More thoughts on bike sprocket / cassette usage

Previously, I discussed how I used the data from my Garmin Edge 500 with GSC-10 pedal and cadence sensor to analyse which sprockets on my cassette I use, and which I don't.

The graphs I produced, such as this one

seem to show clustering of results around what the cassette offers (its a Shimano 105 11-28 so has 11-12-13-14-15-17-19-21-24-28).

The next question is: if these are my results from actual ride data, what would a theoretical approach look like?

So I took the data from a longer ride (roughly 65km over 2.25 hours giving about 10,000 data points), and again plotted speed vs cadence: NB speed in kph, cadence in Hz.

Again, I used Google Spreadsheets to calculate theoretical values. What I did was to create a matrix of speed vs teeth, and each data point is the cadence in Hz, populated using the formula discussed previously:

which I've plotted. Each coloured line represents a particular sprocket

So is the analytical model valid? Here's the two charts overlaid and scaled

Woot! I would say that means yes!

Next: is the pedal cadence I've arbitrarily set OK? I test this in a bit...