Originally Posted by
GamblerGORD53
Maybe I used the wrong terminology BUT ... Pedals ARE levers >> Power or work = F x D.
Math is math. There is nothing wrong with my math as stated. 5/ 165 = 3%.
The math you demonstrate is valid for the effort as exerted over the pedal, not for the power.
And, this is valid only if the rider provided the same torque & power output as with the different length crank.
Hence, your statement is still wrong.
Besides, what you mention is a valid formula for mechanical work, but not for power. The power is the rate of work done, meaning work per unit of time.
And, the "equal torque and power" premise is most certainly wrong, since the rider provides quite a bit different torque and power with a different crank length.
I've ridden with 170 mm cranks for 41 years, and then with 165 mm cranks for the next 10, and my power output is at least 4% better with the shorter cranks.
Looking at the crank as a lever is oversimplifying the entire power delivery chain, as the human body does things better or worse based on a bunch of factors, range of motion being just one example.