Energy Efficient BuildingsSequence of Analysis; Building Energy Balance; Weather Data

Building Energy Use in the U.S.

U.S. building energy use is described in figures below. This class will focus on increasing renewable energy use in buildings and on improving the energy efficiency of space heating, space cooling and lighting.

Source: Buildings Energy Data Book, U.S. Department of Energy

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Sequence of AnalysisThe sequence for designing a building heating and cooling system is shown below.

Our sequence in class:1. Design space to minimize space loads and energy use2. Design distribution system to minimize distribution loads and energy use3. Design primary heating and cooling system to minimize plant energy use

Building Energy BalanceHeat flows into and out of a space are typically called “loads”. To determine the net load on a space, sum the components of the load in an energy balance.

Net Heating LoadDuring winter, the major sources of heat gain/loss into/from a building are shown below.

The net heat loss out is called the heating load. Based on an energy balance, the net heat load out is:

Qnet,out = (Qwalls + Qwindows + Qceiling + Qdoors + Qinfiltration + Qground)out – (Qsolar + Qpeople + Qelectricity)in

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Design Space

Calculate Space Heating/Cooling

Loads

Design Distribution System

Calculate

Distribution Loads

Design Plant

Size Plant to Meet Space and System

Loads

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Heating Energy UseTo maintain the interior of the building at a steady temperature, the furnace must provide enough heat to the space, Qfurnace, to balance the net energy loss from the space, Qnet,out. Because furnaces are not 100% efficient, some of the energy supplied to the furnace, Qnatural gas, is lost in the exhaust, Qexhaust.

Although energy balances can be written in a variety of forms, I strongly recommend writing energy balances in the following form:

∑ E in−∑ Eout=dE Or, on a rate basis:

∑ E in−∑ Eout=dEdt

In this case, an energy balance on the house gives:

Qfurnace – Qnet,out = (dE/dt)house = 0 (if the house temperature remains constant, i.e. Steady State)

It follows that:

Qfurnace = Qnet,out

Efficiency is defined as:

η=useful outputrequired input

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In the case of a furnace, the useful output is Qfurnace and the required input is Qnatural gas. Thus, the efficiency of a furnace is:

η furnace = Qfurnace / Qnatural gas

The efficiencies of furnaces have improved over the years from about 65% to 95%. The efficiency equation can be rearranged to determine the natural gas energy use consumed by the furnace.

Qnatural gas = Qfurnace / η furnace

Example

Consider a building has the following average loads in winter:Qpeople = 13,000 Btu/h, Qsolar = 3,000 Btu/h, Qelec = 3,000 Btu/h, Qwalls = 20,000 Btu/h, Qwindows = 15,000 Btu/hr, Qdoors=1,500 Btu/hr, Qceiling = 12,500 Btu/hr, Qinfiltration = 15,000 Btu/hr, Qground = 5,000 Btu/hr.

Calculate the Qnet,out of the building.

Qnet,out = (Qwalls + Qwindows + Qceiling + Qdoors + Qinfiltration + Qground)out – (Qsolar + Qpeople + Qelectricity)in

Qnet,out = (20,000+15,000+12,500+1,500+15,000+5,000)Btu/hr – (3,000+13,000+3,000) Btu/hr

Qnet,out = 50,000 Btu/hr

The furnace of this building operates 1,000 hours over the winter and is 80% efficient. Natural gas costs $10 /mmBtu. Calculate the cost of fuel for the furnace over a winter.

Qfurnace = Qnet,out = 50,000 Btu/hrQnatural gas = Qfurnace / η furnace = 50,000 Btu/hr / 80% = 62,500 Btu/hrQnatural gas, yr = Qnatural gas x HPY = 62,500 Btu/hr x 1,000 hr/yr = 625,500,000 Btu/yrCnatural gas, yr = Qnatural gas,yr x Cng = 625.5 mmBtu/yr x $10 /mmBtu = $6,255 /yr

Net Cooling LoadDuring summer, the major sources of gain into a building are shown below. Note that ground losses/gains in the summer are typically small and are here assumed to be negligible.

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The net heat load into a building is called the cooling load. Based on an energy balance, the net heat load in is:

Qnet,in = (Qsolar + Qpeople + Qelectricity + Qwalls + Qwindows + Qceiling + Qdoors + Qinfiltration)in

Cooling Energy UseTo maintain the interior of the building at a steady temperature, the air conditioner must remove enough heat from the space, Qac, to balance the net energy gain to the space, Qnet,in.

In this case, an energy balance on the house gives:

Qnet,in – Qac = (dE/dt)house = 0 (SS)

It follows that:

Qac = Qnet,in

To pump heat “uphill” from the cool space to the hot outdoors, electric air conditioners require electrical energy Welec. As before, efficiency is defined as:

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η=useful outputrequired input

For an electric air conditioner, the useful output is Qac and the required input is Welec . Thus, the efficiency of the air conditioner is:

η ac = Qac / Welec

The efficiency equation can be rearranged to determine the electricity consumed by an air conditioner.

Welec = Qac / η ac

The efficiency of air conditioners is measured in several ways. The coefficient of performance (COP) is a non-dimensional measure of steady state efficiency at a single set of operating conditions. The COP of typical air conditioners is about 3, which means that an air conditioner removes 3 units of heat from a space for every unit of electrical work it consumes. Air conditioner efficiency varies with the temperature of the air returned to the air conditioner and the temperature of the outdoor air to which heat is rejected. The average efficiency rating of air conditioners over a season is reported as the Seasonal Energy Efficiency Rating (SEER) with units Btu/Wh. The electricity consumed by an air conditioner can be calculated using either COP or SEER with proper attention to units. Welec = Qac / η ac = Qnet,in / COPac = Qnet,in / SEER

Example

Consider a building has the following average loads in summer:Qpeople = 3,500 Btu/h, Qsolar = 11,000 Btu/h, Qelec = 7,500 Btu/h, Qwalls = 2,500 Btu/h, Qwindows = 3,000 Btu/hr, Qdoors=750 Btu/hr, Qceiling = 750 Btu/hr, Qinfiltration = 3,000 Btu/hr.

Calculate the Qnet,in of the building.

Qnet,in = (Qsolar + Qpeople + Qelectricity + Qwalls + Qwindows + Qceiling + Qdoors + Qinfiltration)in Qnet,in = (11,000 + 3,500 + 7,500 + 2,500 + 3,000 + 750 + 750 + 3,000) Btu/hrQnet,in = 32,000 Btu/hr

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The air conditioner for this building operates 1,000 hours over the summer, with a COP of 3.2. Electricity costs $0.10 /kWh. Calculate the cost of electricity for the air conditioner over the summer.

Qac = Qnet,in = 32,000 Btu/hrWelec = Qac / COP = (32,000 Btu/hr / 3.20) / 3,412 Btu/kWh= 2.93 kWWelec, yr = Welec x HPY = 2.93 kW x 1,000 hr/yr = 2,930 kWh/yrCelec, yr = Welec,yr x Celec = 2,930 kWh/yr x $0.10 /kWh = $293 /yr

ExampleCalculate the cost of operating an air conditioner over a summer if the average net cooling load is 36,000 Btu/hr, the SEER is 12 Btu/Wh, the air conditioner operates 1,000 hours over the summer, and electricity costs $0.10 /kWh.

Qac = Qnet,in = 36,000 Btu/hrWelec = Qac / SEER = (36,000 Btu/hr / 12 Btu/Wh) = 3.00 kWWelec, yr = Welec x HPY = 3.00 kW x 1,000 hr/yr = 3,000 kWh/yrCelec, yr = Welec,yr x Celec = 3,000 kWh/yr x $0.10 /kWh = $300 /yr

Weather DataThe net heat gain or loss to buildings depends on weather. The three most important weather variables are:

Outdoor air dry-bulb temperature Outdoor air humidity Solar radiation

Three types of weather data are commonly used for building heating and air conditioning design and analysis:

Typical weather (for estimating typical energy use or savings) Actual weather (for calibrating energy use calculated by a theoretical model to

measured energy use) Design weather (for calculating maximum expected building loads to size heating

and air conditioning equipment)

Typical Weather Data (TMY2, TMY3 and EPW files)To determine typical weather conditions, meteorologists analyzed 30 years (1961- 1990) of hourly data from 239 U.S. weather stations. Based on this data, meteorologists created “Typical Meteorological Year”, TMY, files for U.S. locations. The second

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generations of these files are called TMY2 files. The third generation of these files are called TMY3 or TM3 files, and are derived from data from 1991-2005. In this class, we will use TMY3 files. TMY3 sites are noted as Class I, Class II or Class III, with the most robust data from Class I sites.

TMY3 files use commas to separate the fields (i.e. they are “comma delimited”), and carry the field name extenstion *.csv. The *.csv files can be read directly into Microsoft Excel. After input into Microsoft Excel, the two header lines and first eight fields of the first three data records of the TMY3 file for Dayton, Ohio are shown below. The first header line indicates site number, site name, site state, timezone, longitude, latitude and elevation (m). The second header line indicates the name and units of each data field. The file then includes 8,760 hourly records (rows) of data, with each record containing 68 fields (columns). TMY3 files use SI units.

724290 DAYTON INTERNATIONAL AIRPORT OH -5 39.9 -84.217 305Date (MM/DD/YYYY) Time (HH:MM) ETR (W/m^2) ETRN (W/m^2) GHI (W/m 2) GHI source GHI uncert (%) DNI (W/m^2)

1/1/1976 1:00 0 0 0 1 0 01/1/1976 2:00 0 0 0 1 0 01/1/1976 3:00 0 0 0 1 0 0

TMY3 files for 1,020 U.S. locations, and a manual which describes the data, can be downloaded from the National Renewable Energy Laboratory at:

http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/tmy3/

Many building energy simulation programs use these files as input, since these files represent the typical meteorological conditions for a given site and contain data on a short enough time interval to quantify many transient effects. Because they represent typical rather than extreme conditions, they are not suited for designing systems to meet the worst-case conditions occurring at a location.

The U.S. Department of Energy is developing a new building energy simulation program called Energy Plus. The weather files for Energy Plus are called Energy Plus Weather, EPW, files. EPW files contain the same data as TMY2 files, with the advantage of being available for many international locations. EPW files, and a manual which describes the data, can be downloaded from:

http://www.eere.energy.gov/buildings/energyplus/

WeaTran Weather Data TranslatorThe weather translator software, WeaTran, can read TMY2, TMY3 and EPW files and create smaller simpler files that still contain the essential solar, temperature and humidity data. The output files from WeaTran are easily loaded into spreadsheets for further analysis. In addition, Weatran can calculate solar radiation on up to four vertical

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exposures from data in the input file. WeaTran reads hourly TMY2, TMY3 or EPW files and makes two types of output files. The first type contains time series data and the second type contains “bin” data. WeaTran can be downloaded from a link on the class homepage.

WeaTran Time Series DataTo produce time series output files, WeaTran translates hourly TMY2, TMY3 or EPW files into either hourly, daily, or monthly time intervals, depending on user specification. In addition, WeaTran also translates hourly TMY2, TMY3 or EPW files into day-type output, which includes one representative day of hourly data from each month. Data output files are named according to the following convention:

First set of characters are the basename of TMY or EPW file Second two characters are either “HR”, “DY”, “MO” or “DT” corresponding to

whether the output file contains hourly, daily, monthly or day-type data. Last two characters are either “US” or “SI” depending on whether the output

data are reported in US or SI unts The filename extension is .TXT

If US units are specified, in each data file: Ta(F) = average air dry-bulb temperatureSol-H(Btu/ft2dy) = total solar radiation on a horizontal surfaceSol-E(Btu/ft2dy) = total solar radiation on a vertical east-facing surfaceSol-S(Btu/ft2dy) = total solar radiation on a vertical south-facing surfaceSol-W(Btu/ft2dy) = total solar radiation on a vertical west-facing surfaceSol-N(Btu/ft2dy) = total solar radiation on a vertical north-facing surfacew(lbw/lba) = average air specific humidityTg(F) = average effective ground temperature

For example, the first 10 records from the hourly time series output file DaytonOH_HR_US.TXT and U.S. units from input file DaytonOH. TMY3 are shown below.

Mo Dy Yr Hr Ta(F) Sol-H(Btu/ft2hr) Sol-E(Btu/ft2hr) Sol-S(Btu/ft2hr) Sol-W(Btu/ft2hr) Sol-N(Btu/ft2hr) w(lbw/lba) Tg(F)1 1 1995 1 32 0 0 0 0 0 0.0032 47.41 1 1995 2 32 0 0 0 0 0 0.003 47.391 1 1995 3 32 0 0 0 0 0 0.003 47.391 1 1995 4 32 0 0 0 0 0 0.0028 47.391 1 1995 5 32 0 0 0 0 0 0.0027 47.381 1 1995 6 30.92 0 0 0 0 0 0.0027 47.381 1 1995 7 30.92 0 0 0 0 0 0.0027 47.381 1 1995 8 30.92 0 0 0 0 0 0.0027 47.371 1 1995 9 30.02 9 5 5 4 4 0.0027 47.371 1 1995 10 30.92 51 81 81 17 17 0.003 47.37

The first 10 records from the daily time series output file DaytonOH_DY_US.TXT and U.S. units from input file DaytonOH. TMY3 are shown below.

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Mo Dy Yr Ta(F) Sol-H(Btu/ft2dy) Sol-E(Btu/ft2dy) Sol-S(Btu/ft2dy) Sol-W(Btu/ft2dy) Sol-N(Btu/ft2dy) w(lbw/lba) Tg(F)1 1 1995 32.39 365 247 281 183 174 0.0029 47.361 2 1995 35.35 281 149 166 151 143 0.0038 47.291 3 1995 24.6 534 253 612 411 206 0.0021 47.211 4 1995 8.93 633 282 890 346 174 0.0009 47.051 5 1995 9.79 420 301 438 273 175 0.001 46.851 6 1995 25.68 627 401 841 275 192 0.002 46.711 7 1995 29.48 360 190 231 194 179 0.0029 46.631 8 1995 4.89 921 476 1823 495 61 0.0008 46.471 9 1995 3.5 900 525 1743 440 74 0.0008 46.281 10 1995 17.73 489 265 470 302 207 0.0015 46.12

The 12 records from the monthly time series output file DaytonOH_MO_US.TXT and U.S. units from input file DaytonOH. TMY3 are shown below.

Mo Yr Ta(F) Sol-H(Btu/ft2dy) Sol-E(Btu/ft2dy) Sol-S(Btu/ft2dy) Sol-W(Btu/ft2dy) Sol-N(Btu/ft2dy) w(lbw/lba) Tg(F)1 1995 24.6 571 288 707 321 173 0.0023 45.682 1995 26.92 824 427 851 410 214 0.0025 43.13 1995 42.48 1164 579 860 548 277 0.004 42.724 1995 51.72 1516 730 809 634 313 0.0052 45.735 1995 63.36 1773 808 694 771 395 0.0072 49.546 1995 70.31 1947 859 643 786 410 0.011 53.697 1995 75.04 1893 844 680 830 411 0.0139 56.548 1995 72.77 1644 773 776 740 365 0.0129 58.799 1995 63.64 1381 630 980 638 285 0.0105 59.1210 1995 51.2 1001 495 1016 492 216 0.0056 56.9611 1995 40.94 614 334 703 317 191 0.0042 53.5812 1995 30.85 485 234 666 259 138 0.0032 49.48

The first 10 records from the day-type output file DaytonOH_DT_US.TXT and U.S. units from input file DaytonOH. TMY3 are shown below. To create day-type files, WeaTran selects the single day in each month with the average temperature closest to the monthly average temperature, and prints all 24 hours for that day. Thus, day-type files contain a header line plus 12 x 24 = 288 records.

Mo Dy Yr Hr Ta(F) Sol-H(Btu/ft2hr) Sol-E(Btu/ft2hr) Sol-S(Btu/ft2hr) Sol-W(Btu/ft2hr) Sol-N(Btu/ft2hr) w(lbw/lba) Tg(F)1 3 1995 1 30.92 0 0 0 0 0 0.0031 47.251 3 1995 2 32 0 0 0 0 0 0.0032 47.251 3 1995 3 30.92 0 0 0 0 0 0.0031 47.251 3 1995 4 30.02 0 0 0 0 0 0.0031 47.241 3 1995 5 30.02 0 0 0 0 0 0.0031 47.241 3 1995 6 30.02 0 0 0 0 0 0.0027 47.241 3 1995 7 28.04 0 0 0 0 0 0.0025 47.241 3 1995 8 26.96 0 0 0 0 0 0.0024 47.231 3 1995 9 26.06 10 7 7 5 5 0.0023 47.231 3 1995 10 26.06 39 38 38 18 18 0.0023 47.23

Time series output files from WeaTran can be loaded into Excel by opening the text file, and specifying that the fields are ‘delimited’ by ‘spaces’.

WeaTran Bin DataWeaTran also translates hourly TMY2, TMY3 or EPW files into temperature bin data. A bin data file created from input file DaytonOH. TMY3 is shown below.

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StrTemp EndTemp T(F) Twb(F) h(Btu/lba) w(lbw/lba) hrs1-8 hrs9-16 hrs17-24 hrs1-24===== ===== ===== ===== ====== ===== ===== ===== ===== =====105 109 107 -99 -99 -99 0 0 0 0100 104 102 -99 -99 -99 0 0 0 095 99 97 -99 -99 -99 0 0 0 090 94 91 75.6 38.8 0.0154 0 5 0 585 89 87.4 74.6 38 0.0155 0 107 16 12380 84 82.2 70.9 34.9 0.0139 11 349 91 45175 79 76.9 68.1 32.7 0.013 53 293 217 56370 74 72.4 66 31.2 0.0126 231 212 263 70665 69 68.1 62.5 28.6 0.0112 308 212 274 79460 64 62.4 55.9 24.2 0.0085 305 288 270 86355 59 57 51 21.1 0.0069 225 208 224 65750 54 51.8 46.8 18.7 0.0058 238 179 253 67045 49 47.5 43 16.6 0.0048 180 120 187 48740 44 43.2 39.7 14.8 0.0041 262 177 244 68335 39 37.5 35.6 12.6 0.0034 308 165 220 69330 34 32.3 31.8 10.8 0.0028 232 235 174 64125 29 27.4 27.9 8.8 0.0021 128 121 141 39020 24 23.1 25 7.5 0.0018 157 87 127 37115 19 17.8 21.3 5.7 0.0014 118 79 105 30210 14 12.1 17.4 4 0.001 74 35 43 1525 9 7.2 14.2 2.6 0.0008 38 35 32 1050 4 2.5 11.2 1.3 0.0006 21 12 20 53-5 -1 -2 8.3 0 0.0005 25 1 14 40

-10 -6 -6.4 5.6 -1.1 0.0004 7 0 4 11-15 -11 -13 -99 -99 -99 0 0 0 0-20 -16 -18 -99 -99 -99 0 0 0 0-25 -21 -23 -99 -99 -99 0 0 0 0-30 -26 -28 -99 -99 -99 0 0 0 0

Dayton_OH.bin

WeaTran Heating and Cooling Degree Day Data WeaTran also translates hourly TMY2, TMY3 or EPW files into heating and cooling degree day data. The first 10 lines of heating and cooling degree day data created from input file DaytonOH. TMY3 are shown below. Tb (F) is the reference temperature from which the degree days (F-day/year) are calculated.

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Tb (F) HDD CDD==== ==== ====

40 1,446 5,56841 1,555 5,31242 1,668 5,05943 1,786 4,81244 1,910 4,57145 2,038 4,33446 2,169 4,10147 2,305 3,87148 2,448 3,64949 2,597 3,43350 2,757 3,228

Actual Weather DataTo improve the accuracy of theoretical models of building energy use, it is useful to compare the predicted energy use of the theoretical model to measured energy use of the building. The process of comparing the predicted energy use from theoretical models to measured energy use, and adjusting the theoretical model to improve the fit is called “calibrating the model”.

Actual Hourly Temperature and Humidity DataThe best source of weather data for calibrating models is measured hourly temperature, humidity and solar radiation data from the period during which the building energy use was measured. Unfortunately, however, it is often difficult to obtain measured hourly temperature, humidity and solar radiation data over specific periods. However, some actual hourly temperature, humidity and windspeed data are available at no charge from the Energy Plus web site at:

http://www.eere.energy.gov/buildings/energyplus/cfm/weatherdata/weather_request.cfm

NASA also operates posts actual weather and solar data at:

http://power.larc.nasa.gov/

Actual Average Daily Temperature DataIn contrast to hourly data, average daily temperature data are widely available. For example, average daily temperature data from 1995 to present for over 300 US and international sites are available for no charge from:

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http://academic.udayton.edu/kissock/http/Weather/default.htm

The first 10 records of the average daily temperature file for Dayton, OH is shown below.

1 1 1995 391 2 1995 19.61 3 1995 20.61 4 1995 11.31 5 1995 6.81 6 1995 231 7 1995 28.21 8 1995 24.71 9 1995 251 10 1995 23.6

Synthesized Hourly Temperature, Humidity and Solar DataBecause outdoor air temperature is typically the single most important weather variable influencing building energy use, hourly weather data files synthesized from average daily temperature data are often the best weather data available for calibrating models to measured energy use. The building energy simulation program, ESim, can synthesize hourly weather data from daily temperatures using solar geometry and the typical relations between weather variables. More information about synthesizing “near actual” hourly weather data from daily temperature data is available in the ESim help menu. ESim can be downloaded from the class homepage.

Design Weather DataDesign weather data sets include the hottest and coldest expected weather conditions for a location. This information is used to size heating and cooling systems so that they can handle the largest expected loads. Design weather data are available in the ASHRAE Fundamentals Handbook for 4,422 sites around the world. The full set of ASHRAE design data for Dayton Ohio, USA are shown below.

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Design Heating and Cooling TemperaturesFor heating, ASHRAE determined the “99.6%” and “99.0%” design conditions. This means that the actual hourly temperatures were greater (warmer) than the design temperature 99.6% or 99.0% of all annual hours. The peak heating load design temperatures for Dayton, OH are shown below. To ensure that the heating system is large enough to handle the coldest expected temperatures, use the 99.6% design temperature.

For Dayton DB99.6% -1 °F99% 5 °F

For cooling, ASHRAE determined “0.4%” and “1.0%” design conditions for temperature (Tdb) and humidity (Twb & Tdp), such that the actual hourly temperatures were greater (warmer) than the design temperatures 0.4% or 1.0% of all annual hours. In addition, ASHRAE determined the mean coincident wet bulb temperature (MCWB) for each design condition, which is the mean wet bulb temperature at the specified dry bulb temperature. MCWB temperature is used for calculating latent cooling loads. The peak cooling load design temperatures for Dayton, OH are shown below. To ensure that the cooling system is large enough to handle the warmest expected conditions, use the 0.4% design temperatures.

For Dayton DB MCWB0.4% 90 °F 74 °F1.0% 88 °F 73 °F

Design Solar RadiationASHRAE recommends the following method for calculating maximum values of solar radiation on a surface, Et. Following this method, the total radiation on a surface, Et, is the sum of the direct radiation ED, the diffuse radiation Ed and the radiation reflected from the ground Er. The method uses local standard time, LST, the local standard meridian, LSM, the local longitude, LON, the angle of the surface from south and the tilt angle of the surface from horizontal as inputs. The method is demonstrated in the example below.

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ExampleCalculate total solar radiation on a vertical, south facing wall at noon in July in Dayton, Ohio.

Hour of day: LST = 12Dayton: LSM=75 ° , LON=84 °W , L=40 ° NJuly: ET=−6 . 2, δ=20 . 6 , A=344 , B=. 207 , C=.136Ψ=surface azimuth=0° for south (−90° for east , 90 ° for west , 180 ° for north )Σ=surface tilt from horizontal=90 ° for vertical (0° for horizontal )

AST=LST +ET60

+ LSM−LON15

=12+−6 .260

+75−8415

=11. 30

H=15×( AST−12 )=15×(11. 3−12 )=−10 .5 °sin β=(cos L×cosδ×cosH )+ (sinL×sin δ )

=[cos ( 40 )×cos (20.6 )×cos (−10 . 5 ) ]+[sin (40 )×sin (20.6 ) ]=. 9312β=sin−1 ( .9312 )=68 .63 °

cos φ=(sin β×sinL )−sin δcos β×cos L

=[ ( . 9312 )×sin (40 ) ]−sin (20 .6 )cos (68 .63 )×cos (40 )

=. 8839

φ=cos−1 ( .8839 )=27 . 89°γ=φ−Ψ=27 . 89−0=27 . 89cosθ=(cos β×cosγ×sin Σ )+(sin β×cosΣ )

=[cos (68 .63 )×cos (27 .89 )×sin (90 ) ]+[ . 9312×cos (90 ) ]=. 3221θ=cos−1 (. 3321 )=71 °

EDN=A×CN

exp ( Bsin β )

=344×1. 0

exp( .207.9312 )

=275. 4[ Btuhr ft 2 ]

ED=EDN×cosθ=275. 4×. 3221=88 . 72[ Btuhr ft2 ]

Y=. 55+( . 437 cosθ )+(. 313cos2θ )=.55+ ( . 437×. 3221 )+[ . 313×( . 3221 )2]=.7232

Ed=C×Y×EDN=. 136×.7232×275.4=27 .09 [ Btuhr ft 2 ]Er=

EDN (C+sin β ) ρg (1−cosΣ )2

=275 .4×( .136+. 9312 )×.2×[1−cos (90 ) ]

2=29 . 39[ Btu

hr ft2 ]ET=ED+Ed+Er=88 .72+27 .09+29 .39 = 145.2 (Btu/hr-ft2)

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