17.1 SECTION 17 SOLAR ENERGY Analysis of Solar Electric Generating System Loads and Costs 17.1 Economics of Investment in an Industrial Solar-Energy System 17.4 Designing a Flat-Plate Solar-Energy Heating and Cooling System 17.6 Determination of Solar Insolation on Solar Collectors Under Differing Conditions 17.13 Sizing Collectors for Solar-Energy Heating Systems 17.15 F Chart Method for Determining Useful Energy Delivery in Solar Heating 17.17 Domestic Hot-Water Heater Collector Selection 17.24 Passive Solar-Heating System Design 17.29 Determining if a Solar Water Heater Will Save Energy 17.36 Sizing a Photovoltaic System for Electrical Service 17.37 Economics and Applications ANALYSIS OF SOLAR ELECTRIC GENERATING SYSTEM LOADS AND COSTS Analyze the feasibility of a solar electric generating system (SEGS) for a power system located in a sub-tropical climate. Compare generating loads and costs with conventional fossil-fuel and nuclear generating plants. Calculation Procedure: 1. Determine when a solar electric generating system can compete with conventional power Solar electric generation, by definition, requires abundant sunshine. Without such sunshine, any proposed solar electric generating plant could not meet load demands. Hence, such a plant could not compete with conventional fossil-fuel or nuclear plants. Therefore, solar electric generation, is at this time, restricted to areas having high concentrations of sunshine. Such areas are in both the subtropical and tropical regions of the world. One successful solar electric generating system is located in the Mojave Desert in southern California. At this writing, it has operated successfully for some 12 years with a turbine cycle efficiency of 37.5 percent for a solar field of more than 2-million ft 2 (1,805,802 m 2 ). A natural-gas backup system has a 39.5 percent effi- Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS 17.2 ENVIRONMENTAL CONTROL Cooling tower Pre-heater Steam generator Superheater Reheater SI Values FC 559 293 C 735 391 C FIGURE 1 Solar-generating-method schematic traces flow of heat-transfer fluid. (Luz International Ltd. and Power.) ciency. Both these levels of efficiency are amongst the highest attainable today with any type of energy source. 2. Sketch a typical cycle arrangement Technology developed by Luz International Ltd. uses a moderate-pressure state-of- the-art Rankine-cycle steam-generating system using solar radiation as its primary energy source, Fig. 1. In the Mojave Desert plant mentioned above, a solar field comprised of parabolic-trough solar collectors which individually track the sun using sun sensors and microprocessors provides heat for the steam cycle. Collection troughs in the Mojave Desert plant are rear surface mirrors bent into the correct parbolic shape. These specially designed mirrors focus sunlight onto heat-collection elements (HCE). Each mirror is washed every two weeks with de- mineralized water to remove normal dust blown off the desert. The mirrors must be clean to focus the optimal amount of the sun’s heat on the HCE. 3. Detail the sun collector arrangement and orientation With the parabolic mirrors described above, sun sensors begin tracking the sun before dawn. Microprocessors prompt the troughs to follow the sun, rotating 180 Њ each day. A central computer facility at the Mojave Desert plant monitors and controls each of the hundreds of individual solar collectors in the field and all of the power plant equipment and systems. During summer months when solar radiation is strongest, some mirrors must be turned away from the sun because there is too much heat for the turbine capacity. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY SOLAR ENERGY 17.3 Solar mode FIGURE 2 Firing modes are shown for typical summer day, left, and typical winter day, right. Correlation of solar generation to peaking power requirements is evident. (Luz International Ltd. and Power.) When this occurs, almost every other row of mirrors must be turned away. However, in the winter, when solar radiation is the weakest, every mirror must be employed to produce the required power. In the Mojave Desert plant, the mirrors focus the collected heat on the HCEs—coated steel pipes mounted inside vacuum-insulated glass tubes. The HCEs contain a synthetic-oil heat-transfer fluid, which is heated by the focused energy to approximately 735 Њ F (390.6 Њ C) and pumped through a series of conventional heat exchangers to generate superheated steam for the turbine-generator. In the Mojave Desert plant, several collectors are assembled into units called solar collector assemblies (SCA); generally, each 330-ft (100.6-m) row of collectors comprises one SCA. The SCAs are mounted on pylons and interconnected with flexible hoses. An 80-MW field consists of 852 SCAs arranged in 142 loops. Each SCA has its own sun sensor, drive motor, and local controller, and is comprised of 224 collector segments, or almost 5867 ft 2 (545 m 2 ) of mirrored surface and 24 HCEs. From this can be inferred that some (5867 /80) ϭ 73.3 ft 2 (6.8 m 2 ) per MW is required at this installation. 4. Plan for an uninterrupted power supply To ensure uninterrupted power during peak demand periods, an auxiliary natural- gas fired boiler is available at the Mojave Desert plant as a supplemental source of steam. However, use of this boiler is limited to 25 percent of the time by federal regulations. This boiler serves as a backup in the event of rain, for night production when called for, or if ‘‘clean sun’’ is unavailable. According to Luz International, clean sun refers to solar radiation untainted by smog, clouds, or rain. Figure 2 shows the firing modes for typical summer (left) and winter (right) days. Correlation of solar generation to peaking-power requirements is evident. As shown in the cycle diagram, the balance-of-plant equipment consists of the turbine-generator, steam generator, solar superheater, two-cell cooling tower, and an intertie with the local utility company, Southern California Edison Co. The Mojave Desert installation represents some 90 percent of the world’s solar power production. Since installing it first solar electric generating system in 1984, a 13.8- MW facility, Luz has built six more SEGS of 30 MW each. Units 6 and 7 use third-generation mirror technology. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY 17.4 ENVIRONMENTAL CONTROL 5. Determine the costs of solar power SEGS are suited to utility peaking service because they provide up to 80 percent of their output during those hours of a utility’s greatest demand, with minimal production during low-demand hours. Cost of Luz’s solar-generated power is less than that of many nuclear plants—$0.08/kWh, down from $0.24 /kWh for the first SEGS, according to com- pany officials. Should the price of oil go up beyond $20/barrel, solar will become even more competitive with conventional power. But the advantages over conventional power sources include more than cost- competitiveness. Emissions levels are much lower—10 ppm—because the sun is essentially non-polluting. SEGS are equipped with the best available technology for emissions cleanup during the hours they burn natural gas, the only time they produce emission. Related Calculations. Luz International Ltd. has installed more capacity at the Mojave Desert plant mentioned here, proving the acceptance and success of its approach to this important technical challenge. That data in this procedure can be useful to engineers studying the feasibility of solar electric generation for other sites around the world. Luz received an Energy Conservation Award from Power magazine, from which the data and illustrations in this procedure were obtained. There are estimates showing that the sunshine impinging the southwestern United States is more than enough to generate the entire electrical needs of the country—when efficient conversion apparatus is developed. It may be that the equipment described here will provide the efficiency needed for large-scale pollu- tion-free power generation. Results to date have been outstanding and promise greater efficiency in the future. ECONOMICS OF INVESTMENT IN AN INDUSTRIAL SOLAR-ENERGY SYSTEM Determine the rate of return and after tax present value of a new industrial solar energy system. The solar installation replaces all fuel utilized by an existing fossil- fueled boiler when optimum weather conditions exist. The existing boiler will be retained as an auxiliary unit. Assume a system energy output (E s )of3 ϫ 10 9 Btu /yr (3.17 kJ ϫ 10 9 /yr) an initial cost for the total system of $503,000 based on a collector area (A c ) of 10,060 ft 2 (934.6 m 2 ), a depreciation life (DP) of 12 yr, a tax rate ( ␶ ) of 0.4840, a tax credit factor (TC) of 0.25, a system life of 20 yr, an operating cost fraction (OMPI) of 0.0250, an initial fuel cost (P f 0 ) of $3.11/MBtu ($3.11/ 947.9 MJ) and a fuel price escalation rate (e) of 0.1450. Calculation Procedure: 1. Compute unit capacity cost (K s ) in $/million Btu per year initial cost of system $503,000 K ϭϭ s 9 E 3 ϫ 10 Btu /yr s $167.67 ϭ ($167.67/ 947.9 MJ /yr). 1 million Btu/ yr Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY SOLAR ENERGY 17.5 2. Compute levelized coefficient of initial costs (M ) over the life of the system CRF TC R,N M ϭ OMPI ϩ 1 ϪϪ ( ␶ ϫ DEP) ͫͩ ͪ ͬ 1 Ϫ ␶ 1 ϩ R CRF R,N is the capital recovery factor which is a function of the market discount rate (R)* over the expected lifetime of the system (20 yr) and is determined as follows: R CRF ϭ R,20 Ϫ 20 1 Ϫ (1 ϩ R) DEP is the depreciation which will be calculated by an accelerated method, the sum of the years digits (SOYD), in accordance with the following formula: 21 DEP ϭ DP Ϫ ͩͪ DP(DP ϩ 1)R CRF R,DP where DP is an allowed depreciation period, or tax life, of 12 yr. Prepare a tabulation (see below) of M values for various market discount rates (R). 3. Compute the levelized cost of solar energy (S), for the life cycle of the system in $/million Btu ($/MJ) Use the relation, S ϭ (K s )(M). Since M varies with R, refer to the tabulation of S for various market discount rates. 4. Compute the levelized cost of fuel (F) in $/ million Btu ($/MJ) and compare to S N P 1 ϩ e 1 ϩ e ƒ0 F ϭ CRF 1 Ϫ ͫ ͩ ͪͩ ͫ ͬ ͪͬ R,N ␩ R Ϫ e 1 ϩ R where ␩ is the boiler efficiency for a fossil fuel system which supplies equivalent heat. Referring to the tabulation, the value of F is tabulated at various market discount rates for ␩ values of 70, 80, and 100 percent. The rate of return for the solar installation is that value of R at which F ϭ S.For ␩ ϭ 70 percent, R is between 7.5 and 8.0 percent. For ␩ ϭ 80 percent, R is between 6.5 and 7.0 percent. These rates of return should exceed current interest (discount) rates to attain eco- nomic feasibility. 5. Compute the after tax present value (PV) of the solar investment if the existing boiler installation has an efficiency of 70 percent 1 Ϫ ␶ PV ϭ E (F Ϫ S) ͩͪ s CRF R,N In order to have a positive value of PV, F must exceed S. Therefore, select a market discount rate (R) from the tabulation which satisfies this criteria. For example, at a 5 percent discount rate, *See tabulation on page 17.6. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY 17.6 ENVIRONMENTAL CONTROL 9 3 ϫ 10 1 Ϫ 0.484 PV ϭ (20.00 Ϫ 13.91) ϭ $117,489.02 ͩͪ 6 10 0.08024 Note that at 8 percent or higher PV will be negative and the investment proves uneconomical against other investment options. F R* CRF R,N CRF R,DP DEP (SOYD) MS ␩ ϭ 100% ␩ ϭ 80% ␩ ϭ 70% 4.5 0.07688 0.10967 0.8210 0.07915 13.27 14.29 17.86 20.41 5.0 0.08024 0.11283 0.8044 0.08295 13.91 14.00 17.50 20.00 5.5 0.08368 0.11603 0.7882 0.08686 14.56 13.71 17.14 19.59 6.0 0.08718 0.11928 0.7727 0.09093 15.25 13.43 16.79 19.19 6.5 0.09076 0.12257 0.7577 0.09511 15.95 13.16 16.45 18.80 7.0 0.09439 0.12590 0.7431 0.09940 16.67 12.89 16.11 18.41 7.5 0.09809 0.12928 0.7290 0.10382 17.41 12.63 15.79 18.04 8.0 0.10185 0.13270 0.7154 0.10833 18.16 12.38 15.47 17.69 *As used in engineering economics, R, discount rate and interest rate refer to the same percentage. The only difference is that interest refers to a progression in time, and discount to a regression in time. See ‘‘Engineering Economics for P.E. Examinations,’’ Max Kurtz, McGraw-Hill. REFERENCE Brown, Kenneth C., ‘‘How to Determine the Cost-Effectiveness of Solar Energy Projects,’’ Power magazine, March, 1981. DESIGNING A FLAT-PLATE SOLAR-ENERGY HEATING AND COOLING SYSTEM Give general design guidelines for the planning of a solar-energy heating and cool- ing system for an industrial building in the Jacksonville, Florida, area to use solar energy for space heating and cooling and water heating. Outline the key factors considered in the design so they may be applied to solar-energy heating and cooling systems in other situations. Give sources of pertinent design data, where applicable. Calculation Procedure: 1. Determine the average annual amount of solar energy available at the site Figure 3 shows the average amount of solar energy available, in Btu /(day ⅐ ft 2 ) (W/m 2 ) of panel area, in various parts of the United States. How much energy is collected depends on the solar panel efficiency and the characteristics of the storage and end-use systems. Tables available from the National Weather Service and the American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE) chart the monthly solar-radiation impact for different locations and solar insolation [total radiation form the sun received by a surface, measured in Btu/(h ⅐ ft 2 ) (W/m 2 ); Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY SOLAR ENERGY 17.7 FIGURE 3 Average amount of solar energy available, in Btu / (day ⅐ ft 2 ) (W/m 2 ), for different parts of the United States. (Power.) insolation is the sum of the direct, diffuse, and reflected radiation] for key hours of a day each month. Estimate from these data the amount of solar radiation likely to reach the surface of a solar collector over 1 yr. Thus, for this industrial building in Jacksonville, Florida, Fig. 3 shows that the average amount of solar energy available is 1500 Btu/ (day ⅐ ft 2 ) (4.732 W/m 2 ). When you make this estimate, keep in mind that on a clear, sunny day direct radiation accounts for 90 percent of the insolation. On a hazy day only diffuse radiation may be available for collection, and it may not be enough to power the solar heating and cooling system. As a guide, the water temperatures required for solar heating and cooling systems are: Space heating Up to 170 Њ F (76.7 Њ C) Space cooling with absorption air conditioning From 200 to 240 Њ F (93.3 to 114.6 Њ C) Domestic hot water 140 Њ F (60 Њ C) 2. Choose collector type for the system There are two basic types of solar collectors: flat-plate and concentrating types. At present the concentrating type of collector is not generally cost-competitive with the flat-plate collector for normal space heating and cooling applications. It will probably find its greatest use for high-temperature heating of process liquids, space cooling, and generation of electricity. Since process heating applications are not the subject of this calculation procedure, concentrating collectors are discussed sepa- rately in another calculation procedure. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY 17.8 ENVIRONMENTAL CONTROL FIGURE 4 Construction details of flat-plate solar collectors. (Power.) Flat-plate collectors find their widest use for building heating, domestic water heating, and similar applications. Since space heating and cooling are the objective of the system being considered here, a flat-plate collector system will be a tentative choice until it is proved suitable or unsuitable for the system. Figure 4 shows the construction details of typical flat-plate collectors. 3. Determine the collector orientation Flat-plate collectors should face south for maximum exposure and should be tilted so the sun’s rays are normal to the plane of the plate cover. Figure 5 shows the optimum tilt angle for the plate for various insolation requirements at different latitudes. Since Jacksonville, Florida, is approximately at latitude 30 Њ , the tilt of the plate for maximum year-round insolation should be 25 Њ from Fig. 5. As a general rule for heating with maximum winter insolation, the tilt angle should be 15 Њ plus the angle of latitude at the site; for cooling, the tilt angle equals the latitude (in the south, this should be the latitude minus 10 Њ for cooling); for hot water, the angle of tilt equals the latitude plus 5 Њ . For combined systems, such as heating, cooling, and hot water, the tilt for the dominant service should prevail. Alternatively, the tilt for maximum year-round insolation can be sued, as was done above. When collector banks are set in back of one another in a sawtooth arrangement, low winter sun can cause shading of one collector by another. This can cause a Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY SOLAR ENERGY 17.9 FIGURE 5 Spacing of solar flat-plate collec- tors to avoid shadowing. (Power.) TABLE 1 Spacing to Avoid Shadowing, ft (m) Њ loss in capacity unless the units are carefully spaced. Table 1 shows the minimum spacing to use between collector rows, based on the latitude of the installation and collector tilt. 4. Sketch the system layout Figure 6 shows the key components of a solar system using flat-plate collectors to capture solar radiation. The arrangement provides for heating, cooling, and hot- water production in this industrial building with sunlight supplying about 60 percent of the energy needed to meet these loads—a typical percentage for solar systems. For this layout, water circulating in the rooftop collector modules is heated to 160 Њ F (71.1 Њ C) to 215 Њ F (101.7 Њ C). The total collector area is 10,000 ft 2 (920 m 2 ). Excess heated hot water not need for space heating or cooling or for domestic water is directed to four 6000-gal (22,740-L) tanks for short-term energy storage. Con- ventional heating equipment provides the hot water needed for heating and cooling during excessive periods of cloudy weather. During a period of 3 h around noon on a clear day, the heat output of the collectors is about 2 million Btu/ h (586 kW), with an efficiency of about 50 percent at these conditions. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY 17.10 ENVIRONMENTAL CONTROL FIGURE 6 Key components of a solar-energy system using flat-plate collectors. (Power.) For this industrial building solar-energy system, a lithium-bromide absorption air-conditioning unit (a frequent choice for solar-heated systems) develops 100 tons (351.7 kW) of refrigeration for cooling with a coefficient of performance of 0.71 by using heated water from the solar collectors. Maximum heat input required by this absorption unit is 1.7 million Btu/h (491.8 kW) with a hot-water flow of 240 gal/ min (909.6 L/ min). Variable-speed pumps and servo-actuated valves control the water flow rates and route the hot-water flow from the solar collectors along several paths—to the best exchanger for heating or cooling of the building, to the absorption unit for cooling of the building, to the storage tanks for use as domestic hot water, or to short-term storage before other usage. The storage tanks hold enough hot water to power the absorption unit for several hours or to provide heating for up to 2 days. Another—and more usual—type of solar-energy system is shown in Fig. 7. In it a flat-plate collector absorbs heat in a water/antifreeze solution that is pumped to a pair of heat exchangers. From unit no. 1 hot water is pumped to a space-heating coil located in the duct work of the hot-air heating system. Solar-heated antifreeze solution pumped to unit no. 2 heats the hot water for domestic service. Excess heated water is diverted to fill an 8000-gal (30,320-L) storage tank. This heated water is used during periods of heavy cloud cover when the solar heating system cannot operate as effectively. 5. Give details of other techniques for solar heating Wet collectors having water running down the surface of a tilted absorber plate and collected in a gutter at the bottom are possible. While these ‘‘trickle-down’’ collec- tors are cheap, their efficiency is impaired by heat losses from evaporation and condensation. Air systems using rocks or gravel to store heat instead of a liquid find use in residential and commercial applications. The air to be heated is circulated via ducts to the solar collector consisting of rocks, gravel, or a flat-plate collector. From here other ducts deliver the heated air to the area to be heated. In an air system using rocks or gravel, more space is needed for storage of the solid media, compared to a liquid. Further, the ductwork is more cumbersome and Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. SOLAR ENERGY [...]... 11,100 ft2 (1032.3 m2) of evacuatedtube solar panels on the roof of their single-level parking structure These panels provide heating, cooling, and domestic hot water for two of the buildings on the campus Energy output of these evacuated-tube collectors is some 3 billion Btu (3.2 ϫ 109 kJ), producing a fuel-cost savings of $25,000 during the first year of installation The use of evacuated-tube collectors... number of days of the month The summation of the heat gains for each space for each Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website SOLAR ENERGY SOLAR ENERGY 17.35 month of the heating season is divided by the summation of the heat... average recovery of 40 percent of 1200 Btu / ft2 (3785 W / m2) of solar energy of sloping surface would require approximately 100 ft2 (9.3 m2) of collector for the 50,000Btu (52,750-kJ) average daily requirement Such a design would provide essentially all the hot-water needs on an average winter day, but would fall short on days of less than average sunshine By contrast, a 50 percent recovery of an average... heat losses of a Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website SOLAR ENERGY 17.30 ENVIRONMENTAL CONTROL space The collector area can be estimated for purposes of heat-loss calculations from Table 8 Table 8 lists ranges of the estimated... and walls, resulting in a weighted average of CS ϭ 0.60 Thus, VM ϭ 35,352 / (144)(0.22)(15)(0.60) ϭ 124 ft3 (3.5 m3) As a rule of thumb for thermal storage wall systems, provide a minimum of 1 ft3 (0.30 m3) of dark-colored thermal storage material per square foot (meter) of collector for masonry walls or 0.5 ft3 (0.15 m3) of water per square foot (meter) of collector for a water wall This will provide... that of the latitude of Grand Forks, Minnesota, or 48Њ, since this produces the maximum performance for any solar collector Next, use tabulations of mean percentage of possible sunshine and solar position and insolation for the latitude of the installation Such tabulations are available in ASHRAE publications and in similar reference works List, for each month of the year, the mean percentage of possible... (47.6 m3) Entering Table 9 at the left for the physical description of the space, read to the right for n, the number of air changes per hour This space has windows on two walls, so n ϭ 1 Thus, Hi ϭ (1680)(1)(65 Ϫ 32) / 55 ϭ 1008 Btu / h (295.4 W) The total heat loss of the space is the sum of the individual heat losses of glass, wall, roof, and infiltration Therefore, the total heat loss for this space... by the editor of this handbook The P chart mentioned as part of the Ps calculation is a trademark of the Solar Energy Design Corporation, POB 67, Fort Collins, Colorado 80521 Developed by Arney, Seward, and Kreider for passive predictions of solar performance, the P chart uses only the building heat load in Btu / (ЊF ⅐ day) The P chart will specify the solar fraction and optimum size of three passive... conductive heat loss of the roof, use the same general relation as above, substituting the U value and area of the roof Thus, U ϭ 0.029 Btu / (h ⅐ ft2 ⅐ ЊF) [0.16 W / (m2 ⅐ K)] and A ϭ 210 ft2 (19.5 m2) Then HC ϭ UA ⌬t ϭ (0.029)(210)(65 Ϫ 32) ϭ 201 Btu / h (58.9 W) To calculate infiltration heat loss, use the relation Hi ϭ Vn ⌬t / 55, where V ϭ volume of heated space, ft3 (m3); n ϭ number of air changes per... h with the nighttime average temperature Table 8 is based on a heat loss of 8 Btu / (day ⅐ ft2) of floor area per ЊF [W / (m2 ⅐ K)] Total building heat loss will increase with the increase in the ratio of collector to floor area because of the larger areas of glazing However, it is assumed that this increase in heat loss will be offset by providing higher insulation values in noncollector surfaces The . reserved. Any use is subject to the Terms of Use as given at the website. Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS 17.2 ENVIRONMENTAL CONTROL. life (DP) of 12 yr, a tax rate ( ␶ ) of 0.4840, a tax credit factor (TC) of 0.25, a system life of 20 yr, an operating cost fraction (OMPI) of 0.0250,