bicycle physics question? (wheel size)
06-09-09, 09:44 AM
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bicycle physics question? (wheel size)
I suppose this is a kind of physics question, but I've been wondering about it, and I'm no physicist, not by a long shot.
Take two wheel sizes - significantly different but not dramatically, such as 584mm ("650b") and 559mm (26"). Now put a narrow profile tire on the bigger wheel and a wide one (or at least "tall" when viewed from the side) on the smaller one, so that the diameter of the wheels+tires ends up the same or very close. Let's say we pump both tires up to max. pressure so they're pretty rigid; not much distortion where the rubber meets the road.
Will these two wheels now have similar behavior, in terms of acceleration, rolling momentum, etc? That is, have we ended up with the same "effective wheel diameter", or is the rim diameter the sole determinant of those characteristics which are said to be effected by wheel size?
I suppose we should leave rolling weight out of the equation: let's say they end up being the same weight due to rim and tire choices.
I always puzzle over these things but lack the brains and math to figure them out.
Take two wheel sizes - significantly different but not dramatically, such as 584mm ("650b") and 559mm (26"). Now put a narrow profile tire on the bigger wheel and a wide one (or at least "tall" when viewed from the side) on the smaller one, so that the diameter of the wheels+tires ends up the same or very close. Let's say we pump both tires up to max. pressure so they're pretty rigid; not much distortion where the rubber meets the road.
Will these two wheels now have similar behavior, in terms of acceleration, rolling momentum, etc? That is, have we ended up with the same "effective wheel diameter", or is the rim diameter the sole determinant of those characteristics which are said to be effected by wheel size?
I suppose we should leave rolling weight out of the equation: let's say they end up being the same weight due to rim and tire choices.
I always puzzle over these things but lack the brains and math to figure them out.
06-09-09, 10:03 AM
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I could be wrong, but I think the smaller rimmed, bigger tired wheel will produce a slightly larger contact patch than the other. Other than that, they should behave the same.
06-09-09, 10:19 AM
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A smaller wheel will have less angular momentum, so it will take less force to accelerate and decelerate, but more force to keep the momentum going.
It's easy to take something smaller and spin it, then take something larger (of the same weight) and see this in effect.
It's easy to take something smaller and spin it, then take something larger (of the same weight) and see this in effect.
06-09-09, 11:17 AM
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So the two have the same diameter because the smaller wheel has a taller tire, right? the overall diameter is the same, their mass is the same, what will differ is how their mass is distributed.
Assuming they both have the same mass, acceleration depends on their angular momentum, or their tendency to resist changing how fast they're spinning (if they're not spinning, its how much they tend to resist beginning to spin).
The smaller wheel with the taller tire will probably have the heavier tire which means that although both wheels have the same mass, the one with the taller tire will probably have a greater percentage of its mass further away from the hub, so more of its mass has to be accelerated and decelerated to greater linear velocity..... i.e. it has a greater 'flywheel' effect.
You can visualize it like this: as the wheel is spinning, if you touch the hub it will rub against your fingers, but if you touch the rim although the wheel is turning at the same revs per minute, the rim would rub against your fingers much faster than the hub. So weight at the rim had to be spun up to a greater speed than weight at the hub, hence it's easier to spin up a wheel that has a thin, light tire on it than one with a tall heavy tire on it (of the same diameter), even if the difference in weight is redistributed to the rest of the wheel.
How important is the weight of your wheels? the answer is 'depends how far away from the hub the weight is' the further from the hub the greater the importance.
Assuming they both have the same mass, acceleration depends on their angular momentum, or their tendency to resist changing how fast they're spinning (if they're not spinning, its how much they tend to resist beginning to spin).
The smaller wheel with the taller tire will probably have the heavier tire which means that although both wheels have the same mass, the one with the taller tire will probably have a greater percentage of its mass further away from the hub, so more of its mass has to be accelerated and decelerated to greater linear velocity..... i.e. it has a greater 'flywheel' effect.
You can visualize it like this: as the wheel is spinning, if you touch the hub it will rub against your fingers, but if you touch the rim although the wheel is turning at the same revs per minute, the rim would rub against your fingers much faster than the hub. So weight at the rim had to be spun up to a greater speed than weight at the hub, hence it's easier to spin up a wheel that has a thin, light tire on it than one with a tall heavy tire on it (of the same diameter), even if the difference in weight is redistributed to the rest of the wheel.
How important is the weight of your wheels? the answer is 'depends how far away from the hub the weight is' the further from the hub the greater the importance.
06-09-09, 02:19 PM
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most interesting
Great responses. I'm now running a 26 inch wheel with a 1.6" slick tire. It's great for darting around urban neighborhoods as the wheels are quick to accelerate, in keeping with assumptions about wheel size.
However when I do my commute, the last four miles of which are a steady, moderate climb - not steep at all, but the fatigue is cumulative over that distance -, I think I can feel the limitations of the small wheel: thrust, fade, thrust, fade... with each pedal stroke, and felt like a bigger wheel (there is adequate standover height) would have a tendency to sustain momentum better.
I don't want to lock into the pedals with straps, etc. and I'm no athlete; age 60, reasonable riding shape for the age.
If I were to switch to 650b I thought it might improve this aspect while retaining some of the responsiveness I like (It'll work on my bike; Ive checked).
But if I went with a lower-profile tire I might end up with a total wheel diameter not much different from what I'm riding, and wondered if the whole thing would just be a wash in that case.
But the theoretical part is interesting apart from all that, and you folks seem knowledgeable.
Chas.
However when I do my commute, the last four miles of which are a steady, moderate climb - not steep at all, but the fatigue is cumulative over that distance -, I think I can feel the limitations of the small wheel: thrust, fade, thrust, fade... with each pedal stroke, and felt like a bigger wheel (there is adequate standover height) would have a tendency to sustain momentum better.
I don't want to lock into the pedals with straps, etc. and I'm no athlete; age 60, reasonable riding shape for the age.
If I were to switch to 650b I thought it might improve this aspect while retaining some of the responsiveness I like (It'll work on my bike; Ive checked).
But if I went with a lower-profile tire I might end up with a total wheel diameter not much different from what I'm riding, and wondered if the whole thing would just be a wash in that case.
But the theoretical part is interesting apart from all that, and you folks seem knowledgeable.
Chas.
06-09-09, 02:35 PM
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The size of the contact patch is not a function of the size of the tire. Instead, it's a function of how much weight is on the tire and the pressure in the tire.
If this tire has 100 lbs on it, and 100 lbs/in^2 of air pressure in it -- the contact patch is one square inch. It's that simple -- weight divided by pressure. Yes, the rigidity of the rubber and the shape of your tread and such affect this to some degree, but the effects are minor.
I believe that rolling resistance is mostly due to rubber being squished and moved back and forth and such, so it would be increased by lower tire pressures and larger tread patterns on the tire (slicks are best.) Air resistance would be increased by having a fatter tire vs. a thinner one.
If this tire has 100 lbs on it, and 100 lbs/in^2 of air pressure in it -- the contact patch is one square inch. It's that simple -- weight divided by pressure. Yes, the rigidity of the rubber and the shape of your tread and such affect this to some degree, but the effects are minor.
I believe that rolling resistance is mostly due to rubber being squished and moved back and forth and such, so it would be increased by lower tire pressures and larger tread patterns on the tire (slicks are best.) Air resistance would be increased by having a fatter tire vs. a thinner one.
06-09-09, 03:16 PM
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so for a stop start commute 26" tyres would be best? as it takes less energy to speed them up and slow them down. but not so good if you have hills?
06-09-09, 06:43 PM
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stop-start commute
I'm sure there are lots of differing opinions, but yes, in my experience the stop/start riding is well-served by the smaller wheels. In theory steep hills ought to be better with these, too, if you want a low effective gear and are willing to ascend slowly. My commute is early morning, on residential side streets, and I can run almost all the stop signs (judiciously, of course, and at my own risk) and stay on the bike and keep moving. The incline is slight but extended over 4 miles and I had the feeling I'd do better with a wheel that would sustain the momentum from each pedal stroke a little longer, and my (crackpot?) theory was that a bigger one would tend to do that. I do like the 26 inch wheels for "scooting around", though. I have grippy platform pedals that allow me to ankle a little bit, and that helps, but I don't want to go to any "trapped feet" arrangements, as I'm just not comfortable with it any more, even though I know it's more efficient.
