Difference between revisions of "Chain Length Calculation"

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(Tabular Example)
(Understanding the Problem)
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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.
 
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. I really have nothing better to do. I like to criticise other people, it makes me feel smart.
+
This makes for some interesting math.
  
 
===The most accurate math===
 
===The most accurate math===

Revision as of 22:27, 6 December 2006

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.png
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

Tabular Example

Center-to-center-table.png

For Single Speed Mountain Bikes

Gear-choice-histogram.gif