Originally Posted by
wphamilton
That's the general misconception that drives this I think. It's completely different from gearing, which allows you to exchange cadence for torque. With different cranks it is the same torque, but exchanges cadence for foot speed.
Torque and force are proportional, for a given crank length. Shorter cranks mean more force to produce a given torque.
How torque and force relate to each other with crank length is analogous to how cadence and foot speed relate to each other with crank length. They're two sides of the same coin.
The actual "force" that you're concerned about is much lower than people would tend to think. When you're cranking along at around 180 watts, it's a few pounds. Maybe 5 pounds. The difference you're concerned about is a few ounces. It's too trivial an amount to make a difference in cadence.
I completely agree that the 172.5 vs 175 different is too small to make a noticeable dent; my original response noted that the length is only a 1.4% difference, and I went on to describe how pursuing cadence changes by altering crank length is pretty silly in any case.
How did you come up with 5 pounds, though? A 175mm crank arm sweeps a path with a circumference of about 2*.175*3.14159 = 1.1m. A cadence of 90rpm would be 1.5 revolutions per second, which means that the pedals are moving at around 1.65m/s. Power is force times speed, so force is power divided by speed. So, 180/1.65 gives 109 newtons. 109N is about 24lbs, or 12lbs per foot. But that's average force: in most pedal strokes, the downstroke is where most of the power delivery happens, and the upstroke is usually ever-so-slightly-negative, so the force should peak at much higher than 12lbs.