It is extremely difficult to calculate the shape of sheets for a parabolic dish, but it is easy to calculate a form. A step form for a parabolic dish would consist of a rising series of shrinking circles.
For total y height and x radius, p = x^2 / y.
For every three to six inch interval for y, x = sqrt(py). The diameter of each rising, shrinking circle is 2x. For a parabolic dish of 24 inches wide & 12 inches high, p = (24/2)^2 / 12 = 12.
|
y
|
x
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x in
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x 16ths in
|
|
3
|
6.000
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6
|
0
|
|
6
|
8.485
|
8
|
8
|
|
9
|
10.392
|
10
|
6
|
|
12
|
12.000
|
12
|
0
|
Formula for the perimeter of a parabolic dish at EFunda Area and Perimeter of a Parabola