Title says it all. From a physics point of view, gravity is a conservative force and so the amount of work done should be the same, and yet one option is a lot more tiring than the other. It's especially odd if we consider friction, since rolling friction is less than static friction, which should imply that cycling up the hill does (slightly) less work. I understand that it's because of friction that if the terrain is flat, cycling is easier than pushing a bicycle.
Here're some hypotheses I've thought about:
- If a person is standing on an inclined plane, he's probably stationary (because of friction). But a bicycle will roll downwards. This constitutes an extra force that a cyclist has to overcome.
- Something to do with the human body, i.e. if we replaced the cyclist with a machine then it'll indeed do the same amount of work both ways.
- Something to do with the human body, in the sense that if we had an Olympic-level cyclist then he'll have no problems cycling up the hill. In other words I only feel more tired because I'm unfit.
- Tiredness correlates to power (physics "power" – work done / time taken). One cannot ride a bicycle slowly up the hill, since the bike won't stay upright; conversely if one is riding the bicycle faster than pushing speed, there's a difference in power.
I find #1 unconvincing since it seems to be double-counting the "roll backwards" force together with gravity. #4 sounds reasonable but on flat ground things reverse, which is contradictory. The other two are plausible. Does anyone know if either (or both / neither) are correct?
Best Answer
The bike's gears are set so that a large force over a shorter distance at the pedal gives a smaller force over a longer distance at the wheel. This is the opposite to most machines, eg. a screw-jack or winch where you put in a smaller force over a longer distance to move a much heavier load.
Normally when you are cruising on the level you want this - the force needed at the wheel to overcome drag and friction is low compared to the force you can easily push with on the pedal. But going uphill you reach the point where to move fast enough to stay upright you have to put a lot of force on the pedal.
Some extreme mountain bikes have low gear ratios <1, so that less force on the pedal than at the wheel - you have to spin to move at a crawling pace.