Many thanks for replies and for taking the time out.
It is unfortuanately going to be a while before I can get back to this 
project.
Certainly have more to think about now though.
Your comment Roman expressed what I felt about it. As the cone is a 
fundamental shape you would think the formula would be some simple (short) 
equation.
I have that sinking feeling that calculus is involved here. I have forgotten 
what little I ever learned of that. (a very long time ago).
Ho hum more "light" reading to do.

Thanks again Bob

"Roman Reiner" <lim### [at] gmxde> wrote in message 
news:web.4528c8e021f68317271c1170@news.povray.org...
> Hi Bob,
>
> This is is far from blindingly obvious! I hope i didn't make a mistake
> though...
>
> the parameterized path function should be:
>
> f(t)=[x(t),y(t),z(t)]=[H*t,(r+(R-r)*t)*sin(2*pi*n*t),(r+(R-r)*t)*cos(2*pi*n*t)]
>
> where t goes from 0 (bottom y=0, r) to 1 (top y=H, R).
>
> if you continue from here the results are getting pretty ugly (tbh i'm
> surprised they are getting *that* ugly) but anyway: the total length of 
> the
> path is:
>
> a) L = (H^2 + (r - R)^2)*LN((sqrt(H^2 + (2*pi*n*r)^2 + (r - R)^2) -
> 2*pi*n*r)/(sqrt(H^2 + (2*pi*n*R)^2 + (r - R)^2) - 2*pi*n*R))/(4*pi*n*(R -
> r)) + r*sqrt(H^2 + (2*pi*n*r)^2 + (r - R)^2)/(2*(r - R)) + R*sqrt(H^2 +
> (2*pi*n*R)^2 + (r - R)^2)/(2*(R - r))
>
> where x^2 is pow(x,2) (and no i didn't calculate this by hand ;-))
>
> I couldn't solve b) and i doubt it would be any nicer than a)
>
> Does this help? :-)
>
> Regards Roman
>
>
>

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