OK...so I couldn't sleep, @
taras0000 and @
brawlo.
I did some research and I didn't need to factor in Torque to figure out how different crank length and chainring cog combinations feel the same.
There is a concept called the ground propulsive force ratio that uses the factors:
- Wheel size
- Crank length
- Chainring
- Cog
and gives a dimensionless number similar to how the coefficient of drag is dimensionless...but can be felt
Long story short, longer cranks allow you to use the same given amount of force to drive a bigger gear.
Well, duh. Everybody knows that
But, can everybody prove it?
Here is a chart I made using a spreadsheet of the formulas that shows which gear ratio you can ride to keep a given amount of force (how hard you mash each pedal stroke) the same. Basically, pushing a 94" gear using 165mm cranks feels the same as pushing a 99.7" gear using 175mm cranks.
Bear in mind, the results of the pushing will be different. With longer cranks, your foot has to travel further each pedal stroke resulting in a lower cadence, but you get more distance traveled per pedal stroke. With shorter cranks, each pedal stroke is shorter resulting in a higher cadence, but the distanced gained is shorter. All of this happens with the same amount of force (feel) on the pedal.
This explains part of why changing crank lengths require one to rethink their gear choices
This also helps explain why cranks are offered in minute 2.5mm increments.