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
I'm not a big fan of approximations. Spreadsheets exist for a reason.
I will add some though, just for comparison.
Considerations for Motorcycles (Simple Swingarm)
For Single Speed Mountain Bikes
Theoretical center distance. Alfa = 1. For a good chain alfa can be in the range of 1.001 and 1.005.