Posted by *Morris Dovey* on July 8, 2010, 5:09 am

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. :)

--

Morris Dovey

http://www.iedu.com/DeSoto/

Posted by *dow* on July 10, 2010, 12:10 am

*> 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. :)*

*> --*

*> Morris Doveyhttp://www.iedu.com/DeSoto/ *

13 seconds ghastly?!

Remember that thing I did a few months ago, calculating the dimensions

of a paraboloidal reflector that has its focus coincident with its

centre of mass? I made the program do the calculation to a precision

of ten significant digits (Why? Because I wanted to see if I could.)

On the ancient machine I used, the program took nearly ten *minutes*

to run.

Good programs give you time to go and make coffee. Really good

programs let you go see a movie. Excellent programs let you take a

vacation.

dow

Posted by *Morris Dovey* on July 10, 2010, 1:29 am

On 7/9/2010 7:10 PM, dow wrote:

*> Remember that thing I did a few months ago, calculating the dimensions*

*> of a paraboloidal reflector that has its focus coincident with its*

*> centre of mass? I made the program do the calculation to a precision*

*> of ten significant digits (Why? Because I wanted to see if I could.)*

*> On the ancient machine I used, the program took nearly ten *minutes**

*> to run.*

*> Good programs give you time to go and make coffee. Really good*

*> programs let you go see a movie. Excellent programs let you take a*

*> vacation.*

Eureka, and thank you (I think). After all these years of programming, I

finally understand why my coffee is _always_ cold - and why I've taken

so few vacations... :-/

--

Morris Dovey

http://www.iedu.com/DeSoto/

Posted by *Steve D* on July 10, 2010, 1:50 am

*> 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*

*> http://www.iedu.com/DeSoto/ *

Posted by *Morris Dovey* on July 10, 2010, 2:51 am

On 7/9/2010 8:50 PM, Steve D wrote:

*> 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).*

Sigh - me too, except that I took the course 45 years ago, and my old

textbook was ruined in a basement flooding 30 years ago.

It should be a fairly simple definite integral, but I'm down to my last

two neurons - one is for breathing and the other... I forget what the

other one does. :)

Between the time I finished the program and the time I posted here I

visited Amazon and ordered a used copy of my old textbook (Abraham

Schwartz's "Calculus and Analytic Geometry"). Perhaps it'll stick better

the second time around.

My iterative approach is to approximate the curve with straight line

segments and sum their lengths. At each iteration I increase the number

of segments by a factor of ten, and when the difference between

successive approximations is less than or equal to the error threshold,

the program outputs the sum and quits. On this old IBM PC the last

non-zero difference (before running out of bits) was on the order of

10^-13 - which is probably close enough for most DIY work.

*> 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.*

I suspect that project would have exceeded my attention span, but I did

write a Z-80 program to control three lead screws to spin dishes from

aluminum disks back in C- and K-band days.

--

Morris Dovey

http://www.iedu.com/DeSoto/

> 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. :)> --> Morris Doveyhttp://www.iedu.com/DeSoto/