;.-'L-iM i^
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
WARTIME REPORT
ORIGINALLY ISSUED
Koyember 19^44 as
Advance Eestricted Eeport IAI21
FEEQUEMCY OF 0CCURKE2JCE OF AIMOSPBERIC GUSTS AND OF
EELATED LOADS ON AIRPLME STRUCTURES
By Richard V . Rhode and Philip Donely
Langley Memorial Aeronautical Lc'^oratory
Langley Field, Va.
I
I-
"424-
UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
RO. BOX 11 7011
GAINESVILLE, FL 32611-7011 USA
NACA
WASHINGTON
NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
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nically edited. All have been reproduced without change in order to expedite general distribution.
* L - 121
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NIC A ARR No. 1)4X21
NATIONAL ADVISORY GOMYITTES '^OR AERONAUTICS
' ADVANCE RESTRICTED REPORT
PREQITliNCY CP OCCURRENCE Or^ ATMOSPHERIC GUSTS AND OP
RELATED LOADS OH AIRPLANE STRUCTURES
By Richard V. Rhode and Philip Donely
STO1MARY
A number of samples of flight acceleration data
taken hy the National Advisory Ccirimittee for Aeronautics
under a variety of operating conditions were evaluated to
determine the total frequencies and the frequency dls-
tribittion of atmospheric ^usts. The sa'nples include
ljl\B hours of operation by several airplanes of the
domestic airlines of tbe United States, a f.'artin M-IJO air-
plane of the Pacific Division of Pan American Airways
System, and the Boeing B-I5 airrslane of the Army Air Forces.
These data are svipplemented by V-G records, so that more
than 9»000»000 miles of operation are represented. Samples
taken on an Aerf^nca C-2 airplane at lovi? altitude in the
turbulent air of the earth's boundary layer are compared
with similar samples ta''cen on the Lockheed XC-35 airplane
at high altitude withjn cumulus-congestus and cumulo-
nimbus clouds.
Similar data of German origin have been reanalyzed
and included for comparison.
It WHS concluded that the distribution of gusts
within turbulent regions of the earth's atmosphere
follows a substantially fixed pattern regardless of the
source of the turbulence. The total frequencies are
therefore governed by the total length of flight path
in rough air, and operating conditions determine the
total frequencies only by affecting the ratio of the
length of flight path in rough air to total length of
the path. Gust-load frequencies were foui'ad to be
inversely'- proportional to airplane size.
It v;as further concluded that the gust frequencies
can be applied with small error to- the estimation of
stress frequencies in the primary structures of airplanes.
The results of the analysis are applicable to the fatigue
NACA ARR No. Lli.121
testing of the primary strucUire of the airframe and to
the estimation of the probability of encountering gusts
of excessive intensity within any stated period of
operation.
INTRODUCTION
The trend in airplane design tov/ard higher vtfing
loading, higher soeed, ctnd larger size - and consequently
toward higher mean stresses and greater severity of loads
on the structure - has resulted in a growing ap-^reclation
h-'T designers of the potential Importance of fatigue in
the prlm^ary structure and of the necessity for designing
on the hasis of fatigue strength for limited "life
expectancy." Reference 1, for exarnple, displays a great
deal of concern about the fatigue life of airplane
structures ,
Life exnectancy is governed not only by fatigue but
also by the ■probability of occurrence of single quasi-
static loads of such high m.agnitude as might endanger
the structure directly. This rjroblem has been made
more acute by the overloading of airplanes due to
wartime traffic demands.
An obvious prerequisite for control of fatigue
strength and for the determination of the probability
of single large loads is flight data that show the
frequency of occurrence of loads or stresses in the
structure correlated with the many factors that Influence
the frequencies. In the flight operations of transport-
type airp].anss the principal source of structural loads
and stresses is atmospheric turbulence, and most of the
required flight data annli cable to transport airr^lanes
may be obtained by measurements of the loads or stresses
during cruising flight in rough air.
Kaul (reference 2) and Fr-eise (reference J) have
presented data on the wing-load histories experienced
by a n-umber of airnlanes both under special test condi-
tions in rough air and in some 600 hours of cruising
flight on several branches of the Deutsche Lufthansa.
Kaul obtained results b'' means of an accelerometer located
near the center of gravity of the airplane and Freise,
by means of a strain gage mounted on a chord member of a
wing spar near the wing root. The results were expressed
in references 2 and 5 i^ terms of applied wing load.
NAGA ARR No. LL.I21
The UACA has from time to ti-fie collected data
slnuMar to these presented by Kaal and Freise . These
data include acceleration ineasureinents fron 1520 nours
of the early operations of the domestic airlines of the
United otates, 515 hours of miscellaneous cross-country
flyinn- oy the Boeing B-lp airplane, a ll^-hour round-
trip flight between Alaneda, Gslif.^and Hong Kong, China,
by a Kartin M-IJO airplane of Pan American Airways Sj^stem,
and two special gust investigations in the vicinity of
Langlsy Field, Va. Data taken with the KACA V-G recorder
(reference I4.) during some 8,300,000 miles of airline
operations are also included to take into consideration
the rare gusts of great intensity that are not normally
encoLintered during the taking of samples of limited
scope. In the precsent paper these data are analyzed and
compared with the Germ.an data of references 2 and 5
to establish a broader basis for the determination of
the frequency of loads resulting from atmospheric gusts.
SYI;:B0L3 AIID i-I0IVl2ITCLATUI^
An acceleration Increment normal to chord of v/ing,
g units
vif weight of airplane
S wing area
a slope of lift curve
p mass density of air at sea level
1/2
V0 ' equivalent airspeed
U.. effective gu.st velocity
K relative alleviation factor
c* mean wing chord
F total frequency, total nuinbor of occurrences of
a phenomenon in a sample
f frequency, number of occurrences of a phenomenon
within a class interval
ll NACA ARR No. iJ+IZl
fj, relative frequency (f/p)
^g^^- average gust inter\'al, average distance along
flight path in turbulent air between
significant gusts
L path of operation, total length of flight path
for any considered scope of operation
R path ratio, ratio of length of flight nath in
turbulent a;ir to r-ath of operation
The class interval Is the range between two values
of a measured quantity within which measurements of like
value are grouped (or classed) for the purpose of tabula-
tion of frequencies . The class mark is the definitive
value, or nid value, of a class.
EPJTECTIin^ GUST VELOCITY AS BASIC ATTRIBUTE
In most investigations of atmospheric turbulence
conducted by the NACA, the acceleration response of
airplanes to the gusts has been utilized in the measure-
ment of atmospheric turbulence. Although much of the
philosophy underlying the concepts involved in the use
of acceleration response in the iiieasurement of turbulence
has not been published, some basic considerations are
discussed in references l\. to 6. These considerations
lead to the relatively simi-nle concept of an "effective
gust velocity," which has been selected as the basic
attribute or independent variable to which the statistical
analysis best ai^piies. The ef f'ective gust velocity is
defined by the relation
PoaKU_VcV23
An = — ^_ (1)
The relative alleviation factor K allows for the
velocity of the airplane normal to the flight oath caused
t>y application of accelerstion during the finite time of
action of the gust. The factor X is given as a function
of the wing loading in figure 1. The derivation of this
curve, which takes into consideration f-r.e lag in transient
development of lift and the gust gradient, is attributable
NACA ARR No. lLiI21
to the authors tub has not 'bssn published. The curve
in figure 1 is -cart of the A^iierlcan design require:nent3
and has been published as figure 11(a) in reference 7«
Although derived at a relatively early date when little
information on gust gradients v/as available, the rela-
tionship described by the curve has remained in excellent
agreement with suDsequently obtained flight data and with
advances in the theory of ujisteady lift.
SGCPE 0? IIE^SI^EMSNTS
Extent of Operations
Domestic airlines .- Acceleration records for
1320 hours, or abo-.it ll^5»0G0 miles, of flight were
obtained during the early da^s of transport orerations
on the domestic airlines of the united States. The
data were taken during routine scheduled operations
over a neriod of about 2 years. The average operating
altitude was atout LOOO feet above sea level. The
airplanes on which the measurements were made included
the following tyoes: Pord 5~AT, Fokker P-IO-A,
Boeing IxO-E, and Boeing 80-A. The routes flov;n covered
most sections of tJ'-e United States and represent all
types of cli?nate and toncgraohy in this country. The
data from these early domestic-airline operations are
referred to subsequently as "sample 1." The charac-
teristics of the airplanes and a sum-mary of the operating
conditions for all the samples are given in tables I
and II, respectively.
A large number of acceleration records were obtained
later on the domestic airlines. These records represent
i|2,105 hours, or about 7>'-0C)»000 miles, of routine
transport operations by Boeing B-2l|.7, Douglas DC-2,
and Douglas DC-5 airplaiies on several airlines covering
most sections of the United States. The data fro:Ti these
later domestic operations are called samples 2, 3, s-^d l\.
for the B-2i4.7, DC-2, and DC-3 airplanes, respectively.
(See tables I and II.)
Alam.eda to Hong Kong .- Records were taken with
number of instr-oments during a round-trip flight in
Jione 193ci from Alameda, Calif, to Kong Kong, China
by a Martin M-I30 airnlane of Fan American Airways
System. The average altitude vras atout 10,000 feet
MCA ARR !To. rJ.}.l21
and the flying time \vas II5 hoiirs, oorre spending to
17,000 miles of flight. The data from this flight
are called sample 5'
Records of acceleration covering 12^232 hours, or
about 1,520,000 miles, of routine operations with
Martin M-I30 and Boeing B-31I4- airplanes are included
in the analysis for the route from Alameda to Hon^ Kong.
The data from these operations are called saraple o.
Boeing P-I3 airplane .- Records of acceleration
v/ere taken on the E-1'3 aTrplane during 315 hours, or
about 14.8,000 miles, of miscellaneous flying including
a number of cross-country flights over various sections
of the United States and one round trip to the Panama
Canal Zone. These flights were made betv/een November 1953
and June 19^0. Tre average altitude of the operations
was aboijit ^QOO feet. The data are subsequently called
sample 7«
XC-33 airplane .- Tre Army Locldised XG-55 alrrlase
was flown in the vTcinity of Langley Field, Ya . during
an investigation of atmospheric turbulence in the
sur;imers of I9I4-I and 1914-2. vleasurements of acceleration
and airspeed were taken only during flight through rough
air, mostly within cumulus-congestus and cumulo-nimbus
clouds. The surveys were made at various altitudes up
to 3li»000 feet. Only two samples from these surveys
are included in the analysis. One of these samples
(sample 8) v;as selected at random from the several sets
of data; the other sample (sample 9) represents the
roughe s t f li ght .
Aeronca C-2 airplane .- An Aeronca C-2 airrlane was
flown auring an investigation in 1957 of turbulence at
very low altitudes in the earth's boundary layer. A
sam.ple (sample 10) was selected at random from the
complete data and is included here for anal^^sis.
Apparatus and Limitations
Domestic airlines (earlv. operations) .- In the early
transport operations only acceleracion records were
obtained. The records were made v/ith commercial vibra-
tion recorders that had been rebuilt into accolerometers
by the NACA. Thiese accelerometers recorded against time
on a waxed-paper disk about I4. inches in diameter. The
instruments were arranged to make one revolution of the
NAG A ARR 'So. Llil21 y
disk in several hours. The time scale was therefore
cramped and only the moderate and the large values of
acceleration could be counted.
As the airspeed was not recorded, effective gust
velocities were evaluated on the basis of the known
cruising speeds of the airplanes.
Although the slopes of the lift curves were known
from available data, the wing loadings of the airplanes
as flown vi'ere not usually known. Effective gust
velocities were, therefore, evaluated on the basis of
the assixmption that the airplanes were flown at normal
gross weight. This assumption leads to somewhat
conservative values, as the airplanes were usually
flown at less than normal gross weight.
Domestic airlines (re ce nt operations) .- In the more
recent domestic transrort o'oe rations" both acceleration
and airspeed were recorded by means of MACA V-G recorders,
which are described in reference l\.. These instrujnents do
not record against time; the accelerations are registered
vertically on a small smoked-glass plate while the values
of airspeed are recorded horizontally. The record is
an envelope of the maximum, and mdnimaira values of accelera-
tion against a scale of airspeed. The sm.all accelerations
are illegible within the envelope and only the larger
values of acceleration that project beyond the envelope
of the small values can be counted.
No assumrtion as to airspeed is required with the
KAGA V-G recorder, as the instantaneous value of airspeed
associated with any observed acceleration is given by
the record.
As in the case of the early transports, the wing
loadings of the more recent transport airplanes as
flown were not Imown exactly. It was determined,
however, that a reasonable aDproximation of the average
operation weight was 85 percent of the normal gross
weight; this value was used in the evaluation of effective
gust velocities.
Alam eda to Hong K ong . - During the round- trip flight
between Alameda and Eon^ Kong of the M-IJO, the airplane
was equipped with an NAGA. V-G recorder, an NAGA recording
accelerometer, an NAGA airspeed recorder, and several
8 MCA ARR No. 1)4.121
NACA scratch-roccrding strain gages. Both the accel-
erometer and the airspeed recorder recorded the measiired
quantities against time with a scale sufficiently open to
permit detailed evaluation of the records. The strain
gages also recorded against tliue, .but the riiotion was of
an intermittent character so that all the strain peaks
could not he counted. Only one strain gage operated
satisfactorily throughout the flight. Many of the strain
values could, hovifever, he correlated v/ith the accelera-
t i on me a 3 ur eme n t s .
During the flight an observer operated the instru-
ments and a comclete log of time spent in rough air, .
total time, airplane weight, and other pertinent detail
was kept. The records therefore permit a complete and
accurate evaluation of the frequencies of effective gust
velocities.
Except for the records taken on this round-trip
flight, all records of acceleration and airspeed taken
on the Alameda-Hong Kong route were made with NACA V-G
recorders ,
B-l~; airplane .- The 3-15 airplane was equipred with
an ITACA recording accelero-^eter and an NACA airspeed
recorder having t'^e time scales sufficiently open to
permit detailed evaluation of the records. A number
of NACA and. L'VL t^-pe scratch- recording strain gages
were installed on shear and chord members of a wing spar
at two stations along the span. The DITL type gages
recorded continiTOUsly against time, and a count of the
strain peaks is rjossible although such a count has not
been made. As in the case of the round-trip flight to
Eong Kong by the ^^.-IJO airplane, the strain records are
used herein only to show the relationship between a
number of meas^ared strains and accelerations.
During the flights of the 3-15 airplane, an observer
operated the instruments and kept a ccmrlete log of time
spent in rough air, total time, airplane weight, and
other pertinent quantities. The records from these
flights t'lerefore rermit a conrlete and accurate
evaluation of the frequencies of effective gust velocities.
XC-35 airr'lane .- The XC-55 airplane was equipped
with an "iTAGA recording accelerom.eter and an NACA air-
speed recorder set to give an open time scale. The records
obtained are amenable to detailed evaluation. The
NAG A ARR ;-'o. l1xI21
CDeratlng weights for all flights are laiown, and effec-
tive giast velocities can be cor.noletely and accurately
evaluated.
Aeronca C-2 air^^lane.- The Aeronca C-2 airplane
v/as also fitted with an KACA recording acceleroneter
and an NACA airspeed recorder, and the operating weiglits
are accurately kno^n. Detailed evaluation of effective
gust velocities is possible from the records.
e\7^lt;ation cf frsou^ncy distributions
AND TOTAL FHS^riENCIES
Method of Count
The r.iethod of counting frequencies used herein
was dictated largely by the type of record available
for analysis and by the quality of the records. Only
the records from the KACA acceleroineter permitted
detailed examination, but even v/ith those records it
was necessarj' for 'Dractical reasons to confine the count
to single maxim-urns and rainimums, or peaks, between any
two consecutive intersections of the record line with
the Ig reference level. This m.ethod of count neglects
the m.inor oscillations suoeri/aposed on those counted.
Kaul (reference 2) emoloj^ed a similar method of count,
and in this respect the German and the American data
are comparable .
From the records for sample 1, in which the time
scales were cramped, and from the records taken with
NACA V-G recorders it was not possible to determine
whether the acceleration returned to or crossed the
Ig reference level after the attainment of a maxim.um
or minimum value. In tiiese cases, therefore, the
evaluation was made by counting the acceleration peaks
standing out from the envelopes of the small accelerations,
Since, excent for the V-G data, it v;as considerably
more convenient to count accelerations directly than to
convert accelerations to effective gxist velocities prior
to the co^jnt, the conversion was made for relatively
short sections of each sample on the basis of mean air-
speeds for these sections. In this way large errors in
airspeed were avoided and the small- deviations of the
airspeed from the selected means v/ere of no great
significance .
10 MCA ARR 1:0. l4l21
Class intervals
The intervals for the classification of frequencies
were chosen at about the sriallest values consistent with
the accuracy of the several acceleration measurements -
namely, about O.lg. For a number of reasons the
intervals v/ere not always quite the same. This fact is
of no consequence for, in any event, since the accel-
eration values were conveniently converted to effective
gust velocities after the count was made, the class
intervals expressed in terms of effective gust velocity
would not rem.ain equal for the various samples because
of differences in air'-'lane characteristics and airspeed.
The class intervals, expressed in terms of gust velocity,
corresponding to the actual evaluation are given in
table III.
Threshold Values of Acceleration
and "^'ffective 'just v'elocity
In co'jr.ting the frequencies in the lowest class
('-hat is, the class containing the s^nallest values of
acceleration), t^e result depends upon the m.inimum values
that can be observed. Cn the records from the NACA accel-
erometer, variations in acceleration attributable to
gusts as small as O.C2g can be ccnvenientl'^ observed,
and all greater values can therefore be counted. This
limit of acceleration for which, the count can be made is
termed herein the "threshold value" of the acceleration.
On the V-j records and the records from the con-
verted cormnercial recorders used in obtaining samiole 1,
the threshold values of acceleration were rather high
because of the lim.itations of the instruments oreviously
described.
The threshold values for the sai?iples are given in
terms of effective gust velocitv in table III.
Relati ve-:^equency Distribution
7t:e frequencies f and tne total frequencies F of
the gusts for the 10 samoles are given in table III as
counted within the selected class Intervals and to the
threshold values of effective gust velocity.
MCA ARR Fo. lJil21 11
In order to arrive at the broadest and most rational
view of gust-frequency dis bribution, all daba were
plotted in the form of relative-frequency polygons
(reference 8). The polygon of relative gust frequencies
is a graph of the ratios f/P = f^ for the different
classes plotted at the respective class marks on a scale
of effective gust velocity. Since the shape of such a
polygorx is dependent upon bhe sl.?:e of the class interval
andi upon the class mark of the lowest class within v^hich
the coimt is made, polygons for the different samples
can be compared only wlien nlotted for a common class
Interval and for a common lowest class. In order to
place all the data on a comnarable basis, a common
class interval of I4..5 feet ^er second, the largest of
the class intervals for wh.l ch cou.nt was made, was chosen.
Since sam"ole 5 ^'"ic. samples 7 to 10 have about the
same small threshold value falling within class 1,
relatj ve-frequency polygons for these samples can be
plotted ii.imediately after conversion to the coiamon class
interval. The polygons for samnles 5 and 7 s.re shown
in figure 2; the polygons for samples 8 and 10, in
figure 5; and the polygon for sample 9? i^ figure []_. A
reference polygon, "relative distribution A," is shown
in these figures to facilitate cornparisons .
In constructing polygons from the remaining data,
samples representing generally similar operations were
combined. The combination of these samples, which
include the V-G data, was rerforraed in such manner as to
bring the relative frequencies of the rarer large gusts
into a proT^er relationship with the other data. The
basic assumption involved in the process was that, for
data covering a large scope of operations, the relative-
frequency distribution follows a single pattern. The
validity of this assixraption is discussed in a later
section.
In the case of sam.ples 1 to []., all of which
represent dom.estic transport operations, none of the
data extended to low values of effective gust velocity
for reasons previously given. The total frequencies
for these samples are, therefore, relatively smaller
than the total frequencies for the more refined samples
because of th? omission of the I'requent low- value gusts.
In order to brir^g the relative-frequency nolygon for the
combined sairiples 1 to Ij. into T:iroi-)er relationship v\?lth
the polygons for the m.ore complete samrles, it was
12 KACA ARR IIo. LliI21
necessary fi.rst to estimate the frequencies of the
missing low-value gusts and the corresponding total
frequencies. For this purpose a mean relative-frequency
distribution from samples 5> 7> 8, and 10 was assumed to
represent the missing low-value gusts of samnle 1, which,
of the combined samples 1 to l^., had the lov/est threshold
value. iVith this assiimptlon, the total frequency of
sample 1, including the frequencies of the lower classes,
was estimated to be 1,6C0,000 gusts for the 1520 hours
of operation.
The frequencies of samnle 2 were then reduced bv the
ratio of the path of operations of sample 1 to the path
of operations of samnle 2 (table IV), Similarly, the
frequencies of samples 3 -^nd l\. were reduced to correspond
to tlie path of operations of s,arrn?le 1, The s'om of the
reduced frequencies within each class of samples 2, 5,
and ).|. was then added to sample^ 1 to obtain the polygon
for the combined samples 1 to 14.,
In combining samples 1 to Ix a pi-e caution was
necessary in regard to class 6 because of the following
considerations. After conversion of sample 1 to class
interval k»5f the highest class in which data fell was
class 6. This class is the lowest in which data from
the V-G records fell. Thus, frequencies were available
from all samples of the combination only in this class.
In arriving at a combined frequency for class 6, two
nossible methods could have been used; namely, either
the reduced freqviencies from samples 2, y, and l\. could
have been averaged with the frequency of sample 1, or
the most reliable sample could have been used without
inclusion of the les^"5 reliable samples. The second
method was actually used and the frequency for class 6
was taken from sample 1 since the obscuration of some
class 6 acceleration peaks within the V-G envelopes of
samples 2, 3, and l\. made these data less reliable for
this class.
The freq^.iarcies for samples '5 and 6 were combined
in a manner similar to that in which samples 1 to 4
were combined. In this case, however, it was
unnecessary* to estimate a total frequency for sample 5f
as the threshold value was comparable to the threshold
values of the other comnlete samples. Also, inasmuch
as the highest gust-induced acceleration for both
samples was recorded within the rather limited scope
of sample 5i this one value j^as assigned a frequencjr
of unity for the combined samples.
FAG A ARR No. lij-Kl I3
Polygons for the ccnbined camples 1, 2, 3> and l\.
and for the combined samples 5 S-^d 6 are shown in
figure 2.
DISCUSSION
Relati ve-Frequency Distribution
Significance of various samples .- Tlie relative-
frequency distribution for any sample of data does not
necessarily represent general average conditions. ?or
instance, the frequency distribution of sample 5 is not
representative of average conditions because of the
occurrence in sample 5 '^^ '^'^^ of the most severe gusts
ever experienced on the Pacific Division of the
Pan American Airways System. Even without other sam.ples
for comparison, this fact mi _2,ht have been suspected from
the form of the relative-frequency polygon for sample 5
in figure 2, which shows a sudden break to large values
of Ue . Sample 9 -i-S anotlier case tl:at is not repre-
sentative of average con-litions, because this sample
was obtained during the roughest of a considerable
number of flights made during a soecial investigation
of turbulence within cumulus-conge stus and cumulo-nimbus
clouds. For sample 9> ^^ can be observed from a com-
TDarison of tbe polvgon in figure I4. v;ith the other
nolygons in figures 2 and 5, the frequency distribution
indicates relative!"" high proportion of gusts of high
intensity.
In contrast to the "fullness" of the frequency
distributions for samples 5 ^ind 9» the frequency distri-
bution for sample 7 shows relatively low proportion of
gusts of high intensity. Tiriis result is in line with
the conditions of ODeration, according to v/hich regions
of high turbulence were avoided as far as possible so
that greater weight v;as given the frequencies of the
smaller gusts .
Since the conditions governing samples 5> 7> ^^'^ 9
are Imown to give rise to more or less extreme frequency
distributions, a sample representative of average condi-
tions a-oplicable to large scoDe of operations would be
expected to lie soinewhere between the extremes. Probably
the most representative of the samples containing
detailed data an the lowest classes are sam.-oles d and 10,
ll^ KACA ARR No. ri;l21
v/^ich v/ere selected at random from a considerable mass
of data. The relative-frequency polygons for these
sainples (fig. 3) may be observed by comparison with
figures 2 and it to lie between the polygons for
samples "^ and 9 ^-^d inside the end point of the polygon
for sample 5-
The combination of samples 1 to L. and of samples 5
and 6 in the manner described greatly extends the scope
of the data ap-oli cable to the respective operating con-
ditions represented. The combined sajiiples are thus more
true than any single small sample in the sense that the
influence of accidental occurrences, such as the sncouin-
tering of an unusually strong gust in sample 5> is sub-
merged In the mass of data; that is, accidental occur-
rences of this oort occur in sufficientlv large number
v;ithln a sam.ple of large scope that they become more
truly representative of the average conditions. Fig-
ure 2 shov/s this effect clearly; the combined sample
5 and 6 and the combined samole 1 to k have relatively
uniform distribiitions Iving betvveen the extreme distri-
butions of samriles 7 and 9'
For comnarison with the samples presented herein,
distribution polygons of JJq have been constructed
from Eaul's data wit^- a clasa interval of 1+-5' It may
be seen from figure 2, v;hich shows the envelopes of the
nol-v'gons for Kaul • s data, t'-at the German and the
American results are in very good agi'eem.ent.
Influence of airDlan e characteristics and source
of turbulence.- it is evident from che -orecedina; dls-
cussion x;ha^the major discrepancies between the fre-
quency distributions for the various samtiles can be
accounted for largely by accidental occurrences during
the operations. 'A'iien the scope of the samples is
sufficiently increased to be representative of average
operating conditions, these accidental influences are
not so strong and the frequency distrioutions tend to
fall into the same pattern regardless of the source
of the data. The results therefore indicate that
individual gusts in turbulent regions of the atmosphere
are distributed on the whole in a fixed manner irrespec-
tive of the location of the turbulent regions and of the
source of the turbulence.
Figure 3 further illustrates the similarity of
different samples. Sample 3 was
NAG A ARR No. 11^121 I5
obtained at high altitude within cujriulo-nirabus and
ciomulus-congestus clouds and represents turbulence
having its origin in thermal convective processes.
Sample 10, on the contz'sry, was obtained at very low
altitude in the absence of thermal effects and the
turbulence arose fro~n the shearing of the wind in the
earth's boijindary layer. Notwithstanding these con-
siderable differences in the aerological conditions,
the frequency distributions are nearly the same and they
are also in close agreement with those from other sources,
Another point, most clearly evident from samples 3
and 10 but also evident fron the other data, is that
the distribution of turbulence as measured is largely
independent of airplane size and other airolane charac-
teristics. The close similarit-'- of the distributions
for saruple 8 (obtained with the Lockheed XC-55 airplane),
sample 10 (obtained with the Aeronca C-2 airplane),
and the samples from the airline operations indicates that
the basic assum.ptions and concents underl^/ing the gust-
load formula (equation (1)) are correct.
Influence of disturbed motion of airplane in
continued s^,vere turbulence.- Although the foregoi n g
remarks aoout the influence of the airplane character-
istics apply on the average, in continiied sovera
tiarbulence the frequency distribution may ampear to
contain abnormal frequencies in che higher classes
unless precautions are taken to eliminate the effect of
disturbed and controlled motions of the airplane. In
the flight from, which sample 9 ^^^^ derived, which was
the roughest of a large number of flights through
curaulo -nimbus clouds, the airplane motion was con-
siderably disturbed from, the desired straight path,
so that the gyroscope of one of the flight instrum.ents
was at times put out o.f action (referer^ce 9). Under
these circumstances the airplane was subject to moderate
acceleration fluctuations of long period upon which the
short-period accelerations due to the turbulence weri
superimposed. .Iilien the count was made in the described
marjier chosen for the general analysis, abnormally high
values of effective gust velocity v/ere ascribed to the
various frequencies and the polygon appeared full
(fig. Ij.) . '^hen bhe count v/as made with respect to the
variable datum caused by the disturbed r.:otion rather
than with respect to the 1 g datum, the frequency distri-
bution confom:ed more nearly to the distributions of the
other samples. The co:^i>ected nolygon retained a certain
l6 MCA ARR No. li|l21
degree of fullness, however, which may he ascrihed to
actual greater frequence of the riiore severe gusts.
rifferences hetv/een two polygons li]<:e those shown
in figure I|. provide 'Tieans of evaluating the effect of
the disturbed motion on the freqtiency of applied loads.
The data given here apoly specifically to the char-
acteristics of the XC-35 airolane and cannot oe safely
applied to other cases. This fact is of small concern,
because large disturbed 'notions are rarelv encountered
in normal operations, so that such effects as are shov/n
in figure I4. would hardly be noticeable in a sample
representing large scope of operations.
Factors Governing Estimation of Total Frequencies
Average and standard gust inte r vals . - The fa c t
that the frequ-fncy distribution follov;s a fixed oattern
for samples of large scope indicates that the total fre-
quency is proportional to the distance flown within tur-
bulent regions. Conversely, the average spacing betv;een
gusts is inversely proportional to the distance flown.
In order to -provide a use'f'ul basis for estimating the
total frequencies of significant gusts (n;:^iely, those
causing measurable acceleration of an airplane), the
term "average gust interval" K^^ is introduced. This
tern is defined as tl-'e average distance along a flight
rath in tu.rbulent air between significant gusts. Nwaer-
ical values of Xg^y have been derived from the total
frequencies of sam.Dles 5> "> 3, 9, and 10 and are given
in table IV. ■ In evaluating X.^^^. the actual path -lengths
in rough air, which are also given in table TV, were
divided by the total frequencies.
The average gust interval \^y is plotted against
mean wing chord in figure 5- The dependence of Xr^y
on airplane size is evident, although the exact nature
of the relationship is not entirely clear from the
figure, Ttie average gust interval for the four samples
shown in figure 5 i^ 11 chord lengths. This value may
be used to estimate total frequency v/hen the path length
in turbulent air and the airplane size are knovm .
Although the joints on figure 5 do not fall on a straight
line, they could probably be made to do so by suitable
correction. Figure 6 of refarence 10, for example,
MCA ARR No. 1J4.12I I7
shovi'3 a marked t'Sndency for average gu3t interval to
increase with gust intensity; corrections for this efi^ect
woi\ld raise the point for sample 7 and Tower the point
for samples 8 and 9*
Pat h ratio.- In order to estimate the total fre-
qnencies~fc5r ac trial operating conditions over a long
period of operations, it is necessary to know something
about the percentage of the total flight path that falls
within regions of turbnlence or about the actual total
frequencies that occur within total paths of operation
of large scope. Information on the relative period of
operation within turbulent regions is given in table IV
for samples 5 and 7 in terms of the path ratio R. The
total frequencies are
? = 5230 rSI:-
' av
or
F s; 5.PJO -^ (2)
lie
when L is in miles, ^^-^ is in feet, and "c is in
feet.
Although the path I'atio is not knovm for the other
samples to which such a ratio Is applicable, the total
frequency of sample 1 is estimated at 1,600,000 gusts
to a threshold value of Ug =0.3 foot per second in
the manner previou.sly explained. Because this total
frequency applies to a nath of operations of l[;S,000 miles
and because the mean choi-d was about 10. S feet, R is
approximatelv G.2I1 from equation (2).
Operating conditions .- Tiae path ratio and therefore
the total gust frequency for any path of operations
manifestly will depend on the operating conditions. A
feeder-line transport operating overland at low altitude,
for example, vvould be expected to enco'unter a greater
percentage of tu.rbulent air than an airplane operating
at high altitude above the mechanical turbulence near
the ground and above most of the conveotive clouds.
Although the operating conditions are important in
defining total frequencies, the data available at this
time are too sketch^^r to permit correlations between
l3 NACA ARR No. l4l21
total frequencies and the factors ccmposing the operating
conditions .
In order to "~'ermit estiinations of total frequencies,
all available pertinent data including those from German
sources have been asseinhled in table V. The first four
sets of Gernan data in table V have been based on the
data of reference 5. Owing to the fact that Freise
presented frequexiclea for noncontiguous classes, the
total frequencies given v/ere obtained by multiplication
of the frequencies co^'onted bv Freise by 2,5, which is
the ratio of the interval between class marks to the
interval within which the original count was made. The
path ratios from the German data were estimated by
application of equation (2).
In applying the data of table V to the estimation
of total frequencies, some nida;m.ont will have to be used
to ensure that values of path ratio most nearly repre-
senting the operating conditions are used. It will be
noted that path ratios range from about 0.006 to O.2I4.,
with an average value of aoout C.l.
APPLICATION 0? GUST FHEQU.^NCIES TO
ESTIVATION OF STRESS FREQUENCIES
Choice of Gust-Frequency Distribution
The relative-frequency polygons representing the
available data permit some latitude in the selection
of a frequency distribTition to be applied in a design
nroblem. Choice o^ a conservative gust-frequency dis-
tribution for use in estimations of stress frequency
depends i;pon the relative significance of the small
and. large stresses in tlie oroblem r'-nder analysis. If
the problem is to determine the probability of occur-
rence of large stresses in excess of the strength of
the structure at the design limit load, a more con-
servative estimate will result from the selection of a
frequency distribution having relatively high frequencies
at the higher values of effective gi^st velocity. For
other purposes, the selection of a distribution having
the higher frequencies at the low effective gust
velocities may give a more conservative estimate. Two
limiting relative-frequency polygons, A and B, representing
MCA ARR No. l1|I21 I9
the approximate limits of the data are shov/n in figure 6.
Polygon A has previo^isly been used as "relative distri-
bution A" to facilitate comparison of the data shown in
figures 2 to J4,. Per some purposes 3i.iiiimation curx'es, or
ogives (reference 3), are ^.lore convenient representations
of frequenc-'-'- distributions than fi'equency nolygons .
Unit svormatlon curves ccrresnondr'ng to polvgcns A and B
of figure 6 are therefore given in figure 7.
Relation betvi/een Effective Gust Velocity
and Stress in the Structure
Direct ap-oll cation of the gust-frequency distribu-
tion and the total frequency by means of equation (1)
with the usual design assujiiption of static load will
yield ap'oroximately correct values of stress frequency.
There are, however, several phenomena that modify'- the
actual stress frequencies fro'-i the stress frequencies
esti^nated in this simple manner. These nhenomena
include ;
(1) Superposition of uncounted small gusts on the
larger gusts counted
(2) Distribution of gust velocity across the span
(5) D^mamic response of the structure
Uncoun ted surfer imposed gusts.- As loreviously m.en-
tionecirj the minor peaks in the acceleration records
were not ordinarilv counted unless they occurred as
single phenomena between tvto consecuta x^e Irtersections
with the Ig datum. A special total count of these neg-
lected peaks was made in one case fr'om a clean-cut
record without reference to the exa-ct m.agnitudes of the
acceleration increments or to the acceleration level at
which they occurred. It was foimd t':at the number of
these s;nall superimposed ■neaks was about twice the "cotal
frequenc:/ counted in the manner adapted for the general
analysis. These superimposed peaks were irregular in
shape, sequence, and time or place of occurrence. The
magnitudes of" th© -superimposed, acceleration peaks with
respect to the ad.iacent acceleration levels were small
and did not in any case exceed a value corresponding to
AUg = I4..5 feet per second. The great majority of these
peaks were -near, the threshold value of O.3 foot per second.
20 MCA ARR No. ri|T21
Discussion of the reason for the consistently
small magnitude of the su^oerimpossd peaks is beyond
the scope of this paper, as the question of the rela-
tionship between gu.-^t intensity and gust dimensions
and the question of the probability of superposition
of randomly distributed gusts are involved.
Kaul (reference 2) reports a similar count of
suTDerlmposed peaks from a record of vifing-tip deflection.
Kaul implied that the acceleration records did not
contain such -neaks and that the extra peaks counted
v/ere due to damped vibration of the wing structure
after disturbance h'T the individual gusts. The ratio
of bhe number of extra -oeaks to the nujnber co^onted
with respect to the Ig datum, was, however, about 2 -
a result that Is in agreement with the authors' count
of the extra acceleration peaks. It seams probable,
therefore, that some additional acceleration peaks due
to 3^^perimposed gusts an-:' some acceleration peaks due
to vibration response of the wing-fuselage system, were
acttially coLinted in both cases.
So far as the mere question of gust frequency
is concerned, without regard to superposition, these
additional small -neaks may be placed in class 1. The
inclusion of such s 'lall peaks in a fatigue test, however,
cannot properly be effected on the basis of this simple
classification. If the superposition of the additional
small peaks is felt to influence the fatigue strength
to an important degree, the phenomenon of superposition
must be taken into account. The superposition may
perhaps be pictured suff Icientlj^^ well for application
to fatigue tests by imagining the periods of the
x'arious stress cycles to be proportional to the
amplitude. Farther, assume the cycles corresponding
to the basic gust frequency distribution to be applied
without super-cosltion. Finallj?-, superim.-cose the
additional small cycles on the basic cycles of class 2
and of the higher classes, distributing the additional
small -oeaks uniformly along the time scale to determine
the numbers to be superimposed on each basic cycle.
The actual anollcatlon of surerlmposed cycles in
fatigue testing is a difficult matter and requires
either the constr't.iction and use of a familv of summation
curves with mean stress as a parameter or the construc-
tion of a comnlex fatigue m.achlne with which the small
MCA ARR No. lM-121 21
cycles can be superimposed on the lar:3er cycles. The
derivation of the surrmiation curves would require that
the basic stress cycles be considered as square waves
.for the purpose of establishing a finite number of mean
stress values, and the actual testing would involve the
difficu.lty of occasionally holding the mean stress levels
at very high values while the small cycles were being
applied.
Dist r ibution of gust velocity along span . - The
distributrbn of gust ve 1 oc ' tj al ong the s -oan o f a wing
is not always uniform, so that the usual assumption of
uniform distribution leads to som_e error in estimation
of stress frequencies from the gust frequencies. The
results of the gust investigation with the XC-35 ai^:"-
Dlane indicate the various typical spanwise distribu-
tions that actually occur and the frequency of each
type. If desired, further refinement of the stress
frequencies can be made from these data, which are
reported in reference 11.
D^Tiamic re spo nse of the structure .- Owing to the
flexibilit" of wing structures, accelei-ations caused by
gusts v;ill not be the same at all points along the
span. The accelerations at the v.'ing tips will be
somewhat greater than and out of phase with those at
the .fuselage. Some calculations pertaining to two
typical large airplanes (reference 12) and tests in
the Langley gust tunnel indicatod that the maximum tip
acceleration at about 200 miles per hour was about
twice the acceleration at the fuselage and occurred
earlier than the fuselage acceleration. The wing
oscillation in these cases damped out in 1 to 2 cycles.
The effect of such dynamic action is to cause, at the
outer portions of the wing primary structure, super-
im.posed stress cycles with a maximum amplitude about
10 percent of the static stress for the uniformly
distributed gust.
Because the natural rierlod of v\f3.ngs increases
almost in direct proportion to the wing linear dim.ensions
and becaiise the size of gusts to vdiich airplanes will
respond also increases as the airplane size, the ratio
of natural i^eriod to neriod of application of load
remains about constant for constant flight soeed. The
d:/namlc response of the structure would, therefore,
aripear not to Increase with airolane size.
22 WACA ARR No. r4l21
If desired, the additional frequencies of the small
dynainic stresses at the cuber portions of the wings can
be Included in the same manner as the uncoijnted super-
imposed gust frequencies.
Exp er imental evid ence .- Sc;ne test results from
the stress 'and acceTeration raeasurements on the 'J-IJO
and the B-I5 airplanes are shovi/n in figures 3 to 10.
Comparative stress frequencies cannot he shov/n, but the
figures illustrate the degree of agreement between peak
stresses as measured and as would be calculated by the
usual assixmption of static load for the corresponding
measured accelerations.
For the Vi-lj>0 airrlane (fig. 8) a datum stress
increment corresDonding to application of a load factor
of 1 was determined by taking the difference between
stress while in level flight in smooth air and stress
while at rest on the water. Correction was made for
wing weight. The olot therefore indicates the agree-
ment between gust-induced stresses as measured and
gust-induced stresses as determined by multiplication
of the datujtn stress by the meastxred acceleration. The
distribution of the points along a line of 1^5° slope
indicates excellent agreement; this result and the lack
of scatter beyond the limlbs of error denote lack of
serious dyiriamic response of the structure.
The results shown for the B-I5 airplane in fig-
ures 9 ^^d 10 are given simply as plots of measured
stress against measured acceleration because a datum
stress increment was not measured. The stress-load
relationships shown are, hov/ever, substantially linear;
this fact, together with virtual absence of scatter
bej-ond the limits of error, shows absence of serious
d;;>Taamic response.
These results indicate that, with the exception
of the small uncounted superimposed stress peaks, the
stress frequencies of the -orimary wing structure will
be given with sufficient exactness, for all practical
purposes, by application of the gust frequencies through
equation. (1) and the usual assuinption of static load.
Application to tail surface s.- Tlae gust-frequency
data given herein are not directly applicable to tail
surfaces. Som.e unpublished flight data on the relative
magnitudes of effective gust velocities on wings and
MCA ARR No. LLi.121 25
tail surfaces Indicate, however, that a rough approxi-
mation of the tail-load frequencies might be obtained
by utilizing the gust frequencies given here and by
multiplying the values of effective gust velocity by 1.6
for the vertical tail surfaces and by O.5 for the
horizontal tail surfaces.
CONCLlTDINa REMARKS
Available flight data are sufficient to indicate
that the distribution of gusts vvithin turbulent regions
of the atmosphere follows a substantially fixed pattern
Vi/hich is independent of the source or cause of the
turbulence. The average Interval betvi/een gusts causing
measurable airplane response is about 11 chord lengths,
and the total frequency of significant gusts in any
stretch of rough air is therefore the length of the
flight path in rough air divided, by 11 times the mean
wing chord.
The total gust frequency to be expected during
the operating life of an airplane depends upon the
operating conditions, v.'hich determine the ratio of
path length in rough air to the total path of opera-
tions. Information on the path ratio as a function of
operating conditions is sketchy at this time and
should be supplemented by fiirther measurements . From
the available informatjon, the average path ratio for
a variety of operating conditions is about 0.1, although
Individual values vary between about O.OO6 and 0.2l|. .
The available data on gust frequencies permit
ar-proximate determination of stress frequencies in
the orlmary structures of airrlanes due to gusts.
These frequencies aroear to describe adequately, for
many design purposes, the stress conditions for
transport-type airplanes in flight. Supplementary
information on stresses in secondary members of the
structure and on the additional frequencies of small
stresses in the primary structure resulting from dynamic
structural response and nonlinear lateral gust distri-
bution is desirable. This information vi/ill have to be
2l| NACA ARR No. ll'^^l
o'bta^.ned by stress measurements correlated with airplane
size, clead-v.'eight distribution, and other factors.
Langley Memorial Aeronautical Laboratory
National Advisory Coinmlttee for Aeronautic:
Langley Field, Va.
NAG A ARR No. l4l21 25
RSFERSNGSS
1. Bland, Reginald B., and Sandorff, Paul E.: The
Control of Life Expectancy in Airplane Structures.
Aero, Eng. Review, vol. Z, no. 6, Aug. 19^3 ^
T.^, 7-21.
2. Kaul, Hans ".V.: Statistical An.alysis of the Time and
Fatigue Strength of Aircraft Wing Structures.
NAG A Tr ::0. 992, 191^1.
5. Preise, Kelnrich: Spitzenv;erte und KMufigkeit von
Boenbelastungen an Verkehrsflugzeugen. Jahrb. 1953
der deutschen Versuchsanstalt fur Luftfahrt, E. V.
(Berlin-Adlershcf ), pp. 2IO-22I4..
\\. Rhode, Richard V.: Gust Loads on Airplanes. 3AE Jour.,
vol. Ii-O, no. 3, Iv'arch 1937, ?" • 3l-33.
5. Rhode, Richard V., and Lundquist, Eugene E.: Prelimi-
nary Study of Apnlied Load Factors in Bumpy Air.
NAG A TN No. 37!^, 1931.
6. Donely, Philip: Effective Gust Structure at Low
Altitudes as Determined from the Reactions of an
Airplane. NAGA Reo. No. 692, I9I4.O.
7. Anon.i Airplane Airworthiness. Pt . O'l of Civil Aero.
Manual, CAA, U. S. Deot. Commerce, Feb. 1, 191^1,
p. .2-2.
8. Rietz, H. L. : Frequency Distrloutlons - Averages and
Measures of Dispersion (Elementary Methods).
Gh. II of Handbook of Mathematical Statistics,
H. L. Rietz, ed,, Houghton Mifflin Co., 192i^,
VV' 20-53.
9. 'flight Research Loads Section: XC-55 Gust Research
Project Bulletin No. 5 - Operations near Gold
Front on August 12, 194-1 - Maximum Gust Intensities.
FACA RE, April I9I+2 .
10. Moskovitz, A. I.: XC-35 Gust Research Project
Bulletin No. 8 - Analvsls of Gust Mi-asuroments .
NAG A RB No. LkD22, \4i^.
26 MCA ARR No. 11^.121
11. Moskovitz, A. I.: XC-55 G'^i.st Research Project
Bulletin No. 7 ~ Preliminary Analysis of the
Lateral Distritution of Gust Velocity along the
Span of an Airplane. NA.OA RB, March I94.3.
12. Pierce, Harold 3. : Dynamic-Stress Calculations for
Two /^irolanes in Various Gusts. NACA ARR,
Sept. 191^1.
NACA ARR No. L4I21
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