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A Fresnel model (was "a stupid question.")

N

Nick Pine

Jan 1, 1970
0
This could be made with 9 1'x1" strips from a 1'x1' mirror tile
and explored with a laser pointer...

10 PI=4*ATN(1)
20 AXISELD=12'axis elevation above horizon (degrees)
30 AXISEL=PI*AXISELD/180'axis elevation above horizon (radians)
40 FL=6/16'focal length (feet)
50 HEIGHT=1.333/16'reflector height (feet)
60 N=9'number of strip reflectors
70 PRINT"strip #","bottom (cm)","top (cm)","spacer (cm)","tilt (deg)"
80 PRINT
90 A=ATN(HEIGHT/FL)'initial est angle to focus (rad)
100 FOR STRIP=1 TO N'reflector strip # (from bottom)
110 TILT=(A-AXISEL)/2'reflector tilt from vertical (rad)
120 D=HEIGHT*SIN(TILT)'spacer (feet)
130 TH=TB+HEIGHT*COS(TILT)'upper strip edge height (feet)
140 AH=ATN(TH/(FL-D))'new estimate
150 IF ABS((A-AH)/A)>.001 THEN A=AH:GOTO 110'iterate to 0.1%
160 SPACER=D'spacer width behind top of strip (feet)
165 S=2.54*12'change to centimeters
170 PRINT STRIP,TB*S,TH*S,SPACER*S,180*TILT/PI
180 TB=TH+D*TH/(FL-D)'next bottom edge height (feet)
190 NEXT STRIP
200 CONC=N*HEIGHT/FL'concentration ratio
210 OHB=100*D/FL'overhead sun blocking (%)
220 PRINT
230 PRINT"height=";TH,"conc=";CONC,"ohb=";OHB;"%"

STRIP # BOTTOM (cm) TOP (cm) SPACER (cm) TILT (deg)

1 0 2.539338 .011651 .2628863
2 2.54193 5.066413 .2745153 6.206025
3 5.191088 7.679055 .5083288 11.54745
4 8.036462 10.47552 .706654 16.15757
5 11.16584 13.55161 .8697661 20.03007
6 14.66775 17.00119 1.001728 23.23352
7 18.6343 20.91928 1.107826 25.86555
8 23.16443 25.40604 1.193142 28.0251
9 28.3672 30.57077 1.262002 29.80009

height= 1.002978 conc= 1.9995 ohb= 11.04114 %

Nick
 
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