Does your geared bike have a matching gear to a fixed? If so, the flywheel 
effect should be notacible, though there are multiple levels of getting more 
and more scientific to compare the two efforts. But if you ride them both on 
the same day, two days in a row, alternating which one is first, then compare 
times and percieved effort level, the result would be interesting.

My own macro observations are that my average speed is nearly identicle to 
freewheel, but my climbing speed is increased while my descent speed has 
decreased. Sincle climbing speed increased immediately on switching to fixed 
gear, with a similar gear to my freewheel ss, that points to the flywheel 
effect. Like you though, the physics of it baffle me, but I don’t really care. 
The difference it makes for my brain when riding is enormous. Grin.

With abandon,
Patrick

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