I would say that the relation is :

sin(pi / n) = r/(R-r)

where n is the number of small circles, r the radius of the small circles
and R the radius of the big one.

for n=6 this gives r = R/3 which is true !

Philippe



<374baac0.0@news.povray.org>...
>Hi all,
>
>    I'm trying to make a simple cable macro. The macro is supposed to make
a
>straight cable from 2 given end points such that the cable is made up of a
>number of given strands twisted smothly around one another. Also given to
>the macro is the radius of the cable as a whole and the twistiness of the
>strands. In use it looks like (will look like) the cable is solid even
>though it is actuall a hollow tube. A very small image is attached showing
>what a 7 strand cable should look like when viewed from the end (an unusual
>place to view such a cable).
>    The problem that I am having is calculating the radius of the small
>inner strands. In the attached picture the inner strands are yellow and the
>outer red is simply for reference and won't show up in a real cable. In the
>image I guessed the yellow radii by trial and error just to make the
>picture. In real use this needs to be an automatic calculation.
>
>    I've been working on the math a lot and finally derived this formula:
>
>z^2 = -8r^4 - (4R + 10)r^3 + (5R + 12R^2)r^2 - 6R^3r + R^4
>
>Where z is a known constant that is related to the number of strands and R
>is the given radius of the large red circle and r is the radius to be
>calcuated. The problem is solving the 4th order polynomial. I also solved
>the problem for the case where there are 3 strands only and got this:
>
>r = R / (2 + ((2 - sqrt(3)) / sqrt(3)))
>
>The problem with this is generalizing it to more strands.
>
>Once I get the radius I need the part of twisting the strands is easy.
>
>Any ideas?
>
>
>Thanks,
>
>--Rainer
>

Post a reply to this message