Chain Length Calculation

Understanding the Problem

A chainwheel is not round. Rather, it is a polygon with facet lenth of the chain pitch. The chain leaves the chainwheel, at maximum, tangent to the pitch diameter. The chain then travels in a (theoretically) straight line to the other chainwheel, meeting it in a similar fashion.

This makes for some interesting math.

The most accurate math

Here are some quick facts:

Some Approximations

I'm not a big fan of approximations. Spreadsheets exist for a reason.

I will add some though, just for comparison.

Some Data

Considerations for Motorcycles (Simple Swingarm)

For Single Speed Mountain Bikes

Theoretical center distance. Alfa = 0. For a good chain alfa can be in the range of 1.001 and 1.005.