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Re: parabolic trough edge's length
From: nospam_steved94@comcast.net (Steve D)
Someone came to my web site looking for a way to calculate the length of a parabolic trough edge. On the off-chance that it was someone who reads this group, I've written an MS-DOS program to do that job and am willing to email a copy of the executable to anyone wanting it.
It provides as close an approximation as anyone is likely to want, and it gives the length of y = Ax^2 + Bx + C between a pair of x limits to a user-specified error threshold (on my machine an error threshold of zero causes it to run for a ghastly 13 seconds).
It isn't beautiful, but the price is right. :)
Are you talking the length along a parabolic curve? If you are, I know there is an exact math solution to this one. It involves a curve integral. I'm sure of it since I calculated it when I was in college. Of course I can't remember how to do it any more, but if you find an appropriate egghead I'm sure you can get the formula. If I was more ambitious I'd try to re-fire those old neurons (it's been more than 20 years).
I remember using the calculation to make something resembling a parabolic dish. Knowing the length along the parabolic curve I cut paper into wedges that varied in width based on the length along the parabolic curve. I taped the wedges together and got a dish.
Regards,
Steve
-- Morris Dovey
