I decided to build my own bike, waited until I could get shorter cranks at a cheap price.
I don’t believe there is a reasonable cost/benefit to spend a lot of money on this element. But it is all about belief when it comes to bikes.
If it was really bonus watts the fitter wouldn’t be calling it optional.
I generally agree with you, but your fag packet maths - does that translate outside the UK? - is excluding the human part of the mechanics which is the point of shorter cranks - they allow better delivery of power to the pedals by reducing unfavourable angles/stresses in the human.
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If only I had touched on the physiological side in the same reply you snipped down to 5 words… oh wait 
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Generally it doesn’t translate to the US. But it brought back a great memory of a young American who got tapped on the shoulder his very first night in Britain, “Oy! no fags on the dance floor!” With all his sputtering, it definitely didn’t translate for him!
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I don’t think you did, hip angle? Force production?
Key phrase, touched on, not meaning all inclusive not hitting on those specific ones you highlight. I tried to leave an open door without trying to cover all the potential reasons.
Without writing an entire diatribe here, I have done any and all of the common tricks with crank lengths in fits, to include mixed lengths on the same bike to handle ROM and impingement issues. There are many reasons like those angles, joint use and more that can justify certain crank length choices.
I am all for long, short, in-between & mixed. The reasons to choose between those vary widely while many people can and do perform well with the “standard” sizing mentalities that existed for many, many years. I will swap any crank for someone as long as I don’t see it creating a problem worse than the intended goal.
I just question the somewhat fuzzy claims (questionable short term data or complete lack there of) and think the “performance” side of these changes is not entirely clear or positive for all. From the bits I’ve taken over the years, outside of the more notable ROM type things I have done, the power & efficiency related items are more unknown than known to me at least.
If we rewind this to the OP (which was really my focus despite wandering a bit), I don’t see anything concrete here worth a clear endorsement that shorter = better in a way that justifies the expense that seems at least questionable to the OP in the first place. When it comes to a recommendation where someone else is looking at a notable expense, I tend to keeping $ in the wallet unless there is a clear benefit to be had. I don’t see that here nor in many of the offshoot comments, while some are well worth it. I certainly didn’t say never, but I also don’t think always is right either. “It depends” yet again shows as a concept where there is no single answer for everyone or every use case.
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I’ve experimented with cranks between 180mm and 152mm over the last year and was shocked how good the short ones worked for me. But I abhor the idea of staring at numbers when I ride so all I can do is offer anecdotes.
Small changes was another story - going between 175 and 170 I always went back to 175.
The other catch to my story is that I had to make some radical changes to the bike to get a good fit so we have to start wondering how much is the crank itself and how much is the fit around the crank. Until I figured out the fit side going shorter than 165 felt just dumb to pedal. Then there’s the accommodation side - are you willing to spend the money and then stick it out for 6 months? I had a mule bike and a bunch of cheapo cranks set up 1x to play around with.
RIght now it’s a hot topic so you probably wouldn’t have much trouble offloading the cranks if they don’t work out.
From what I’ve read it sounds like there is little risk of going to 165mm. So it’s tempting. My concern would be trying to sell the 172.5mm cranks if people are looking for good prices on shorter cranks. I think I’ll keep an eye on some ebay sales and see how quickly they go and for how much
I don’t think this is right. Same cadence, same resistance, you’re putting out the same torque and the same power. If going with shorter cranks meant you had to put out more power to go at the same speed then everybody would be riding around on giant cranks!
What has changed isn’t power but force at the pedal. Shorter crank means a shorter lever which means to maintain that same cadence you need to apply more force at the pedal, but you’re applying that force with a slower pedal speed (because you’re on shorter cranks, hence shorter circles, so same cadence means lower pedal speed) so power is the same.
If this is true I would guess the reasons are as likely to be about aero as they are pedalling mechanics. E.g. Let’s say you’re on 170mm cranks and already have good pedalling mechanics I.e.hip angles are good, etc. If you switch to 165mm cranks then you can potentially drop the saddle 5mm while maintaining same hip angle over the top of the pedal stroke. And at the bottom of the pedal stroke your feet are now 5mm higher. So you’ve effectively reduced the size of the hole you have to make in the wind by 1cm vertically - back is 5mm lower, feet are 5mm higher. I understand from people who spend time testing aero positions that that can lead to measurable aero improvements, so assuming that change can be achieved without compromising power output or biomechanics it’s worth doing.
He said they measured increased power at the same cadence, to overcome the same resistance. I didn’t understand at first how that was possible - as you said, power should be the same, given those constraints, and then thought they must mean higher torque (with the shorter lever) at the same cadence.
Just reread the original comment and yes there’s definitely some crossed wires somewhere in terms of either the methodology or the terms being used!
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I wouldn’t get hung up on cadence - what matters is foot speed and leg force.
Let’s say you run a 6 minute mile on a standard track. Your “lap cadence” is 40 laps/hour. If you then go run on a shorter track, your “lap cadence” will increase but you’re not running any faster.
You can also get hung up on oversimplified power = force times cadence models but your body is not a jacuzzi pump that runs at a constant load. You are constantly changing your force and velocity within the pedal stroke and then numbers your Training Overlord are showing are averages.