Originally Posted by
Carbonfiberboy
Thanks. Yes, I suppose I do have a specific idea about crank torque. That would be whatever I think my legs can handle for the anticipated duration of the stress. So I've done a 3000' climb at 55 cadence just for fun because I was accompanying a slower rider and still wanted a good leg workout. The low cadence increased crank torque enough to produce adequate leg pain by the end of the climb. Usually I'll climb at 78-82 cadence because my 90%LT power combined with that cadence will cut crank torque enough to allow my legs to keep functioning for a couple hours anyway. [...] So I'm saying that in my mind, power is a function of torque * cadence. If power is limited, then each rider has to find a balance between torque and cadence that suits their physiology and current goal, assuming that gearing is unlimited, which of course it's not, so we can't always choose just what we want even if we know what that is.
Does that make sense?
Well, perhaps it does but I've never been able to understand why, which is the reason I was asking.
On steep hills, we know that the aero component of drag is pretty small and the main component of power is just to lift the weight of you and the bike. That part of power is linear with speed (the aero component is, of course, cubic with speed). For any given gear ratio, speed is linear with cadence -- so for any given gear ratio, on a steep hill power varies linearly with cadence. As you say, power = torque * cadence so if power varies linearly with cadence on a steep hill for any given gear ratio, crank torque is constant.
So once you're in your lowest gear, it doesn't matter whether you pedal at 50 rpm or 80 rpm (or 40 rpm or 90 rpm) -- the crank torque is almost constant. In fact, pedaling faster doesn't reduce crank torque, it increases it (slightly). That is, once you're in your lowest gear, pedaling at 80 rpm doesn't put less strain on your legs than pedaling at 50 rpm -- it's almost exactly the same.
So you can see why I've been puzzled about appropriate cadence. On a steep hill, crank torque is almost entirely determined by gear ratio, and almost entirely independent of cadence.