I bought a Fuji Professional with 175 cranks in 1977 because the mechanic in the shop I worked said I should buy the boxed one in the basement. I did. I knew nothing about fit; that bike was a radical departure from anything I had ever ridden and from day one I was faster than I had ever known. That fall I had a serious crash. The next March I was training to race again in my fix gewar with 168 cranks. Switched to the Fuji to ride 100 miles in prep for the first race that weekend. That was a crank length change combined with poor fitness, lack of stretching and the cold weather of New England. My knees have never been the same. Now switching crank lengths is a big deal so big I don't. I ride 175s on all my bikes, even my three fix gears.

Not saying there is any magic to 175s. They work well for me and there is real risk to my knees making any changes. (I used to be 6'1/2" with long legs. That first dimension is now shrinking.)

Ben

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.

I've always run 175s because, well, that's what the bikes came with from the factory. When I replaced the factory 48/34 crankset on my touring bike with a 39/26 unit, though, I also opted for 180mm crankarms. That extra 5mm per arm translates to a 10mm (4/10") larger circle by the pedals, and basic physics tells us that the longer arms provide additional torque. Unloaded and/or on flat ground the difference is so slight as to not be noticed, but when loaded and/or climbing, that additional leverage adds incremental torque.

Thanks for the comments. My experience is the same. Mostly seems to matter very little. Seems a bit less pressure on my knees with shorter cranks and a higher cadence. But something to say for more leverage on hills and cranking out long miles with longer cranks.
I don't mind intelligent disagreements but Shelbyfv really needs to take his insults somewhere else.

Harassment/Trolling other forum members is a violation of BF Guidelines.