 1.00
Macon 15 1.00 Stone 15 1.67
Marion 15 1.00 Sullivan 15 1.00
Mercer...Mississippi 15 20 1.00 1.00 Taney Worth 15 15 1.67 1.00
Monroe 15 1.00
New Madrid 20 1.25 All Others 15 1.33
MONTANA
All Counties 8 1.00
NEBRASKA
Antelope Arthur 10 10 1.50 1.00 Dixon Dundy 10 10 1.50 1.00
Banner 8 1.00 Frontier 10 1.50
Blaine 10 1.00 Furnas 10 1.50
Boone 10 1.50 Garden 8 1.33
Box Butte 8 1.33 Garfield 10 1.00
Boyd Brown 10 10 1.00 1.00 Gosper Grant 10 10 1.50 1.00
Buf'falo 10 1.50 Greeley 10 1.50
Cedar 10 1.50 Harlan 10 1.50
Chase 10 1.00 Hayes 10 1.00
Cherry Cheyenne Custer 10 8 10 1.00 1.33 1.00 Hitchcock Holt Hooker 10 10 10 1.00 1.00 1.00
Dakota 10 1.50 Howard 10 1.50
Dawes 8 1.33 Kearney 10 1.50
Dawson 10 1.50 Keith 10 1.00
Deuel 8 1.33 Keya Paha 10 1.00
D-15
NEBRASKA
COUNTY CFM FACTOR COUNTY CFM FACTOR
Kimball 8 1.00 Scotts Bluff 8 1.00
Knox 10 1.00 Sheridan 8 1.33
Lincoln 10 1.00 Sherman 10 1.50
Logan Loup McPherson 10 10 10 1.00 1. 00 1.00 Sioux Stanton Thomas 8 10 10 1.00 1.50 1.00
Madison 10 1.50 Thurston 10 1.50
Morrill 8 1.33 Valley 10 1.50
Perkins 10 1.00 Wayne 10 1.50
Phelps 10 1.50 Wheeler 10 1.50
Pierce 10 1.50
Red Willow 10 1.50
Rock 10 1.00 All Others 15 1.00
NEVADA
COUNTY CFM FACTOR COUNTY CFM FACTOR
Churchill 8 1. 00 Lyon 8 1.00
Clark 15 1.00 Mineral 8 1. 00
Douglas 8 1.00 Nye 10 1.00
Elko 8 1.33 Ormsby 8 1.00
Esmeralda 10 1.00 Pershing 8 1.00
Eureka 8 1.33 Storey 8 1.00
Humboldt 8 1.00 Washoe 8 1.00
Lander 8 1.33 White Pine 8 1.33
Lincoln 10 1. 00
NEW HAMPSHIRE
Coos 8 l.CO All Others 10 1.00
NEW JERSEY
Atlantic 15 1. 00 Gloucester 15 1.00
Bulington Camden 15 15 1. 00 1.00 Mercer Ocean 15 15 1.00 1.00
Cape May Cumberland 1.5 15 1. 00 1.00 Salem All Others 15 10 1.00 1.50
D-16
NEW MEXICO
CCXJNTY CFM FACTOR COUNTY CFM' FACTOR
BernaJ.illo 8 1.33 San Juan 10 1.00
Colfax 10 1.00 San Miguel 10 1.00
GuadaJ.upe 10 1.00 Santa Fe 8 1.33
Harding 10 1.00 Socorro 10 1.00
Los Alamos 8 1.33 Taos 8 1.33
McKinley 10 1.00 Torrance 10 1.00
Mora 10 1.00 Union 10 1.00
Rio Arriba 8 1.33 VaJ.encia 10 1.00
Sandoval 8 1.33 All Others 10 1.50
NEW YORK---
Bronx 10 1.50 Putnam 10 1.50
Clinton 8 1.33 Queens 10 1.50
Essex 8 1.33 Richmond 10 1.50
Franklin 8 1.33 Rockland 10 1.50
Kings 10 1.50 St. Lawrence 8 1.33
Nassau 10 1.50 Suffolk 10 1.50
New York 10 1.50 Westchester 10 1.50
Orange 10 1.50 All Others 10 1.00
NORTH CAROLINA
Alexander 15 1.00 Onslow 20 1.25
Alleghany 15 1.00 Pender 20 1.25
Ashe 15 1.00 Person 15 1.00
Avery 15 1.00 Robeson 20 1.25
Bladen 20 1.25 Rockingham 15 1.00
Brunswick CaJ.dwell 20 15 1.25 1.00 Sampson Scotland 20 20 1.25 1.25
Caswell 15 1.00 Stokes 15 1.00
Columbus Cumberland Duplin 20 20 15 1.25 1.25 1.67 Surry Watauga Wilkes 15 15 15 1.00 1.00 1.00
Forsyth 15 1.00 Yadkin 15 1.00
Hoke 20 1.25 Yancey 15 1.00
Mitchell 15 1.00
New Hanover 20 1.25 All Others 15 1.33
D-17
NORTH DAKOTA
COUNTY CFM FACTOR COUNTY CFM FACT<R
Dickey 8 1.33 Ransom 8 1.33
Emmons 8 1.33 Richland 8 1.33
La Moure 8 1.33 Sargent 8 1.33
Logan 8 1.33 Sioux 8 1.33
Mcintosh 8 1.33 All Others 8 1.00
OHIO
Ashtabula 10 1.00 Lake 10 1.00
Belmont 10 1.00 Ma.honing ~0 1.00
Columbiana 10 1.00 Monroe 10 1.00
Cuyahoga 10 LOO Trumbull 10 1.00
Geauga 10 1.00 Washington 10 1.00
Jefferson 10 1.00 All Others 10 1.50
OKLAHOMA
Adair 20 1.25 Greer 15 1.33
Alfalfa 15 1.33 Harmon 15 1.33
Atoka 25 1.60 Harper 15 1.33
Beaver 10 1.50 Haskell 20 1."50
Beckham 15 1.33 Hughes 20 1.50
Blaine 20 1.00 Jackson 15 1.33
Bryan 25 2.00 Jefferson 25 1.60
Caddo 20 1.25 Johnston 25 1.60
Canadian 20 1.25 Kay 20 1.00
Carter 25 1.60 Kingfisher 20 1.00
Cherokee 20 1.25 Kiowa 20 1.00
Choctaw 25 2.00 Latimer 20 2.00
Cimarron 10 1.00 Le Flore 20 2.00
Cleveland 20 1.50 Lincoln 20 1.25
Coal 25 1.60 Logan 20 1.25
Comanche 20 1.25 Love 25 2.00
Cotton 20 1.50 McClain 20 1.50
Craig 20 1 ..25 McCurtain 20 2.00
Creek 15 1.33 Mcintosh 20 1.50
Custer 15 1.33 Major 15 1.33
Delaware 20 1.25_ Marshall 25 2.00
Dewey 15 1.33 Mayes 20 1.25
Ellis 15 1.33 Murray 25 1.60
Garfield 20 1.00 Muskogee 20 1.25
Garvin 20 1.50 Noble 20 1.00
Grady 20 1.25 Nowata 20 1.00
Grant 15 1.33 Okfuskee 20 1.25
D-18
OKLAHOMA
COUNTY C:FM FACTOR COUNTY C:FM FACTOR
Oklahoma 20 1.25 Rogers 20 1.25
Okmulgee 20 1.25 Seminole 20 1.50
Osage 20 1.00 Sequoyah 20 1.50
Ottawa 20 1.25 Stephens 20 1.50
Pawnee 20 1.00 Texas 10 1.50
Payne 20 1.25 Tillman 20 1.25
Pittsburg 20 2.00 Tulsa 20 1.25.
Pontotoc 20 2.00 Wagoner 20 1.25
Pottawatomie 20 1.50 Washington 20 1.00
Pusmataha 20 2.00 Washita 20 1.00
Roger Mill 15 1.33 Woods 15 1.33
Woodward 15 1.33
OREGON
All Counties 8 1.00
PENNSYLVANIA
Adams 15 1.00 Lehigh 10 1.50
Bedford 10 1.50 Luzerne 10 1.50
Berks 15 1.00 Mifflin 10 1.50
Bucks 15 1.00 Monroe 10 1.50
Carbon 10 1.50 Montgomery 15 1.00
Chester 15 1.00 Montour 10 1.50
Columbia 10 1.50 Northampton 10 1.50
Cumberland 10 1.50 Northumberland 10 1.50
Dauphin 10 1.50 Perry 10 1.50
Delaware 1.5 1.00 Philadelphia 15 1.00
Franklin 10 1.50 Pike 10 1.50
Fulton 10 1.50 Schuylkill 10 1.50
Huntingdon 10 1.50 Snyder 10 1.50
Juniata 10 1.50 Union 10 1.50
Lancaster 15 1.00 York 15 1.00
Lebanon 10 1.50 All Others 10 1.00
RHODE ISLAND
All Counties 10 1.00
D-19
SOUTH CAROLINA
COUNTY CFM FACTOR COUNTY CFM FACTOR
•
Abbeville 15 1.33 McCormick 15 1.33 Anderson 15 1.33 Newberry 15 1.33 Cherokee 15 1.33 Oconee 15 1.33 Chester 15 1.33 Pickens 15 1.33
Greenville 15 1.33 Spartanburg 15 1.33 Greenwood 15 1.33 Union 15 1.33 Lancaster 15 1-33 York 15 1.33 Laurens 15 1.33 All others 20 1.25
SOUTH DAKOTA
BOn Homme 10 1.00 Lawrence 8 1.00 Butte 8 1.00 Lincoln 10 1.50 Charles Mix 10 1.00 McCook 10 1.00 Clay 10 1.50 Meade 8 1.00 Custer 8 1.00 Minnehaha 10 1.00 Douglas 10 1.00 Moody 10 1.00 Fall River 8 1.00 Pennington 8 1.00 Gregory 10 1.00 Perkins 8 1.00 Hanson 10 1.00 Turner 10 1.00 Harding 8 1.00 Union 10 1.50 Hutchinson :..J 1.00 Yankton 10 1.00 All others 8 1.33
TENNESSEE
Benton 20 1.00 Hardin 20 1.25
Campbell 15 1.00 Hawkins 1.00
15
Carroll 20 1.25 Haywood 20 1.25
1.00
Carter 15 Henderson 20 1.25 (,"hester 20 1.25 Henry 20 1.00 Claiborne 15 1.00 Hickman 20 1.00 Cocke 15 1.00 Houston 20 1.00 Crockett 20 1.25 Humphreys 20 1.00 Decatur 20 1.00 Jefferson 15 1.00 Dickson 20 1.00 Johnson 15 1.00 Dyer 20 1.25 Lake 20 1.25 Fayette 20 1.25 Lauderdale 20 1.25
Gibson
20 1.25 Lawrence 20 1.00 Giles 20 1.00 Lewis 20 1.00
Grainger 15 1.00 McNairy 20 1.25
Greene 15 1.00 Madison 20 1.25
Hamblen 15 1.00 Maury 20 1.00
Hancock 15 1.00 Obion 20 1.25 Hardeman 20 1.25 Perry 20 1.00
D-20
TENNESSEE
COUNTY CFM FACTOR COUNTY CFM FACTOR
Scott 15 1.00 Unicoi 15 1.00
Shelby Stewart 20 20 1.25 1.00 Union Washington 15 15 1.00 1.00
Sullivan 15 1.00 Wayne 20 1.00
Tiption 20 1.25 Weakley 20 1.00
All Others 15 1.33
TEXAS
Anderson 40 1.50 Cherokee 40 1.50
Andrews 15 1.00 Childress 15 1.33
Angelina Aransas 40 50 1.50 1.20 Clay Cochran 25 10 1.60 1.50
Archer 20 1.50 Coke 15 1.33
Armstrong Atascosa 15 30 1.00 2.00 Coleman Collin 20 30 1.25 2.00
Austin 30 2.00 Collingsworth 15 1.33
Bailey Bandera 10 20 1.50 1.50 Colorado Comal 30 25 2.00 1.60
Bastrop 25 2.00 Comanche 20 1.50
Baylor Bee 20 40 1.25 1.50 Concho Cooke 20 25 1.25 2.00
Bell 25 2.00 Coryell 25 1.60
Bexar 25 1.60 Cottle 15 1.33
Blanco 20 1.50 Crane 15 1.00
Borden 15 1.33 Crockett 15 1.33
Bosque Bowie 25 30 2.00 2.40 Crosby Culberson 15 15 1.33 1.00
Brazoria 40 1.50 Dallam 10 1.50
Brazos 30 2.00 Dallas 40 1.50
Brewster 15 1.33 Dawson 15 1.00
Brooks 50 1.20 Deaf Smith 10 1.50
Brown 20 1.50 Delta 30 2.00
Burleson 30 2.00 Denton 30 2.00
Burnet 25 1.60 De Witt 30 2.00
Caldwell 25 1.60 Dickens 15 1.33
Calhonn 40 1.50 Dimmit 30 1.60
Callahan 20 1.25 Donley 15 1.00
Cameron 50 1.20 Duval 50 1.20
Camp 30 2.00 Eastland 20 1.50
Carson 10 1.50 Ector 15 1.00
Cass 30 2.40 Edwards 20 1.25
Castro 10 1.50 Ellis 40 1.50
Chambers 40 1.50 El Paso 10 1.50
D-21
TEXAS
COUNTY FACTOR COUNTY grn FACTOR
.9ft!
•
Erath 25 1.60 Hunt 30 2.00
Falls 30 2.00 Hutchinson 10 1.50
Fannin 30 2.40 Irion 15 1.33
Fayette 25 2.00 Jack 25 1.60
Fisher 15 1.33 Jackson 40 1.50
Floyd 15 1.00 Jasper 40 1.50
Foard 20 1.00 Jeff Davis 15 1.00
Fort Bend 30 2.00 Jefferson 40 1.50
Franklin 30 2.00 Jim Hogg 50 1.20
Freestone 40 1.50 Jim Wells 50 1.20
Frio 30 2.00 Johnson 30 2.00
Gaines 15 1.00 Jones 20 1.25
Galveston 40 1.50 Karnes 2.00
Garza 15 1.33 Kaufman zg 1.50
Gillespie 20 1.50 Kendall 20 1.50
Glasscock 15 1.33 Kenedy 50 1.20
Goliad 40 1.25 Kent 15 1.33
Gonzales 30 2.00 Kerr 20 1.50
Gray 15 1.00 Kimble 20 1.25
Grayson 30 2.00 King 15 1.33
Gregg 30 2.00 K~nney 20 1.60
Grimes 30 2.00 Kleberg 50 1.20
Guadalupe 25 1.60 Knox 20 1.00
Hale 15 1.00 Lamar 30 2.40
Hall 15 1.33 Lamb 10 1.50
Hamilton 25 1.60 Lampasas 25 1.60
Hansford 10 1.50 La Salle 40 1.50
Hardeman 20 1.00 Lavaca 30 2.00
Hardin 40 1.50 Lee 25 2.00
Harris 40 1.50 Leon 40 1.50
Harrison 30 2.00 Liberty 40 1.50
Hartley 10 1.50 Limestone 30 2.00
Haskell 20 1.00 Lipscomb 15 1.33
Hays 25 1.60 Live Oak 40 1.50
Hemphill 15 1.33 Llano 20 1.50
Henderson 40 1.50 Loving 15 1.00
Hidalgo 50 1.20 Lubbock 15 1.00
Hill 30 2.00 Lynn 15 1.00
Hockley 15 1.00 McCulloch 20 1.25
Hood 25 2.00 McLennan 30 2.00
Hopkins 30 2.00 McMullen 40 1.50
Houston 40 1.50 Madison 30 2.00
Howard 15 1.33 Marion 30 2.40
Hudspeth 15 1.00 Martin 15 1.00
D-22
TEXAS
COUNTY Qfl! FACTOR COUNTY CFM FACTOR
Mason 20 Matagorda 40 Maverick 25 Medina 25 Menard 20 Midland 15 Milam 30 Mills 20 Mitchell 15 Montague 25 Montgomery 30 Moore 10 Morris 30 Motley 15 Nacgdoches 40 Navarro 40 Newton 40 Nolan 15 Nueces 50 Ochiltree 15 Oldham 10 Orange 40 Palo Pinto 25 Panola 30 Parker 25 Parmer 10 Pecos 15 Polk 40 Potter 10 Presidio 15 Rains 30 Randall 10 Reagan 15 Real 20 Red River 30 Reeves 15 Refugio 40 Roberts 15 Robertson 30 Rockwall 40 Runnels 20 Rusk 40 Sabine 30 San Augustine 40 San Jacinto 40 San Patricio 50 San Saba 20 1.50 1.50 1.60 1.60 1.25 1.00 2.00 1.50 1.33 1.60 2.00 1.50 2.40 1.33 1.50 1.50 1.50 1.33 1.20 1.00 1.50 1.50 1.60 2.00 2.00 1.50 1.33 1.50 1.50 1.00 2.00 1.50 1.33 1.50 2.40 1.00 1.50 1.00 2.00 1.50 1.25 1.50 2.00 1.50 1.50 1.20 1.50 Schleicher Scurry Shackelford Shelby Sherman Smith Somervell Starr Stephens Sterling Sonewall Sutton Swisher Tarrant Taylor Terrell Terry Throckmorton Titus Tom Green Travis Trinity Tyler Upshur Upton Uvalde Val Verde Van Zandt Victoria Walker Waller Ward .Washington Webb Wharton Wheeler Wichita Wilbarger Willacy Williamson Wilson Winkler Wise Wocd Yoakum Young Zapata 20 15 20 30 10 40 25 50 20 15 15 20 10 30 20 15 15 20 30 15 25 40 40 30 15 25 20 40 40 40 30 15 30 50 30 15 20 20 50 25 30 15 30 30 15 20 50 1.25 1.33 1.25 2.00 1.50 1.50 2.00 1.20 1.50 1.33 1.33 1.25 1.50 2.00 1.25 1.33 1.00 1.25 2~40 1.33 1.60 1.50 1.50 2.00 1.33 1.60 1.25 1.50 1.50 1.50 2.00 1.00 2.00 1.20 2.00 1.33 1.50 1.25 1.20 1.60 2.00 1.00 2.00 2.00 1.00 1.50 1.20
Zavala 26 1.60
D-23
,,_ UTAH
COUNTY CFM FACTOR COUNTY CFM' FACTOR
Box Elder 8 1.00 Rich 8 1.00
Cache 8 1.00 Salt Lake 8 1.00
Carbon 8 1.00 San Juan 8 1.00
Daggett 8 1.00 Sunnnit 8 1.00
Davis 8 1.00 Uintah 8 1.00
Duchesne 8 1.00 Wasatch 8 1.00
Grand 8 1.00 Weber 8 1.00
Morgan 8 1.00 All Others 8 1.33
VERMONT
Bennington 10 1.00 Windham 10 1.00
Orange 10 1.00 Windsor 10 1.00
Rutland 10 1.00 All Others 8 1.00
VIRGINIA
Brunswick 15 1.33 ,Nansemond 15 1.33
Dinwiddie 15 1.33 Prince George 15 1.33
Gloucester 15 1.33 Southrunpton 15 1.33
Greensville 15 1.33 Surry 15 1.33
Isle of Wight 15 1.33 Sussex 15 1.33
James City 15 1.33 York 15 1.33
Mathews 15 1.33 All Others 15 1.00
WASHINGTON
All Counties 8 1.00
l'ffiST VIRGINIA
Berkeley 10 1.50 Mineral 10 1.50
Cabell 10 1.50 Mingo 10 1.50
Grant 10 1.50 Monroe 10 1.50
Greenbrier Hampshire 10 10 1.50 1.50 Morgan Pendleton 10 10 1.50 1.50
Hardy 10 1.50 Pocahontas 10 1.50
Jefferson 10 1.50 Putnam 10 1.50
Lincoln Logan 10 10 1.50 1.50 Raleigh Sunnners 10 10 1.50 1.50
McDowell 10 1.50 Wayne 10 1.50
Mason Mercer 10 10 1.50 1.50 Wyoming All Others 10 10 1.50 1.00
D-24
IHSCONSIN
COUNTY CFM FACTO.:\ COUNTY CFH FACTOR
Ashland 8 1.00 La Crosse 8 1.00
Bayfield 8 1.00 Lafayette 10 1.50
Buffalo 10 1.00 Marinette 8 1.00
Crawford 10 1. 50 Hilwaukee 10 1.00
Dane 10 1.00 Fepin 10 1.00
Douglas 8 1.00 Pierce 10 1.00
Florence 8 1.00 Racine 10 1.00
Forest 8 1.00 Richland 10 1.00
Grant 10 1. 50 Rock 10 1. 50
Green 10 1. 50 Trempealeau 10 1.00
Iowa 10 1.50 Vernon 10 1.00
Iron 8 1.00 Vilas 8 1.00
Jefferson 10 1.00 Walworth 10 1.50
Kenosha 10 1. 50 Waukesha 10 1.00
All Others 8 1.33
WYOMING
All Counties 8 1.00
OTHER AREAS
AREA CFM FACTOR
Alaska 5 1.00
District of Columbia .15 1.00
American Samoa 40 1.50
Canal Zone 35 1. 70
Guam 35 1. 70
Hawaii 20 1.00
Midway 15 1.00
Puerto Rico 30 1.67
Virgin Islands 30 1.67
Wake 35 1. 70
D-25
SUGGESTED FLOOR AREA USABILITY FACTORS
(Recommended by DCPA based upon inspection of a large sample of shelter
facilities. Since shelter methodology is based upon exterior building
dimensions, percentages shown in the "0" column pertain to SAF survey
procedures and may be used as a guide for determining net shelter areas.)
BASEMENT FIRST STORY UPPER STORY % Usable Ave. % Usable Ave. % Usable Ave.
(I) (0) Area (I) (0) Area (I) (0) Area
Residential Housing 84 79 5400 88 84 8700 86 82 8500
School Buildings 87 82 7000 89 86 14300 87 83 12000
Religious Buildings 86 81 6400 87 83 8600 88 83 7600
Gov. and Public s~rvice 86 81 6300 87 84 14300 89 86 16000
Commercial Building 86 81 7600 90 86 12100 90 86 11000
Industrial Building 81 77 12300 84 81 18300 82 79 14700
Amusement and Meeting 79 74 7500 92 88 9300 86 80 5200
Transportation 84 74 1604 94 89 7100 98 94 12500
Miscellaneous 100 91 1900
NOTES: (1) %Usable I=% Usable Area Using Inside Building Measurements
(2)
%Usable 0 =%Usable Area Using Outside Wall Dimensions
(3)
Area = Outside Wall Dimensions
(4)
The survey assumed that all items (such as desks, files, etcj)/~/ that could be removed (not permanent) were removed. /
D-26
U. S. GOVERNMENT PRINTING OFFICE : 1976 0 -208·401
Distribution: Architects & Engineers Qualified in Fallout Shelter Analysis National Academy of Science Advisory Committee