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, on average, 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.

Here are some quick facts:

The most accurate math

Another formula:
File:Emerson-ept-math.gif

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

Tabular Example