Uy\ 5s / US.—Wgir Production Board --Office, of Production , Research and pevelppment e Solar energy,, utilization for house heating. RESEARCH REPORT SOLAR ENERGY UTILIZATION FOR HOUSE HEATING OFFICE OF tODUCTION RESEARCH AND DEVELOPMENT -WAR PRODUCTION BOARD WASHINGTON, D. C. Engineering Experiment Station Laboratory Work Conducted By JJtaiifiCfitty_ftt_Cfilor*dP Work Coordinated By_ Jndu_atarlal_ and Coneuaer Products Branch Date May_18^_1946 Report No. Px? jtplLflfl* .452. J&Ltc&ojLJta*. \qq Copy No. 6m 7; May 18, 1946 ^Jilr. Ely C. Hutchinson Production Research and Development Division Office of Declassification and Technical Services Department of Cor..n.erce Washington 25, "D. C. . Dear I r r. Hutchinson: w In accordance with the requirements of contract '7PB-100, re- search and development work has been conducted on the Solar Heat Trap proposed by the Consumer Products Branch) Office of Production Research and Development of the War Production Board. The details of this investigation and the results thereof are hereby submitted i-n« the accompanying Final Report Very truly yours, fyjh G. Lof George Associate Professor of Cher. ical Engineering, P GOCL:LJ II pa. 253T5 SOLAR ENERGY UTILIZATION for HOUSE HEATING (Contract 7/PB-lOO) Distributed by Office of Hie Publication Board * Department of Commerce Washington U, D. C. Ail secrecy restrictions on the contents of tbis document have been lifted. In quoting or citing the report, please give proper credit to the authors and the sponsoring agency. In distributing this report, the Office of the Publication Board assumes no responsibility for its completeness and accuracy or for any opinions expressed. Products and proc- esses described may be the subject ef 0. S. patents, and the usual patent search is recommended before making practical applications. i.-**™-, ..o University of Colorado Engineering Experiment Station Boulder, Colorado May 18, 19*6 Submitted byt ii George 0. G. L6f, Associate Professor of Chemical Engineering R. Wi Hawley, Junior Research Engineer, Engineering Experiment Station E. R. Irish, Junior Research Engineer, Engineering Experiment Station » Supervisory and Laboratory Associates! C. W. Bcrgmann, Director, Eng. Exp. Stn, C. H. Prien, Asst. Research Engineer W. B. Pietenpol, Professor of Physics B. H. Spurlock, Asst. Prof. Kech. Eng. tf» l'. David, Junior Research Engineer J. P. Pohlenz, Junior Research Engineer Ill ACKNCTLEDGEIiENT In most research projects having a rather broad scope in a relatively unex- plored field, numerous workers may each contribute a part of the complete solu- tion. Such has been the case in the performance of the research covered by this report. The authors, therefore, wish to acknowledge the excellent v work cf these without whose services this research could not have been conducted. The performance of a large part of the preliminary testing and the initial studies on the indoor unit were very ably handled by LIr. L'ort on David. His successor, Kr. Jack Pohlenz, assisted in the carrying of this v/ork tc its con- clusion, and the developing of data for construction of the outdoor laboratory unit. The junior authors of this report then aided i'n the construction and operation of the full scale laboratory unit, aided in designing the house unit, and performed the calculations of their perf ermance. Particular recognition is given tc the services cf Professor C. H. Prien of the Chemical Engineering Department, who was in active charge cf the experiner al work on the indoor unit and the outdoor laboratory unit durinf most of the period cf their operation. He was responsible for securing the major portion of the data on which the results are based, and numerous features of construction and techniques of operation were developed under his direction. Thanks are also accorded to Professor 7 r . B, Pietenpol, Frofessor of Physics, and Professor B, H* Spurlcck, Assistant Professor cf Lechanical Engineering, who, with the senior -author, constituted the c cut it tee which planned initial phases of the v/ork. Advice and encouragement received from Professor C. Y. r . Eorgmann, Direc or of the Engineering Experiment Station, have been greatly appreciated. The authors also wish to express their appreciation for the assistarce given by members of the Geology Department of the University of Colorado, and by the technical personnel of the Boulder and Valrcnt offices of the Public Service Company of Colorado. The information on various phases of the weather and house heating requirements proved invaluable. Thanks are also tendered to fc'r. I. F. Har and his associates of the Solar Radiation Section of the U. S. leather Bureau for their calibration of the pyrheliometer and for considerable data crncerning its use. To Mr. K. W. Miller, forr.er consultant to the OPED, who devised this princip] of solar energy collection, and to Vr . Ely C. Hutchinson, chief of the Consumer Products Branch of the OPRD during most of the period of this study, go the prais of the authors for their excellent services to the people of the United States, and their continued interest and advice concerning the perf ormance of this work. IV TABLE OF CONTENTS Pag© I SULfliARY 1 II . INTRODUCTION * III THEORY 6 IV CONSTRUCTION AND OPERATION OF SOLAR UNITS 10 General Procedure 10 Indoor Unit 10 Cmtdoor Unit 12 House Unit 18 V PRIMARY RESULTS 22 VI SECONDARY RESULTS AND CORRELATIONS I? VII GENERAL SIGNIFICANCE OF RESULTS 57 VIII DISCUSSION OF RESULTS 61 Table of Results I 61 Primary Graphical Results 69 Table of Results II '74 Table of Results III ' 76 Table tf Results IV 77 Table of Results V 79 Seoondary Graphical Results and Correlations 82 IX CONCLUSIONS 86 X STATUS OF SOLAR RESEARCH PROGRA1.! 89 XI APPENDIX 90 A.. Preliminary Investigations 91 B» Patent Application 94 C« Methods of Calculation 109 D. Literature Citations 153 1. I SUMMARY The work described in this report was undertaken at the request of the Con- sumer Products Branch of the Office of Production Research and Development of the War Production Board. The specific problem was the experimental invest i ra- tion of a proposal advanced by K. "'. Miller (lG), consultant to the OPRb, for the practical utilization of solar energy, principally for purposes of house heating. L'iller's proposal involved a design consisting of a group of partially blackened, overlapping glass plates, mounted on a house roof. The arrangement is similar to that of shingles, separated by small air spaces. A semi-cent inucus glass cover over the staggered plates was also proposed. By virtue of the high transmissivity of glass for solar radiation an*; the lew transmissivity for long wave thercal radiation, the black, and clear glass surfaces in the unit would be- come heated when exposed to sunlight, and the reradiated heat therefrom would have no avenue of escape. Air passing between the plates could then be heated and supplied to the house. By this nethod, it v/as claimed that heat c:uld be collecte at a higher tei.psrature level than is attained in other types of collectors, A. second proposal, not covered by contract nor studied experimentally, ccr. cerned the storage of the collected heat by passing the hot air through a bed of loosely packed, cheap solids, to which the sensible heat of the air could be transferred. Delivery of hot air from the storage bed could then provide heat when no solar energy was being received.. The first experimental unit was constructed indoors and irradiated artificiall with a bank of tungsten lamps. In a complete study of the operating character- istics of this unit, it was found that i.iller's principle v/as actually workable and that a construction involving two-thirds overlap of plates blackened cne-third their length on the upper surface and space i l/4 inch apart resulted in the best performance. Repoi ts covering this phase of the investigation have been previeuol presented. (11, 12, 13, 14, 15) The results obtained with the indoor unit were next used in the design cf a large scale collector, which was constructed on the laboratory roof. This unit was operated intensively over a three -month pc-rio 3 in the fall and run intermittent ly throughout the winter. The large number of variables measured and correlated included the solar heat input, heat collected, efficiency of collection, entrance and exit air temperatures, air flow rate, plate spacing, an 1 various temperatures needed for establishing heat balances. The principal results of the invest irat i were obtained in this way. A third unit was then constructed on a small house and connected by uots to the regular hot air heating syster. , This collector covered about one-tfcii J of the entire roof area and occupied the usable surface on the south side cf the r Electrical connections and automatic controls completed the installation x*d per- mitted its completely automatic operation. By reans of this installation, the numerous problems associated with the combination of the solar heating un : . normal heating system were solved and the fuel savings affected by the solar unit were measured throughout one winter. A systei , designed to utilize the solar hi .ir to supply hot water for household use in the summer, was also installed and oper- ated for a short period. 2. Fror. the data experimentally obtained in tests on the three units, numerous results were calculated; several predictions, not based specifically on experi- mental data, were made. The latter included principally those concerning heat storage, operation of the equipment in ether localities, air conditioning, and cost . The results shew that Tiller's principle, although too idealised, is workable, and that by it solar heat can be recovered with efficiencies of 35 per cent to 40 per cent, with exit air temperatures ab^.ve 150 C F. at no<-n on a brirht day. Higher temperatures can be secured, but at lower efficiencies. Tilting cf the collector to the south is desirable, and roof slopes ranging fror.. the one e r qual to the latitude, up to approximately 10 degrees groator than the latitude, are near the optimum. Preakare cf glass plates exposed to sclar radiation, re:. airs the greatest problem. The way in which thermal stresses cause this breakage is subject cf a new investigation. Operation of the house unit during one winter showed that a fuel s .ving cf .\ib-:*ut 20 per cent was being realized, even though ideal arrangements had not yet been made. Very satisfactory automatic equipment controlled the unit, and the collector showed excellent weather resistance. Calculations show that if the heat load carryable is to be increased, the ducts will have to be insulated; and to secure a sizeable change, storage of heat for a maximurr economic. 1 period of one day should be provided. Under these circumstances, and with the roof area errplcyed, 50 per cent to 60 per cent of the fuel used in the test house cculd be saved. A storage bed containing about 6 tens cf solids would suffice, and if air recirculation between collector and storage unit were provided, the storage bed might be appreciably smaller. Very limited data indicate that the house hot water can be supplied by the sclar vnter heater during the summer. Locations north of the 40th parallel are generally unfavorable for economical sclar house heating. Because of the possibility for using the solar heated air to operate an absorption type of air conditioner, it is felt that the greatest applicability cf this system would be in the southern belt of the states. It is also believed that the net cost of the solar heating apparatus cnuld be kept below $500 on large scale production. The greatest advantages of this type of solar heat collector are its simplicit cf construction and low cost. It appears to have an officiency in the same range as that of the flat plate collectors in which water is heated (9), and its opera- tion is more efficient and flexible than the method employing large south windows. The outlook for commercial development of this apparatus is highly f.-..v rablo. 'York being sponsored by a private manufacturing company is new under way at the University cf Colorado. It is expected that this work will lead tc (l) the Sevelo ment ci' a practical design suitable for factory production of solar heating units, (2) the determinatirn of the most satisfactory means of heat storage, and (3) the elimination of plate breakage. 3. Applications for patents 'on the basic principles and the improvements have been made by K. W. Miller and §. 0. G. Lof , and licenses to the government have been granted. ^A copy of the Lof patent application has been included in -this report to show the design of the entire apparatus in its present stage of develop- ment. II INTRODUCTION During the last 70 years . \ at1 mpte have been made to bring about more effective utilization of the gi . t quantity of solar-energy incident on the earth' surface. A few of the names connected with those attempts to prove the economic feasibility of converting solar energy to heat and transferring that hc.it to the working fluid of a heat engine, cr storing it in some suitable fluid for subse- quent utilization aret Mouchot (l, 2), Pifre (3, 2), Shuman (4), Ericsson (5)i ' Llsie (6), Shuman (7), Abbot (8), and Hottel and V.'oertz (9). Solar heat collectors might be classified in three ways; according to the pe of insulation used, the degree of concentration of 3unshine obtained, and th- nature of the orientation of the collector with respect to the sun. Insulation o: the heat collection surface is acccr.pl is hod in several v/ays. In the flat plate collector the insulation may consist of one or r.ore spaced glass panes placed parallel to the absorbing surface and the sides and bottom could bo covered with a layer of a commercial insulating material. In the case of the tubular collectoj one or nore concentric glass tubes may surround the heat absorbing tube and in some cases a. vacuum is maintained betweon the tubes. In the flat plate collector there is usually no concentration of the suns rays but in other types of collecto- ref lectors are sometimes employed. Any collector might be built with three types of orientation. It might be mounted permanently in one position so selected to gather the maximum amount of solar energy over the desired period; to improve its efficiency the unit might be mounted so that its angle of inclination might be varied day to day so that it would always be perpendicular to the suns rays; further elaboration may bo used in the mounting to permit the unit to follow the hour angle of the sun so that it is at all times aligned in the position to obtai the maximum amount of radiant energy from the sun. In the design of a solar heat collector, two factors of major importance mus 4 be considered. One is the quantity of heat available at the earth's surface, and tht- other is the temperature level at which it is collected. Mirrors which focus the heat of sunlight and allow it to be collected at relatively high temperature levels have been devised but these have a disadvantage in that they collect 'only ■-:. small portion of total energy. On the other hand large quantities of heat can be lected at low temperature levels by th "greenhouse effect". This effect utilizes the fact that glass is transparent I visible and r 1 ngths which make up the predominate portion of sunlight and is opaque to long infrared wave lengths. When the sunlight enters the greenhouse, it impinges on the contents ar. is changed to low temperature long wave length heat which is trapped inside the glass enclosure. Since focusing devices of large area are quite expensive to build and to operate it seems desirable to devise a method to utilize the greenhouse effect in su^ that the temperature level of collection is greater than previous designs have allowed. A modification of the greenhouse effect v/as suggested by K. "'. Miller (10) of th.e Office of Production Research and Development of the War Production Board by Lch he proposed to raise the temperature level of the heat collected to several hundred degrees Fahrenheit. This plan involves the use of a large area covered by overlapping plates of glass. The area of each sheet of glass which extends in 5. the space on the under side. is coated with a radiation absorbing medium such as lamp-black. Air is drawn slowly through the space between the plates, becomes heated, and is removed from the unit. It is the purpose of this investigation to ascertain the workability of the scheme presented by Mr. Miller and to determine the optimum dimensions and con- figuration of the heat collecting unit. After it was found that the scheme offereo an improvement over previous methods of solar heat collection, it was decided to place a unit in operation as an auxiliary heating unit in a private residence to determine its economic feasibility. The following report describee in detail the work done and the results ob- tained during the course of the investigation with the exception of the preliminar* tests - on an experimental indoor heat collector. The latter is covered in previous reports (11, 12, 13, 14, 15). 6. Ill THEORY The theory of the solar heat trap as proposed by K. \7. Miller will be des- cribed in connection with Figure I which has been modified slightly from Miller's original drawing. A large area is covered by overlapping sheets of glass and enclosed within heat insulating wall3. Solar heat impinges on the upper glass, part of it is multiply reflectod back towards the sky, part is absorbed in the glass, and the remaining transmitted portion impinges on the black surface of the opaque glass where it is absorbed and changed to heat. As the black surface absorbs heat its temperature rises and i-t reradiates in the far infrared region to which radiation glass is opaque. Air is slowly drawn inward through or between the glass plates. This air at base temperature picks up the solar heat energy absorbed in the glass. This air is passing counterflow to the heat flow by conduction through and along the glass plates and by radiative heat transfer upward between them. Thus most of the heat attempting to escape upward from the high temperature end of the opaque glass plate is picked up by the air stream which, therefore, onters tho opaque glass section at an elevated temperature. Very important is the fact that this air flow maintains the upper surface of the glass plates at a temperature not much greater than air temperature. This reradiation of heat energy back toward the sky from the glass is thus very materially reduced since, quantitatively, it is proportional to the fourth pov/er of the absolute temperature of the outer glass surface. Mr. Miller has made a nathamatical analysis of the operation of the above described- solar heat trap and has derived equations of use in the calculation of the possible heat recoveries and temperature levels of heat collection! The principal derivations made and the resulting final equations are shewn below. To analyse the existing conditions in a solar heat trap, steady state, tempera- ture and air flow conditions must first be. assumed. The calculations are made for a zenith position of the sun. A heat balance is first established. A value for the absorption and reflec- tion of a single sheet of glass is determined and from the following equations the reflection and absorption of the series of overlapping plates are found. r n ♦ 1 = r n ♦ t n 2 r /(l - rr n ) (l) a n ♦ 1 ■ a n * t n ( ra n * a)/(l-rr n ) (2) *n ♦ 1 " V/* 1 " rr n> (3) r n ♦ 1 + a n ♦ 1 * *n ♦ 1 = * * * < 4 ) where i = incident light ow radiation r 3 fraction reflected a = fraction absorbed t = fraction transmitted n = subscript referring to number of plates Reradiation back to the sky from the top plate is found by assuming a tempera- ture for the plate and applying the following formula: Q = .172 e| t + 460 | 4 (5) V 100 " ) where e = emissivity of the glass plate (.95) t = temperature of the top plate ^F. In the above equation, it has been assumed that the surface is radiating to a sky having a temperature of absolute zero. It was found that a temperature of the surrounding air was a much better approximation. An initial air temperature and a spacing between plates are first chosen in carrying out the following calculations. A value is assumed for the ratio of actual spacing to critical spacing s = 2h and a value is assumed for the heat flowing into a single air film/* * ^ T a :at d ; /s f c : ---•..- With the new values of J and e, new values of 9i and $2' tne nea * entering the air stream from eacH plate may be calculated and a new corrected heat balance set up. With the above heat balance, tha mats air flow can be calculated and from that the velocity of the air stream. By the above analysis it was found that exit air temperatures of 300^. could easily ^e obtained in a unit built a3 described and shown in Figure 1. It was assumed, however, that no convection loeses took place at the cover plate surface and that no heat was lost by oonduotion through the sides or floor of the unit. These assumptions, along with the basic one that streamline flow prevails, make the actual predicted numerical results questionable even though their general order of magnitude may be correct. 10. IV CONSTRUCTION AND OFIRATION OF SOLAR UNITS I. General Procedure The investigation of the collection and utilization of solar heat by the method which involves the use of overlapping glass plates as suggestec by K. W. Miller was taken up in three phases. The first phase consisted of building an experimental collection unit and an artificial light sourer indoors. Tests on this unit were to furnish such information as general workability, optimum plate spacing, optimum overlap, optimum plate length, and optimum air rate. The data made available through the indoor unit studies v/ere used in the design of a larger heat collection unit which was constructed on the south roof of the laboratory, and the data were checked under natural sunlight. The effect of the changing, solar angles was studied along with the effect of clouds and haze. Exit air temperature and overall heat recovery efficiency were correlated with air rate and other operating variables. These tv/o phases being completed, the final phase of the investiga- tion was to place a typical unit in operation in a local home and deter- mine its usefulness in supplying heating requirements. II. The Indoor Experimental Unit--Summary A. Construction The indoor solar heat collection unit was built for the purpose of obtaining design , information to aid in the selection of the proper glass plate arrangement in the proposed outdoor unit. A drawing of the completed unit is shown in Figure I of "Progress Report V" of the Solar Radiation Investigation ( 15 ) and a des- cripticn is also given. Only a brief summary is given here because the work with the indoor unit yielded only preliminary design results The unit consists of a rectangular box 2-1/2 feet wide, 12 feet long, and 1-1/2 foot deep, well insulated against heat loss. Air at room temperature enters one end of the unit and passes through a finned tube air heater where its temperature is adjusted to the desired value by allowing steam or water or a mixture of both to flow on the inside of the tubes. After leaving the air heater, the air passes through a short section of duct of reduced cross section where it is thoroughly mixed and its temperature measured by a high-velocity iron-constantan thermocouple. As 3hown in the drawing, the air in the mixing chamber is protected fro:- direct radiation from the light source by partitioning the duct and drawing a stream of air through the upper half; this insulating air after being partially heated by radiation from the source is discarded into the room. The air leaving the mixing chamber enters the heat collection chamber through a perforated baffle. 11. The heat collection chamber consists of a number of glass plates defining a plurality of zones or passages through which the air is passed. These plates are arranged in staggered relation to each other and lie in a horizontal position. A section of the top surface of., each plate adjacent to the trailing edge was mads opaque by the use of black paint, and the corresponding bottom surface was coated with a layer of aluminum foil. This assembly is sealed from above by a continuous sheet of glass laid into a cover support. The construction is similar to that of* the outdoor % unit described in Section III 'below, and further details are presented in that section. An artificial source of solar energy. in the form of a bank of 84 - 1500 watt electric tungsten lamps is situated 10 feet above the cover glass of the heat collection chamber, and interposed between.. * the source and the, cover glass is a sheet of double strength window glass which absorbs the excess infrared radiation so that the radi- ation impinging on the collection plates more nearly approximates • that from the sun. The heat collection chamber described makes up a length of 6 feet of the total length of the indoor unit. Methods of measuring temperatures in this chamber make. use of high-velocity iron-con- stantan thermocouples and chromel-constantan foil surface thermo- couples. Their positions, are described below. The heated air leaving the heat collection chamber passes to a tapered exit section which is well insulated against radiant heat. At the apex or outlet of the tapered section is a shielded iron- constantan thermocouple for the measurement of the exit air tempera- tures. The air is then routed through a calibrated rotameter where the flow rate is. measured; an ircn-constantan t her mo couple is also installed at this point. The air leaving the rotameter is then exhausted outdoors through a forge type blower which induces the necessary air flow through the system. All temperature measurements are recorded on a Brown 12-point recording potent iometric pyrometer. B. Operation To made a run on the indoor unit, the independent variables are chosen and the unit set in operation. These variables are: Spacing between plates, length of plate overlap, entrance air temperature, and air velocity. When equilibrium is reached^as shown by the attainment- of constant temperatures .the run is discontinued, and a new set of independent variables is chosen. At equilibrium the following readings are taken: 1. Air velocity, CFM (760 mm. - 70°F.) (Fischer and Porter Rotameter) . 2. Entrance air temperature. 12. 3. Exit air temperature . 4. Temperature of air leaving black surfaces cf two plates near the center of the stack. 5. Temperature of air leaving black surfaces of bottom and second plates. 6. Temperature of air parsing through the rotameter. 7. Surface temperature in center of blackened portion f ctntrel plate in stack. (Bottom plate temperature) 8. Surface temperature three inches behind leading edge cf central plate in stack. (Top plate temperature) 9. Cover plate temperature, under side. From these data it is possible to calculate the efficiency of heat recovery if the heat input from the lamp bank is known. This input was obtained by placing an EppTjr pyrheliometer on the unit and measuring the heat input in calories per square centimetar per second. The data gathered as a result of the above procedure were correlated by a series of graphs an shown in Progress Reports IV and V. (14,15) The important conclusions of the tests on the indoor unit were ^l) the general principle of the heat collector as sot forth by K. W. Miller was shewn to be workable, (2) the optimum plate spacing was found to be l/4 inch, (3) the optimum plate overlap was found to be 2/3. The plate length factor was not investigated thoroughly enough to draw any definite conclusions, but it ie believed that a variation in plate length would net materially affect the operating characteristics of the unit, all other factors being constant. III. The Outdoor Laboratory Unit A.. Construction The outdoor unit was constructed on the roof cf the Chemical Engineering Laboratory just over the balcony on which the indoor unit was built. The construction v/ill be described with reference to Figure No. 2 and the accompanying photograph. The dimensions of the collector arc 15 f^ot .vide and l8-l/2 f iot lor.", the oxposed p -rti n m.king up* 15 feet of the overall length. Components of the collector are; a floor laid on a double layer of balsam-wool insula- tion, two supported wood sides adjustable in height, a windshield at the lower end to damper the inlet air from sudden drafts, a board at the upper end with five exit air ports, and five cover glass frames running the width of the unit. Each cover glass support consists of a rectangular framework of 2" x 4" lumber divided into three section PC Ul w s DC O O »- o UJ o o < < -I o ifi O o < O .J O a u. O en a: UJ > < c/> z n > UJ 1" • 2 ss • In a. / o K OC ul o x Z K P P /* . 15. The top edges of the timbers are grooved to hold the plates of glass, and each plate is puttied into place. The cover glass supports are doweled together in position and sealed with adhesive tape % The glass collector plates used in the unit are 3& inches wide, 48 inches long, and l/8 inch thickj they were supplied by the Jeanette plant of the American V/indow Glass Company. One third (sixteen inches) of each collector plate was painted with black paint on one side and coated with aluminum foil .00025 inch thick on the other. The black paint contained a solvent made of 60 per cent by volume of turpentine and 40 percent bronzing fluid, and. 15 grams of lampblack pigment in 100 cc. of solvent. This paint was com- pounded after making a series of tests which are explained in Appendix , A, The glass collector plates are supported in the following manner: the bottom black plate is laid flush on the floor at the lower end of the unit and a strip of wood 1-3/4- inches wide and the thickness of the glass is placed on the floor directly behind the glass and extending to the top of the unit where it is secured by a 1 inch spindle. These strips are placed so that their longitudinal center is in line with the junction between two adjacent glass plates. On top of these strips are placed similar strips the thickness of which represents the plate spacing desired. These strips extend from the spindle at the top of the unit to one-third the distance from the bottom end of the bottom plate to the top end of the plate for an overlap of 2/3*. At the end of these strips are. secured small protruding strips which form a ledge to support the next glass plate. This method of stacking is carried out until all the collector plates are in place. To prevent air flow over the top of the top plate thus short-circuiting the space betv/een the plates, a piece of sheet rubber material compounded from heat resisting neoprene was fastened to the cover plate support and the trailing edge of the top plate. This method of stacking the glass plates may be visualized by in- specting the drawing and photograph. The air to be heated is drawn into the windshield through the top and ends and through the perforated end board into the collector proper. After passing through the heat collector plates the air is drawn through the exit ports, which are equipped with adjustable dampers, and through a ten inch galvanized iron duct through the roof and into the building. After passing through r. -.suring devices described below, the air passes to the main floor of the laboratory and into a large blower (American Blower, type 2 C >0 E) from which the air is exhausted either outdoors or* directly into the laboratory when heat is required. Three -types of thermocouples are installed in the unit to measure the necessary temperatures. The surface temperatures are measured with surface thermocouples made of chromel-constantan bright metal foil, 0.0009 inch in thickness and l/l6 inch in width held firmly against the surface by a microscope cover glass glued down with shellac. Chromel and constantah No. 36 B. and S. wires are 16. soldered to the ends of the- foil and pass to the cold junction ice bath. Air temperatures are measured with iron-constantan thermo- couples, No. 3& B. and S. Gauge, mounted in l/8 inch i. d. x l/2 inch 0. d. bakelite cylinders and provided with copper tips having a 3/64 inch opening, through which a small stream of hot air leaving the plates is rapidly drawn by a water aspirator. This high- velocity thermocouple is used to reduce radiation errors. Air temperatures at the rotameter and blower are measured with bare iron- constantan thermocouples inserted in the duct. All thermocouples are connected to a Brown 12-poirrt recording potentiometric pyrometer which is calibrated for iron-constantan thermocouples, and is cold junction compensating. To evaluate the temperatures of the surface couples which are equipped with an ice bath cold junction, it is necessary to subtract the temperature of the potentiometer box from the recorded temperature and convert to chromel-constantan tempera- ture by means of the chart shown in the appendix (Figure 32 ), which was constructed from tables furnished by The Leeds and Northrup Company. B. Operation During a day's run of the solar heat collecting unit, the following temperatures are taken in the manner described above and automatically printed on the potentiometer chart with the numbers given in parentheses: entrance air (10); air leaving the trailing edge of the center plate in the west section or section A (4); air leaving the trailing edge of the center plate in the section adjacent to the we.st section or section B (5); the air leaving the trailing edge of the center plate of the center section or section C (6) j the exit air in sections A, B, and C, (7, 8, and 9) J air temperature at the orifice, rotameter, or blower (8); center black plate temperature in sections A, B, and C, (4j 5» 12); center clear plate temperatures in sections A, B, and C, (l, 2, 11); cover glass temperature at the geometric center of the unit (3); cold junction temperature at the recorder (3)» The rate of air flow through the unit is measured in two separate^ ways. For flow rates up to 150 CFM a Fischer and Perter rotameter equipped with a guided plumb-bob float is used for measurement. The rotameter was calibrated at the factory to read in CFM at 76O mm. and 70°F. when measured at 630 mm. and 70°F. For flow rates above 150 CFM a thin plate 3*inch orifice installed in the ten inch duct was used. The orifice was calibrated against the rotameter up to flow rates of 250 CFM and the curve extrapolated to 400 CFM. An alignment chart was prepared for rapid calculatiqn of the flow rates. In order that flow rates could be calculated, static pressures were measured by water manometers, and the pressure drop across the orifice was read with a vertical 20 inch water manometer and an inclined water gauge (not shown). In order to make it possible to obtain flow rate measurements, over the entire period of a run, a thermocouple was installed in the blower and by considera- tion of the fact that a constant volumetric rate is handled by the blowsr, the actual flow rate measured at 7&0 mm. and 70°F. could be calculated. 17. The heat input to the solar heat collector 'was measured by an Eppley 50-junction (23) pyrheliometer which was previously calibrated by the U. S. Weather Bureau. The readings were taken continuously on a Leeds and Northrup continuous recording potentiometer and in- tegrated hourly with a polar planiraeter. Th> instrument was in- stalled on the peak of the roof in a horizontal position as required by spepifications of the U. S. Weather Bureau. Before the unit was 6et in operation, measurements were made io determine if the flow through each section was equal.. This was approximated by determining the static preBSAtre at the exit ports of the five sections. The dampens were -then adjusted to obtain equal static pressure, The unit was first stacked with the optimum plate spacing and overlap as determined by tests on the indoor unit (l/4 inch spacing, 2/3 overlap) and a series of 40 runs was made from July 24 to September 23, 1944, with air rates varying from 53 to 369 CFl: and with heat input varying according to the position of the sun and pre- vailing weather. This procedure was then repeated with l/2 inch spacing, and a series of 28 runs were made from October 7 to October 31 * 1944. The unit was then run periodically through the winter months to determine the variation of performance with time Of year. At the end of the following summer (194J>) a final run was y made with the unit in a bad state of disrepair. Approximately 85/* of the plates were broken, water had washed a considerable amount of paint off and all of the air seals were broken. Following the runs, all pertinent data were calculated and put in usable form (see Tabulate^ Results). Finally, important correlations were made and conclusions drawn as to the performance characteristics of such a solar heating unit r Data that were necessary for a proper heat balance but that were not directly available were gathered from other sources of informa- tion. The atmospheric air temperatures were secured from the U. S\ Weather Bureau station on the University Campus. Wind velocity figures were obtained from the Valmont plant of the Public Service Company and corrected for the difference between Boulder and Valmont. . using figures available a few years ago. These data were necessary v for the calculation of -convection losses from the top of the unit. is. IV. The Experimental House Unit The experimental house unit was constructed on the roof of the home of Dr. G. 0. G. Lof at 1719 Mariposa Street, Boulder, Colorado. Figure No, 3 and the accompanying photograph illustrate the construction of the unit. Lying on the slope of the roof are sixteen supports constructed of 2" by, 6" lumber supported and separated by iron strips which also act as supports for the cover glasses (a) % In the sides of these pieces are cut appropriate slots into which are driven narrow strips of composition board; the slots and strips are positioned so that they will support the glass plates (t) in their proper relation. At the end of each strip is fastened a small wood block which prevents the glass plates from sliding down the roof. The assembly is built directly on top of the shingles of the roof but before the glass is laid, a l/2 inch layer of celotex insulation is placed ever the shingles. The supports are spaced on 32 inch centers and the glass plates are 29 inches wide by 36 inches long. The glass plates are placed in the optimum arrangement found in the tests on the outdoor unit which v/as found to be l/4" spacing, 2/3 overlap with 12 inches of each plate painted black. The cover glasses are put in place in groves cut in the top side of the supports and sealed with putty; the ends of the cover glasses overlap in the manner of a green-house glazing. A cap strip of sheet metal is placed on the top edge of each 2 by 6 to protect the seal from weathering. A flashing made of sheet metal covers the top and bottom ends of the unit. The entrance air inlet (b) is cut through the roof at the bottom end of the unit and a duct (c) is built from the house cold air return (r) to these openings in the roof. The heated air is drawn from the top of the unit through similar holes (d) cut in the roof. The duct system employed for the hot air £s shown in the drawing and consists of a large duct (e) leading from the hot air outlets of the unit to the center of the attic where it branches into two. One branch (f) leads to the bottom of the furnace (s) and thence to the fan (g) and into the house hot air circulation system (h). The other branch (i) leads through a finned tube water heater (j) and thence to a natural circulation vent (k) through the roof, the top of which is higher than the top of the solar unit. The finned tube heater is used to heat water when the heat is not needed to heat the house. This heated water is stored in a 120 gallon tank (m) installed in the attic as shov/n in the drawing. This tank is connected directly to the inlet of the automatic hot water heater. Installed in this duct system are suitable controls in the form of thermostats, dampers (n), damper motors (p), and relays which permit the unit to be operated in the following manner automat icallyj Case I. 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U • 4m Z O O O -O O X *4H • 4* T) 4» J • OJPb 41 C J= 4» « H I 3 • VH §• u l • »v 3t) J( • ♦» m r-t m «ih k V b o • 4 J 5Sgu»oBH • • . w > . i_ ■ o »_ »> o ■** m \- B a i 4j ** •Xaio«)whh]oiia4|«i4ii4i«i<4ixoaxoz xlcc o o ac o h i ' fl« t; t s I • • • 3 « o 9": § § i t I u o ac => i I i JillJ^l^iiiiii^l HKAT INPUT A*D HKAT RXCOTOUD, BVU/W. ,•«•'*• y^ TXMPERATURI OF AIR IKTKRINO AMD HAVING, F. ■ ■■»■«■■• MMtlMMIMH ■■•■••»■•■■••■■■ ■ ■■■iumiMiiJii iitiiiiiiiriinivi ■•■■•••••• •■■•■••««• ■■•••■■■■« ■■■■■■■■■•■ ■■■■■■■•«■ ■■•■■■■ ■*■■■•■■■■■■■■■•■•■■«■■■ ■■■■•■••••»•■••■■■ j* ■•■«»■■■■■•■•••■■■■•• ■■■■■■■•■■■■■■■•■■■■■a !■■■■•■*• ■■*•«■•■«■■■■ ? sr % A0N3I0UJ3 ssoue M. ; }{UH:tt J : " % ' kOH3\3\d A 3 13N 28. TABLE OF RESULTS II House Unit Calculated Storage Heat in Oct. Nov. Dec. Jan. Feb. 1,'arch April May Tilt Capacity BTU x 1C~3 15*4 1944 1944 1945 1945 1945 1945 1945 Tota! (Time) , j Heat req'd 5416 i 1C393 15036 14657 13471 11403 j 1C402 1 4229 •■ 8500 1 j Solar rec'd 8400 ; 6703 7110 6154 6087 ; 9193 j 7963 7983 5964 None ! Solar used 1620; 3688 <462 4604 4024 . *3TJD 1(1) (1) 237b; • j load cr'd 30.0 ; 35.5 36.3 31.4 30.0 40.2 (l) ■ (l) 34. 1 27° ! Solar used 4530 i 6198 -7110 6154 6029 78l6 5813 2916- 4656' 1 day 2 day j load cr'd 83.6 59.6 47.3 42.0 ; 44.8 68.3 55.8 69. 54.7 Solar used 4723 6793 7110 6154 6087 8358 6627 3&21 4947 i load cr'd 87.2 65.4 47.3 42. C 45.2 73.4 63.6 85.8 58.2 Solar used 4723 7036 7110 6154 6087 8382 7536 4053 5108 3 day j j load cr'd ' 87.2 67.7 47.3 42.0 45.2 78.3 72.3 96.0 60.1 1 . Solar rec'd 9105 7707 8308 7250 7003 9635 8053 7515 6463 ; None Solar used 1623 3804 5647 4760 4204 4416 (l) (l) 2445 j load cr'd | 30.0 36.6 37.5 32.5 31.2 40.6 (l) (l) 35.1 Solar used -4566 69H 8291 71&7 687O 8085 5825 2805 5051 . 1 day i 40° j load cr'd 1 84.2 66.5 55.1 49.0 51.0 70.8 56 66".4 59.? Solar used j 4726 7413 8308 7250 7003 8614 6685 3582 5358 ; 2 day | j load crJd £7,2 71.3 55.3 49.5 52.0 75.5 64.3 84.8 63.0 Solar used ! 4726 7727 8308 '7250 7003 8679 7644 4017 5535 3 day j load cr'd ! 87.2 74.4 55.3 49.5 52.0 76. 73.5 95.0 65.1 (l) Data not available for April and Llay. Totals based on requirements through March only. Collector Area 463 sq. ft. Overlap 2/3 Plate length 36" Black length 12" 29. TABLE OF KESULTS III FRELICTED SIZE OF KEAT STORAGE UIIIT St or are { „ For s to rage of aver are load " | For s trr ar;; ci' :..ax i.~:u;y 1 tir..e |Heat st'd BTU ["lbs :..'It ' l"^ heat load Heat Stored 1 Lbs. t/at ' 1 j ? heat I i ■ car r ied , 3tu ■ lead cr'dj 1 day : 300,000 11,500 53-5 A00£C0 15,400 54.8' 2 day j 500,000 19,200 i 5^.5 740,000 26,500 5f .2 i_Jay [ 800,000 : 30«30C j SlPjCCO ;_ 37^.3.00 [ - foil ' Note: Heat capacity of material 0.2 Btu/y°F (brickwork, carbon, clay, flass, granite, stone) Available temperature rise 130 r 'F Yet efficiency of sclsi unit 45/= Solar unit tilt from horizontal 27 u 30. TABLE OF RESULTS IV House Unit Performance Data 1945-46 A. Basis; Comparison with identical house Period 1945-46 Uss used - C u f t. (19) (Sept.lO-Oct 12 Oct 13-Kov 10 Nov 11 -Dec 12 •Dec 13-Jan 12 |Jan 13-Feb 12 •Total Solar House I Identical House 11,200(19) 14,400 23,600 29,800 29,10c ,,108,100 9,900 13,400 23,900 26,500 24,100 i * > Gas savedl,, 1 b u Identical ♦40.5/-J in Solar House 13,900 18,800 33,600 37,200 33,800 11,17 1 loo 2J00 ,'4,400 10,000 7,40C 4,700 J> heating oc.d cr'd y solar nit 19.4 23.4 29.8 19.9 13. 9 21.2 B. Easisj Derree Day Data 1 2 3 4 5 6 7 8 >f' JL ■ , ■ ■ ' < ' II ■ ill I I. :Peried |°Days ; °Days * Gas jGas Gas for • Nat gas Gas 1945-46 j (1 9) j»15.5#j Necessary! Used hot water" Used Saved Sept 1*0- ' 1 301 I 348 j 8600 [ 11,200 '• 2433 342 395 . 970C 14,400 ; 2433 900 11039 25£5c ; 23,600 2433 Oct 12 ;oct 13- 1 Nov 10 Nov 11- Dec 12 :Dec 13- Jan 12 1 1052 1218 , 3Q100 j 29,800- 2433 Jan 13 -: 1198 I 25»600 j 29,100 ! 2433 41 9S ? 103.7 10 : 108.100 [12J.65 % Heating load Carried by Unit Fob 12| 1038 Total 36 33 C. Operatinf Data 1 88OC ; I ! 12CC0 .| C ! i 21200 ! 4450 .27,400 1 2700 I •26,700 j 2900 ;96,100 JL QC5Q • Area cf Unit, sq. ft. Air rate, CFli (760 kj3-70°F) Air terperaturo rise at noon C F JCro8s efficiency f. T 463 168 67 10 12.8 Uet eff iciency ; i Predicted heatin- load carriable ^ i 20.0 i 17.4 s.o 9.8 Solar house used 25/* -' ore heat than identical house durinr winter of 1944-45. During wir.ter 1945-46 solar house maintained 5 egrees higher than winter 1944-45. Public Service figures indicate heat requirements will be l$*5% hirher for this : degree raise, making a total of 40. 5f higher than the identical house. 31. TABLE OF RESULTS V Comparison of Actual and Theoretical Results Experimental Theoretical Incident Solar Radiation Btu/hr 'ftT o Top Plate Temperature F Heat Lost Btu/hr ft convection reradiation reflection unaccounted Heat Recovered Btu/hr ft* Black Plate Temperature °F Air leaving Black Plate C F Air Rate (CFI.I, 760 bk -70°F) Gross Efficiency % (2 clear plat es plus cover) 3 plates 4 plates Actual Ad.iusl :ed (2 clear plates) (3 clear plates) 329 327 329 32S 100 100 100 ICO 57 57 57 57 27 27 27 27 63 63 47 63 24 158 182 158 182 225 — — 243 2S0 186 2C1 224 278 312 — 224 *38 48 55-* 60.2 5' -4 32. VI SECONDARY RESULTS AND CORRELATIONS Figure 8 Ail* rate vs. temperature rj.se, l/4" spacing, const, net heat input 9 Air rate vs. temperature rise, l/2" spacing, const, net heat input 10 Gross efficiency vs. temperature rise, l/4 M spacing, const . net heat input 11 Gross efficiency vs. temperature rise, l/2 M spacing, const , not heat input 12 Net efficiency vs. temperaturo rise, l/4 M spacing, const .net heat input 13 Net efficiency vs. tonporaturc rise, l/2" spacing, const .not htat input 14 Entrance temperature vs. gross efficiency, l/4 M spacing, constant rate 15 Entrance temperature vs. gross efficiency, l/2" spacing, constant rate 16 Entrance temperature vs. net efficiency, l/4" spacing* constant rate 17 Entrance temperature vs. net efficiency, l/2" spacing, constant rate 18 Gross heat input vs. gross efficiency, l/4" spacing, constant rate 19 Gross heat input vs. gross efficiency, l/2" spacing, constant r?.te 20 Net heat input vs. gross efficiency, l/4 M spacing, constant rate 21 Not heat input vs. gross efficiency,* l/2 M spacing, constant rate 22 Gross heat input vs.net efficiency, 1/4" spacing, constant rate 23 Gross heat input vs. net efficiency, l/2" spacing, constant rats 24 Net heat input vs. net* efficiency, l/4 H spacing, constant rate 25 Net heat input vs. net efficiency, l/2" spacing, constant rate 26 Cloudiness vs net efficiency, l/4" spacing, constant rate 27 Cloudiness vs net efficiency, 1/2" spacing, constant rate 28 Cloudiness vs. tomperature rise," l/4" spacing, constant rate 29 Cloudiness vs. temperature riso, l/2" spacing, constant rate 30 Angle of declination vs. gross efficiency, l/2" spacing, constant rate 31 Angle of declination vs. net efficiency, l/2" spacing, constant rate 53. 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J. r ,^IH»ji»dw -»(_ 'dm •••'8 »*o^ "• 4«<|lu-»_L SI. 40. 41. y m /iui.»i)j3 >»/v 42. • £ ' X->\* »JO.'-H 3 Y»N 4*. * * * 44. ft * * 4ft* •/ '/»«ti*jf4 3 %*•**) 46, "/ (m ».'»,)•}•$ 3 t»#-4*l 4T. T ST 48. Jot m *£'S*4i0i'*t$jf& f/t y/ mmm ^ ,.: : __J } f ) 3 ^ »N f>0. 3 5 */ m ' /** *! ?) u 3 ^»K 5i. % r /"-> *»!■>.»■$ -S3 }»N 62. 68. ^ • ' • *•' H •■•^•*'» J »^ Lu3 'j_ 54. 66. 66. asj | r iq^ ; .« *3 4 — I KB ft: :55 ffij • ttt zzz ^z U i mq r±^ ffi m 5= S^ MTTTn ton N •/. ^ u »! 3 !|j3 j^h 57. VII GEI^RAL SIGNIFICANCE OF RESULTS One of the c ost important results of the entire investigation is the proof f the workability of the principle advanced by Tiller (10). Although experimental leat recovery efficiencies and exit air temperatures are not as high as predicted heoretically, the results indicate that solar energy can be used to heat air to emperatures in excess of 200°F and that overall heat recovery eff-iciencies of at east 357* °f total input can be secured. Of perhaps the greatest practical significance is the fact that a solar heat- ng unit was constructed and installed in a typical small heme; was provided with oropletely automatic controls; was tied in with che normal heating systen.; and as operated satisfactorily throughout one complete winter. A fuel saving of pproximately 20 per cent was realized. Other important specific results involve the details of construction and opera- ion of the equipment. Such factors as the use of two-thirds overlap of plates ainted one-third black on the upper surface, ■£ inch spacing between plates, plate engths of three to four feet, support of plates on strips driven into wood section ides, and i;.ethod of supporting cover plates, are practical results of building r.d testing the equipment. The recirculation of house air through the unit, laintenance of air rate at the optimum value, available temperature of air, heat- ng load carryable, equalization of temperature in the various sections, are use- ul results obtained from operating studies on the equipment. The results indicate that there are good future possibilities for utilization f this solar heating principle, and that further 'work to develop the apparatus nto commercially marketable units is justified. Indications are that with an ex- enditiire in the general range of $500, the owner of a moderately sized house could ave solar equipment installed which would save two-thirds of his winter fuel in climate having considera le winter sunshine, but rather large heating require- tents. The relatively low cost and simplicity of construction of the equipment re probably its greatest advantages; and- since the efficiencies are comparable o those secured with flat plate collectors heating water (9)> and much greater han those obtained with simple large south windows, it is felt thut commercial evelopment nay be possible as soon as the few remaining problems have been solved. It is to be realized that all data, calculations, and results have been based n observations r ade at one location, Boulder, Colorado, 40 decrees min North atitude, 105 degrees 16 min West longitude, 5428 feet elevation. All the results n general, and those of the house operation in particular cannot be applied to ther locations 'without discretion. Certain generalizations can be made however, hus , in locations in which either the solar radiation received is greater than n Boulder (because of lower latitude, for exar pie) or the heating requirement s less (because of higher winter temperatures), either the fraction of the heating oad carryable by a solar unit of the sane size would Le rreater in the other loca- ion, or a collector to carry the same load could be smaller or tilted at a lower ngle. For prediction of size of collector needed to carry a certain heating load n another location, data on latitude, solar radiation, winter te. peraturcs , and ouse heating requirements are necessary. 58, .Its o: : with the collector clone, as in the- case of the lal oratory runs, can be appl -re r-. to ether locations; and ccn parable perforr. ance d if consideration is giver, to the different angle at which the sun strikes the collector at t Lfferent latitude. Thus, for the sar. e projected area of collector, er : equivalent averarc cloudiness, heat recovery efficiencies should be very similar at ti B air rates, even in widely different locations. It is probablo that although the conditions for utilizing solar energy at Boulder, Colorado are considered to be good, they are close- to the severity be- yond which it would be uneconomical to attenpt solar heating. It is therefore felt that in localities north of the fortieth parallel, the cost of heating house by solar radiation would generally be too high for economical application of this principle. Collector and storare units would have to be unduly large and their cost would be a considerable drawback. It is possible, however, that in a few northern localities, where considerable winter sunshine is obtained, and where temperatures aro not extremely low, econoi. ical use mif.ht extend considerably above the fortieth parallel. This would bj particularly true where fuel is ex- pensive. As further explained below, the greatest applicability of this solar energy collector should be in the southern portion of the United States. Certain considerations of other uses of the collected solar energy have also been rade. Th3 first of these involves the possibility of using the heated air to operate an absorption type of refrigerating air conditioner. 3uch a unit is available com; ercially, and the application of solar energy to its operation is considered to have excellent possibilities . It is apparent that the period in which the greatest energy is received corresponds exactly to the period in which the greatest cooling is required. The apparatus woulr? therefore be able to pro- vide the most cooling at the tire it is needed. It is felt that perhaps the region of greatest applicability of this equipmer is in the southern half of the U.S., where winter heating loads are not too sever and where surr.rr.er cooling is greatly desired. The heating of water for household uses has also been considered, and equip- ment for this purpose has been installed in the house unit. Ko cor. plete results of its operation are available became of its late installation, but a few ob- servations s' o\v that, particularly in the summer, it should be possible by using solar-heated air to heat sufficient water to the te. perature required for house- hold use. Other possible uses for Solar energy might be to provide a continuous supply of clean, heated air or other gas to certain industrial processes, such as drying or crystallizing. Numerous factors have not as yet been investigated because of certain limita- tions. The most important of these problems is that of heat storage, KTost of th envieioned usee for the solar energy recoverable by this process are predicated on the assumption that storapo of the heat for at least 24 hours can be success- fully and ecoro ically provided. Thie.pioblen has not yet been investigated experimentally, because it was considered beyond the scope of the study covered by this report. It is expected , however, that studies now being planned will sh that storage of heat can be accomplished satisfactorily. On this assumption, resu of heat storage calculations have been included in this report. They indicate th 59. storare of heat only overnight in a bed of crushed solid, will more than uouble the heating load carryable by the solar unit, and will not require a storage unit too large for practical use. An additional benefit, not yet determined quanti- tatively, is the higher storage temperatures which can undoubtedly be obtained when hot air is recirculated between collector and storage unit. An important practical problem, not yet solved, because of lack of time, is the discovery of the fundamental cause of, and the method of eliminating, the excessive breakage of glass in the collecting unit. The frequent breakage of plates exposed to sunlight is no doubt caused by thermal stresses set up in the glass, but the way in which these stresses cause breakage is not definitely known.. Tests are be- ing planned which should show whether small edge cracks grow into large ones , wheth- er lack of proper annealing is responsible, pr if some other cause exists. Although considerable progress has been made toward designin: a collector entirely practical for the average home, more work needs to be done to r. ake possible the large scale production of units which then can be easily installed in the house. Certain simplification and standardization in design is necessary before wide usage ban be realized. Another subject meriting study is the possible use of glass which has been surface-treated to reduce reflection. It would perhaps be possible, at con- paratively low cost, to reduce materially the amount of energy reflected back to the sky fror the unit, and thereby increase the efficiency. The black coating used on plates in all the tests v/as very satisfactory. It had a high absorbtivity for solar radiation and reasonably good adherence. Future work, however, will be directed toward the development of a coating with extremely perm.anent characteristics and one which could be easily applied at the glass factory. leather resistance of the equipment was generally very good. The use of putty for sealing the cover glasses on the house unit proved very satisfactory, except when it was necessary to replv.ee broken glass. In such instances, the hardened putty, prevented easy re oval of the cover plates. The use of a rubber or felt' sealing strip is being conte; plated and will be investigated. The house unit was found to withstand a high wind very satisfactorily, but the frar.es holuin^ the. cover f lasses on the laboratory unit were blov/n off and de olished in the sar.e wind storm. As a result, the type of construction originally used in the labora- tory unit has been abandoned. Snow removal constituted no problem, for the smoothness of the glass caused the snov; to slide off the roof as socn as a thin layor next to the glass had melted. The -£ inch mesh screen (hardware cloth) was considered adequate pro- tection against hail da a^e in the surmor and was used only in that season. Ideally, a very thor ourh study of numerous fundamental problem.s should have preceded, or at least accorpaniod, the designing and tostiny of the whole solar collector. The limitations of time, personnel, and fund3 prevented, this , however. Such studies as those directed toward learning the true character of the air flow between the heated plates, whether str eamline, turbulent, or eddying because of then al gradients, r/ould be extremely valuable in establishing an optimum design. I.ieasurei. ents of air flow and ter pcrature should be made by careful explorations across the cross section of the space, between plates. Further theoretical develop- ment of the heat transfer relations should also be made and correlated with the experimental results. 60. It is hoped that so- e of these funds; er.tal characteristics of the solar un: be investigated in a nrw project, alon.r v.'ith the overall factors previousl; tioned. V.'ith this rr.ore cor.plete knowledge, it is felt th: t t the rrost practi< de6irn can be devoloped ard the optin-.uir. operatinr conditions established. ei. ?:. VIII DISCUSSION OF RESULTS The results of the study are divided into seven main sections! (l) a table showing: results obtained with the outdoor laboratory unit, (2) graphs of these results plotted to show importance of certain variables, (3) a table showing house heating load carryable, calculated from laboratory outdoor unit data and house heat ing data, (4) a table showing size of heat storage system needed, (5) a table of actual fuel saving in the experimental house installation, (6) a table in which experimentally determined performance and the performance theoretically predicted are compared, and (7) a section of secondary results and correlations in which the results shown in table I and Figures 2 and 3 are plotted in numerous ways so as to show clearly the importance of certain operating 1 variables. TABLE OF RESULTS I In Table of Results I, it is seen that runs 1 to 45 were all conducted with a spacing between plates of l/4 inch. In these tests, the principal controlled variable was the rate of air flow which was Varied between 32 cubic feet per minute and 3^9 cubic feet per minute, measured at 7&0 mm pressure and 70°F. Other condi- tions which varied because of weather and solar position were the inlet air tempera' ture, the amount of incident radiation, and the angle at which the radiation struck the collector. In runs 46 to 74, the spacing between pl?.tes was l/2 inch, and air rates were varied between 33 and 354 cubic feet per minute. Most of the runs were made in 1944 during August, September, and October, and a few were made in the winter and spring of 1945.' In the discussion immediately following, the various items in Table I are explained, and particularly significant results are discussed. The overlap of 2/3 was employed because the results of tests on the email scale, indoor unit showed this to be the best arrangement* Plates '48 inches in length and blackened for 16 inches were employed simply because such a size was a convenient one with which to work, and not so small as to require an unduly large number of plates to fill the unit. The area of 209 square feet is actually the "black area", and does not include the area of end pieces and supports. The spacing of 1/4 inch was found to be the optimum. in the indoor tests and was utilized in .the first runs on the outdoor unit. The spacing was later changed to 1/2 inch for another set of runs and the performance compared. As is seen in Figures 5 and 6, the 1/4 inch spacing proved to be superior, thus confirming the result of tests on the indoor unit. ' # Figures on time of sunrise and sunset were obtained from solar tables,, and were not- corrected for irregularities in the horizon. Such irregularities exist principally to the west of the unit and may cause the sunset to be as 'much as 30 minutes before the time shown. 62. The time at which the first direct sunlight strikes the collector is .later than sunris pd. summer , betv/ecn March 23 and September 23 because the sun rises to the/east durir.r® those seasons. Since the unit slopes directly to the south, the tire at which the first sun strikes the collector is v:hen the sun '-as risen to a height such that it is due east of the unit. The sane considera- tions apply in the afternoon, when the last sunlight strikes the collector as the sun crosses a position due west of the unit. In the fall and v/inter, the tirr.e at which the first and last sunlight strike the collector corresponds exactly to the tine of sunrise and sunset, because the sun's position is always to the south of the unit during these seasons-. All the figures dealing with time of day are solar time, which at the longi- tude of Boulder, Colorado, corresponds roughly to Mountain Standard Time. Solar tine varies from fiftsen minutes ahead, to fifteen minutes behind, Mountain Standard Time, depending on the season of the year. Statistics on sunrise, cunset, and time of first and last sunlight on the collector were used as a guide for establishing the duration of runs, and for an indication of the thermal lag or heat storage in the collector. The cloud loss was calculated as shown in Appendix C, Methods of Calculation; the figures represent the percentage of the total possible radiation with com- pletely clear sky which has been absorbed by clouds and not supplied to the collector on a given day. It is seen that the radiation lost because of cloudiness varied from zero to about 70 per cent. In most of the runs, however, the clouds reduced the solar input less than 2C per cent. The cloudiness figures were used in determining whether any appreciable dif- ferences in over all heat recovery efficiency could be attributed to the extent of cloudiness. As shown in Figures 26 and 27 > and as discussed below, very little difference ir. efficiency was found to be caused by clouds alone, even though they naturally reduced the overall heat supplied and recovered. Since the calculation of heat balances required the determination of the heat lost by convection from the cover of the unit, and since the rate of air flow past the surface profoundly affects the rate of heat lost by convection, it was necessai to secure data on wind velocity. These data were not available at the site of the collector, so values from a station about 5 miles distant were used, after correc- tion by the method shown in Appendix C. Although subject to some error, these > data were sufficiently reliable to permit calculation of convection losses within the accuracy of the equations for determining convection coefficients. Moreover, those figures were needed enly for the heat balances and are not involved in the efficiency colculat ions . For the computation of convection and radiation losses in the heat balances, it is necessary to know the temperature of the main body of air external* to, but in the vicinity of the unit. It was found that this tempera- ture was not the sane as the temperature of the sir entering the unit. Local weather bureau records showed that the atmospheric air temperature was always low- er, sometimes as much as ten or twelve degrees, than the entering air temperature as measured by the thermocouple at the collector inlet. This difference can be attributed to the fact that the unit is surrounded by a large expanse of black roof which, when exposed to the sun, causes considerable heating of the adjacent air. Veather station records were, therefore, employed in the determination of the mean daily air temperatures for use in the calculation of convection and radia- tion losses. 63* Entrance air temperatures ware measured as described previously and were used in the calculation of heat recovery. Since a stream of entering air was aspirated past the thermocouple junction at high velocity, the measured temperatures should be in error less than a degree. Variation of the temperature took place during the day, and the daily mean temperatures varied between 57° s.nd 66°F through the main period of testing. Mean entrance air temperatures as low as 3^ F were re- corded in the winter tests. Exit air temperatures were measured in the same manner as entrance air temper- atures, but the effect of changing operating variables caused them to vary a great deal more. The exit air temperature is most markedly affected by solar heat input, air rate, and entrance air temperature. It is seen from the results that the daily mean- exit air temperatures varied between 64 and 156 F., which values cor- respond to mean air temperature rises through the unit of 24° and 75° respectively. The maximum measured exit air temperature was 231 F. As is explained in greater detail below, the exit air temperature bears a direct relation to air rate and to heat recovery efficiency. Since no recycling of warm air to the unitwas em - ployed in these tests, entrance air temperatures were occasionally very low, es- pecially in the winter, In the house installation, air is supplied tothe unit from the house itself, and is therefore at an approximately constant temperature of 70°F. Thus, a temperature rise as small as 25° would allow delivery of air at 95° to the building. The mean air temperature rises may appear surprisingly low, but it is to be realized that they are calculated simply by averaging the hourly exit temperatures and hourly entrance temperature, and taking the difference; whereas, a better picture, insofar as heat delivery is concerned, would be obtained by using a mean which is weighted according to the heat delivered. Thus, the temperature rises during the' middle of the day, when high heet recoveries are being obtained, are .particularly high, and of greater impotence than those secured early and late in the day. In other words, for purposes of heat storage, it is more impotent to have particularly high air temperatures during the period of high heat re- covery, than it is to have a moderately high air temperature throughout the entire day. V.'hen the mean temperature rises are calculated in this manner (obtained most easily from the total heat recovered and the air rate), they are 10 tc 2C degrees higher than those shown in Table I for most runs. A second point in this connection is that the temperature rises during only the 4 or 5 hours in the middle of the day are considerably greater than either of the means mentioned above, and since roughly 2/3 of the daily heat recovery is in this period, the effective exit air temperature available to a heat storage unit is considerably above the averages shown. A third consi deration of the reported exit air temperatures indicates that these could be greatly increased by the use of a heat storage unit in a manner such that recycling of hot air fror the collector to the storage unit, and back to the collector could be employed. With this system, most of the heat in the air leaving the collector is transferred to the storage bed, which results in heating of the bed and cooling of the air. As the bed's temperature increases, the temperature of the air leaving it also increases. If this warm air is circulated back to the collector, its temperature at the collector 6xit is raised consider- ably abo'"* that secured with the use of cold inlet air. The bed's temperature could be progressively increased by this recirculation method to the point at which the heat losses from the collector became equal to the sclar input. It is expected that this point of maximum air temperature would be at least 25C°F, and perhaps considerably higher. 34. Cover plate temperatures are probably subject to greater error than air temp- itures because of radiation errors, and imperfect contact between the thermo- couple strips and the glass. The cover temperatures were used only in calculat- ing losses for the heat balances and probably are within the maximum probable error in the heat loss equations. It is felt that cover plate temperatures are generally within five degrees of the exact value. From the data, it is seen that the cover plate temperature is usually about 20° higher than the temperature of the surrounding air. Temperatures of black surfaces were also measured so that the heat lost through the bottom of the unit could be calculated, and so that the exit air temperature and black plate temperature could be compared. The reliability of these figures is probably about the same as that of the cover plate temperatures, since the same method of measurement was employed. The data indicate that the average black plate temperature is 20° to 30° higher than the exit air temperature in most cases where reasonably high air rates were used. At lower rates the dif- ference is greater and the plate temperature is higher. Thus, with a lower air rate, less heat is recovered, higher air temperature is obtained, - and the unit operates at a higher temperature throughout. It is, therefore., apparent that the heat transfer coefficient is much lower at the low rates. Convection trans- fer, at least at the high rates, must therefore, take place. The air rate was varied over a wide range in order to determine its effect on exit air temperature and efficiency. The rate was controlled by adjusting a damper in the duct leading to the exhauster and measured either by the use of a calibrated rotameter or an orifice. Since equipment for continuously recording the air rate was not available, one or more measurements of air rate were made during each run by reading the rotameter or orifice manometer and the correspond- ing air temperature. Since the volumetric rate at the fan inlet remains constant throughout the day, even though the air temperature is steadily changing.) the continuously recorded temperature at the fan inlet along with the above flow and temperature measurements were used in the calculation of air rates throughout the day. This method involved possible errors in the calibration of the meters,, in temperature measurement, and in fluctuating voltage to the fan motor. It is felt that the maximum probable error in the mean air rates is less than 5 per cent, k'ore than a ten-fold variation in rate was secured, ranging from 32 to 369 cubic feet per minute. The total heat recovered during a day was calculated from the values of air flow rate, temperature rise through the unit, and the heat capacity of the air. To express the value on a basis of 1 square foot, the total was divided by 209, the area of the collector. Values were greatly affected by air rate, as further discussed below, and ranged up to approximately 1000 Btu per square foot of collector per day. The accuracy of these results is approximately the same as the flow rate accuracy and therefore within a maximum probable error of 5 per cent. Gross heat input was calculated from the pyrheliometric data by integrating the recorder chart each hour and converting the results to engineering units. The recorder clock was set in accordance with the calculated solar time; the calibration of the pyrheliotneter was directed by I. F. Hand of the U. S. leather Bureau, Solar Radiation Section (23). Correction was also made for the seasonal variation in e.m.f. per unit of solar energy as caused by change in angle of solar incidence. Ey consideration of the possible sources of error in the above fBcaeurerwnts and calibrations, it was concluded that the solar measurements could- have a maximum probable error no greater than 2 per cent. 65. By the method described, the energy received per square foct of horizontal area was calculated. It was then necessary to convert these results, by a simple cosine relationship, to energy received per square foot of roof area sloping at a 27° angle. Reflection losses were calculated from data on reflection from multiple glass surfaces (9) by the method outlined in the appendix. Since these 1-osses vary with angle of incidence of sunlight, and since such angle varies throughout a day, hourly calculations were made and then totaled. The accuracy of these figures is high because of th.e reliability of the data and equations. The maximum probable error is thought to be less than one per cent. Because diffuse radiation strikes the collector with a different effective angle than direct radiation, it was necessary to determine experimentally the por- tion cf the total radiation which was diffuse. By shading the pyrhelicmeter with a small disc held several feet away, the diffuse radiation was easily measured. The presence of clouds causes a considerable change in the proportion of diffuse radiation, but because of the variability of this factor, and the small overall effect mentioned below, the mean angle of incidence during daylifht hours was calculated on the assumption that all radiation was direct. Diffuse radiation is of most importance early in the morning, and late in the afternoon when the amount of direct radiation may be si all or even zero, whereas the diffuse radia- tion is a large portion of the total and strikes the collector at a much more favorable angle than the direct. However, the total reflection during the day is not apprciably affected by the portion of diffuse radiation because this portion is such a small fraction of the 1 total, and its mean angle of incidence does not differ greatly from the, mean angle for direct radiation. Further discussion cf reflection losses nay be found below, in the section devoted to heat balances. Net heat input was calculated by subtracting the reflection losses from the gross heat input.. The principal use cf the net heat input results was in the correlation of efficiency data. Since the reflection loss is affected by the mean angle at which the sun strikes the collector, and since this r.;ean angle varies from day to day and season to season, the basing of performance on net heat input eliminates the effect of this seasonal variation when the effect of another variable, such as air rate, is being studied. Gross efficiency is the percentage cf the total radiation striking the collect- or which is actually recovered as sensible heat in the air stream. It is the primary index by which the performance of the collector is judged and should obvious- ly be as high as possible. As explained iri more detail below, it is most affected by air rate. In the tests shown in the Table of Results, gross efficiency varied from about 8 per cent at low air rates to approximately 40 per cent at high rates. Net efficiencies are approximately 50 per cent at the high air rates. These values mean that about 50 per cent of the net heat input (gross input minus reflec-r tion) was recovered in the air stream* The usefulness of these figures is twofold: first, as described above in connection with net input, they allow a better com- parison of perf err ance on different days than do gross efficiencies, because the effect of change in solar position is minimized; secondly they represent more accurately the efficiency in terr s of a fraction of the ultimata obtainable per- 56. forrance with this collector. The latter consideration is valuable, because the lected energy is not available for useful recovery, and therefore the unit could never have a pross efficiency of IOC per cent no matter what, conditions prevailed. However, the unit could have a net efficiency approaching 100 per cent if the air rate were increased sufficiently. The net efficiency figures also in- dicate what overall performance (gr*ss efficiency) might be obtained if surface reflection could be eliminated as by one of the surface treating processes for lenses and other types of glass. Further discussion- of the factors affecting efficiency is presented in the explanation of the various plots. In order to compare the total measured heat input with the measured useful output plus reflection, convection, conduction and radiation losses, a nunber of heat balances were calculated. In addition to showing the distribution of heat losses, these results five information on the reliability of the data and method of computation. When the heat balances are studied it is seen that the unaccounted-for losse were frequently less than five per cent of the total los.ses (being therefore less than three per cent of total heat input). In view of the great amount of data ar calculations on which this result depende , and in consideration of the v/ide hour] variation in conditions frequently encountered and the resulting necessary appro mations, it is felt that th3 heat balances are highly satisfactory. Several heat balances, in which widor deviations are noted, are perhaps not quite sc reliable, but certain faotors, particularly wind velocity, have such important bearing on particular losses that these rssults seem well within experi mental error. The distribution of losses is probably not so exact in these runs as in those with lower unaccounted-for losses, but the efficiency, which is based n measured heat recovery, should be just as reliable as in the runs with less discrepancy in the heat balance. There are two reasons for not calculating heat balances in all runs. In the first place, the overall recovery is the important practical item, whereas the distribution of losses is of considerably lesser importance in equipment performs Secondly, certain data, particularly cover plate temperature, necessary for heat balance calculations were not obtained in all runs. In the table are shown the actual total daily heat losses by reflection fron glass surfaces, convection fror the cover glass into the surrounding air, conduct through the bottom and sides of the unit, and re-radiation from the warm cover pi into the surrounding air. The sum of these losses subtracted from the total (ob- tained by subtracting measured heat recovery from gross heat input) yields the unaoeounted-f or losses. Each of these losses was also computed as a percentage of the total. It is seen from the heat balances that roughly one third of the loss is by reflection from tho glass surfaces, another third is by convection from the cover plate > and the remainder is partially by conduction through the walls and floor of the unit and mainly by reradiation from the cover plates. The distribution of these losses, of course, varies considerably with such factors as wind velocit cover plate temperature, air flow rate through the unit, and solar intensity. 67. Reflection from multiple gXass surfaces represents a large portion of the total losses, but there is little or nothing that can be done to reduce this, ex- cept by providing coated or etched glass (glass treated with certain agents to pro- duce a coating of molecular thickness, to minimize surface reflection), a process as yet probably impractical for large glass surfaces. The glass could be made essentially non-reflective for certain wave lengths, but could not be made non-re- flective to both the visible and infra-red radiation in the solar spectrum. Reradiation and convection from the cover plate constitute together the great- est heat less, and are dependent or the difference in temperature between the cover plate and the surrounding air. The convection loss also depends on the wind velocity. The above temperature difference must exist if heat is being recovered, hence its magnitude should be maintained as low as is consistent with sufficiently high exit air temperatures. In other words, the higher the air rate through the unit, the lower will be the cover plate temperature and the resulting losses; and the higher will be the efficiency of heat recovery. If, on the other hand, high exit temperatures are desired, with no attention being paid to heat recovery efficiency, low air rates can be used, as for example in run 45, which result in high exit termperatures, high cover plate temperature, and hi^h convection and reradiation losses. High outside v/ind velocities increase the rate of heat loss by convection, but do not affect the re-radiation losses directly. A correction for wind velocity was made by the method shown in Appendix C, and should yield reasonably reliable results. The equations which were used in calculating the various losses are based upon the standard methods used in heat transfer work, and are reasonably accurate. The calculation of the convection heat transfer coefficient is probably subject to the greatest error because of numerous factors, particularly wind velocity. The coefficient is markedly affected by wind velocity, and the estimation of velocities right at the glass surface is difficult. Jhe accuracy of the heat transfer co- efficient ■ equation is also somewhat lower than could be desired. It is estimated that the figures on heat loss by convection have a maximum probable error of 10 per cent. / Radiation losses can be calculated reasonably exaotly by the Stefan-Boltzman equation, provided that the cover plate temperature, air temperature, and surface emissivity are accurately known. In some runs, reliable cover temperatures were available, and it is believed that these were within one or two degrees of the exact surface temperatures. As explained previously, Weather Bureau data were used f'or calculations of the temperatures of the surrounding air. It is felt that the radiation losses have a maximum probable error less than five per cent. Knowledge of reflection losses is obtained entirely by calculation of reflec- tion from multiple glass surfaces. These figures should be even more exact than those described immediately above, because the only complicating factors are dirt •n the plates, and change in angle of solar incidence. Dirt on the plates has been shown (9) to have negligible effect on the reflected energy; and small changes in angle of incidence, in the ranges involved, cause changes relatively small in the portion reflected. 60. Conduction losses through the floor and walls are small, and calculation of their values has been made by simple and fairly exact methods. Errors would not exceed those mentioned above. The unaccounted-for losses do not represent other types of losses, but rathe additional losses of one or more of the above types. In two or three instances, negative unaccounted-for losses indicate that one or more of the other reported losses is no doubt high. In general, the heat balances show a remarkable correlation of the data and lend strong support to conclusions based thereon. They also show how the various losses are distributed, and which ones should first be investigated further in an effort to improve efficiencies. 69. PRIMARY GRAPHICAL RESULTS In the numerous graphs of results, several variables have been correlated to show more clearly than does the table how the performance of the unit is affected by changes in its arrangement and operation. These graphs have been divided into two separate main sections, the first of which may be considered to contain the principal basic plots, and the second to contain the secondary graphical results and numerous correlations. The purpose in this division is to show clearly the overall performance of the solar unit by a few simple graphical analyses, and then to show the specific effects on exit air temperature and efficiency of varying air flow rate, entrance air temperature, plate spacing, heat input, cloudiness, and season of the year. The graphs in the first section may be further classified as follows: 1) A sample graph showing how the performance of the unit varies with the hours of the day. (Figure 4) 2) Graphs showing relation between air rate and efficiency for different plate spacings. (Figures 5 and 6) 3) A graph showing the relation between angle of collector tilt and the winter radiation collected. (Figure 7) The graphs in group 2 probably show in simplest form the general overall per- formance of the equipment. Figure 4 is included to show how the heat recovery and air temperature vary throughout a clear day, and is an example of the sort of data which were used in the calculation of final results shown in the tables and other graphs. Figure 7, on the other hand, is a graph of the relative effectiveness of collectors at different tilts, and would therefore be useful in the design of solar heating units. By reference specifically to Figure 4, it is seen that the heat input rises rapidly to a maximur. at noon, then drops off in the afternoon nearly to zero at sunset. On cloudy days, the curve is not perfectly regular, of course. The heat recovery curve is of a shape similar to the input curve, but lower and displaced somewhat to the right. Its lov/er height is / due to the heat losses previously dis- cussed, and its displacement is caused by the thermal lag in the unit. In other words, the heat capacity of the glass and other components of the unit is such that approximately one hour is required tc heat the equipment to operating tempera- ture. Thus, trends in the heat input curve are not evidenced in the eut put curve until about one hour has. elapsed. In the morning, this effect causes a delay in useful heat delivery, whereas in the afternoon, a prolonged heat delivery is noted. This extra heat delivered in the afternoon hours, some even after sundown, can be looked upon as morning heat stored in the unit. The areas under the heat input and output curves correspond to the total re- spective heats for the day, and the ratio of the two areas can be used to obtain the heat recovery efficiency, 37«4 per cent in the case shown. Temperature variation throughout the day is also shown in Figure 4. It is seen that the exit air temperature curve has a shape and position almost identical to those of the heat recovery curve. . In other words, the same lag exists in the attainment of elevated air temperature as in securing heat recovery, because the one quantity depends on the other. In the case shown, the temperature difference 70. i between enterinr and exit air wis at a maximum of 72 decrees at 1 p.m., solar time Moreover, exit tamperat urea were at leaat 20 degrees higher than entrance tempera- tures for mora than eight hours during this particular day. The entrance air temperatures showed a natural rise and fall during the day. In Figures 5 and 6, gross and net efficiencies are plotted against air rate, for two different plate spacings. For Figure 6, the calculated reflection losses were deducted from the total heat input, and the resulting net heat input figures were used in computing net efficiencies. Gross efficiency, plotted in Figure 5, is the -\ctual heat recovered divided by the total heat input. In these plots, as in others, there is very little difference between the trends in the net and gross efficiencies. This means that the reflection losses from the unit ac a percentage of input were sufficiently constant throughout the several months of recorded runs that the net efficiencies are simply proportionate ly greater than the gross efficiencies. Th3 seasonal change iri the sun's position caused practically no difference in the percentage reflection. It is seen in Figures 5 and 6 first that the l/4 inch spacing yields decidedl greater efficiencies than the l/2 inch spacing. This is in complete agreement wit the results of tests with the small scale indoor unit. The superior performance o the unit with l/4 inch spacing is no doubt due to the decreased eddying of the air passing between plates and the resulting lower convection heat transfer upwards from plate to plate. A second important conclusion drawn from Figures 5" and 6 is that efficiencies are low at low air rates, rise nearly linearly as air rates are increased to a moderate value, and then rise more slowly as air rates are increased to a compara- tively high figure. It is also seen that with l/4 inch spacing, efficiencies in- crease only slightly .above 37 per cent gross and 50 per cent net, as air rates are greatly increased. This fact points toward the conclusion that with the apparatus tested, there is practically- no advantage in going to excessively high air rates in order to secure slightly higher efficiencies. That this point is particularly important is realized when it is noted that the maximum exit air temperature de- creases almost in inverse proportion to the air rate. It is of course true that if the air rate were increased to a sufficient de- gree, the net efficiency would very nearly reach 100 per cent. The net efficiency curves are therefore not approaching maxima near the values shown in Figure 6. That net .heat recovery efficiency should approach 100 per cent at high air rates is obvious because the higher the air rate, the lower the temperatures in the unit, and hence, the lower the reradiation, convection, and conduction losses. These los9ee would approach zero at sufficiently high air rates. It is felt that the apparent slowness of the approach to 100 per cent net efficiency is caused by the increased aij? turbulence at high rates, and the resulting increased ease of heat transfer by convection from plate to plate. Thus, as air rate is increase although the temperature in the unit is reduced, the convection heat transfer from plate to plate is facilitated, the cover temperature does not decrease greatl and the losses remain relatively high. Hence, efficiency does not increase markedly aven with large increases in air rate. 71. A third fact apparent in Figures 5 and 6 is that cloudiness has no noticeable effect on efficiency. Points differentiated according to clarity of sky show no noticeable trend, and the curves were therefore drawn through the whole group of points. Another plot of this effect is presented in. Figures 26 and 27. In Figure 7, the relation between total radiation collected and change in angle of tilt of collector is presented. For a given collector tilt, readings on the vertical scale indicate the ratio of the total radiation which v/ould be collected during the period October 1, 1944 to June 1, 1945 to the radiation which would be collected during the s-ams period by a collector of the same area, but tilted at 40 degrees from the horizontal. The graph vas constructed from results of two complete heat recovery calc.ulQtio.HS . In the first of these, solar energy received each hour per unit of horiionial area, as recorded by the pyrheliorreter equipment, was totalled each 4ay, Thi-S result was then converted to heat re- covered by a roof unit tilted 40 degrees to the south from the horizontal and col- lecting heat with an overall daily net efficiency of 45 per cent. The total radia- tion thus collectable by the 463 sq, ft, unit over the winter period would be 64,630^000 Bttu A similar calculation was made for the case of a roof sloping 27 degrees from the horizontal, and the ratio of the total heat recovered by the 27 degree roof to that by the 4C degree roof was determined. It was also found by calculations based on the relation between solar .position and season (22) that at a latitude of 40 degrees the angle of / ■fi'ne $aximuin radiation can be collected during this period is 43 degrees. This result is obtained as shown in Appendix C by graphically integrating an equation in which the total radiation received by a tilted collector during the winter season is equated to a function involving latitude, angle of collector tilt, solar declination, and atmospheric trans- missivity. By repeating the calculation for several collector tilts, the one for which the maximum radiation is received is determined. Although the final result is based on the .solar position at noon of each day, it is valid for the entire day, because -optimum exposure at noon is accompanied by optimum exposure all day. •Even though the calculation of the optimum angle vof tilt in Figure 7 is based on calculations of solar position whereas. the 27 degree and 40 degree points are israed on actual radiation received, the correlation appears very good. . This re- lation indicates in turn that such factors as cloudiness reduced the monthly radia- tions 'isynmetric ally throughout the period between October and taay, and did not predominate heavily during any month* The points at 46 degrees and 59 degrees. tilts -are obtained by analogy and involve the same ratio of radiation collected as do the 4-0 degree and 27 degree points. Such is the case because the collectors are merely tilted by the same numb- er of degrees beyond the optimum., hence they receive radiation at the same angle but simply oblique in the opposite direction. The remaining two points which arc used to construct the curve are located in accordance with the fact that the mean angle of 47 degrees (90 degrees minus 43 degrees) which the sun's rays make with the horizontal through these months would cause the rays to be parallel to the surface of a unit sloped 47 degrees to the north. Thus, if a collector's surface is tilted 47 degrees to the north, and if the sun v/ere stationary at its average noon winter position, the sun's rays would simply graze the surface of the unit and do not enter it. Hence the ratio of radiation recovered would be zero. Actually, some small amount of radiation would be c611ected because the 47 degree solar angle of elevation is simply a mean, and there would be periods in the fall and spring in which some radiation would be 72. cc i_ ., However | this effect would bi anall, and has not been computed in this analysis. Similarly, if the unit were tilt 3 bo the south, considerably beyond • 1 position bo that its cover surfaco faced down at an angle of 133 de- . essentially zero collection would result. Although the seven points described above do not constitute a complete ana precisely accurate set of results, the curve drawn through then has considerable meaning and value. It is seen that at 40 degrees latitude, a tilt of 30 degrees i per cent as effective as one tilted at the optimum 43 degrees, and a unit tilted at 40 degrees is only about 1 per cent less effective than the optimum." Thus, the effectiveness of tilting the units to different degrees, as for example, to correspond to the roof slopes of different houses, can be readily observed in Figure 7.. Tho graph clearly shows the importance cf tilting the collector, becaus if a horizontal position were used at the 40 degree latitude, the energy collector during October through Kay would be less than 70 per cent of that collected by a unit cf equal orea tilted at 43 degrees. The graph can also be used to cal- culate directly the relative areas of units . collect ing the same radiation, but tilted at different angles. Thus, a collector tilted at 27 degrees should be 8 per cent (100-92) larger than one tilted at 40 degrees, if the sar.ie total radir: tion is to be collected. It is tc be recognized that a tilt of 43 degrees is the optimum fcr heat col * lection , but not necessarily for heat use in a house. In the fall and spring, a large portion of the collected heat would be discarded, because the heating lead is light in these seasons. Hence, the optimum tilt would be somewhat steeper than 43 degrees in order tc favor heat collection in the winter months when essentially all the collected heat is needed in the house. In order to calculate such an optimum, the fraction of the collected heat which would actually be used in the experimental house each month was obtained from T-.ble II. Values for a 40 degree tilt and one day storage were employed. By using these fractions as multipliers in the previously mentioned radiation equation, integration :f the functim for various tilts could be performed. It was found that with collector size and heating requirements analogous to these in the experimental house, a collector tilted at 47 degrees would carry a greater portion cf the annual heating load than would a collector at any other tilt, provided that hoat could be stored fcr a one day period. Theoretically, the values for monthly fraction -of collected heat used by the house should be recalculated for a 47 degree tilt rather than 40 degrees, but the effect on the final result would be negligible. The variation in solar raliation caused by clouds has net been considered, but the effect of such variation is relatively small. The use cf collectors larger than the one on the experimental house, relative to the heating requirements woul .': require tilts scmev/hat greater than 47 degrees if the optimum were to be maintained* Smaller collectors, or larger heating requirements, would entail the use of an angle 0* optimum tilt less than 4? : egrees, but not less than 43 degrees. In general, ther fere, a house at 40 legroe latitude, in which approximately the same monthly frac- tions cf collected energy are actually usei as in the experimental house, should be prcviiei with a collector tilted at 4? degrees if the collector area is to be at a minimum, kt latitudes other than 40 Agrees, Figure 7 would be somewhat different, but ighly, the optimum tilt for heat collecti on luring this winter period could be no by adding approximately 3 degrees to the latitude. Thus, at latitude 30 degrees, the collector shcul . be tilted about 33 degrees from the horizontal to 73. receive the maximum radiation in this period. The 3 degree figure is the approximate m:an declination of the sun during this period, that is, its average i»sition is 3 degrees below the equator. To collect and utilize the solar heat in a house having a heating requirement and collector area similar to the experimental .house and having one^-day heat storage capacity, the col- lector should ideally be tilted at an angle equal to the latitude plus approxi* mately seven degrees. If the collector were used primarily to supply energy to an air cooling unit operating in the summer, it should, of course, bo .oriented more favorably for summer exposure. Tilts of 20 decrees to 25 degrees would probably be near the optimum during this season. 74. TABLE OF RESULTS II Tsble of Results II contains tha calculated values of the percent of the toti heating load carried by the solar unit from October 1944 through L'ay 19^5- The ta are given for the conditions that (l) no heat storage is "used, and that (2) excess heat is stored for one, two, or three days. Data for both a 27 and a 40° tilt of the unit from the horizontal are given. The calculations ei' the data fcr operation with no storage involved the use ' degree-day figures for the daylight hours only.. These figures were determine from daily temperature charts available fror. the Geology Department at the Univei sity. The heat required per degree day was originally calculated on a twenty-fci hour basis, but since eunlirht adds to the house heat supply, there would be lesi heat required in the hours of daylight" per degree-day than would be required during the night. In calculating? the heat required during the daylight hours, this difference was neglected because of the complexities involved in- deterrinini the correct values. The calculated heat requirement during the daylight hours ii therefcre, somewhat higher than actually would be needed. The heat storage -calculations were made en the assumption that there was stora.e capacity sufficient to hold all of the excess heat collected for r. certa period of time, in this case one, two, or three days. The calculations could have been rrnde on the assumption that storage capacity was provided that would hold a certain maximum -quantity cf heat, but this method would require a longer set of calculations* By examination of the results obtained by the first method of calculation, the necessary capacity of the three sizes of storage units could easily be determined. These storage unit sizes are shewn in Table of Results III All of the original calculations were mado with the further assumption that then was no loss fror the storage unit until the one, two, <~»r three day period had elapsed. At the end cf the storage period, all hoat which had not been used was ssuned to be lost. This assumption is net strictly* true, as the heat is gradu- ally dissipated, but it rreatly simplifies the calculations without introducing serious error.- The data show the advantare of incorporating a storage unit into the solar eating system. Fcr the 27 tilt, the audition of a storage unit capable of stoi ng all the excess heat for one day, wcul i increase, the percent heating load arried from 3^.0 to 54.6, but increasing the storage capacity the amount necess; store heat for 2 or 3 days would increase the percent heating load only to and 60.1 respectively. These data show, therefore, that the greatest ad- ntage is obtained with a small storage unit capable of storing heat for one y, end that the U3e of larger units may be impractical. The final design, how er, will depend on an economic balance which will show if the added cost of lai Lorage facilities will be greater or smaller than the value of the additional heat saved. It is interesting to note that in October more heat was collected in the solj than was req\ ired to heat the house, but when no storage- was provided, only of the heating load was carried. The - reason for this anomaly is that the ex- 33 heat was collected during the day and discarded, and was, therefore, not able when heat was needed in the evenings and early mornings. If storage 75. facilities had been provided, this waste heat could 'have been saved and used when needed. During the remaining months, the heat received was not enough to carry the entire heating load, 'but, if desired, more heat could be collected by employing a solar heat trap of greater surface area* An economic balance of cost of solar unit versus fuel cost would be of assistance in determining the optimum size of solar unit to use. The angle the collecter makes with the horizontal is shown to have a definite influence on the operating characteristics of the heating, system. To receive the maximum amount of solar radiation at any time, the unit should be normal to the sun's rays. Since the unit is in a fixed position, the angle of incidence of the sun on the unit must be chosen.-tc give the maximum ai: cunt of radiation over the period considered. For the period shown. in the table, this angle- has been found to be about 47 degrees, when the house heating needs ere considered and one-day storage is provided. The table shews that a 5% increase in heat recovered could be expected if the angle of tilt were increased from 27° tc 40°, Forty degrees roof tilt was chosen as about the maximum practical angle. 76. TkHLE Of RESULTS III » In Table of Results III are shewn the necessary sizes for heat storage units packed with a material having a heat capacity of 0.2 Btu/lb.°F M such as brick- work, ccke, clay, rlass, granite, or stone. A rac'ximum available terperature dro of 130°F. was assumed. Thus, the unit may be considered to have a r.aximum quanti of heat stored when at a terperature of 210°, and no useful heat when at 60°F. If the exhaust air froi the storage unit were to be recycled back to the solar unit intake, the ir.axirr.un. useful temperature drop might be considerably increased As reported in the literature, water or some other liquid might also be used as a heat storage r.ediuru. Since much more elaborate equipment would be required fo the use of a liquid storage medium, it would probably be cheaper to store the heat in a chamber of lcose solids. For this reason, heat storage in v. liquid ha not been considered in this calculation. The amount of excess heat recovered each cay by the solar unit and stored for subsequent use was first calculated. At infrequent intervals an abnormally large amount of excess heat was recovered. The fipurec in column 5 of Tc.ble III are these maximum quantities of stored heat, regardless of whether or not the heat is needed. It wouls seem unnecessary to design a storage unit with capacit sufficient to store this abnormal an' cunt of heat if satisfactory results could be obtained by using a unit which would store a normal maximum or average high quantity. Columns 4 and 7 of the table shew clearly that the difference in stor- age sizes would effect a difference in heating load carriable of only 1 to 2 per cent, whereas the larger unit would require at least 33 P Q r cent mere material. The difference in storage unit size required for one, two, and three day heat storage is also shown in Table of Results III. The final design of the •storage unit would be dictated by an economic balance, but superficial exar.inati of the data leads one to believe that the economical unit would be designed to store heat for one day. To store heat for three days, a storage unit nearly thr times larger would be required, and only 4 to 6 per cent increase in heating loa carriable would be realized.. The approximate volume of a unit designed to stcre the normal maximum of excess heat for one day would be five cubic yards* . TklLE OF RESULiS IV In table rf K.asu] s I\ t, , and' C, itinj .' house heating system are presented. Th staniar i house comprises a furnace in which natural gas is use ! as fu 1, a fun a: for delivery of hot uir'tc the rooms cf the house, and ' ' ■ •. c controls ;' r temperature adjustment. Intc g system was incorporated a solar heat collector ana the necessary ducts, dampers, and additional controls for automatic operation. Fuel saved ii. the experimental house after the solar unit was install* 3 is de- termined by comparing the gas consumption in two identical houses over the same period (Table IV A) and 1 y comparing fuel requirements in the solar heated house before ana after the solar installation (Table IV B). In Table of Results IV A, the pas consumption of the solar heated house is compared with that of an identical house not equipped with a solar heating system. The second house has the same floor plan and volume as the experimental house, and is situated adjacent to it. During the year preceding the installation of the solar heating unit, the average gas consumption in the test house was 21 per cent greater than in the identical house next door. The mode of living of the re- spective occupants and the temperature level maintained in the two houses combined to cause this difference in heating requirements. Durinr the period shown in th,; table, the temperature of the test house was maintained about 5 degrees higher than it had been the previous year. This increase in temperature would increase the heating load, and hence the gas consumption, of the system. The amount of this increase was estimated by the Public Service Company of Colorado to be 3-1 per cent for each degree increase in temperature (19). For the 5 degree increase in temperature, the eras consumption should be increased 15.5 per cent. The gas consumption for the test house, if the solar unit were not used, should then be 25 per cent plus 15.5 psr cent or 4C.5 per cent greater than that for the identical house. A number of errors are inherent in the calculation of the results shewn in the table. The figure used in the comparison with the identical house was only an approximation since (l) the heating load increase of 25 per cent was based on data for only one winter, and durinr that time it varied considerably; (2) the five degree increase in temperature maintained was an assumed average for the entire heatin; season, and probably somewhat inaccurate; and (3) the gas consumptio increase of 3.1 per cent per degree was an average for many houses and may not have been exact for this particular one. Other errors which night havn been of consequence were possible differences in the gas consumed In the two automatic hot water heaters and in the kitchen range of the identical house during the two years of comparison. The last column in Table of Results IV A shows the per cent heating load carriable as determined from the amount of pas saved (Column 4). It would seem that in the spring and fall, when a large amount of heat was collected, the per cent heating load carried would have been greater than in the winter when smaller quantities of heat were recovered. The table shows that in reality the reverse was true. In the spring and fall, most of the heating was required at night and a great amount of heat was thrown away during the daylight hours, but in the colder months the per cent of the total heating required during the dayli'ht hours increased and more of the collected heat was utilized. It is , therefore , seen that in the absence of heat storage facilities a greater per cent of the heatin? load 'was carried in the winter months. 78. The discrepancy between the per cent heating load carriable shown in Table II and that shown in Table IV A may be attributed to factors other than those mention- ed above. The figures in Table II were based on an air rate of 180 CFM and the corresponding net efficiency of 45 per cent obtained with the laboratory unit . Since the area of the laboratory unit was 209 sq. ft. and that of the house unit was 463 sq. ft., an air rate of 400 CFM should have been maintained in the house unit, if it were to operate at an efficiency of 45 per cent. From experin.ental measurements made at noon, an air rate in the house unit of only 168 CFl! and an efficiency of 12.8 per cent were calculated. If the galvanized iron ducts in the house unit were insulated, the shading effect of the chimney eliminated, and the broken glass replaced, the efficiency should be about 29 per cent. This value can be read from Fifuro 6 at a laboratory unit air rate of 85 CFM, which cor- responds to the-house unit air rate of 188 CFM. The efficiency of the house unit, 12.8 per cent, may be somewhat in error as it was assumed that the efficiency at noon was approximately the same as the efficiency for the whole day. This approximation was found 'to bo reasonably valid by examining the laboratory unit data. An additional difference lies in the fact that the figures for heating load carriable shown in Table II are based on only one year and would, of course, change from one year to the next. Results of calculating house unit performance by use of degree-day heating requirements, instead of by direct comparison with the adjacent house, are shown in Table IV B. Since the number of degree-days of heating is only one of many heating load variables ,• such as wind velocity, sunshine, mode of living, and thermostat settings, the heating load carried shown in column 9 is subject to considerable error. The fact that the heating load carriable in September, October, and November is recorded in the table as zero, is a good indication that the method of calculation is not reliable, because it was known that some of the required heat was furnished by the solar unit. The actual operating data for the house heating system, as determined ex- perimentally, are shown in Table TV C. The predicted heating load carriable is based on the assumption that all the heat collected at the low efficiency cf 12.8 per cent was used during the day and that lack of storage was not a disadvantage. Since tbe first method of calculation, that of comparison with the identical house, and the method involving the 12.8 per cent efficiency figure are in the same range, and since the degree-day method is known to be seriously in error, the most probable average per cent heating load carried by the present house solar unit is about 20 per cent. Though this figure is low in comparison with the 34 per cent heating load carriable shown in Table II, it could be increased simply by supplying the correct air flow and insulating all the hot air ducts. 79. TABLE OF RESULTS V Comparison of Actual and Theoretical Results In the report of i. iller (10), theoretical consideration of the operation" of a solar heating unit was made, and 'quantitative results of its operation were pre- dicted. In the calculations, it v/as assumed that (l) no heat transfer took place by convection fron plate to plate, (2) no heat was lost to the surroundings by convection fron the cover plate, (3) the radiation loss fro: the cover plate was to a space temperature of absolute zero, (4) no heat losses from the sides and bottom of the unit took place, and (5) certain simplifications of the rigorous mathematical solution could be made without introducing large errors in tl-e re- sults. In order to rake a comparison between experimental and theoretical results, it was necessary to use filler's method in the calculation of a set of results based on a specific outdoor unit run. Since convection from the top plate was known to take place, the amount of heat lost in this manner was determined as shown in Appendix C. The reradiation from the top plate was assumed 'to take place to the outdoor air tei. perature, since this has been found to be a better approxima- tion than the one proposed by 1'iller, which states that radiation takes place to a space tenperature of absolute zero (9). l.iller's assumption (4) in which he stated that there was no loss of heat from the sides and bottom of the unit is, of course, not rigorous. In the present calculations, however, it was unnecessary to consider this loss because it would take place from the heated air after the air left the black plate, whereas the air temperature was measured at the plate end before any heat loss took place. Outdoor unit run 0-42 was chosen for the comparison because it was made on a clear day for which all necessary heat balance data v/ere available.' The calcula- tions a re made for the hour ending at solar noon. Average values for the hour were used in every case. L'iller's analysis was based on a unit with no cover plate. To- make a rigorous comparison of the experimental and theoretical heat traps, it would be necessary to determine the heat interchange between the top plates and the cover plate, and to determine the amount of heat picked up from both plates by the entering air stream. The complexities involved in making the above calculations make it im- practical to include them in the present comparison, hence it was decided to make' two theoretical calculations in order to obtain a basis for comparing the experi- mental results. The first analysis was made on a theoretical unit with three plates in a stacks which is essentially a blackened plate insulated with v*° clear plates (2/3 overlap); and the second analysis was made on a unit with four plates in a stack (3/4 overlap). In the first analysis the unit had the sarre number of ideal heat transfer surfaces as the experimental unit, but less radiation insula- tion and reflection. In the second analysis the unit had more heat transfer sur- faces than the experir ental unit, but the saj. e ar ount of radiation insulation and reflection. Since all calculations v/ere based on the sai. e top plate temperature, convection and reradiation losses were the same. 80. The results of the* calculations are shown in Teble of Results V. If the theoretical analysis were entirely vali'i, the experimental .temper atures should have fallen between the two calculated ten peratures in each case. This gen- eralization is seen when it is realized that the temperature3 in the experimental unit should have beer, below those in the theoretical 4 plate unit because thoro was actually one loss ideal heat transfer air film but the sane amount of ref lectio and reradiation, and that experimental -emperatures should have been higher than those in the three plate theoretical unit because there was actually one more glass plate opaque to reradiation to the sky; this effoct may have been partially counter-balanced, however, by the additional reflection caused by the extra glass. Since the experir ehtal temperatures did not fall between the two sets of theoretical terporatures , one correction was thought to be In order. The unaccouni ed for loss of 24 3tu in the experimental unit should have been included in the heat balances in either bf two ways. The 24 Btu might have been added to the losses in the theoretical calculation and a njv/ calculation of temperatures made, or, this loss might have been added tc the heat recovery of the experimental unit. Though neither of those methods is strictly accurate, either could have been employed to i:ake possible a better comparison of the experimental and theoretical units. The latter method was chosen. After adding the 24 Btu to the 15& Btu heat recovery in the experimental unit, the revised heat recovery and efficiency were calculated to be 182 Btu and 55»4$ respect i/ely. These values are necessarily the sate as those obtained in the 4 plate theoretical calculation since both units had the sar. e number of plates and the same top plate terperature. Inder these revised conditions, the temperature of the air leaving the black plato was calculated to be 201°F. This value is higher than the experir. ertally determined value of l86°F., but it is still below cither of the theoretical values. If the 24 Btu had been added to the losses in the theoretical calculation, the theoretical tepperatures would have been lowered so: evhat,but probably not enough to alter the corparison greatly. The differerce between the experimental results and the revised theoretical results ray be attributed largely to the assumption that no heat transfer took place by convection froi plate to plate. If th<: air flow wore strictly laninar, no convection would take place, but the very large temperature gradient across the air film is a good indication that laminar flow aid not exist. It should be mentioned that the difference in air rites in the experimental and theoretical results in Table V does net constitute a reason for the observed disarreerent- of temperatures. All calculations are b-;sed on equal top plate tem- peratures, and any change in air rates fror. these listed would change this top plate temperature and herce chance the reradiation loss. If the theoretical an- alysis were precise, therefore, the experimental air temperature and rate would be identical with those calculated, provided that the Bstme* top plate temperature prevailed. In teste on the experii.ental unit, two inaccuracies which may be partially responsible for the discrepancy in the results just noted are (l) inaccw ecles temperature reaeureLent, and (2) the time lag fro, radiation received and heat recovered. The air temperatures were meesur.d by high-velocity thermocouples, out may be slightly affected by the usual errors encountered in thermocouple pyro: etry. The solar trap necessarily shdws a considerable ti, e lag between the orent the solar rays strike the unit. and the tir.e it attains a temperature cor- responding to this input. This tine lag is due to heat storage in the glass plates 81. and in the side walls and hottoi. of the unit. It has been noticed that the air traversing the unit would show its rr.3xin.1u2 temperature rise about one hour- after the tire of maximum solar input (solar noon), and, it has therefore been .concluded that the time lae is approximately one- hour. Because of this lag, the air temp- eratures and surface temperatures are undoubtedly not. in equilibrium with a particular incident solar radiation, nor does this equilibrium ever exist with a changing sun. The assumption of equilibrium is therefore, no doubt, in error. A better correlation might be obtained in the calculation of theoretical perform- ance by using the average incident solar radiation for the hour preceding the temperature readings. Since the unaccounted for loss includes heat stored in the one-hour period, the above method would, however, be an inclusion cf a loss correction/which has already been made. Therefore, correction for the time lag has not been separately made. 82. SEC0VD/,2Y GRAPHICAL R2SULTS AND C0FR3LATI0NS Figures 8 to 31 comprise the secondary results and correlations obtained with the laboratory unit and may be further classified as follows: 1) Graphs showing how efficiency, air rate, and air temperature rise are related at constant heat inputs (Figures 8 to 13) 2) Graphs showing how efficiency, entrance air temperature, heat input, temporature rise, cloudiness, and angle of solar declination are related at constant air rates (Figures 14 to 31). The above graphs are based on the data and results presented in Table I. They are used to show in detail the specific effects of changes in certain variables and are therefore of consi .arable value in explaining certain de- viations from the .-vera,,e noticed in the general table of r3sults (Tablel) and in Figures 5 and 6. They also show cloariy the particular effects of changing one operation variable while holding the others reasonably constant. In several cases, graphs are presented which because of similarity to each other, show essentially the same facts and from which the same conclusions are drawn. These similar graphs have all been included however, so that a complete" picture of the results could be presented. In Figures 8 and 9, air temperature rise is plotted against air rates at the two plate spacingS and at several constant daily heat inputs. The reason for correlating these variables at constant net heat input is that air rate and temperature rise could not show a simple interdependence under all oonditvons of small and large heat inputs, whereas at a certain heat input, temperature rise should vary systematically -with change in rate. Comparison of the two figures shows that air tomperatures are higher with the l/4 inch spacing than with the l/2 inch spacing at corresponding air rate3 and heat inputs. Each figure shows also that the temperature rise is greater with the larger heat inputs, and that at constant input, the air temp- erature rise decreases linoraly with increase in air rate. The latter effect is to be expected qualitatively, and is or value in determining quantitatively what air rates should be utilized in order to obtain partieular daily average air temperature rises. Maximum averagu daily rises of about 70 degrees F can be secured at low air rates, and average rises of 30 degrees to 40 & degrees can be secured at high rates, with resulting, high efficiency. In Figures 10 to 13 correlation of efficiencies with temperature rise at constant net heat input is made-. As mentioned previously, the same trends in net efficiency and Tress efficiency are noted, and Figures 12 and 13 are therefore very similar to Figures 10 and 11. - 86. It is seen in Figures 10 and II that better performance is obtained with l/4 inch spacing than with l/2 inch. In other words, at a fix* ut ani e given efficiency, a better temperature rise is secured with l/4 inch spacing; cr for a given temperature rise better efficiency is observed. In each of the four graphs,, the lines are relatively nine, together, i there is considerable scattering of the points. It thus appears that the relationship between daily average air temperature rise ant! efficiency is net markedly affected by snail variation in heat input. It would be expected, however, that with ; greater difference in sclir input, wider variation in efficiency-would be observed. Three such points are shewn in Figures 10 and 12 at net heat inputs of oOC Btu/ft'. If the air temperature rise is tc be the same with this lcw:r input as with the higher inputs, the air rate r.ust be considerably lower. For the same temperature rise, approximately the same cover temperatures exist and hence the same rate of heat less. Those losses therefore constitute a larger percentage of the input and cause a lower efficiency. This poorer performance is observer, in Figures 10 and 12 at the net heat input of GOC 3tu/sq.ft. There is act enough variation in the other inputs to cause a marked difference in the relationship between efficiency and temperature' rise. Il is ,oi course, seen that a high efficiencies (corresponding to high air rates) the temperature rise is comparatively lew, on i that as air rate is decreased, the temperature rise increases, losses inert-use, and efficiency decreases. These plots can be useful in establishing the conditions for operation of a soler heat- ing unit because they shew clearly the balancing d th< two most important variables ter.-.perature rise an. 1 efficiency. Thus, it can be immediately seen fro;.: Figure 10 that a 50 degree temperatui ; rise can be obtained with about 2£ per cent gross efficiency or a 40 degree rise with "\C per cent to 35 per cent efficiency. The air rates corresponding to these conditions can then be ascertained from Figure 5. Figures 14 tc 17 show the relation between entrance air temperature and ef- ficiency. Figures 14 and 15 show how gross efficiency varies with entrance air temperature at the two spacings, and Figures 16 and 17 show the variation in net efficiency.' These factors have been correlated at several c.nstant air rates in order tc. eliminate the effects of this variable. It is seen in all four figures that a change in entrance air temperature has only a slight effect on efficiency, and that the efficiency decreases slightly as entrance air temperature is raised. This effect is explained by the fact that with higher entrance air temperatures, the unit, as a whole, operates at somewhat higher temperatures, which causes higher losses and slightly lower efficiencies. In practical use, some advantage is gained by this effect, because with the low entrance air temperatures encountered in the winter, efficiencies are at their highest values. 8*. In Firures lC to 25, the relation between hso.t input .nd efficiencies is pre- sented. As in the preceding plots, all comparisons fire made at constant air rates. toss input vc grccs efficiency, not input vs. gross efficiency, • tticieney, nd net input vs net efficiency at the twe different ohs show essentially the same general trends. In Figure lC, for le, it is seen that as input is increased, while air rate is held eonstan lency iecreases slightly. The doubling of heat input appears to decrease the iciency by only five ncr cent. This change is due to the higher temperatures 88 at the higher heat inputs ar l : the mere rapid increase in losses than it input. That is, if heat input is ioy.blei, the losses are more than double. thus slightly reducing the r ry efficiency. In Figure 19, the changes ar in seen to be slight. The lines in the case these runs with l/2 inch plate sr , however, have a slope opposite to t of the lines obtained in the runs with l/4 inch spaced plates. Very little significance is attached to this difference because the points are so few and scattered that a small error in one or two of them could easily change the slopes of the lines to correspond to those in Figure 18.- As a ratter of fact, there is probably equal justification for drawing the lines in Figure IS with a slight negative slope. It can therefore be said, in general, that with l/4 inch and l/2 inch spacing, efficiency is not appreciably affected by change in solar heat input ; constant air rates, and if there is a slight ef f ect ; it is a decrease in ef- ficiency as heat input is increased. The practical value of this fact is that cloudy skies and hazy atmosphere do net appreciably lower the efficiency of heat recovery, alth-ugh the tctal in- put, the output, are msiderably decreased. This point is furtheriis- cussed below in crnnecticn with Figures 26 to 29. Figures 2C to 2^ shew the identical facts as 18 and 19 iescribed above and -ely involve the plotting of net heat inputs and not efficiencies rather than the totals used in Figures lS and 19. As explained previously, trends in net heat effects are seer tc parallel those of gross heat effects. The effect of cloudiness on efficiency is shown in Figures 26 and 27. It is seen that there is practically no change in the efficiency, even when cloudiness reduces the ncrr.al radiation by one-half. There appears to be a very slight in- crease in efficiency at high cloudiness, possibly because of lower exit air temper:, tures and resultant disproportionately low heat losses. There jsny also be a slight improvement in the mean angle of incidence of solar radiation, causing slightly lower reflection losses. The constancy of efficiency is advantageous in the practical operation of solar uni : . s, because the unit works as well in cloudy weath. as in clear, but of crurse less neat is delivered because of lower input. In contrast to the slight effect of cloudiness on efficiency, Figures 28 and 29 show the rarked effect of cloudiness on air temperature rise at constant air rates. As would be expected, the air ter.perature rise is not as great when radian' . reduced by clouds, provided that the air rate is unchanged, ".'ith a lower input, a lower recovery is secured; at a uniform air rate, therefore, the rature is decreased. This effect is observed in the runs at differer con3tart uir rates and with the two different plate spacings. 85. If it is desired tc secure a constant exit air temperature, the air rite should be varied accordingly. Thus, if input drops, the air rate should be de-- croased,' This means, of course, that the efficiency would also drop, as would be predicted by. comparing efficiency at two different rates in Figure 5 or Figure 6. Figures 30 and 31 show tne basic reason for the close parallelism between gross and net efficiencies observed in many cf> the preceding; figures. It is seen in Figure 30 that within experimental error there is practically no change in gross efficiency even with a change in solar declination of almost 15 degrees. Such a change in declination corresponds roughly to the change in solar position during the period from the middle of October to the middle of February. , An entire' similar independence of net efficiency .on solar position in this rarige is seen in Figure 31« It is naturally expected that net efficiency would not bo affected by change in declination because the calculation of net efficiency involves the deduction fron total input of *ref lection lbss, the only los^s appreciably affected by solar position. The nearly horizontal lines in Figure 31 bear witness to the validity of this conclusion. The identical trends in the gross efficiencies ob- served in Figure 30 show that they too are relatively unaffected by seasonal chang in solar position. Comparisons of performance , whether in terms of grosser net efficiencies, must therefore show the same general results. The lack of strong dependence of gross efficiency on entrance temperature an solar position (season) is fortunate in that efficiencies can be secured in the winter, which are approximately the sane' as those secured in the. summer. Further- more, although most of th6 reported runs were made in the fall, the results ob- tained should apply very satisfactorily to Winter operation. If the flow Tate is maintained approximately constant, exit air temperatures are of course lewer in the winter because of the lower solar input, and if it is desired to hoi* the exit air temperature constant, the air rate must be reduce- in the winter. This latter step Would lower the winter efficiency, so a balance of efficiency against exit temperature woul ' have to be established in orler to obtain optinun operation, 86. IX CONCLUSIONS A. Fundamental 1. The principle of solar heat collection which has been theoretically de- vised by Miller (10) is workable on a practical scale. 2. Although performance of the full scale collector is not as good as theo- retically predicted, solar heat can be recovered in the form of hot air, with an. overall efficiency of 35 to 40 per cent and an average daily exit air temperature of approximately 110°F. 3. During periods of high heat input, as in the middle of the day, exit air temperatures of 175° can be secured witii an overall efficiency of 35 to 40 per cent. 4. By reducing the air rate to a comparatively low value, air temperatures of at least 225° can be secured, but at an efficiency reduced below 10 per cent. 5. Keat recovery efficiencies which have been secured are comparable with or greater than those previously obtained by the use of other methods. 6. The, optimum plate arrangement is with 2/3 overlap, l/3 of the top surfao coated black, l/4 inch spacing between plates, and cover plates forming a complete enclosure. 7. The optimum tilt of a collector for s-olar heat collection at 40 degree latitude, from October through May, i3 43 degrees; optimum tilt in other localities is approximately numerically equal to the particular latitude. 8. Only a small reduction in radiation collected is observed when the tilt, is greatly reduced; a tilt of 27 degrees at 40 degree latitude permits the collection of nearly 92 per cent as much heat as a unit of the same size would -collect at a 43 degree tilt. N 9. A collector tilt of 47 degrees is the optimum at 40 degree latitude for winter heating of a house having collector area and heating requirements similar to the experimental house and having a unit storing heat for one day; in ether localities would be the latitude plus approximately 7 degrees. 10. As long as the problem of plate breakage remains unsolved, practical application of the equipment cannot be made. 11. The immediate cause of plate breakage is thermal stress resulting from unequal heating of the plates; the manner in which thermal stress initiates breakage is unknown. B. Secondary Air flow through the unit is not streamline as predicted by Miller, but eddying because of the high temperature difference between plates. 87. 2. The time lag in the outdoor units, because of heat storage in the unit itself, is between one hour and 1.5 hour. - 3. In the collector tested, 1 cu« ft. of air supplied per minute for each square foot of collector results in a heat collecting efficiency" of about 35 per cent, if the atmosphere is reasonably clear. 4. Any? decrease in solar input, such as that caused by clouds, causes no change in efficiency If the air rate is not altered, but results in a lowerer exit air temperature. 5. Heat recovery efficiency is only slightly affected by changes in entranc air temperatures. 6. On a clear day, in the test location, solar reflection and heat con- vection from the cover each constitute - about one-third of the losses; radiation from the cover plate and conduction through sides and bottom of the unit make up the balance of the losses. • C. House Unit 1. A solar heat collector jof the type herein described can be installed on the roof of a suitable house and employed in conjunction with the' standard hot air heating system to supply a portion of the heat required by the house. 2. The household solar heating *unit can be regulated entirely automatically, so that when heat 'is required in the house, fuel will be used iii the furnace if insufficient solar heat is available. 3. Although the operating variables have not yet been fully regulated to secure the optimum performance, approximately 20 per cent fuel saving has resulted during one winter from the use of a solar heat collector, covering about one-third of the roof, in the one dwelling installation. 4. Results of the operation of a water heater, utilizing the solar heated air, although based on limited data secured over a short period during which heat insulation was not in use, indicate that the domestic hot water needed during the summer can be supplied from the solar unit. 5. The construction employed in the house unit, shown in Figure 3 and Plate 2, is the most practical yet devised and is superior to the construction of the laboratory unit. 6.. The weather resistance of the collector employed in the house installa- tion was good; snow slid from the roof, a screen gave protection from hail in^the summer, and high wind caused little damage. D. General Conclusions and Indications 1. Cheap heat storage, although not studied experimentally, can be provided vin order to store excess heat collected during the day for use at night. 2. Use of the solar heat- -collector without the auxilliary heat storage unit is probably impractical in most locations. 88. 3. "ith proper adjustment and insulation of the experimental house unit, proximately 34 per cent of the annual heating load should be carryable by the solar unit alone; with the installation of a heat storage unit of a size ade^.ute for overnight storage of nearly all the heat collected which is required by the house, the combined collector and storage unit should be able to carry approximately 5$ P^r cent of the annual heating load. 4. A well insulated chamber containing approximately 6 tons of crushed rock, coke, staggered cinder block, hollow tile, or similar material would provide heat storage capacity adequate for the requirement set forth above; the dimensions of such a chamber could be roughly 3 f t x 3" ft, x 15 ft. 5. As an alternative, heat storage in the form of heated water could be provided. 6. The advantage in providing sufficient storage material to store heat for two or three days is slight and is probably more than offset by the increased cost of the larger storage unit. 7. 'Vhen heat is not being supplied to the house, the recirculation of air from solar heat collector to the storage unit and back to the collector would be advisable, because this procedure would permit higher storago temperatures and greater heat storage per unit weight of storage material, 8. Heat recovery effioiency should not be appreciably different in widely separated localities, provided that the same air rates are employed and the same area of collector is presented normal to the sun's mean position at the particular latitude. $, In general, locations in which. greater winter sunshine or lower heating loads prevail, (as in most sections further south than Boulder), greater fuel savings will result if collector and storage sizes are made the same as herein described; for the -same savings, the units can be smaller. 10. Economic advantages of installations north of the 40th parallel of latitude are doubtful, unless in regions of unusually favorable weather conditions or high fuel costs. 11. The applicability of the solar heated air as the energy source in the operation of an absorption refrigerator type of air conditioner is possible; air cooling should thus be cheaply obtained in the regions where most needed. 12. The cost of a complete solar heating installation under the conditions encountered in the experimental units should, on a large production basis, be no more than $500 over and above the cost of the installed standard hot air furnace, ducts, ^and auxilliaries. 89. X STATUS OF SOLAR RESEARCH PROGRAM At about the .time experimental work on the laboratory unit was being completed, an application for a patent covering - the construction and operating features of the solar heating apparatus was made. This application is in the name of George Q, n . 93. Measurement of diffuse radiation was made during several clear days. Data for one day appear below: bate 9-6-1944 rime Total Radiation, 8.7 mv. mr Diff-use Radj .ation of tot! Solar 1 Per cent il 11:05 A.M. C35 4.0 12:55 P.M. 8.65 c.5 -. 5.8 2l50 P.M. 6.35 0.5 7.9 4:00 P.M. 4.1 0.4 9.8 The above results show that diffuse radiation was a small fraction of the total radiation received from a clear sky. It was, therefore, neglected when data were' secured during clear hours. Obviously, radiation received during hours when the sky was overcast was entirely diffuse. Reflection losses from the collector during cloudy hours were calculated by assuming that the effective angle of incidence of the diffuse radiation falling on the collector was constant at 58 degrees (9). From Figure 42, the sum of transmittance and absorption of three glass plates for radiation striking the surfaces at an angle of incidence of 58 degrees was found to be 72.5 per cent of the total radiation. This sum of 72.5 P©r cent was equivalent to a reflectivity of 27«5 per cent. Radiation received from a cloudy sky was therefore considered to. be reduced by 27.5 per cent, regardless of solar position. XI Appendix B Patent Application The following patent application was made on December 3» 1945 under the Serial Number 632, 5G4. It is quoted here in full, exclusive of the claims. "This invention relates to solar heating apparatus and methods and more particularly relates to solar heating systems for household and similar installa- tions. "Solar heating and the use of solar heat traps has been well known and ex- tensively used for such purposes as greenhouse heating and the like, but in the past, little effort has been made to utilize this heating source effectively in household installations. However, in recent years considerable study of the sub- ject has been undertaken and with the changes and innovations being incorpo: atsd i present day architecture, solar heating systems are now recognized as a possible adjunct of future homo building. "The present invention represents the culmination of a series of investiga- tions undertaken to provide a suitable system for household heating and the like, which is adapted both for installation in existing structures and also for incor- poration in new construction. is t of tne present invention to provide a simple, efficient and economical method of heating homes or similar structures. abject of the invention is to provide a simple, efficient and economical method of conditioning the circulating air of homes or similar struc- ture both a3 to temperature and moisture content. object of the invention is to provide a simple, durable and econof system adapted for installation in homes or similar structures, which ia adapted to utilize the maximum effect of solar heating as an energy source in the temperature regulation, water heating, and other appliances of the heating and water pupply installations of the structure. "Still another object of the invention is to provide a solar heat trap adaptei for installation in existing homes or the like, which may be utilized as a heat exchange medium to heat air, water or other fluids. "Other objects reside in novel combinations and arrangements of parts and in novel steps and treatments, all of which will be described in the course of the following description. sntion resides in the discovery that a solar heat trap may be installations or the like, which contains a plurality of "The present invent provided in household zones or passages, within which heat rays are caused to travel in opposed direction between heat transfer surf aces defining the passages or zones. Within these zones, fluid, such as air or water, is circulated in contact with the heat transfer surfaces and after heating in this manner, the fluid is circulated to other por- tions of the structure to be there utilized as a source of heat for the structure 95. or for appliances, the operation of which is essential in the use of the structure. Preferably, there" is also incorporated in the system, means for limiting heat radiation within the confined zones and other means for storing excess heat re-* leased through said zones. "Having thus described in general th6 features of the present invention, reference will now be made to the accompanying drawings illustrating typical em- bodiments and practices of the invention. In the drawings, in the several views of which like parts have been designated similarly Fig. 1 is a vertical section through a structure utilizing the features of the present invention;. Fig. 2 is a vertical section through a heat trap unit embodying features of the present invention; Fig. 3 is a vertical section through another form of heat trap unit al3o embodying features of the present invention; Fig. 4 is a fragmentary section through a Heat trap installation illu- strating a preferred construction for use in existing structures; Fig. 5 ia a similar section illustrating a preferred arrangement for in- stallation in structures under construction; Fig. 6 is a similar section illustrating a preferred installation built as a prefabricated unit; Fig. 7 is a side sleyation of one of the heat exchange elements utilized in the heat traps of the present invention illustrating a preferred method of surface treatment and drawn to an enlarged scale; Fig. 8 is an enlarged perspective viev/ partially broken to show interior construction in section of one form of heat trap used in the practice of the present invention; and Fig, 9 is a schematic assembly view showing arrangement of parts in an air conditioning unit adapted to be operated by a solar heat trap of the type shown in Fig. 1 in a circulating system of the type shown in Fig. 1., "Fig. 1 illustrates an installation in a house or other habitation in which the various forms of solar heat utilization of the present invention have been combined in a single installation. It will be understood that for most purposes, liquid and air room heating installations will not be combined within the same structure, although under certain circumstances, it may be necessary or advisable to do so, for which reason both forms have been described or illustrated in the drawings. The air conditioning circuit illustrated is intended for use inde- pendently of or as an adjunct of the household heating system and a typical in- stallation has been shown in Fig. 1. Also, the use of the solar heat source for heating the domestic water supply has been illustrated and this may either be a 96. ntcn 01 * air ». Normal riir Cniiittd air ^ uxfornal Hoi w jter — — - Cold water - INVENTOR. BY FIG. I -J en "v= ; / / - rO v^ * ? O .O 0> ro f s ^00 ro O r / / / / / / / / / / / / / / A ro - ! U A / / / / / t / / / / 'rO >V ro ro o5 \ ro 1/ / / CVJ (3 > ro ^ rO INVENTOR. CHi .. . _. ! FKv fa IXl K\T0R. BY 94 *° 98 FIG. 9 INVENTOR. V BY 85 100 separate installation or incorporated as an adjunct to the existing household installation. "In Fig. 1, a building designated generally by the reference letter B is in- tended to illustrate a home or business structure and as shown embodies a tv/o story construction, but which may be any number of stories within the capacity limits cf the system to heat. . As illustrated, the building has upright walls 12 covered by a roof 13 with a floor 14 partitioning the interior space into a basement 15 and other partitions 16 cooperating with the floor 14 and a ceiling 17 to divide the first floor space into a plurality of rooms designated X and Y. The basement is provided with a floor space 18 of any suitable material, such as concrete, ar.d the foundation structure 19 for the building also may be any suit- able material such as concrete. "A section of the roof 13 preferably located so as to have good exposure to the sun in both summer and winter is suitably apertured to receive a heat trap T, the details of which will be described hereinafter. V'hen the heat trap T is to be utilised as a heating source for the building, it may be necessary to have it operating in conjunction with a stand-by heating plant and utilize a common system of conduits, outlets and the like and systems of this type have been illustrated in Fig. 1. n the basement 15 or in some other suitable area of building B, a furnace 21, preferably v. blower-type circulating air heater, is located to deliver heated air through a valve controlled conduit 22 into a distributor 23 from which a series of cenduite 24a and 24b deliver the heated air to room outlets 2^, The furnace 21 also has a valve controlled intake 26 preferably supplied by a cold air duct 2 Its inlet opening 28 located as in the floor of room Y to provide culating system. However, it should be understood that if desired, an rp^r. circuit circulation may be employed, in which case the duct 27 would inlet located to receive atmospheric air from a point outside the The furnace 21 may utilize any suitable type of fuel, such as coal, °il t such times, for example during the night hours, when the system may not uti solar heating, the furnace is operated as in conventional installa- tions eat the rooms X and Y through discharge of heated air through outlets -25. "In utilizing the solar heating source in this circuit, at least a portion of the ntering through duct 27 is by-passed from the intake 26 through regulation of suitable valves 31 and 132 into a conduit 32 which in turn connects with the lev/.jr portion cf heat trap T through a suitable opening 33 preferably located at the lower end of said trap. At the upper or opposite end of said trap, another opening 34 connects with a valve controlled conduit 35 which delivers heated air from the trap into furnace intake 26 and thence through the circulatory system as hereinbefore described. 7'ith this understanding of the general arrange- ment of the circulatory system, reference will now be made to the details of construction of the heat trap and its function and operation. The arrangement shown in Fig. 2 illustrates a preferred construction for in- allations of the type just described. The unit comprises a framework having a bottom 36 and side walls 37 preferably forming a rectangular enclosure. The bottom and side walls may be formed of any suitable material, such as wood or metal, and preferably are of a dimension not requiring too great an unsupported 101. surface for the glass parts now to be described. The top closure for the heat trap comprises a glass plate 38 supported at its sides and ends by the side walls 37. Although not shown, it will be understood that where it is necessary to protect the cover plate 38, as from hailstones or the like, a suitable wire screen or other protecting means permitting light penetration may be mounted in over- hanging relation to plate 38. Within the enclosure thus formed, a series of glas.r. plates 39 are mounted in spaced and substantially parallel relation and prefers staggered lengthwise of the enclosure. in the manner shown. Each of said plates except special end plates 39a and 39b are provided at ona end with an opaque and essentially nonreflecting area 40 preferably formed as by covering the sai'd sur- face of the glass with black paint. "The opaque area thus provided preferably will be of a uniform length Which is an even division of the total length of the plates 39. As here shown, the length of the opaque area is ohe third the length *of the entire plate except at the lower end whore ono plate 3Sx is four times the length of its opaque area and another plate 39y is five times the length of its opaque area. Also at the lower end of trap T, the surface 41 of bottom 36 underlying the transparent portions of plates 39* and 39y is blackened in a manner similar to the plates 39 » or a sheet of material, mounted on the bottcm will have its upper surface blackened, as shown. Through the arrangement just described, solar heat rays entering through plate 38 are at all times directed against a blackened surface throughout the extent of the plate assembly. Obviously, the length of the opaque areas may be increased or decreased for a given sized- plate and as long as the overall effect is similar to that just described, satisfactory results will bo obtained^ "While the arrangement of the heat trap T thus far described is adequate for mest purposes, more satisfactory results will be obtained by providing a reflec- tive medium throughout the opaque area of the glass plates 39* Such an arrange- ment has been shown in Fig. 7» in which a glass plate 39M having an opaque area provided by applying, black paint 40a to its top surface has tho portion of its undersurface underlying paint 40a covered with a reflective material such as aluminum foil 41. Through the use of the light reflective medium, a uniform reflective surface or surface effect is obtained which serves to retard heat losse occasioned by temperature differentials between glass plates 39 and bottom 36. "The arrangement of opaque and transparent surfaces just described has the further advantage that as viewed from underneath, the blackened areas provide a uniform reflecting surface. Because of this, the heat emanating from the blackenc surfaces by reason of the stoppage of the solar heat rays travels in a reverse direction to said rays with tho result that with respect to any given plate, both its top and bottom surfaces are substantially heated. Therefore, when cold air flowing through duct 32 enters into the enclosure and passes between the several plates 39» a heat exchange action rosults which imparts an upward flow tc the entering air and aids its travel to a point of escape at opening 34, although the primary air movement is induced by the blower in furnace 21. Due to the aforesaid heat exchange action, a substantial increase in temperature results so that the heated air passing through opening 34 comprises an adequate heating medium for the building. This air travels through conduit 35, enters furnace intake 26 and is then moved by the blower actuation to the distributor 23 and circulated through the rooms in the manner hereinbefore described. 102. Lther type of he-.t trap as herein described, the parallel arrangement cf the glass plate3 having, opaque and transparent areas provides a multiple air filD therr.al insulation, as well as providing heat transfer surfaces to the air flow between the plates heated by solar radiation. Consequently, the solar heat is transformed to warm air at temperatures high enough to be adequate for house heating purposes even in extremely cold weather, and by providing sufficient capacity through the use of a battery of such heat traps, preferably arranged in adjoining relation, it is possible to generate sufficient heat units to function as a heat source for various household appliances, in addition to supplying the required amount of heat for house heating purposes. "For most purposes, the hent trap will be utilized to heat a circulating air stream in the manner just described. However, it is practical to utilize this heat source in heating other fluids, such as water for example. Fig. 3 illustrates such an arrangement in which the trap T' is arranged to have liquid flow between the parallel plates 43 which are generally similar to the plates 39 cf Fig. 2 and pass from the enclosure through a lower outlet 44 in the bottom 45 of an enclosure similar to trap T, having side wall9 46 and a transparent cover plate 47. As in. the other form, the plates have opaque areas 48 preferably applied by black paint and the surface of the bottom 45 undorlying the transparent portion of 6nd plates 43x and 43y is. covered with black paint as shown at 49. "In this form of assembly,, the upright walls 46 and bottom 45 will have to be joined in. water-tight relation to confine the liquid and prevent leakage into other parts cf the structure in which the heat trap is located. As installed, trap T 1 will be located in an inclined position with the outlet 44 constituting the lev/ point through which the released .liquid will flow. The liquid is intro- duced into trap T" by a series of pipes 50 supplied from one or mere headers (not shown) and the conduits have a series cf jet or spray outlets from which liquid passes on to the upper ends of the respective plates 43> 43*, 43y and 49. "These plates are heated in the same manner as previously described through the arrangement of transparent and opaque surfaces and the liquid flowing down- wardly along the plates is subjected to an intense heat -transfer action with the result that when it collects at the lower end of trap T' and passes through outlet 44, it is at a ter.iper°ture adequate for the requirements of the household system. Any vapors generated in the heat exchange action will rise in contact with the undersurface of the overhanging plate and thus are subjected to further heat exchange action. Other vapors passing out of the upper ends of the passages be- tween parallel plates and heated air v/ithin the enclosure tend to collect in the upper end of the enclosure and act as an additional heat source to assist in the overall heat transfer action of the Unit. Loisture condensing at any point in the upper part of the enclosure will ultimately fall on to one of the heat transfer surfaces and then descend along sume to reach the outlet 44. "In use, the outlet 44 will be connected with a suitable conduit to deliver the collected contents to a storage receptacle or some other point of ultimate use within the structure. Y/here the units of this type are to provide the circulating water for a household radiation system, for example, it usually will be necessary to have several of such units arranged as a battery to provide the necessary capacity. V/hen a lesser quantity of heated water is required, as for. example in / supplying a hot water storage tank, a single unit will provide the required amount of heated water. 103. "From the foregoing description, it will be apparent that the structural arrangements of the present invention may be utilized in heating a variety of fluids of which air and water are typical. Referring again to the arrangement of the circulating system shown in Fig. 1 hereinbefore described, it will be apparent that the various controls of valves, hampers, blower and the like may be automati- cally controlled as by thermostat regulation, for example. "It will be apparent that in the operation of the system thus far describod, the heat trap T on clear days may produce an excess amount of heated air during at least a portion of its operating period. Two satisfactory methods of handling this excess have been shown in Fig. 1. For example, in the roof installation, a valve 55 raay be operated to close conduit 35 and cause the heated air passing therethrough to enter a by-pass conduit 56. Through suitable regulation of other valves 57 and 58, a portion of the hot air flowing through conduit 56 will pass into a stack outlet 59 while the remainder will flow back into conduit 35 and thence pass to furnace intake 26. If tha aforesaid by-pass arrangement is not being utilized in the system, valves 57 and 58 are closed and valve 55 is open to permit the direct flow of air through conduit 35. After delivery into furnace 21, a portion of the heated air may be diverted through suitable damper regulation and passed into a conduit 6l which discharges into a heat storage bin 62. "Preferably, this bin is sealed and insulated from the atmosphere except for the inlet and outlet openings hereinafter to be described and a large portion of the volume of the bin is filled with a heat absorbing and retaining material 63 which preferably is a loose or spaced solid, such as sand, gravel, or stacked brick, but which may be a fluid, such as tar, oil, water or the like. Consequent!; when the excess of heated air discharged by furnace 21 into conduit 6l is delivere through a suitable opening 64 into bin 62, the bed 63 is gradually heated and functions as a heat storage unit of the system, and the air, after heat extraction, is recirculated to the heat trap through conduit 32. Subsequently, when heated air is no longer supplied to the furnace from heat trap T, warm air flows back through conduit 6l until diverted by a gate 130L and through a branch pipe 131 to pass into furnace 21 and is then distributed through the heat outlets in the manner previously described. The air after passing through rooms such as X and Y then returns to bin 62 via duct 27 with suitable adjustment of valves 75 > 132, 31 and 133. Thus, it will be seen that excess heat produced in the operation of the solar heat trap may be utilized in the household system, if desired, or if not, may be wasted to atmosphere to prevent undue heating of building B. . "It will also be desirable to provide an arrangement for heating a portion of the domestic water supply of the building at such times as the heat trap is in operation. As shown in Fig. 1, this is accomplished by providing a heat exchange unit 70 mounted about conduit 35 with a portion of the heated air passing there- through diverted through a system of flues or similar water jacketed passages to heat the contained water of the unit. A portion of the heated water then passes to a storage tank 71, which tank has a ccld water return to unit 70. The remain- der of the heated Water passes through a line 72 which empties into storage heater 51 located in the baser. ent of building B. Suitable draw-off connections may be provided for both tank 71 and storage heater 51 and it will be understood that whenever the heat trap is unable to supply water at the required temperature, the storage unit 51 will be operated in the usual manner to heat the water required in he household supply. 104. "The heat trap T also cay be utilized to provide cooled, conditioned air when required for distribution throughout the building. To. accomplish this, the furnace operation is stopped and the heated air delivered through conduit 35 is passed from furnace 21 into :.. refrigerator unit R through the opening of a suit- able valve 76. After passing through generator 90 of refrigerator R, the air passes through duct 137 "to duct 32 and recirculates to trap T, damper 135 being suitably adjusted for this operation. Air to be circulated by refrigerator R is drawn into same from duct 27 by a suitable blower unit, the course of flow of air through duct 27 having been changed by operation of a suitable valve 75* The air stream passing into refrigerator R after being suitably cooled is delivered to distributor 23 and then circulated through the various conduits 24a and 24b to the room outlets 25 to reduce the room temperature of rooms X and Y. "It will be understood that any suitable refrigerator unit may be used for this purpose and in order to clearly describe the practice of the invention, a suitable air conditioning unit has been illustrated in Fig. 9. This unit comprise a casing 80 having a partition 8l dividing its interior into a cooling chamber 82 and a second compartment 83 in which most of the operating parts are located. The cooling chamber 82 contains a blower 84 preferably having its intake 85 below the casing to receive the returned air flow diverted from duct 27 as previously described. Preferably, compartment 82 will have means for filtering incoming air which may be located at any suitable place, such as the area, 86, and a means for humidifying air which nay be located at any suitable place, such as the area 86a. An outlet for the air delivered to chamber 82 is provided at its top, as shown at 87, and in the installation shown in Fig. 1, this outlet will deliver the cold air past valve 22 to distributor 23. A conduit 88 having its intake 89 located within compartrent 82 extends through partiti.on 8l and discharges its contents within chamber 83 in a manner that will be hereinafter described. The mechanism of this air conditioning unit is of a conventional design of the type used in certain commercial refrigerators except for the generator unit 90 shown in chamber 83 f the construction details and operation of which will now be described. "The generator has an air inlet 91 and an air outlet 92 at one of its ends and adjacent thereto a dome 93. The interior of the generator contains a tube section 9* of the general arrangement of conventional boiler construction. The end of the generator opposite inlet 91 contains a space 95 beyond the end of tube section 94 through which the hot air flows to pass into the return passages of tube section 94. A wall 9.6 divides the tube section into a main heating portion 97 and a secondary heating portion 58, and assists in forming a pressure head in dome 93. "This generator unit is used to vaporize ammonia from an aqueous ammonia solution by a heat transfer action and utilizes hot air supplied from heat trap T in the system shown in Fig. 1. To accomplish this, a conduit 100 delivers aqueous .onia solution into the enclosure of tube section 94 where i% is boiled by the - heat transfer action and the resulting vapors rise in the main heating section 97 to pass from the unit through the same conduit 100 through which the solution is delivered to the unit. This counter-current circulaticn has the further advantage of preheating the solution flowing to generator 90. The gases rising through conduit 100 pass into a rectifier 104 which releases freed ammonia into a line 105 supplying a condenser 106 while the water condensed by rectifier 104 'returns to :uit 100. 105. "The gaseous ammonia entering condenser 106 is condensed to the liquid form and passes tc evaporator 113 through conduits 116 and 117 . Any uncondensed ammonia rises tc condenser" 106a and the liquid ammonia formed therein passes to the evaporator 113 through cnnduit 120. The downf lowing streams of liquid ammonia meet an upf lowing stream of hydrogen gas entering evaporator 113 through conduit 134 hereinafter described, the liquid ammonia being evaporated by said hydrogen accompanied by an extraction of heat from the circulating air^in body 82 and thu3 providing cool air for rooms X and Y. The mixed hydrogen and ammonia vapors then pass from the evaporator through conduit 114, and the inner conduits of 115> and heat exchanger 112, to bulb 111. The gases then pass upward through absorber 135 ccuntercurrent tc a downward stream of water hereinafter to be described. The absorber 135 absorbs ammonia from the gaees and the remaining hydrogen passes up the outer conduit of heat exchanger 112 to reenter evaporator 113 through conduit 134. The hydrogen reserve tank 119 serves to keep the pressure in the hydrogen system constant during room temperature changes. "When most of the ammonia has been foiled from the aqueous solution in heat- ing section 97 the solution has a higher density and flows to the bottom of the generator 90 and underneath the baffle 96 to the secondary heating section 98 where further evolution of ammonia occurs. The ammonia gas rises into dome 93 creating a pressure which forces the dilute amr.onia solution, .hereinafter called water, up through conduit 101 into head tank 102. The ammonia "vapor accompanying the water continues down conduit 103 to join the main ammonia stream going upward to the condenser from conduit 100. From head tank 102 the water flows by gravity down conduit 109, through the inner conduit of heat exchanger 108, and into the top of absorber 135» The water then flows down the absorber 135 countercurrent to the stream of mixed gases flowing upward and absorbs the spent ammonia gases hereinbefore mentioned. The aqueous ammonia solution then flows into bulb 111, down conduit 110, through the annular space in heat exchanger 108, and into con- duit 100 through the connecting conduit 107. The aqueous ammonia then flows into the generator 90 to complete the cycle. , The flew of aqueous ammonia from the absorber 135 to the gonerEtcr 90 is actuated by gravity from head tank 102. "The air diverted from chamber 82 which passes through conduit 88 reaches a distributor 121 which directs it across the surfaces of condensers 106 and 106a after which it passes into an outle.t 122 to be exposed to atmosphere in any suit- able manner as through a stack (not shown). "In the operation of an installation such as that shown in Fig. 1, it fre- quently will be desirable to store heat generated at heat trap T without circula- ting hot air through the rooms of the building, as for example, when the tempera- ture of the room is sufficiently high through a preceding heating operation and additional heat is passing from the discharge of the heat trap. Under these circumstances, a damper 130r in furnace 21 is moved to close the passage through valve 22 to distributor 23 and a damper 130L is opened to allow the gases entering the furnace through intake 26 to pass into conduit 6l, the valve in branch conduit 131 being closed. At the same time, damper 75 is moved to shut off the flow of cool air through duct 27 and another valve 132 is closed to block the passage be- tween duct 27 and intake 26 while a valve 133 is open to permit art outward flow of heated air from storage bin 62. 106. "When so arranged, the hented air leaving trap T flows dov/nwardly through conduit 35 and into furnace 21 through intake 26. Having no escape except through conduit 6l hot air passes through duct 6l into a storage bin 62. Through the open- ing of valve 133, a pronounced flow of air through bin 62 is obtained with the air returning therefrom entering conduit 32 past valve 31 which also has been open and thus the air returns to the entrance 33 °f heat trap T. "So long as this operation is allowed to continue, the circulating air will be progressively heated, thus raising the temperature of the bed 63 in bin 62 and as this circuit is insulated from other portions and particularly the occupied portions «f the building, no appreciable temperature rise occurs in these occupied portions. This circulation will be allov/od to continue so long as the solar heat trap is functioning and whenever there is a further demand for heat, either from furnace 21 or air conditioner R or the water heating stages previously described, the circulation can be discontinued and the generated heat made available where required. "When stored heat is to be used for the opyration of air conditioning unit R, hot air is drawn through duct 6l from storage bin 62. This hot air proceeds to duct 35 through duct 131 by suitable adjustment of dampers 131 and 130L. The hot air then flows into furnace 21 and into refrigerator R by suitable adjustment of damper 76 and after being used flows through duct 137 and 138 and back into heat storage unit 62 by suitable adjustment of vane 139 and damper 133* I* is possible, if desired, to operate the refrigerator R by applying heat from natural or arti- ficial gas or other similar fuel when the heat storage unit is cold and trap T is cold. "In the operation of the system previously described, the location of by-pass conduit 56 provides a convenient arrangement to prevent overheating of the storage water supply which otherwise might occur if heat exchange unit 70 were 'operated at all times when hot air was flowing through conduit 35» Whenever the temperature of the water in tank 71 reaches an established maximum, the valve 55 may be closed and valve 57 opened to permit the flow of the hot air through branch 56 and thence back to conduit 35 without heating the water in the heat exchange unit 70. Preferably, a thermostat control will be utilized to provide automatic regulation at this stage, although manual or other' types of operation may be used, if desired, "In Fig. 1, no attempt has been made to show the insulation of the heat trap, conduit, storage bin and the like. Hoy/ever, it will be understood from the fore- going description that suitable heat insulation may be provided for all of the conductive' parts of the system and the insulation to be used for this purpose may be any one of a variety of materials available on the market for such purposes. "Noxt referring to Fig. 2, it will bo understood that if desired this form of construction may bo utilized as a water hosting unit rsther than >as air heating unit as described. In ordor to do so, it will be necessary to make the entire closure, inclusive .ef bottom 36, ,side walls 37 and cover plate 38, into a water- tight assembly and then pump water in under pressure through the opening 33 to effect its movement across the heat exchange surfaces and its ultimatB discharge at outlet 34. As the production of such a unit would involve construction diffi- culties in providing sufficient structural strength to carry the load and to with- stand the pressures required in the pumping action, I prefer to use the form of 107. construction illustrated in Fig. 3 whenever the heat trip is to be used in heating water -rather than a gaseous fluid. "In assembling the heat trap in the roof of a structure, various arrangements may be employed. Where the installation is to be made in existing structure, the arrangement shown in Fig. 4 is particularly suitable and comprises upright walls 37x which cooperate with end walls 37 (not shown) preferably of similar width and thickness to form a box-like enclosure. The enclosure has a bottom 3& of "the type hereinbef ore.described which preferably comprises the roofing material and the . interior space of the enclosure is insulated from the building enclosure by a strip or bed of suitable heat insulating composition 3&a» "As previously explained, it is necessary to have some suitable transparent cover for the enclosure and this is most conveniently effected by arranging a plurality of glass plates in tiers or layers with a portion of an end surface of one plate overlying another end portion of a second similar plate, a greater portion of which projects beyond the first said plaife in a direction lengthwise of the enclosure. When it is necessary to brace the respective plates to support the weight of the cover assembly, suitable straps or bars of wood or metal may be arranged to bridge the space between the members 37* in supporting relation to the cover plate glass. "The arrangement just described will be best understood by reference to Fig. 8 which is a perspective view partially broken away to illustrate an assembly of this character. While the arrangement shown in Fig. 8 is illustrative in general of all the arrangements shown in Figs. 4, 5 and 6, it is more exactly a representa- tion of the construction shown in Fig. 4 and consequently has been given corres- ponding reference numerals. In the preceding description, the arrangement of transparent and opaque surfaces has been described as being embodied in a plate of glass. While this is a preferred arrangement because of the simplicity of con- struction and assembly, it will be understood that the opaque black areas may be any suitable material which is nor -reflecting, and if desired, may be separate pieces arranged in end to end relation with the transparent plates of glass or other suitable composition. "Where the heat trap units are to be installed in new constructions, it is possible to use the rafters 37y of the roof structure as a part of the trap en- closure, mounting thereon a cover plate 38 in all respects the same as the cover plate 38 shown in Fig. 4 and providing insulation 362 of the type previously described with a bottom portion 3&x preferably attached to and in underhanging relation to the rafters 37y. Within the enclosure, the arrangement of transparent and opaque surfaces previously described will be provided. "Still another arrangement has been illustrated in Fig. 6 in which the en- closure is formed to seat upon rafters 37z and has end walls (not shown) similar to those previously described. A bottom piece 36z encloses the space between two adjoining rafters 3?z while the usual type of transparent cover plate will be provided at the top of the enclosure. As clearly shown in Fig. 6, the material of the bottom portion 36z is U shaped in section and fits against the top and side surfaces of the rafter 37z. Through this arrangement, it is possible to order any required number of such trap units and mount same on rafters or other upstanding supports with the respective units joined in side by side relation as indicated in Fig. 6. 108. om the foregoing description, it will be apparent that the solar of th sntion is well suited for incorporation in new constructions or in existing structures, end only a minor amount of the habital of the house or other structure is occupied by compone . When desired, the solar heat trap may be supplemented a heat source by standard type furnaces, water heaters and refrigerators, . with proper capacity in the heat trap and heat storage units such iances will be unnecessary in manyi installations. iccompanying drawings illustrate typical installations J or carrying out the purpos the present invention, and it will be understood that the construction and operation are within contemplation of the invention. Therefore, the construction and arrangement of parts shown and scribed is not intended to liait the invention 109. XI APPENDIX C METHODS OF CALCULATION I. Calculation of Charts and Nomograph A. Thermocouple Conversion Chart Temperatures of couples were recorded by a Brown potent iometric pyrometer which was calibrated and compensated for iron-constar.tan couples with a cold junction temperature at the instrument temperature. A calibration for iron-constantan couples with a C°F. reference temperature was used and the .potentiometer compensated to allow for the difference between the instrument' temperature and 0°F. Chromel-constantar, couples, used for measuring surface temperatures, with a cold junction ice b-ith, were also connected through the pyrometer. Assuming an average instrument temperature to be 1C0°F. and constant, a conversion chart was made to give chromel-constantan temperatures from the temperature difference between indicated temperature and instrument temperature. (Figure 3Z , Appendix) For a temperature difference of 90°F. Indicated temperature « 10C°F. + ?C°F; = 1$'0°F. From iron-constantan calibration: t = 190°; - mv, * 5 .** t = 100°; mv = 2.88 At = 50°; m* = 2.66 From chromel constantan calibration: At *nv = 2.66; t = 108.5°F. Therefore, 108.jr°F. is plotted versus 50°F. B. Charts and nomograph for calculation of air rates. 1. Rotameter a. Calibration curves. Calibration curVes for both rotameters were furnished by the Fischer and Porter Company of Hatboro, Pennsylvania. (Figure,55 , Appendix) r — rr—i TTT — i — r — n — TTl ! !| •• 7 ; Ll ■ 7:1 •= -".4: ■ ■ N 1' ' \ . ' fr -: • !l '" { ■ ■ "I — i : ." • i ■ ■ - - • ; : - : 73 _ • • . '- S> •7 77 — ~ '- -• U 5C - : :: : ■ '•■ ' :v . : " : - "7" ■ a * : , ■ - '■■ , . . - . ;. -:. --: ":.^ - 7':. -.- I| .7: .. - T" - ~i - .- _.- it. h i^ . -- £t b ..: 1 " - : •\ . :.ti; .- - -t*_ . *v --♦V !g "7 ; . 3 • -'■'- •~- r~ -.'■ stij &~ :^ - i^l j .., £ 3% z\: Z J !t;" :7:: ;.:. "77^ i' 1 TTrl .... ji ; i -' : • '--■ - '■-.• -': I ' ¥ -.: 7::- 7-- : 1-: 11 :.'■ is rrrr s ■ ■ - s : ' -rl $ ■ :.;. ;- : . . : .■'- -" •• f 1 : 7 "Til £ . : :.- Hi 'U. .... - ■ u: " : 7 3g L .-_ I 4 fc _.. " ' : ■■^ .77 .::* — - •- |_ ■ ;._. — r? ■ : 13 * •'_: *3 -5 - :i -h 1 • ■ 5 — ■'- : ;-.- __ . : - _ *H . - . -«. | 5 -- £S : ; ; ! . 1; " 5rE 7 "7" § a 5 - ■y: !:-; F. h .. ; ; E777 -t 11 ; 55 fg32 SH § .- 77" — - — . t; -'- :-... :. : "S #1 j Tjji s | i i i -: — — •-• '£ " _: ,r. • .:?- ~... • : ■ -.- — ... ._, .-' " ■? 5T t : 3 __. - - trr- < i ,! ■ 7" . \ « ■ . T-' h :- - ■-"-. .:; L. ":_ ^ 511 Hi i >* \ ■ ! ± / : ~: : .;^ - - -i /: t r ■ - ■"_: j 7- _ i-1 . liJit ■ -- ■ - VJ ■ --- igj ;"-. fg? SB /" : : rT; ; i-: - :7_ "^ 5JE tii 1 -.. 775 3 - -7 :r. •■ ^ 77 , -_ :-. . ■W j - : :1- >~ ::1 '-'- (..... k& ^t Ct -75 ■--r R 1 - 1 v fe - -■'" - ' ; : :- : .. i -_ - --■ ? f£= : ' r " P^ 1 Ir ---^-f s - - •]• - £~ £T_i =£ A =~ = r ■ . IE! ■-- I ; : ;:> ;;;;_ g i": Ms ifi Si A- ^ T | 2i ■-" : r - \ ;r: : r 775 .'-: : : " ;/-_ - — is p __- ---4^ a| | ^ : \ ~M S _ r ^ tt^t-^ ~- : ? 7: .77 — .y - - 77' =fFi .:: T 7 i ?« — -- -'- ■ 5JH '-" i - ~: #p?= 7S ^ s ■ - : t - p - i s 777 4 ."■■ • ■ ^ 2S - -A-- g -.7 tM 7 - ^ ■. ^ : 7 1 7- : ' ,~ -:- \ ■ | : £ 7 .- - r ■-_- 7 - V - — , ■ ■ B - - - - - ' ■ . - - "- ■5 - -^it — . :: s - £ ^:- -1 _: ■ - ■ - - -- -.^1.' .-■: :r.: : — =J 1 , • •-- ii i- , — ■■- i^ -_ 7^1 » - J± ^:_ '-- .; -^7 — -"- - - T - \ . '-'_ \2r : -;7 £ St -■ - . - -- - ■ ^. _ - .: . : ■j~i - - ■ '/: ■j -_ r -' - --_7 :■ ri - - \ r: 3 ._ - -5 1 1 1 1 ; I ? i i p : \ I | i )- < p > . - t3 r 1 '! • -1 - - i - 1 •i ' F • l - g TT Jc t u&n \LV± ^ YJU (VI ^iV j. yoo - 7, 7/v v± /// P ■ - ■ j , i i i T; ..i: ;. - - 7:5 i r -i ..Z ■ i 1 ' i ■ 1 i ..- i ! , ; : 9 . . ; 1 i i - --7 - f- .75 111. b. Pressure correction Since the above calibration curve was made to read volume of air at (760 mtn. - 70°F.) measured at (6}0 mrn. - 70°F.), correction must be made for measurements at pressures other than 630 miti. Hg. and temperatures other than 70°F: (10) Correction factor * - (p actua^ = (6loU-= 0.984 \ 63c / \630/ A plot of the factors versus P actual was made. (Figured Appendix) c, Temperature correction Similarly, a correction must be applied if the &%r rate is not measured at 70°F. Correction factor = f :^ q°K \? = ! 510 \ ? = 0.971 \* 6 ^ctual° F / • \460n00j A plot of these factors was also furnished by the Fischer & Porter Company. (Figure 35 ; Appondix) 2. Nomograph for 3«5 M air orifice. A nomograph for finding air rate from the orifice data was made from the following equation. (Figure-?/, Appendix) ■'/'■.?• 142.fr K; ' 515 (B-1.87P-0.9^ftl) ' 485 . T 0.485 where ' LI = pressure drop across orifice, inchos H^O B = barometric pressure, mm Hg. P = upstream static pressure, inches M ? T = temperature of fluid, °F. . V » volume of air f c.f.m. (760nu-.70°F.) The above formula was derived from the basic orifice equation and a calibration curve for the orifice which was obtained by calibrating the orifice with the -above mentioned Fischer & Porter Rotameter. (Figure 36* 9 Appendix) References feo), (21) 112. Hill : 111. • .■>l«ittltifllllllll»llllllt« •IIIIIHIPIIIMl»IMII*lll*lttiall*lllllll«IIIIMIIIIIIIIIIIMIIIIPUIMnil**^I^IIIIIIMI|tl|»|llllll ■■■■■•■■•■•■■■■•••••••••»■••••••■•■■••■#■•#•■■••••»■••■••••■•••■••••••••••••••■• ••■•■•■■•■■■■•■•■■■■■■■••••■•■•r (Mi-iiirp»*illl' d" ■■■■■■• • ■■«I1IIII*MMIII«IMI Ilflltlllt Ill IMIIItlltll IIUIIMIIIIIIItll Mill *«■ I ** *« J •--••rt* b . ■■■«■■■ ■***■■■■■■■■«•■«*■■•■■•■■•••■■■•■■■•«■■••■ iiiMMiiMi riiiittMiiiiiiii niiiiiiui iiiiniiiiiii.ikaii.iiii.4i .■■■•«■■■ ■ ■■(■•■•■■IIIIIIIIIMlllllllUIIMIIIMIIIMlkllllltlllMlllliMIM Ililllll •••■■■■■■■«•■••■■■•■• «•••••■■••■■•*' ••■•■•■■■•••■•■••■■■■■« ■•*■>*«•■■•■■•■>««••«•■■■•■•• llllilliOlMIMIItlllilllllllMIIIIIIMIIIIIIIIIIIIIIHII llllimillHIIIIIIMIIUflllllllllllimllMIII ■ ••■•■«■* ■••■»•■■••■■■■■••■•••■•■■•••*■■■■■■•••••••«■•#•■■•■*■•■■•«■■■•••■•••••■•• •■■«■■■ •■«■■■■■■■!■■■ ■■■■■■ ■ »* a ■■*. ■■ iiiiiiiiiiniiimi • ■•IMtltllllMltlllllllllllllll n*IMJMIIItll JIIIIIIIIIIIIIIMIIIIIMIIIIIIMIIIIIIIIII ■ I' l»IFIT • * 1 ■■•■■■»■■ ■ ■ ■■■•■■*« iiiiiiiiii ■■■•■•■■aim ■•!■«■■■■■ ■■■•■•■■•■■»■■■■•■■•••■•■■•■••■■■■•■•■•■ ■■•■■■■«■•«■■■■■■■■■■■■«•■■•/■ -- 'at *■■■•■■■•■■■« 114. I 116. onrF)CE c/libratiom, it" ^ )oi"Juct IUBL 20 2.5 30 40 bO 60 7C? 80 90 ICO 1.50 200 2.50 300 4*0 5» bOO 7 8 9 10 Z^H — Fe,e.t *y FluiJ f) e ^infl| Figure 36 fiMH* //6 NOMOGRAPH FOR ^5' AIR ORIFICE TMCCTIOMS ' COWMCT MAM »U3S B *>TH STATIC ***** P. *AOn ,«rWA*cno* ifl^pTTl,** » AM" ""' TO OKMCI **«*»,. f"» I»™MCT»« . OH m7»»m * ***» *■** r»*v J*»* T to *e/>. UN** ****. maw urn mm "Jrwrnucr,** c oN, tT m> omm* •* ** "•"* "*« *"»: '"Tester** OaI V /«■ DfSiMb AIR **TM AT *3e>A1», 70 F n,"K-siM.H t o T/oo*r Set a/: V3**Cfft. V ■ I4t.% n*** (m- I. HP -oo*rt\)*' ttr BAftoneiR\c patssuac AIM MJ .54- *3J • SI •M 6i» as v$ - a til % T OAiricc *H r Tf i IN M.O r \ OPS r MAM STATIC HRCZZoAE, IN h,Z * t r o to ID to I" ; i • ! " ~ i QfHFICC 4H IAI. NtO ,1 l» II 1.1 u J.4- i.S /•* II /« i 20 Zoo 2 5 3C 3 S ♦ c *s Xf ft < ft T ZIP 220 230 260 lie J"4< S6C 3TO J So 390 40e ; 4.0 4*> 4*> r f*> 4 4JD f-4*> -#- ♦*> --£-<•» -*■ *» -J— Joe f^t'aure 37 117. C. Solar Charts 1. Angle of declination versus cosine angle of incidence. This plot was rr.ade up for the collector tilt. (£) = 27°] and latitude ' ( *: ) = 40 ; . Lines for C, +0.5 --+6.5 hours from solar noon \;ere plotted for the entire year. Calculation of one point should suffice in showing the relations used. Nomenclature used in following sections: •©■p = angle of incidence of direct sunlight on tilted surface "&* = angle of incidence of direct sunlight on horizontal surface q = angle of declination of sun $ = latitude = 40° P = angle of tilt of collecter from the '. o: JUrncal to ard the equator = 27° (-0 = hour angle, degrees (15 per hour from noon) Angles of declination were obtained from the Solar Ephemeris and Polaris Tables for 1944 Angles of incidence of direct sunlight have been calculated by the following equations: ( 9 ) Cos -"i x = sin /f sin j ♦ cos i> cos ( j cosiO If an artificial latitude ( .J> --• 3 ) is substituted for tb , cos <9f becomes cos Gt from which 3y03X\ be found. cos f'^. = sin (# - (o ) sin,} + cor, ( ft - ? ) cos<) cos»0 For.^ = -22 , ±5-5 hrs. from solar noon U) = 5.5 x 15 = 82.5° cos & = sin (40-27) sin -22 + cos (4C-27) cos -22 cos 82.5 = (0.225 x -0.375) + (0.974 x 0.927 x 0.131) = -0.0844 + 0.1182 = 0.034 cos £ is plotted against ^ (Figure 50 , Appendix) No. 320-N .119. 2. Daily interval of exposure to sunlight. a. pyrhelioraeter (Figure 59 , Appendix) cos 6/ = sin sin ^ + cos (p cos^ cos ^ &£- 90° at first and last exposure cos (p E = sin .re - 1'. i 9i- #\- ± i i 3 ct L -p- 1 : ;-:| "~r ^. '*l i » / y— § fW-P- 5 \.' p. - / . ;-::= 1 ^ j it| r 1 / \: i *, ! > ^v - 1 1 1 JL _Z_j * 3" § ru' k 1 1 !■ II | j 'I ■ g 8 1. J 1 i ', . \f t •*'- p -*- Ir 1 K ! ft 1 ■ ■ | . ■ : III / i -;!^ L^ 51- -;s ! -H— . 1 , hi / -:j— 1 ■ *[ ' ff\j t ' j , "■ S - _ — - - . 1 1 1 "I . ' ■ * 4,. V | ! i • \ r l / /^ • 1 i 1 ^ 1 - ! i - -\- I . I /\-y» 1" i ! * - - _L _1_ — - — ! ■ • t 1 ' * i>^" ii u': ' ■ p ^ - 1 f ji !H ;■ < ' t i. — i - — 1 4" ; ;:. J H J i ; ' i- ' -1 _ » • — (i ' :: ''•I * — 1 t i. T*f :. j ':: 1 ' * - X ^l; £ 1 * \f N i j: - ', 1 ■ */- *5 ! ■:|i / ;■■. *s. ^ - s« / Jj ' i • \y\ ' ; i 85 T j . I \ . i ft- ji ■ ; I . > i_«_ 5? i; ji! . . ! I I i r TT V . :j i i.! ttli . ■; •'-'■ ^ ; : : • : it I ! y V /a :^ ■ .. . .j rr- S! • . ;■: "/ $ /$i 1 .' 'h: // ' i 4 »» ; !i J « j « \ •* 1. . SI 1 <* ■ * \ i i s v » 1 ■ I I < i * § v. \ \ y b * ? < i »*r > V ► t .. 1 i *,il ,'.- 3L 1 Lr V 1 ! ' i 1 ^ 1 < [ ■ , ' •I- j.- ,... .■ ; i 3 f ■ i-w. } < 9~ , F»r [ -<* / 1! .: . ■ r- ; . i fir ; . | M ;■' HL "; ■ :- j • ■ ; iri : t::i ■ r: i ;. ; ; ;. : ";■ .:: ■ . ':■. . ■ :.' § 1 1 ff . .:;. \ '. : .; ■ i tttt S3 1 ; iff] iiii . i ■ ' '- , : t ti : i '.' ■ ■ * ^ || |$e i £g n;: ;;": 3p :: : i ,;i: :.' !■•: ' i.... ■ :i; ' 1 ■, riff - ■;• 1 ■.•! • ; ;; ti : 1.! i;;i I2U. tit! ::l: lii: . ,:■; ill' '!■■ m • ■ ,,• ■ 124. i | X . ., , ? 5 • *| p « * ? - . m HI I* H IS ; i* *~»y ^> ^ $i >§£*$« • :: \ f ~^> ' 28 . h g \ r -| 4-1 4_ \ \ ' _ \ tr* 4 r. :\ ■ SO * I : ! . F ~.:\\ 1 . .. z ■■ r * 1 " «r 1 r... ■ i • : : : J V ; . w . T<.- A - : L[-:H%. ' J '"7l ; - " ~T— A. •f V -A M "if \ i ..17/ . | . , m k "I ~ l ~ 4i , . \ 1 . 1 : . " pS If lZ.-^Li ' V ■ -1 T ■ V f-- - 1 / fyf f£ 1 i • life 3 ^^ ; i ■ ■ •■ " . - ■ ':---: i > - W^ i . ; in.. -- -X - id? i f- SF 1 "- ■ .-J*. . I • / : i- ■ /-^v 5 i 7 | j- ■ g= * i t ' 1 1 "i ^ -* / - ' | 1 1 tt - , y1. 3 f | ■ tu- r 7 * < ; . ■ ' : . 7 L . 1 . J 1 I". e. j | I : f \ -,^: 1 I j i ■ l_i r " — **—-» f*~afh r» aJtc ^^1 Ml for < i -r ^v 3*/ ^ **? 1lw l» ? ^ *. » t ■ ■ ! VI • i u Li. ! "♦• r*7 1 , i J 1 n ; ■ - _L I ^ 1 . i ' 1 > v 1 1 z , » s !••■■•■ ^ i — i — 1 1 ' v* o_ 1 J ' "* i :' . i ■ : I 1 ! , . :* 5 -fc > > £ - 1 / v^ 3L ~ ; i ■ 5Q I" 1 h * •'T i ■ 127 II. Calculation of Results of Run Calculations for a typical run will be shown for the hour ending at solar noon. The following data from run 0-50 made on October 12, 1544, will be used: Entrance air temperature 92°F. Exit air temperature l84°F. Bulk air temperature 67 °F. Coverglass temperature 123°F. Blower temperature 1C9°F. Solar Input 6l.5 2§£ Cm 2 Hr. Bar omct er 625 Km . Hg . Area of heat collection, black area ...205 sq. feet Rate data (secured at 4:00 P.l:.) Rotameter static pressure 0.4" H2O Rotameter temperature , 53°F» Rotameter reading 107 nan. Blower temperature 94°F. Blower static pressure 21 mm. Hg. The temperatures mentioned above (except the temperatures given with rate data) are mean values obtained over the period from eleven o'clock until noon. They ire the arithmetic mean values for the several readings taken during the hour. A.. Air Rate -Rotameter From the calibration curve for the rotameter, a reading of 107 mm indicates that 51. 5 standard (760 mr. Hg. - 70°F.) c.f.m. of air if measured at 63C mm. of Hg .absolute pressure and 70°F. would be flowing. Since the air was measured at an absolute pressure of (625 mm Hg.- 0.4 M H2C and at a temperature of 93°F., pressure and temperature corrections must be applied to the 51.5 standard c.f.m. Correction factors for pressure and temperature were obtained from Figures 3*}- and S'~ . Appendix Rate = 91.5 x 0.596 x 0.579 = 85.2 c.f.m. (76c ma - 7C°F.) Rate at blower conditions = 89.2 x 760 x ( 460 + 94 ) (625-21) (46C + 70) = 117 c.f.m. (604 mm - 94°F.) Since the blower displaces the same volume of air constantly, the mass of air depends on the temperature and pressure' at the blower. The rate calculated above is an instantaneous value based on data taken at four o'cl©«k # An average *s*t for the hour 1b calculated using an hourly mean value of the blower temperature rath r than the instantaneous temperature recorded when the rate was measured. 128. Actual rate at noon = 117 x ( 460 + 70 ) x ( £-25-21 ) (460 + 109) 760 =86.7 e.f.m. (760 ran - 70°F.) Two other methods were, used for determining air rates. L 3«5 inch air orifice was used for which a nomograph (described previously) was made. Run 0-17 may be used to explain this method. Barometer 629.5 mm Hg. Orifice static pressure .....,., 0.35" H2O Pressure drop across -orifice 1.73" H^O Orifice temperature 79°F. Using the above data, a value of 217 c.f.m. (760 mm - 70°F.) was obtained from the nomograph. The hourly rates were obtained from the instantaneous value above by the same method described under the section on the rotameter. The other method involved the dilution of CO^ injected into the stream of air. Run 0-1 will be used to demonstrate this method. Barometer , 24.6 inches Hg. Static pressure, CO2 line 26.2 inches Kg. Pressure drop 6.4 inches Hg. Percent COp • 1.0$ Temperature, C0 2 line 41°F. Total' pressure = 24.6 inches Kg. Static pressure - 26^2 " " CO^ line pressure = 50.8 inches Hg = 1291 mm Hg. Density of C0 2 .« 44 moTe x ft). 8 x 46c + 32 \ ft3_ 25.9 460 + 41 J 359 r^ole = 0.204 -£— ft Pressure drop = 6.4* Hg x 13.6 x 62.4 -ft^ ~Hg. 12 C.204-#/ft3 C0 2 = 2210 ft. of C0 2 From calibration curve (£0), c.f.s. of 1 CO? = 0.0215 ft 3 C0 ? sec c.f.m. of air ■ C.0215 sec x 6o n -.in x 12^1 x ^0 x ££ parts air 760 501 1..0 part C0 2 = 229 £ * air (760 mm. - 7C°F.) min 129, B. Cover Plate Temperature Calculation of the cover plate temperature is as follows-. Indicated temperature s 192°F. Instrument temperature ■ 86°F. Temperature difference - 192 - 86 = 106°F. From chart (Figure-52) actual temperature = 123°F. C. Heat Recovered tt min Btu Heat Recovered= CFM( 760-70 )x492 x 29molex60 Hrx0.24F Fx At°F. fti 530 209 ft 2 359mole Btu cjpHrft 2 * Cn:( 760-70) x 4?2 x 29 x 6Q x 0.242 xat 530 x 359 x 209 0^ * CFM(760-70) x At x 0.00522 q- = 86.7 x (184-92) x 0.00522 " Btu =41.7 Hrft 2 D. Heat Input Heat Input * Solar Innut x R Where: R = cos Br cos fa. Pr = angle of incidence of direct sunlight on a tilted surface, Pr.~ angle of incidence of direct sunlight on a horizontal surface. (Zenith angle) R is obtained from Figure ' i rO Appendix and equals 1.39 at noon on October 12. The solar input to a horizontal surface was measured continuously by an Eppley fiftjp-j unction pyrhelioneter and recorded by a Leeds- Northrup recording potentiometer. The chart records were integrated with a polar planimeter which was calibrated to give a reading in calories per square centimeter per hour.. Solar Input cat x ( 2.54 x 12 ) cr.2Hr 252 cal 2 SZ2 ft2 x R Btu = Solar Input x R x 3»69 = 61.5 x 1.39 x 3.69 Btu = 315 Hrft 2 130. E. Gross Efficiency ( Overall for day) , Gross Efficiency s Total Heat Recovered x 100 Total Gross Heat Input = 3J8 x 100 « 17.4^ 2056 F. Net Heat Input (equals gross input minus reflection loss) Net q = Gross q x t , TChere t * transmitted radiation obtained from Figure tS Appendix For noon on October 12, t ■ O.78 Btu . Net qj = 315 x 0.78 « 246 Hr.ft. G. Net Efficiency (Overall fpr day) Net Efficiency * Total Heat Recovered x 100 Total Net Heat Input s 2S& x 100 « 23.3^ ■ 1531 H. Cloud Loss Cloud Loss = Input with clear sky - actual input x 100 Input with clear sky = 220? - 2056 x 100 = 6.6$ 2202 The input with clear sky is tho solar input obtained on a clear day a few days before or after the indicated day. A sample data sheet of a similar run (Run 0-39) is shown on the following page 3 i vn ^ >* r*- > $ > 0) > !> O rH i < i u > > < 33 s0 %R r-\ L'\ CNJ C"> 3 vO o> o o • -4 3 +3 -P UO i> ON sO CO f> w >i o o c - ^ m • 0) CM rf> rw ON Q .. t> c ). oj 0\i 3 00 rr> {> x^ 3 -a ON rH CO sB w *- r- H 00 sO C a oo CM m 4- 2 •«s Eh < 4 o si 3 o < a> - Os 0% sO rH co a 3 1 1 u 3 • 3 o 1 vD xO • L- i xO t> ro- 1 ^O sO • C\J 00 CO OJ rH A O a O ^0 1 sO sO H vO i sO s0 o sO 1 35 sO o o ^cf • • co ro CO rH OJ UA C rH rH St rO vl 3 o 0> cti O i> r ' sfC 3 r- a 3 « < 00 1 vO ITV sO i 5 sQ o 00 ^g ; >- \ E- sD sj 3 sO C - sO •"" •> O o O vO 1 st) sO H o » sfi o sfi sO sO o o • rH 00 lOc ON On 0) ■t rH o O a> CO C 3 sO o "N 00 U 3 • • H 1 O 00 • o i 0^ oo o-- o 00 t> - Cvi a o ( . o 1 %0 ^o ! £> sO f — i E> i o o 00 t> O O xO CO o • CO 00 rH 00 Sf Sf • • CM -v 6 OJ Oi CO O r-\ rH ST • * • 00 r-\ ^D • • • uo -p sO rH t> - ww 3 so r - rH • • H sD 1 ah o o o i CJN rH to i> ON HD ON rH ■ sw C*- a 3 C- t* 3 r- o A r<-\ o 0^ r»> 00 1 t> o o^ 00 i I> TO CO 00 t> o o ~o tM • fjc, . -o -S • C\i H c*> H c\ rH o oo O" *N J- a 3 C 3 • i • » ur\ 0> o o • ■^ o o c-- ■ i> sO- O st • • U XJ -p a *E 03 co co r- h >o c 3 OW 3 CO 0> IT, to o o o rH H OJ <-{ o rH r->. o O CM 'O. vO u m oj s h o C0 r H 00 r- H C^ o A VTv rH 00 sO rH f-\ rH l-A ■si rH H H rH o r-^ rH rH rH vO C»> -P 2> -P O o (U r-i CO Eh ^ Jh. o u> E <1) Q) oj -vt u> ^ n • u\ oo O • • • 5t £ vX 3 P ■s C 3 • • o o 00 tf> o • t> sO (3> st c~- CM C st o • Ih I> f» H CM ro rH LO 00 "vT lf> rH sO o St P^l OJ t> XO SJ Cfj U fn *H H H • • O0 r H! 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IS ■ C 4 • o CM O LO • C> st CM 03 St 00 ON O r-A vO • Eh CO co u n, O o ^o^ :-A «"N - -t sO 00 .^i 0^ OJ lf> St CO O H ^r O r H rH r- A f- O ■\ r~i sT> N •st H H H H 00 rH H H rH rH rH r-i rH OJ rH CO O 00 H • f" cr\ • H » O C V t- v r •{ \D • sO • -. f Cxi O cv cv 00 03 O - rH rH rH CM rH H rH rH OJ rH OJ rH rH rH OJ H CM sO • • -p • C\i n • • sO :C CO sO sj 3 O C r* r H -0 • CM • -4 CM H rH Tvi 00 rH 3 o ON kf> st ^ st st • P H 5 o p \ta - i cv 00 rH o ^> -••. ■sj CM CM ^D O OJ C4 sO nO OJ OJ 00 o tiO O r H rH r- ^ t> v- A rH O r»> -s4 rH r : ^ H rv H H CM rH OJ rH rH rH rH OJ rH sO |X4 •H G -st U"> o OJ _} tJ O C > sO vl 3 o "N • f^l CVJ 1 • | • co C O cOsi 3 O c "i\D - ^ CJs • CM • o CM eg »* ON H ir« 00 O-s rH O rH O OJ O • H W S > r ^H- H r> r> A H O CM !> sO 0^ c*> CM rH -43 c> 3 -t OJ sC J vO st CM H o Eh rH c* n r*> rH H rH CM rH H H CI r-i rH rH rH CM r-t o Oi H CM sO. CO CO co, Oh > rH c > rH \i 3 o 3 • • CM • <4 O O-v Q£ f^ OJ UA r-- o * OJ r> O CO • • r-l rH rH - toe 4 O - 4 - rv O a 4 !> OJ o OJ sj st CO o OJ sQ •p c t> r A <-{ r- H C- »? A v> ^ O'A r-\ H H (V rH H H CM ■ON r^ rH rH OJ ON sfl C H -4 c^ OJ CM OJ H o C ^ c 3 C h • ■ o- • <4 ^ rH 00 • r-\ vO sO £> * r~\ St CM 8 • rH sr r >i O r- H O u "N rH O tf> vD CM rH o ^f Oi s| o NO On OJ CM H 0> oo o 22 O 00 r ^ co r- ■IsO r ^ c- m CM OJ H rH H H L^ rH H rH H sO H rH rH rH vO ciA O u ">vJ3f C 3 -i - oo o Q O O -4 X' rH sj o CO • ro ro O o O OJ 4 CO 00 ~ C ^ C- C in ir\ o ^ ^t CM CM o H O rH ^o O^- H QT> rH ON c> ON H CO CM OJ 3 sj O • ' o • o • a0 OJ 3(\C ^ -sfO rH r- CM • rH t»> H rH 00 t> st H o o o OJ st CO d rH vD vJ 3sor - IT\ r r\ H CM H 0> t- I> t> ON rH sO o £> CO H vO C> [> 00 H UN 5 _3 t> vO - st r\j .; j -4 ; : > h 8 vXJ I cTv OO c*> 1 UA oo p> > st ."O • • • • • < < PL, Oh CC ir\ l C\ U%vJ D vr\ r ^ o rH c»> o sTN I LO IfN o u^ 1 ^O UN o IC v-O SO CO O m w rH 00 CM CO > t, r> U^ 00 oo liMAOO o sO co r r » h r - ua C P» • • U"\ I r-\ O OJ t r-] rH CNJ st o ON • CO V n> kr> w ( "> o - Eh 1 Cx. o Cti H M tH o W\ i W\ U\ a N r-t UA 1 Efa o ir\ ur\ o NJ 6- ft. CTN cr\ uo st o NJ Eh Ph rH DO wo lOvO sO • • Cl* o c s CC .'"5 cc u •H o- 0£ U •H ct cc ii fr i 1 Q] C r ; 3 co CQ O E i- ' C - X ^ < ^ re •-j; CQ (h sj r< ^ c ) P.- - £2 " SB < ->=> «ft ?' Q ct *• ^ 0) O^ t) p u c? o tj> O ^3 U O O -P •H C O. 1) I o Eh r- -P 4J H •P P Eh o- +5 p> H P> O H -C 61 ♦i id PQ eq * a) PQ C U 0) - B 0) •• »^ ♦3 P O •s H 0) rH »■ • l-H u rH rH a> rH O rH 03 U Oi i H ^ 0) o a ■P a rl CL< p a H 0. p Ph U u CH p Oh rj ■H •• rH H « -^ O • H Eh •H - P o O h L cl 1 ■H a a) -,H m IU •H cO I) P 0) H O •• C 5 c ■ < rH <5 s* c •H -: u rH g K < 0/ H e PC < Q] rH H pS O «n o o h- 5 g E- • H •H -p xi p -P 4^> >' p P -a P p rH (-< -P !fi c > -p ■ H > 5^, rH CO H • c^ •H ■0 u p « •rH Xi D p CD •r-( XI a p a) CV. 3 w dj p > > " > > ' => > > > > o S Q) T < O D O D O D O O o O -•c < < -*: •^ PQ PQ PQ PQ PQ p e 1 o C3 p c •\ co +■ > c > c > rH :m c^n -^ IA> X) £> ro 0- .'3 r* CM ■-o t ir> ■0 r- 00 o O r—. CM P"\ St Ci'\ v5> 1 s 1 rH H M H H rH |h H r-i H CM CV CM CM CM CM (M 131. 132. III. Heat Balance The heat balance was divided into the following divisions: input recovery total losses reflection N convection conduction re-radiation unaccounted Each item was calculated for each hour of the day and the hourly values were added to give a daily value. A sample calculation for the hour ending at solar noon on October 12, 1944, (Run - 5°)f°Hows: A. Total losses gross input - recovery * total losses Btu 315 - 42 = 273 H? * B. Reflection losses reflection ■ gross input x (l-t) = 315 x (1-.78) - 69. C. Convection losses Using the data of Jurges ( 1 J) and Schack's ( \£ ) } temperature . conversion factor, the heat transfer coefficient from the cover glass to the air is found by the relation / , \ h « 0.99 * 0.21V [ 460 + 7 \ where V is velocity of air in feet per second over the surface. Then the total heat lost per square foot is £c = *c <*' '*' • ) (17) a cover air For V = 4.4- ft/sec* tkir ■ *7°F. t' cover = 123°F. Btu h. = 0.99 +"0,21 x 4.4 / 460+10 \ = 1.92 Hr ft 2o F. V 460+67J q^ = 1.92 x (123-67) = 107 Hr ft 2 Btu _,. = 1.92 x (123-67) = 107 A * Next page . 133, *Since wind velocity data were not available on the site of the solar heating unit at the time of the runs, an approximation was made, " ind velocity records regularly available at Valmont Steam Power Plant four miles east of the Boulder location of the unit were corrected to local v/ind velocities by a factor. This factor was determined from data in 1942 when data were available locally and and at Valmont. It was found that the velocity on the campus averaged approximately 0.6 that at Valmont, D, Conduction losses Losses by conduction v/ere divided into three parts: (l) side losses (2) top board; (3) floor. i Btu ft. q - KAAt ; ( | 7 ) K =: thermal conductivity, Hrft^°F. L . A = area of transfer, ft2 L = thickness At = temperature difference, F. 1. Side losses per square foot of collector area. A = 3(15 x 1) = 45 ft 2 L = 1 inch (wood) K = 0.12 ^3kti= exit -+ entrance - entrance air 2 = exit - entrance air = 184-92 = 46 2 2 q s •= 0.12 x 45 x,46 = Btu 209 x 1/12 i4 Hr.ft^ .2. Top losses A =■ 15 x 2.1 = 31.5 ft* L = 4 inches (insulation) 1 inch (wood) K = 0.04 (insulation) , 0.12 (wood) ^t 2 = exit air - entrance ai.r = 184-92 = 92 q. = 15 x 2.1 x 92 209/ 4 + 1 \ U2x0.04 12xC.12j Btu Hr.ft^ 134. 3. Floor losses A = 15' x 18' = 270 ft 2 L = 8" (insulation) 2" (wood) K = 0.04 (insulation) f 0.12 (wood) At 3 = (bottom plate - 70) = (274 - 70) s 204 q. = 15 x 18 x 204 * ,. Btu 209 / 8 + 2 " \ ° Hr.ft 2 [ 12x0.04 12x0.12] Conduction losses • 14 ♦ 2 ♦ 15 ■ 31 2£S Hr.ft 2 £• Re-radiation losses q/A-oa73eV[*fr(fe)-^(^J J 0-7 ) Where e' s = t.>+ 1 = 0. 94 ♦ 1 = 0.97 2 2 6 5 = emissivity of surface 6^.= emissivity of surrounding air ;£r- | iX,= absorptivity of surrounding air t£r ^ T,= absolute gas temperature, °R. Tj~ absolute surface temperature, °R. q/A = 0.173 x 0.97 f f 123 * 46o ) A - ( 67 * 46o \ 4 1 V ioo / \ loo I J = 64 Btu Hr.ft 2 F. Summation - Daily totals input - recovery = losses 2056 - 358 1697 Btu ft*" % of total losses reflection 525 convection 577 conduction 220 re-radiation 363 unaccounted 24 31.0 34.0 12.9 21.4 0.7 135. IV. Calculation of Predicted Performance of Collector for House Heating (experimental house unit) " o The solar heat trap on Dr. G..0. C. Lof's house is at a tilt of 27 with the horizontal and has an area of 463 square feet. From the plot of net efficiency versus air rate obtained from studies made- on th ] moratory unit, (also at a tilt of 27° with the horizontal; A$% net efficiency at an air rate of l60 CF1I with a 40°F. mean temperature rise were deemed optimum conditions. A. Heat recoverable Calculations for each hour from sunrise to sunset for every day from October, 1944, through May, 1945, were made to determine the quantity of heat recovered under the above conditions. Hourly Heat Recovered = Hourly Net Heat Input Btu x G.45 x 463 ft 2 Ft? B. Heat necessary 1. Degree-day method The heat necessary t was calculated using the degree-day method. A temperature of 65°F. was the reference, i'^ 1 day with an .average temperature (arithmetic average of maximum and minimum temperature) of 42°F: I i Degree-days = (65-t av ) x ?'o. of Hour" : t av <^ 65. 24 = (65-42) x 1 = 2J For calculation of heat necessary during the daylight hours alone, the same method was used. with one ex on. The average temperature was an arithmetic averaj ..peratur^ calculated from continuous chart -recorded temperatures for the daylight hours only. The above relation was used for the calculation of degree-days. 2. Heat required per degree day. The heat required 'per degree-day was obtained from the gas consumption data for the Lof house. Btu Heating value of gas = 630 ft3 at (630mm-70 u F) Btu 90,000 - ft3 Furnace input ((? ) S0,C0C Hr . " 83C 1C£ Hr . ft3 s Input to pilot = 3 Hr. — nl 1 Total input ]ti Hr . Btu Heat available to hou: ) C7,5C0Hr. Equivalent heating = 67.500 = £ 8 Btu 111 fP 136. The quantity of gas used for hot water heating was found by averaging the gas consumption during the summer months when house heating wis unnecessary. Ft 3 Gas used for water heating - 2430 mo. Period of gas consumption for this calculation only Sept. 11 - March 12 No. of degree-days - 4412 Days Gas consumption - 123,700 ft 3 Gas consumption for water heating = 6 x 2430 c 14,600 ft Gas consumption for house heating = 123,700 - 14,600 = 109,100 ft3 Heat furnished to house ■ 109,100 ft- 3 x 6o8~^r = 66,334,000 B.T. 0. ftj> Btu used/ Day = 66.^34,000 - 15,035 4412 ' 3. Total heat necessary Heat Necessary = Degree-days x Btu/ D,ay = 23 x 15,035 = 3^5,000 Btu C. Percentage of heating load carried by collector 1. No storage The following example taken from the calculation for November will suffice with a short explanation. (1) (2) ONLY DAYLIGHT HOURS (3) T (4) (5) (6) Date °Days 1 Heat Necessary ! °Days j Heat Necessary . He^.t Recovered I Heat Used Fron Nov. 24 20 25 35 26 37 27 33 26 31 29 26 30 40 Monthly Totals xl0"3 301 527 557 497 467 391 602 10,390 Btu xlO-3 Btu xlC-3 I Sun xl0"3 7..9 ! 114.6 1 15.0 113.8 13.3 110.8 19.6 119 125 220 166 226 265 208 197 200 197 16"2 146 296 101 4025 6700 119 166 226 197 197 146 101 3688 137. The method for calculating the values in columns 1-5 are shown previously. Column 6 is composed of the vsmaller value from either 4 or 5» The total of the column for the month are as shown. % load carried (Nov. 1944) = (6)^100 = 3688 100 = 35.5$ (2) * 10,390 % load carried (Oct. 1944- = 2 3. 7 70.000 ^™ s 34.0^ Mar 1945, inc) 69,820,000 2. One day storage A similar table made up for one day storage is as follows: (1) (2) (3) (4) Date °Day Heat Necessary Heat Recovered Heat Used Nov. Btu xl0"3 Btu xlO' -3 Btu xl0-3 1 10 150 291 150 2 16 241 268 241 . 3 20 301 262 262 4 19 286 214 214 5 16 240 . 195 195 6 16 240 120 120 7 13 196 265 196 Monthly Totals 10,390 6?C0 6200 Column 4 is composed of the smaller values of either (2) or (3). % load carried (Nov. 1544) = U) 1Q0 = 6200 100 = 59. 6/0 (2) 10,390 % load carried (Oct. 1944- = 46.570.000 ;:1QO = 54. 8£ May 1945, inc.) 85,000,000 3. Two ar.d three day storage 138, 2 DAY FROM SUN 3 DAY frck: sun I Date'! • D Days ' Heat 1 Heat Heat Used 1 Heat Stor 1 •ed ' i Heat Used 1 1 • JHeat stored i Necessary Recover ed Btu xl0~3 Btu xl0"3 Btu xlO" ' j Btu xlC -3 Btu xlC-3 Btu xlO" ■3 Nov. i 1 256 1 10 i 150 291 150 291 ' 150 291 ^ ! | . "291 2 ; 16 241 268 241 268 241 268 i i ' 258" . 3 2C \ 301. 262 .... 3C1 . 229 • 3d .. 262 \ 234 4 19 266 • 214 286 157 286 214 •. 1 1 1 , 208 _5 ! 16 240 195 240 i 112 II 24 ° : 195 ! i j t t; 163 6 | 16. . 2fO 120 232 1 1 I: 240 120 j 8 ? 7 I 13 196 1. 265 196 69 S_ 156 1 265 l/.onthi y 1 1 1 ' 1 Totals 10,393 6700 i 6790 1 ! 7C40 1 Method of calculation Example - Date - 3rd 2 day storage Heat necessary was 301 xlO 3 BTU and since there was 268 xlO 3 BTU stored from the previous day, 33 xlO 3 BTU were necessary to carry the total load, these were taken from the 262 xlO-* which were recovered for the day, leaving 22$ xlO^ BTU in storage for use on the following day. 3 day storage The heat in storage from two days previous to the third was 291 xl0 3 BTU from the first and 268 x.ic3 BTU from the second day. Therefore, the 291 xlO BTU were used first, leaving 10 xlo3 BTU to be taken from the 268 xlo3 BTU. After this was used there remained in storage 258 x"lo3 BTU and 262 xlo3 BTU were added to this from the day's recovery. Two day store' 1 % loud cnid C^v,1944) = g.ffi.OOO x 1Q0 . gj ^ 7 1 dad carr'i e d ( Oc t . 194 << - j9i<70iQCQ -■*» &¥* inc) 35 ; ooo ] ,cco x lco " ^- c/ - Th ree day stcrare ,J. , E-. % £ load carried (Nov. 19*4) = 7.040,000 1QC a ^ ? 7 ^ ic,3S 0,000 k yi ;. load carried (Oct. 1$44«- . r ,c n , w L-v 1945 inc) g 1 ' 000 ^ 00 : x IOC - 60.1J* u^y i,«0, L ncj £5 ? 000, 000 D. Correlations for c6ilectore at tilts ether than 27 Similar calculations as these shown for the actual collector have been r. ide for a collector of squal area tilted 40° fro::, the horizontal. Ey .use of the results calculated for collectors at tilts of 27 ' and 40°, an atter.xt to approximate the radiation collected by a neat trap at any tilt h .is been r.ade. The correlation shown in -Figure 7 covers the solar eneny obtainable ever the period fron October through 'fty» the aionths in which collection is desired. • r x = 0.73 x 64, 63C, COO Btu for 463 ft 2 . = 47,26C,000 Btu for 463 ft 2 . 141. . ■• .i ation of the tilt of a heattjap for collecting: the maxi i r.ost desired, rather t v> an collecting the crjcimuc; total he it for . n was obtained in the follcwinr manner. Dat- for thi I fat I by trap tiltod at 40 and the heat used Lr the .:->.■ 1 ,if one-d«;y storage is provided, were obtained i i fraction vf heat used for each rent of 1 ating s as a multiplier in the graphical integration of the follouii ec . -j >.June 1 " " J ccs [f$ - c - p) x + ransrrittar.ce x fraction i Uoed '! (da-). October 1 For exar.plc, on October 15 at $ - AC C and j3 = <0 C : A - _C;0 o — — ^ trr.nsii.ittar.ee = 0.59 heat used = 45oO = C.501 heat collected 5105 Q «*■ cos {0 - A - J3) x transrittar.ee x fraction cf heat used. Q * cos (40+8-10) x C.59 x 0.501 Q -. ccs £ x C.59 x C.501 Q ^ 0.293 (plotted versus October 15) GraphioA/interrations of this equation for tilts of -0°, 43°, 47°, and 50° I , and the results were plotted in Figure 45c. A tilt of 47° is i the optimur. for collecting heat usable during this season, he i.'onthly fractions cf collected energy actually used are the sane as in the experimental hcuse. 143. V. Predicted Size of Heat Storage Unit k. One day storage Frcrr. the previous calculation (Sec. IV C 2), it was observed that an average of the high quantities of heat used from the sun over a one day period was 300,000 Btu. The maximum quantity of heat used from the sun over a one day period was 400,000 Btu. The size of storage bins large enough to store these quantities could be estimated as follows: 1. assume a value of 0.2 —^ for the specific heat of the storage #°F material. 2. assume an available temperature rise of (200-70) = 130°F. Storage of 300,000 Btu 3 00,000 Btu Btu = 11,500 pounds of material 0.2^F x 130°F % heating load carried = 53«51> Storage of 400,000 Btu 400.000 Btu Btu = 15,400 pounds of material 0.2JPF x 130°F £ heating load carried = $A,fQ% B. Two day storage Storage of 500,000 Btu, average high quantity of heat stored over a period of two days. 500.00 Btu Btu = 19,200 pounds of material 0.2#°F x 130°F % heating load carried « 56.52/° Storage of 740,000 Btu, the mrjeimum quantity of heat stored over a two-day period. 740.00 Btu Btu = 28,500 pounds of material 0.2fT x 130°F i heating load carried = 58.19/C 144. C. Three day storage Storage of 800,000 Btu, an average high quantity of heat stored over a poriod of three days. 800.000 Btu Btu = 30,800 pounds of material 0.2#°F x 130°F Storage of 970,000 Btu, tho maximum quantity of heat Btorod 1 throe-duy period. 970.000 Btu Btu = 37»300 pounds of material 0.2^F x 130°F D, General Comments From the above calculations, it is seen that two sizes of storage units have been ostimated. Survey of the day-by-day collected heat that could be stored shows that storage of the maximum quantity of heat is unwarranted because the overall percentage heating loud carried would not be increased sufficiently. Therefore, it was proposed to use a storage unit capable of storing an average high value. 145. Btu VI. Calculation of Theoretical Perf ormance of Unit A. Heat balance (based en data of run 0-42) Incident radiation = 329 Pf^t 2 Radiation reflected fror.: top surface = 0.04 x 329 = 13-2 Hfft 2 Btu Radiation transmitted to piste = 315-8 H?Tt 2 Radiation absorbed = 315.8 x 0.03 + i ^c"^ ' * 2 * ****) x °*°3 = 10 * 6 IrTt 2 t 2 pistes (filler) = 0.798 for a=0.03, r-C.08, t=0.8? (l plate) Radiation absorbed on black lur'faee" 0.798 x 329 = 262 $7^2 a 2 plates = 0.059 i *0) Radiation absorbed (total) in glass ■ 0.059 x 329 ■ 19.4 §n*t 2 Radiation abs6rbed in 2nd plate * 19.4 - 1C.6 = $.8 $|rt 2 Heat into air stream = 329 - losses r 2 pi a tes = 0,14 3 (Killer) for a = 0.03, r ■ C.08, t = 0.89 (l plr.it e) Radiation reflected = 0.143 x 329 = 47 ppy t 2 Radiation convected fror.; top surface = 57 nr7+2 (fror pi avioua calculation) Et u Radiation reradiated from top surface= 27 HPTt 2 ( frorr * previous calculation) Btu ieatinto air stream = 329 - ^7 - 57 - 27 = 198 §p£ t 2 MILLER ANALYSIS - RUN 0-42 (5th calculation) 146. filn (2) (1) Q=329 13.2 \L 84 Outdoor Air Assumed 47 ?7 2f 75°F o u < 315.8 < ! (72.8) 9. 5+1.1= 10.6 (a) J 72.8 t £ V 96 £ (160) 145. 6f 7 8.8(a) Single . S Strength ? \L 14.4 i 329x0.798=262 ^116.4 Calculated T,°F f,°F 100 96 1.0 102 0.76 101.3 158 160.7 243 115.8 93 ivl" 186.3 105 0.76 B. Calculations based on I ilier's analysis 1. Assume Q n & s n s 2 = 1.0 Q 2 = ° 6 btu '* ft Cover temp = 100 Q F 9j = O.78 Q x = 102 Btu/tlrft 2 196 ntu/hrft 2 Film 2: *-f^- Q. , ill 96 a C 92 2s !s 2s ^ 7 * * Hr^t 2 Filfr. 1: - qi = -||i- Ql = |jl§yl x 102 = 14.4 ^2 (frQ? . a±r tc plat e) B+u ^2 = -5li--Q n = ~^~i x 102 = 116,4 ud; t 2 (fro;.: plate to air) 2. Run heat balance aroun I file for each film. (See diagram) 3. Calculate ter.peratures of plates. Cover temperature (exp.) = 100 F Cover temperature (batten) T c nor <- ^c +A /2 iul r — q _ hea t cord': K • plate.-Pi :cted through = 100 ♦ 1.3 = 101. 3°F Fj-ft* A. = heat absorbed in plate. 3tu BffV K = Conductance of rlass = 60 ^ u Mddle plato (top) T = 100 °o = 100 / T o +460 V 100 , J*L >,4 0.172 2 ^- 1/4 Hr c F ft- 1 1/4 -460; / 101.3+460 ) + 72t e " \ 100 / 0.1555 = 158°F Liddle plate (bottom) T = 156 ♦ i6 ?a 4 '^ '%460 0,.= heat radiated be- Btu tv;een plates, Hrft sc = 160.7 °F >lack plate (tcp) T = 100 r/ 00 , e= s eru: issivity of £lass surface = C. 95 T - ten.pero.ture of bot- ,0 r > . , \4 4 tor. of ut per ] ; 160.7^ 14LJL -460 °F. V 100 j ♦ 0.1553 0_ 3 = 243 F per plate, (>3t,o$t Calculate. air ter.pcr v.turos, Llm2l T 2 = - R s ( Tn .. Tn ) + TegJ^ / d^TsVy- »c+.nal input x 10Q percent . ir«rut •"1 + > clear sVy Degree-day - a unit, based upon temperature difference and time, used in specifying the nominal heating load in winter. For any one day there oxist3 as many degree-days as there are degrees Fahrenheit difference in temperature between the moan temperature for the day and 65°F. Gross efficiency - (heat recovared) (lOO)/(gross heat input), percent. Gross heat input - solar input x R, Btu./(hr)(ft ). Net efficiency - (heat recovered )(100)/( net heat input), percent. Net heat input - gr.oss heat input x t, Btu./(hr)(ft ), 153. XI APPENDIX D LITERATURE CITATIONS 1. Mouchot, A., Gauthier-Villars, "Solar Heat,- Its Industrial Applications," Paris, (l879). 2. Abbot, C. G., "The Sun and the Welfare of Man," Smithsonian Scientific Series , vol. 2, pp. 1^6, 203, (1934). 3. Man^on, M.H., "New -Results on the Utilization of Solar Heat at Paris," Comptes Rendus, vol. 91, ?. 3^8 (l88C). 4. Ackermann, A. S. E., "The Utilization of Solar Energy," Journal of the Ro yal Society of Arts . vol. 63, p. 538, (1514-15) 5. Ericsson, J., "The Sun Motor and the Sun's Temperature,", Scientific American Supplement . vol. 17, p. 6727 (l884). 6. 7/illsie, H. -.7., "Experiments in the Development of Power From the Sun's Heat," Engineering Nev;s , vol. 6l, p. 511 (1909). 7. Shuman, "Power from the Sun's Heat," Engineering News, vol. 6l, p. 509, (1909). 8. Abbot, C. G., "Utilizing Heat From the Sun," Smithsonian Miscellaneous Collections , vol. 98, No. 5, ( 1 9 3 9 ) • 9. Hottel, H. C. and V'oertz, B. E., "The Performance of Flat -Plate Solar Heat Collectors," American Soc . Me c h . Eng . Trans . , vo i £,4 P. 51, (1942). 10. tiller, K. '7., "Solar fteat Trap," a :. r..ofafldur to the Office of Production Research' and Development, "ar Production Doard, July 12, 1943. 11. Enrinoerin; Expcri. ent Station, University of Colorado "Progress; Report I, Solar Radiation Investigation," I'ov. 1, 1S43. 12. Ibid. M r'ro~ress Report II, Solur RaUiatior. Investi -tion," Dect: ber 23, I943. 13. Ibid. "Prorrecs Report III, Solar Ka istion Investigation," February 21, 194<1 . 14. Ibid, "frorreue Report IV, Solar Radiatior. Invest i«-aticn," Juno 2C, 1$4<, 15. Ibid, "Progress Report V, Solar Radiation Investigation," December 16, 1944. 154. 16. Fisher and Porter Ccrr.pany, "Theory of the Rotameter," Catalog Section 98-Y, Hatboro, Pennsylvania. 17. Mc Adams, "'. H. , Heat Transmission , Second Ed., McGraw-Hill Book Company, Inc., New York, (194-2). 18. Schack, A., "Der Industrielle Warmeubergang," Verlag Stahleisen, Dusseldorf, (1929). 19. Public Service Company of Colorado, Private Communication, August, 1945. ?0. Prien, C.'-H., Private Communication, September, 1944. 21. Davis, D. S,, Empirical Equations and Nomography , First Ed., McGraw-Hill Book Co., New York, '(194-3)"" 22. C. L. Berger. and Sons, Inc., Boston, -ass., " Solar Ephcr.eris and Polaris Tables ", 1944, 23. I. F. Hand - Private Communication, Dec. 30, 1943, June 5, 1944