Originally Posted by jschen
Energy = Mass * Vertical Gain * Gravitational Pull
Neglecting parasitic forces (wind resistance, rolling resistance, drivetrain inefficiencies, differences in pedaling efficiency, etc) makes for pretty good and pretty easy approximations on steep enough a hill. Once we make that approximation, what we find is that it takes the same amount of energy to get up that hill no matter how you go about it. After all, your mass doesn't change with how you climb, the vertical gain isn't changing, and the earth's gravity most definitely isn't affected by your climbing technique.
Correct...that's the answer I was expecting on a logical basis.
(On the other hand, once Mars gets terriformed, climbing Olympus Mons wouldn't be nearly the challenge it would appear to be since the gravitational pull on Mars isn't as great.)
True, but climbing out of Valles Marineris might make the lungs collapse a scoch.
Energy = Power * Time = Power / Speed
The first part is simple physics. The second part is pretty obvious since time and speed are inversely related. The faster you climb, the more power you need. Climbing 50% faster takes 50% more power. Plain and simple. But notice that climbing 50% faster gets you up there 50% faster, so your total energy expenditure stays the same. This is why the mountains are where huge time gaps are made.
Power = Torque * Cadence = Pedaling Force * Crank Length * Cadence
Here is why gearing matters. For the same speed, you can do it in different gears, resulting in different cadences. Your cardiovascular system (again neglecting parasitic forces) doesn't care because the same amount of power is needed at that speed no matter how you go at it. (In reality, higher cadences have slightly higher parasitic forces.) But your leg muscles may care, because you can only pedal so hard without getting tired really fast.
Ergo, the way to benefit from a Compact and stay with the Standard guys who are hammering is to just pedal faster and more efficiently in the smaller gear available to you.