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.
The basic equation for a parabola is x^2 = py. 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 | p*y | √ p*y = x | x inches | (fraction of inch) * 16 appx= 16ths in |
| 3 | 36 | 6.000 | 6 | 0 / 16 |
| 6 | 72 | 8.485 | 8 | 8 / 16 |
| 9 | 108 | 10.392 | 10 | 6 / 16 |
| 12 | 144 | 12.000 | 12 | 0 / 16 |
Formula for the perimeter of a parabolic dish at EFunda Area and Perimeter of a Parabola
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