3

I am trying to drill holes in a bicycle hub to fit it on a different style rim. I currently have a 36 hole rim with 18 holes on each side, and I'm transitioning to a 32 hole rim with 16 holes on each side. I need to drill new holes in the rim, and I need the 16 new points to be far away from the old 18 holes for stability.

Picture of bicycle hub similar to mine; for reference.

Here is a summary of what I think I am trying to do: Given x points on the circumference of a circle equidistant to each other, find y other points on the circumference of the circle which are equidistant to each other, farthest away from the x points.

Here I drew a graph and plotted points to illustrate what I am trying to do: https://www.desmos.com/calculator/mdzqhqhhwb

On my graph the red X's are existing holes, and the blue points are the holes that I plan to drill. I have used variable h to shift the points about the circle. I have used variable k to change the distance between two pairs of holes (I realize this breaks the condition of equidistant points that I mentioned earlier, but it would work in my bicycle application). Currently I'm going by eye and just punching in random shift (variable h) values. It is possible to re use existing holes (ie overlap).

James Meas
  • 31
  • 1
    If you have a blue point exactly on top of a red point, does that also compromise stability, or can you just reuse the existing hole? I ask because it changes the mathematical formulation a bit, since then you would exclude those coincident points from the objective. –  Nov 24 '18 at 09:30
  • I was thinking about that after I posted the question; yes, I suppose it is possible to reuse existing holes. – James Meas Nov 24 '18 at 19:01
  • 1
    I think the theory of approximation by rationals might be connected with this. If you have two drummers drumming at different rates, & you want their beats to be maximally separated, then the ratio of their tempi is to be the golden section. I think the theory for deciding your problem might be something of that nature. – AmbretteOrrisey Dec 03 '18 at 20:49

0 Answers0