Informative article on crank arm length
Nice little article on ST's front page about crank arm lengths and gearing: http://www.slowtwitch.com/Tech/Crank_Length_and_Gearing_4095.html
Take home lesson: If you shorten your cranks, you make your gears "harder" because of the shorter lever arm. (You have to increase the Torque/Force, but over a shorter distance, so it's the same total energy...just more force = "harder".. I did a calculation on my bike when I went to 165s that suggested that all gears would be about 1 gear "harder". For me it seems to have been a good trade off, because it allowed me an aggressive low fit without squashing up my torso angle and lowering FTP. You'll see a discussion of this.
Nonetheless, going "one cassette easier" is something to consider if you make the change.
Comments
It's enough to make my head hurt. There are two many variables to make a reasonable equation, much less guesstimate in some sort of logical fashion.
I switched last year from 172.5 to 167.5 cranks. I kept the 650 wheels and the 53/39 chain rings. I alternated between 11/28 and 11/32 cassettes. And, as a result of the shorter cranks, I was able to lower my front end substantially - either 5 - 10 mm, with a higher saddle to account for the shorter crank.
So my hip angle was more open - "stronger" - and my position was more aero. It's very hard to know if those two effects more than made up for the increased force I needed to apply due to the shorter cranks. Which I calculate @ 1.7% when riding @ 20.3 mph, a common speed on the flats in an IM for me.
Anyway, I came away from the article not convinced that I needed to change my gearing at all when going 5 mm shorter in my crank length. The change in position (lower front end, more open hip angle) I believe enables me to go the same speed with less fatigue (the only metric that matters to me: how fast can I run afterwards?). It's kinda like comparing road to tri power - the aero position changes more than compensates for the decrease in power which the TT position imposes.
Given how easy it is to change Cassettes or pick a different gear, I don't see how it would really matter for "most" AG'ers anyways.
And As Tim observed, these differences are so minute that most people wouldn't notice them anyways.
But what Al commented on is spot on. Going to a shorter crank nets you 2x the difference in length in lower bars, assuming one of of your limiters is your knees hitting into your belly at the top of your pedal stroke. This also allows you to open up your hip angle as well like he noted.
The Geeky BioEngineer in me loves this topic...
I have a 165 ultegra crank set that I am selling if anyone is interested in trying it out
John...be careful with your units. :-) there has to be the same amount of energy per full rotation. (Imagine the case that you are going on a 100% grade with an otherwise frictionless system.)
Lets imagine a super extreme example, where the circumference of the shorter cranks was exactly half of the circumference of the long cranks. In this case, at the same foot speed, the shorter crank would need to make 2 full rotations for every rotation of the longer crank. Then if we were going up the same 100% frictionless incline, the same amount of work would certainly need to be done, but the shorter crank would need 1/2 as much work per rotation but do 2x as many rotations to get there. Now I haven't actually muscled through the equations to determine if that's better or worse, but it's not as obvious as he makes it sound in the article. I would think that If I were doing bench Press and needed to lift 2,000lbs, I'd be less tired after doing 20 reps at 100 lbs than I would be after 10 reps at 200lbs. And I know I couldn't even do 8 reps at 250lbs.
My nuance is I'm assuming the same effective foot speed. This will simple help to promote a "slightly" higher cadence at caonstant power. Obviously there would be limitations to this as you get to the extremes, but the difference we're talking about in circumference is not that great when we're only talking about a 5-10% change in crank arm length. But I'm guessing that the it makes the differences mostly negligible.