Rainer Mager wrote:
> 
> Hi all,

>     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?

Well, I was thinking quickly about the circumference of the red and
yellow.
It seems there is  the following approximate relation:

   2.n.r = 2.pi.(R-r)

which is :
 the sum of the diameter (2.r) of the yellow circles (.n) is
equal to the perimeter (2.pi) of the circle going through all the
centers 
of the yellow circles.
The difference between this circle and the red circle is the
radius of a yellow circle. (R-r)

 So the relation is :
 
 2.(n+pi).r = 2.pi.R

or 

   r = pi.R/(n+pi)

Caveat : n should be big enough so you can consider a segment as an arc.
         (at least 6, so that make 12 segments ?)

calculation for n=6 give:

  r = R * .34365903524

instead of the awaited r = R / 3
only a 3 % error !!
         
> 
> Thanks,
> 
> --Rainer
> 
>   ------------------------------------------------------------------------
>             Name: 7.jpg
>    7.jpg    Type: JPEG Image (image/jpeg)
>         Encoding: base64

Post a reply to this message