Chain Length Calculation

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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.

The most accurate math



Some Approximations

Some Data



Tabular Example