Larger wheels - easier to turn?

I've seen it mentioned that larger wheels are easier to turn - is that actually the case? How would that work?

The way I see it, larger wheels will have more angular momentum, meaning they'll take more energy to start turning, but while spinning, will be easier to keep at the same speed?

• Good question. I added the folding-bicycle tag, since this is obviously going to apply to them. Nov 10 '10 at 4:38

Larger wheels have lower effective rolling resistance. That is, they roll over obstacles more easily and smoothly because the larger diameter doesn't allow them to fall into gaps as easily. Which means on actual roads you'll roll more easily with a larger wheel. Everything else is much smaller differences.

However, I think the angular momentum may work out about the same: at the same speed, a bigger wheel will have a lower rpm than a smaller wheel. And the ratio of the difference in rotation speed is the same as the ratio of the the angular momentum. To put it another way: I'm too lazy to work out all the math, but I think the angular momentum cancels out and you get the same linear momentum regardless of wheel size. (and having the same linear momentum is an intuitive result. If you're going 15mph, relative to you the bottom of the wheel is going 15mph back, the top 15mph forward, the front 15mph down, the back 15mph up. Relative to the road it's 0, 15, 15 and 30. All independent of wheel size)

Constructing a larger wheel will generally require slightly more mass and might therefore slow your acceleration slightly.

Also, all else being equal, a larger wheel is geared higher and may give you a higher top speed.

• Good point about the rolling resistance. As for the momentum, I think I figured the larger wheel has more MASS at the rim than the smaller one -- but it's been a while since I did that kind of math. Nov 5 '10 at 18:08
• For a fixed geometry (mass distribution), the moment of inertia `I` of a wheel of mass `m`, radius `r` is `kmr^2`, where `k` is some constant (less than one). At a speed `v`, the angular velocity of the wheel is `v/r`, and so the angular momentum is `Iw = kmvr`. So, for a larger wheel, you do have more angular momentum. But momentum isn't what's important - energy is. The kinetic energy is `1/2 Iw^2 = kmv^2 / 2`. This means it takes the same amount of work (energy) to get up to the same speed on the different wheel sizes. Nov 5 '10 at 21:25

It mostly has to do with gearing. Imagine we have a big wheel of 26 inches and a small wheel of 10 inches.

The 10 inch wheel will have a circumference of 31 inches.

The 26 inch wheel will have a circumference of 163 inches.

This means that to travel 163 inches the big wheel will need to spin once and the smaller wheel will need to spin 5 times.

Another way to put this is that the bearing on the smaller wheel will need to travel a distance 5x further than the bearing on the larger wheel.

My physics is too rusty to calculate the force of friction from the bearing but physics public beta opens in 4 days we should ask them.

• Oh, sure, wheel size is calculated into the gear ratio, basically, but the sentiment I get is that even if the gears compensate for the different circumference, the larger wheels are "easier". And that's the part that confuses me. Nov 5 '10 at 18:06
• Traveling farther on the bearing doesn't mean it's any harder - force of kinetic friction doesn't usually have a strong dependence on velocity. Nov 5 '10 at 21:30
• Actually, I'm not sure of the math/physics behind it, but smaller wheels generally require a lot more maintenance. From what I've heard, if you tow a trailer with small wheels behind a car, you have to be sure the bearing are properly greased, or they can seize up. Higher (rotational) speed results in increased friction, which causes excessive heat, and causes the grease to break down faster. Nov 8 '10 at 1:00