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umop3pisdn
frankenbike
Fair warning to all: mathematical speculation below.
Your cadence at a given speed will be the same with any crank length. However, the speed at which your feet move (around the circumference of the circle traced by the pedals) will change. Power is given by P = F v where F is force on the cranks and v is the speed of your feet/the pedals moving. So if your power stays the same on the new cranks you're putting in more force on the pedals but moving your feet slower. Is this bad? I have no idea. But intuitively I feel like your knees might be more sore than usual.
If you want to maintain the same foot speed/force/power on the new cranks your cadence will have to increase by a factor of 172.5/160 (so from e.g. 90 to 97), as the distance travelled in one crank revolution is just 2π r where r is crank length. To maintain the same foot speed, power, force on pedals, bike speed etc. you would therefore have to gear down to about 39/24 or 36/22.
To take it to an extreme, if you switched to cranks that are 1mm long, you'd have to put a massive amount of force through them to maintain the same ground speed, so you'd gear way down. If you switched to cranks that are 1m long it would take next to no force to move them but you'd have a really jerky motion as your feet would be moving so fast, so you'd gear up. Makes sense?
Is it more important to maintain downward force at the pedals or cadence? I have absolutely no idea. Would be interested to hear anyone else's thoughts on the matter. I would be especially interested to hear what you think if you try riding the same bike with a 24 and your current 22 and see which you think matches the current feel best.
But this is all speculation and I really wouldn't recommend spending any more than a very small sum of money based on some dodgy maths done by an internet weirdo (me)