Chain Length Calculation

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Understanding the Problem

Chain-layout-model.gif

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

Chain-length-math.gif
Here are some quick facts:

Chain-math-details.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

Chain-data.png

Considerations for Motorcycles (Simple Swingarm)

Center-to-center-table.png

For Single Speed Mountain Bikes

Gear-choice-histogram-possible.gif

Theoretical center distance. Alfa = 1. For a good chain alfa can be in the range of 1.001 and 1.005. Bicycle-Magic.gif

See Also

http://www.gearingcommander.com/