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thermal performance model

I'm building a house and am looking for a computer model (Linux or Windows, free or inexpensive) that can *accurately* predict my HVAC heating loads given my exact residential floor plan, building envelope construction, glazing, occupancy and location (near Reno).

One that I've tried (eQuest) is wonderful in its detail and ease-of-use. Unfortunately, there must be a flaw in the underlying model calculation because increasing the south facing (double pane, high SHGC) glass from 12% to 70% *increases* the HVAC heating requirements. Other software (e.g. the Canadian Hot2000, RESFEN 3.1 ) does not seem to allow one to input the exact floorplan, unique building materials (e.g. ICF's) and other data necessary for an accurate estimate of heating requirements. Some also have artificial limitations (e.g. unable to specify 80% of the south facing wall as windows)

Can anyone suggest a good *accurate* program? What do energy consultants use?

Lee Elson

Reply to
lelson
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You might write your own. Third-graders can learn BASIC :-) Here's a start, which reads the Reno Typical Meterological Year (TMY2) hourly weather data file (available from NREL's web site) and makes another simplified file called "winter."

10 PI=4*ATN(1):SCREEN 9:KEY OFF:CLS 20 LINE (0,0)-(639,349),,B:DF=.434 30 FOR TR= 60 TO 80 STEP 10'temp ref lines 40 LINE (0,349-5*(TR-10))-(639,349-5*(TR-10)):NEXT 50 F$="23185.tm2"'NREL TMY2 file name (Reno) 60 OPEN F$ FOR INPUT AS #1 70 OPEN "winter" FOR OUTPUT AS #2 80 LINE INPUT#1,S$'read header 90 CITY$=MID$(S$,8,25) 100 LAT=VAL(MID$(S$,40,2))+VAL(MID$(S$,43,2))/60 110 LON=VAL(MID$(S$,48,3))+VAL(MID$(S$,52,2))/60 120 PRINT#2,CITY$,LAT,LON 130 GOSUB 190 140 PASS=1 150 CLOSE #1 160 OPEN F$ FOR INPUT AS #1 170 LINE INPUT#1,S$'ignore header 180 GOSUB 190 190 FOR H=1 TO 8760'hour of year 200 LINE INPUT#1,S$ 210 MONTH=VAL(MID$(S$,4,2))'month of year (1-12) 220 IF PASS=0 AND MONTH=1 THEN PHIS=-1.570796327#:GOTO 440 430 PHIS=ATN(X/SQR(-X*X+1))'sin^-1(x) = sun azimuth angle (radians) 440 FOR PHIPD=0 TO 180 STEP 90'azimuth angle of plane (degrees) 450 PHIP=PI*PHIPD/180 460 X=SIN(THETAS)*COS(PHIS-PHIP) 470 THETAI=-ATN(X/SQR(-X*X+1))+PI/2'incidence angle to surface (radians) 480 IF THETAI>=PI/2 THEN THETAI=PI/2 490 RHOG=.2'ground reflectance 500 IGLOP=IDIR*COS(THETAI)+IDIF/2+IGLOH*RHOG/2'radiation on surface (Btu/ft^2) 510 PRINT#2,IGLOP; 520 'IF PHIPD = 0 THEN PSET(H-8030,349-IGLOP) 530 NEXT PHIPD 540 PHIP=PI*270/180 550 X=SIN(THETAS)*COS(PHIS-PHIP) 560 THETAI=-ATN(X/SQR(-X*X+1))+PI/2'incidence angle to surface (radians) 570 IF THETAI>=PI/2 THEN THETAI=PI/2 580 IGLOP=IDIR*COS(THETAI)+IDIF/2+IGLOH*RHOG/2'radiation on surface (Btu/ft^2) 590 PRINT#2,IGLOP 600 IF HOUR=.5 THEN LINE (DF*(WH-8030),349)-(DF*(WH-8030),345) 610 NEXT H 620 RETURN

Here's the start of the winter file, with the month, day, hour, dry bulb temperature (F), and Btu/ft^2 of sun falling on the ground and south, west, north, and east walls for the months of October through January. The worst- case months are December and January. I start simulating in October to make sure house temperatures have stabilized by December.

RENO NV 39.5 119.7833 10 1 .5 44.06 0 0 0 0 0 10 1 1.5 43.52 0 0 0 0 0 10 1 2.5 42.08 0 0 0 0 0 10 1 3.5 39.74 0 0 0 0 0 10 1 4.5 39.74 0 0 0 0 0 10 1 5.5 40.28 .634 .2433778 .2218999 .2218999 .8492084 10 1 6.5 41 20.288 20.40661 6.466783 6.466783 110.9118 10 1 7.5 48.92 79.884 78.2263 16.23037 16.23037 211.7582 10 1 8.5 57.02 142.333 137.1752 25.48676 25.48676 228.2724 10 1 9.5 64.94 194.638 186.9535 33.09476 33.09476 201.9825 10 1 10.5 69.98001 232.361 223.7174 38.29355 38.29355 149.5433 10 1 11.5 75.02001 247.577 240.1501 40.44915 40.44915 78.724 10 1 12.5 80.06001 245.041 240.2293 78.39368 40.03705 40.03705 10 1 13.5 80.06001 221.583 221.1326 147.2574 36.74025 36.74025 10 1 14.5 80.06001 178.154 183.0438 197.6003 30.65386 30.65386 10 1 15.5 80.06001 121.094 130.7123 218.4883 22.25336 22.25336 10 1 16.5 74.12 56.743 67.68118 185.0582 12.64827 12.64827 10 1 17.5 68 11.412 10.40487 49.15384 4.311193 4.311193 10 1 18.5 62.06 0 0 0 0 0 10 1 19.5 60.08 0 0 0 0 0 10 1 20.5 57.92 0 0 0 0 0 10 1 21.5 55.94 0 0 0 0 0 10 1 22.5 51.26 0 0 0 0 0 10 1 23.5 46.76 0 0 0 0 0 10 2 .5 42.08 0 0 0 0 0 ... Here's a program that simulates an 8' R32 cube with an R2 south wall with 80% solar transmission and a huge thermal mass using the winter file as an input. There are much more efficient solar heating schemes (eg those using simple air heaters or low-thermal-mass sunspaces), but this direct gain scheme is simple to simulate with a 21 line program.

10 CLS:SCREEN 9:LINE (0,0)-(639,349),,B:DF=.43 20 FOR TR=20 TO 70 STEP 10'plot temp ref lines 30 LINE (0,349-5*(TR-10))-(639,349-5*(TR-10)):NEXT 40 RV=32'wall R-value 50 C=20000!'house capacitance (Btu/F)

Increasing the R-value or capacitance raises the worst-case temperature...

60 TI=70:TIMIN=1000'Initial house air temps (F) 70 OPEN "winter" FOR INPUT AS #1:LINE INPUT#1,H$ 80 INPUT#1,MONTH,DAY,HOUR,TA,SH,SS,SW,SN,SE 100 SOLGAIN=.8*64*SS-(TI-TA)*32'net south window solar gain (Btu)

The solar gain is 80% of the south sun minus the heat loss to the outdoors.

110 IH=SOLGAIN-(TI-TA)*5*64/RV 120 TI=TI+IH/C'find new house temperature (F)

Divide the net heatflow by the capacitance to find its temperature change.

130 IF TI>70 THEN TI=70'limit house temp

An exhaust fan might enforce this 70 F upper comfort limit.

200 IF TIease-of-use. Unfortunately, there must be a flaw in the underlying

Windows lose heat at night and on cloudy days, as DJ mentioned.

You might try making this south window a simple air heater that loses no heat at night, or move it to a low-thermal-mass sunspace that's isolated from the living space and let warm air circulate between the sunspace during the day and stop the circulation at night and let the sunspace get cold, so the window loses little heat at night, IF your simulation program permits. Lots of them don't, even DOE's latest and greatest ENERGY 10.

Changing the window to an air heater in the cube above reduces the required thermal mass from 20K to 3.5K Btu/F, for a 65 F min temp. Putting in the ceiling with a larger temp swing reduces it further, especially with a nighttime heat setback.

Those are the kinds of limitations and bugs and unclear assumptions that led me to write my own hourly simulation programs. Also, being able to change the fundamentals can give much deeper insight as to what's going on, compared to canned programs.

Nick

Reply to
nicksanspam

Here's a simulation for a Philadelphia row house using NREL's hourly Typical Meteorological Year (TMY2) weather data... The first program makes a simplified output file called "ecayear."

10 SCREEN 9:KEY OFF:CLS:PI=4*ATN(1) 20 LINE (0,0)-(639,349),,B:XDF=.073:YDF=3.88 30 FOR TR= 60 TO 80 STEP 10'temp ref lines 40 LINE (0,349-YDF*(TR-10))-(639,349-YDF*(TR-10)):NEXT 50 OPEN "13739.tm2" FOR INPUT AS #1'NREL TMY2 file name (Phila) 60 OPEN "ecayear" FOR OUTPUT AS #2 70 LINE INPUT#1,S$'read header 80 CITY$=MID$(S$,8,25) 90 LAT=VAL(MID$(S$,40,2))+VAL(MID$(S$,43,2))/60 100 LON=VAL(MID$(S$,48,3))+VAL(MID$(S$,52,2))/60 110 PRINT#2,CITY$,LAT,LON 120 FOR H=1 TO 8760'hour of year 130 LINE INPUT#1,S$ 140 MONTH=VAL(MID$(S$,4,2))'month of year (1-12) 150 DAY=VAL(MID$(S$,6,2))'day of month 160 HOUR=VAL(MID$(S$,8,2))-.5'hour of day 170 N=1+H/24'day of year (1 to 365) 180 TDB=VAL(MID$(S$,68,4))*.18+32'dry bulb temp (F) 190 TDP=VAL(MID$(S$,74,4))*.18+32'dew point temp (F) 200 PSET(XDF*H,349-YDF*(TDB-10)) 210 IF DAY=1 AND HOUR=.5 THEN LINE (XDF*H,349)-(XDF*H,345)'tick months 220 WIND=VAL(MID$(S$,96,3))*.22371'wind velocity (mph) 230 IGLOH=VAL(MID$(S$,18,4))*.317'global horizontal radiation (Btu/ft^2) 240 PRINT#2,MONTH;DAY;HOUR;TDB;WIND;TDP;IGLOH; 250 IDIF=VAL(MID$(S$,30,4))*.317'diffuse horizontal radiation (Btu/ft^2) 260 IDIR=VAL(MID$(S$,24,4))*.317'direct normal radiation (Btu/ft^2) 270 L=PI*LAT/180'Phila latitude (radians) 280 T=HOUR'solar time (EST) 290 X=-SIN(PI*23.45/180)*COS(2*PI*(N+10)/365.25) 300 D=ATN(X/SQR(-X*X+1))'sin^-1(x) = declination (radians) 310 W=2*PI*(T-12)/24'hour angle (radians) 320 X=COS(L)*COS(D)*COS(W)+SIN(L)*SIN(D) 330 THETAS=-ATN(X/SQR(-X*X+1))+PI/2'cos^-1(x) = sun zenith angle (radians) 340 X=COS(D)*SIN(W)/SIN(THETAS) 350 IF X^2 >=1 THEN PHIS=-1.570796327#:GOTO 370 360 PHIS=ATN(X/SQR(-X*X+1))'sin^-1(x) = sun azimuth angle (radians) 370 FOR PHIPD=0 TO 180 STEP 90'azimuth angle of plane (degrees) 380 PHIP=PI*PHIPD/180 390 X=SIN(THETAS)*COS(PHIS-PHIP) 400 THETAI=-ATN(X/SQR(-X*X+1))+PI/2'incidence angle to surface (radians) 410 IF THETAI>=PI/2 THEN THETAI=PI/2 420 RHOG=.2'ground reflectance 430 IGLOP=IDIR*COS(THETAI)+IDIF/2+IGLOH*RHOG/2'radiation on surface (Btu/ft^2) 440 PRINT#2,IGLOP; 450 'IF PHIPD = 0 THEN PSET(XDF*H,349-IGLOP) 460 NEXT PHIPD 470 PHIP=PI*270/180 480 X=SIN(THETAS)*COS(PHIS-PHIP) 490 THETAI=-ATN(X/SQR(-X*X+1))+PI/2'incidence angle to surface (radians) 500 IF THETAI>=PI/2 THEN THETAI=PI/2 510 IGLOP=IDIR*COS(THETAI)+IDIF/2+IGLOH*RHOG/2'radiation on surface (Btu/ft^2) 520 PRINT#2,IGLOP 530 NEXT H 430 IGLOP=IDIR*COS(THETAI)+IDIF/2+IGLOH*RHOG/2'radiation on surface (Btu/ft^2)

Here's a sample of its ecayear output file, with the month, day, hour, dry bulb temperature (F), wind velocity (mph), dew point temp (F) and Btu/ft^2 of sun that falls on the ground and south, west, north, and east walls for every hour of the year. It starts just past midnight on New Year's day...

PHILADELPHIA PA 39.88334 75.25 1 1 .5 33.98 4.69791 30.92 0 0 0 0 0 1 1 1.5 33.98 9.172109 30.92 0 0 0 0 0 1 1 2.5 33.98 10.29066 28.94 0 0 0 0 0 1 1 3.5 32 23.04213 19.94 0 0 0 0 0 1 1 4.5 28.04 19.68648 15.98 0 0 0 0 0 1 1 5.5 24.98 20.80503 8.06 0 0 0 0 0 1 1 6.5 21.92 19.68648 10.04 0 0 0 0 0 1 1 7.5 15.98 24.16068 -.940 7.92 26.5 2.6 2.6 41.2 1 1 8.5 14 25.27923 -5.08 41.5 131.8 9.0 9.0 145.2 1 1 9.5 15.08 21.92358 -5.08 88.4 205.2 15.6 15.6 154.0 1 1 10.5 15.08 26.39778 -5.08 83.6 102.9 33.8 33.8 62.7 1 1 11.5 15.08 25.27923 -4.00 66.2 54.4 34.8 34.8 37.5 1 1 12.5 17.06 25.27923 -5.08 109.3 150.8 51.9 36.4 36.4 1 1 13.5 17.06 23.04213 -2.92 99.8 146.3 79.9 32.4 32.4 1 1 14.5 15.98 25.27923 -2.02 64.3 103.3 81.3 21.8 21.8 1 1 15.5 15.08 25.27923 -4.00 44.6 118.3 129.9 11.6 11.6 1 1 16.5 12.02 21.92358 -7.06 10.1 32.1 49.8 3.7 3.7 1 1 17.5 10.94 23.04213 -7.96 0 0 0 0 0 1 1 18.5 10.94 23.04213 -7.96 0 0 0 0 0 1 1 19.5 10.94 23.04213 -5.98 0 0 0 0 0 1 1 20.5 10.94 18.34422 -5.08 0 0 0 0 0 1 1 21.5 10.94 18.34422 -4.00 0 0 0 0 0 1 1 22.5 12.02 20.80503 -2.92 0 0 0 0 0 1 1 23.5 12.92 20.80503 -.940 0 0 0 0 0 ...

Skipping to the 4th of July...

7 4 .5 64.94 3.35565 55.94 0 0 0 0 0 7 4 1.5 64.04 3.35565 57.02 0 0 0 0 0 7 4 2.5 62.96 4.69791 57.92 0 0 0 0 0 7 4 3.5 62.06 3.35565 59 0 0 0 0 0 7 4 4.5 60.98 2.2371 59 1.9 1.3 1.1 1.1 1.4 7 4 5.5 62.96 2.2371 60.0 21.8 26.7 9.9 9.9 50.7 7 4 6.5 66.92 5.81646 59 72.2 50.7 22.1 22.1 140.5 7 4 7.5 71.06 2.2371 60.0 134.4 47.7 34.6 34.6 189.0 7 4 8.5 73.94 5.81646 53.06 195.9 59.3 46.2 46.2 202.4 7 4 9.5 75.92 9.172109 53.06 246.6 94.5 54.9 54.9 185.1 7 4 10.5 78.98 6.93501 53.06 283.7 121.4 61.0 61.0 146.9 7 4 11.5 80.06 8.05356 51.98 304.3 136.0 64.1 64.1 94.2 7 4 12.5 82.04 8.05356 48.92 306.5 136.7 94.8 64.7 64.7 7 4 13.5 82.04 8.05356 50 289.1 122.7 148.4 61.8 61.8 7 4 14.5 82.94 10.29 51.08 254.8 96.5 188.3 56.2 56.2 7 4 15.5 82.94 5.81646 50 206.0 61.4 208.0 47.8 47.8 7 4 16.5 82.04 10.29 51.98 146.1 50.5 198.3 36.9 36.9 7 4 17.5 80.06 11.63292 53.06 82.7 55.5 153.7 24.2 24.2 7 4 18.5 75.92 10.29066 51.08 28.8 35.2 68.6 11.9 11.9 7 4 19.5 71.06 8.05356 53.06 3.8 2.7 3.2 2.1 2.1 7 4 20.5 68 6.93501 53.06 0 0 0 0 0 7 4 21.5 66.02001 5.81646 55.04 0 0 0 0 0 7 4 22.5 64.94 5.81646 55.04 0 0 0 0 0 7 4 23.5 62.96001 5.81646 57.02 0 0 0 0 0 ...

Here's a program that simulates the house, using the ecayear weather file as an input. We can try out various improvements to make it more comfortable and save energy, eg airsealing (line 80), more roof insulation (line 90), roof reflectance (line 100), a whole-house fan (line 110) and making some of the south wall into a simple Trombe wall (line 120.) Trombe walls are inefficient solar heaters, but they might be cheap retrofits.

10 SCREEN 9:KEY OFF:CLS 20 DAYSTART=0'display start time (days) 30 DS=DAYSTART*24'display start time (hours) 40 RANGE=8760'dISPLAY RANGE (HOURS)

We can expand the display range above, to look at a few days or hours...

50 LINE (0,0)-(639,349),,B:XDF=640/RANGE:YDF=3.88 60 FOR TR=60 TO 80 STEP 10'temp ref lines 70 LINE (0,349-YDF*(TR-10))-(639,349-YDF*(TR-10)):NEXT 80 ACH=.3'air infiltration (house volumes per hour) 90 RROOF=40'roof R-value (F-h/Btu) 100 REFROOF=.1'roof reflectance (1=mirror) 110 CFM=2470'whole-house fan cfm (Lasko/Air King 9600) 120 ATROMBE=64'area of Trombe wall (ft^2, with no int. insul.) 130 AROOF=30*40'roof area (ft^2) 140 GROOF=AROOF/RROOF'roof conductance (Btu/h-F) 150 AWALL=2*30*16'wall area (ft^2, excluding common and basement) 160 RWALL=2'wall R-value (F-h/Btu, including windows) 170 AINTWALL=0'area of interior wall insulation (ft^2, with no ext. insul.) 180 RINTWALL=10'R-value of interior wall insulation (F-h/Btu)

Adding insulation inside the brick walls is an option...

190 GINT=AINTWALL/(GWALL+RINTWALL)'int. wall section conductance (Btu/h-F) 200 GWALL=GINT+(AWALL-ATROMBE-AINTWALL)/RWALL'wall conductance (Btu/h-F) 210 GAIR=ACH*30*40*24/60'air infiltration conductance (Btu/h-F) 220 GH=GWALL+GAIR'house conductance (Btu/h-F, excluding roof) 230 CH=15000+(2*30*24-AINTWALL)*5!'house capacitance (Btu/F) 240 GASCAP=50000!'furnace capacity (Btu/h) 250 TA=30'initial average outdoor temp (F) 260 TH=65'initial house temp (F) 270 OPEN "ecayear" FOR INPUT AS #1:LINE INPUT#1,H$ 280 OPEN "ecaout" FOR OUTPUT AS #2

This also makes an output file for a spreadsheet...

290 FOR H=1 TO 8760'hours of typical (TMY2) year 300 INPUT#1,MONTH,DAY,HOUR,TDB,WIND,TDP,IGLOH,SS,WS,NS,ES 310 TA=.99*TA+.01*TDB'3-day moving average outdoor temp (F) 320 TT=86-.32*TA'target temp (F)

The fan target temp varies from 75 in winter to 65 in summer...

330 GWIND=2+WIND/2'roof airfilm conductance (Btu/h-F-ft^2) 340 TSAR=TDB+IGLOH*(1-REFROOF)/GWIND'sol-air roof temp (F) 350 RGAIN=(TSAR-TH)/(1/(AROOF*GWIND)+1/GROOF)'roof solar gain (Btu) 360 IF MONTH>4 AND MONTH80 THEN HOTHOURS=HOTHOURS+1

Count the number of hours per year over 80 F, assuming no AC...

540 IF HDS+RANGE THEN GOTO 610 550 'PSET(XDF*(H-DS),349-YDF*(TDB-10)) 560 'PSET(XDF*(H-DS),349-YDF*(TT-10)) 570 PSET(XDF*(H-DS),349-YDF*(TH-10)) 580 IF QGAS>0 THEN LINE (XDF*(H-DS),300-QGAS/1000!)-(XDF*(H-DS),300)'gas energy 590 LINE (XDF*(H-DS),320-QFAN/2000)-(XDF*(H-DS),320)'mark fan energy

Display furnace and fan usage...

600 IF DAY=1 AND HOUR=.5 THEN LINE (XDF*(H-DS),349)-(XDF*(H-DS),345)'months 610 PRINT#2,MONTH;DAY;HOUR;TDB;TH;GASHEAT,FANHEAT,FANCOOL 620 'IF H>4310 THEN PRINT IGLOH,tdb,tsar:end 630 NEXT H 640 CLOSE #1 650 PRINT ACH,RROOF,REFROOF,CFM,ATROMBE 660 PRINT GASHEAT/100000!,FANHEAT/100000!,FANCOOL/100000!,FANHOURS,HOTHOURS 670 LIST 80-120 680 END 690 'Th Tt and Th> 65 and Th> Tdb cool with fan towards Tt 860 IF LASTHEATQHMAX THEN FANTIME=QHMAX/QFMAX:QFAN=-QHMAX:RETURN 900 FANTIME=1:QFAN=-QFMAX:RETURN

  1. ACH Rroof Refroof Fan cfm Trombe area .7 13 .1 0 0 Gas heat Fan heat Fan cool Fan hours Hot hours 1099.73 0 0 0 298

Case 1 above is the unimproved house, which uses about 1100 therms of gas heat at 100% furnace efficiency and has 298 h/y of indoor temps over 80 F.

  1. ACH Rroof Refroof Fan cfm Trombe area .3 13 .1 0 0 Gas heat Fan heat Fan cool Fan hours Hot hours 859.8806 0 0 0 283

Reducing air leakage without changing anything else lowers the gas bill by 22% and reduces the number of hot hours slightly.

  1. ACH Rroof Refroof Fan cfm Trombe area .7 40 .1 0 0 Gas heat Fan heat Fan cool Fan hours Hot hours 1040.083 0 0 0 207

Adding roof insulation without changing anything else lowers the gas bill slightly and reduces the number of hot hours significantly.

  1. ACH Rroof Refroof Fan cfm Trombe area .7 13 .9 0 0 Gas heat Fan heat Fan cool Fan hours Hot hours 1122.53 0 0 0 192

Making the roof white without changing anything else raises the gas bill slightly and reduces the number of hot hours significantly.

  1. ACH Rroof Refroof Fan cfm Trombe area .7 13 .1 2470 0 Gas heat Fan heat Fan cool Fan hours Hot hours 1101.208 7.445226 61.50649 895.0826 121

Without changing anything else, a whole-house fan for heating and cooling reduces the number of hot hours significantly.

  1. ACH Rroof Refroof Fan cfm Trombe area .7 13 .1 0 64 Gas heat Fan heat Fan cool Fan hours Hot hours 1049.856 0 0 0 297

Without changing anything else, a 64 ft^2 Trombe wall reduces the gas bill slightly.

  1. ACH Rroof Refroof Fan cfm Trombe area .3 40 .1 0 0 Gas heat Fan heat Fan cool Fan hours Hot hours 800.3312 0 0 0 181

Combined airsealing and roof insulation saves lots of gas.

  1. ACH Rroof Refroof Fan cfm Trombe area .3 40 .9 0 0 Gas heat Fan heat Fan cool Fan hours Hot hours 807.8726 0 0 0 131

Adding a white roof raises the gas bill slightly and keeps the house cooler.

  1. ACH Rroof Refroof Fan cfm Trombe area .3 40 .9 2470 0 Gas heat Fan heat Fan cool Fan hours Hot hours 806.815 9.980721 48.20572 806.8318 34

Adding a whole-house fan can keep the house a lot cooler.

10.ACH Rroof Refroof Fan cfm Trombe area .3 40 .9 2470 64 Gas heat Fan heat Fan cool Fan hours Hot hours 757.1798 8.498159 49.49792 797.0345 33

Adding a Trombe wall still saves some gas.

11.ACH Rroof Refroof Fan cfm Trombe area .3 40 .1 2470 64 Gas heat Fan heat Fan cool Fan hours Hot hours 750.3186 7.776429 52.50024 816.752 41

And leaving the roof black saves a bit more...

With a few more lines we can add internal heat gain from electrical use, ventilation constraints based on dew point, and so on.

Nick

Reply to
nicksanspam

And your are Bill, and Steve Baer and trolling as usual

Reply to
m Ransley

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