Can it be easier to cycle uphill?

[Breakout Hit]

I am a lay person trying to solve a bet. I contend that pedalling a bike uphill can easier than pedalling on a level plane at a 1:1 gear ratio, if:

[a] The bike is put in a higher gear ratio such as 10:1
The rider accepts travel at a reduced speed and therefore a longer duration ride, if equal distances
[c] The incline is limited to keep the assertion feasible

Certain friends insist it is always harder.

Knowing this forum's members will bring science to bare, I nervously await your replies...

Thanks,

BH

 

[ideasrule]

This is probably the most disappointing answer possible, but it depends on what you define as "easier" or "harder".

If you define difficulty based on the force it takes to keep the bike moving, it's certainly true that peddling uphill could be easier if you put the gears on a higher ratio. Frictional forces like air resistance and rolling resistance don't depend on the gear ratio, so using a higher ratio would help you combat these forces as well as the force of gravity.

If you define difficulty based on the energy it takes to get from A to B, the answer is less clear. If A and B are separated by a vertical distance of "h", the energy it takes to move an object of mass m from A to B is always going to be greater than mgh. There's no way around this, no matter which path you take or how cleverly you move the object. So in an ideal world with no friction, going uphill will take you E=mgh, and traveling level will take E=0. It's possible that when going uphill, frictional forces on the bike change so that the total resistance to the bike's movement is lower than on level ground. For instance, if you're going more slowly while traveling uphill, air resistance would be lower. This might mean it takes less energy to go uphill, but it could be equally true that frictional forces don't change enough to make up the mgh loss, meaning it would take more energy.

Another option is that you can define difficulty based on how easy it is, subjectively, to go from A to B. Again, there's no clear answer. At least for me, subjective difficulty isn't proportional to force--riding a bike for 10 minutes isn't as easy as riding it for 5 minutes, even if I'm applying the same force throughout the ride. It isn't proportional to energy, either--I find it much easier to bike up a hill by circling around it rather than going straight up, even though it actually takes more energy to circle around due to frictional losses. I suspect subjective difficulty also varies from person to person, so there's no easy answer to this question.

 

[DaveC426913]

How do you define effort of pedaling on a flat plane?

At first blush, effort expended could be zero, so pretty hard to beat that...

 

[NascentOxygen]

Surely, if you stop to think about it...

Isn't it always going to be true--that cycling with gearing is more effortless than cycling without gears--until the incline is made sufficiently steep that it isn't more effortless??

I'm valiantly trying to not get tied in knots, here.

 

[Breakout Hit]

Surely, if you stop to think about it...

Isn't it always going to be true--that cycling with gearing is more effortless than cycling without gears--until the incline is made sufficiently steep that it isn't more effortless??

I'm valiantly trying to not get tied in knots, here.

That's my position... just wondering if someone can show why that is not the case.

 

[Breakout Hit]

How do you define effort of pedaling on a flat plane?

At first blush, effort expended could be zero, so pretty hard to beat that...

Good question. In an effort to keep it really simple I'm going with amount of force expended to cycle for ten seconds; uphill with optimum gearing vs level with 1:1 gear ratio.

 

[DaveC426913]

Good question. In an effort to keep it really simple I'm going with amount of force expended to cycle for ten seconds; uphill with optimum gearing vs level with 1:1 gear ratio.

Again, cycling for ten seconds on a level plane theoretically takes zero effort, so how do you propose to beat that?

There are variables unaccounted for in your setup.

 

[Jobrag]

It will ALWAYS be harder going up a slope (unless the gradient is very very small). When going up hill you have to keep on working all the time otherwise you will stop, on the flat you can always freewheel for a while to give some respite.