re: another 12' non-cube SOLAR.KnowledgePublications.com

re: another 12' non-cube
17 mar 2001
>the reflector needs (sqrt(4x^2+y^2)+y^2/(2x)ln((2x+sqrt(4x^2+y^2))/y)/2
>= 17.75' long curved kerfed 2x4 rafters...

here's where to cut the kerfs:

kerf width (in): 0.125              kerf depth (in): 2.367
 
kerf     x             y            distance along beam

(#)      (feet)        (feet)       (feet)         (cm)

0        .008          .317          .327           9.980
1        .034          .636          .658          20.041
2        .076          .958          .993          30.267
3        .138         1.286         1.337          40.746
4        .219         1.621         1.692          51.577
5        .322         1.966         2.063          62.867
6        .450         2.323         2.452          74.742
7        .605         2.695         2.866          87.347
8        .793         3.085         3.309         100.859
9       1.019         3.496         3.789         115.490
10      1.290         3.934         4.314         131.506
11      1.616         4.404         4.896         149.239
12      2.010         4.911         5.549         169.121
13      2.487         5.463         6.290         191.709
14      3.072         6.072         7.144         217.755
15      3.796         6.749         8.145         248.273
16      4.702         7.511         9.340         284.682
17      5.854         8.381        10.794         329.008
18      7.347         9.390        12.606         384.235
19      9.326        10.579        14.925         454.909

nick

10 xmax=12'parabola depth (feet)
20 ymax=12'parabola height (feet)
30 n=21'number of line segments
40 w=.125'kerf width (in)
50 f=ymax^2/(4*xmax)'focal length (feet)
60 ap=2*atn(1)-atn(2*f/ymax)'final slope (radians)
70 al=ap/n'lower kerf angle (radians)
80 au=ap/(n-1)'upper kerf angle (radians)
90 a=(al+au)/2'average kerf angle (radians)
100 xl=0:yl=0
110 ah=a/2
120 for k=0 to n-1
130 d=4*f*tan(ah+k*a)'quadratic term
140 yk=(d+sqr(d^2-4*yl*(d-yl)))/2'next kerf height (feet)
150 yl=yk'last kerf height (feet)
160 next k
170 if abs(yk-ymax)/ymax<.001 goto 200'iterate to 0.1%
180 if yk>ymax then au=a else al=a
190 goto 90
200 dl=0:yl=0
210 print "kerf depth (in):";w/2/tan(ah)
220 for k=0 to n-2'number of kerfs
230 d=4*f*tan(ah+k*a)'quadratic term
240 yk=(d+sqr(d^2-4*yl*(d-yl)))/2'next kerf height (feet)
250 xk=yk^2/(4*f)'next kerf x-coordinate (feet)
260 dk=dl+w/12+sqr((xk-xl)^2+(yk-yl)^2)'kerf distance along beam (feet)
300 drm=int(dk*30.48*1000+.5)/1000'kerf distance along beam (cm)
310 print k,xk,yk,dk,drm
320 xl=xk:yl=yk:dl=dk'last kerf coordinates (feet)
330 next k