physics of bike wheel

[Ray(GB)]

Hello All,
How does a thin-spoked bike wheel stay stiff?.
Thin metal spokes bend in compression ,so they must all be in tension.
Which means that the whole weight is borne by the spokes at the top quarter of the wheel,the rest cannot give support,can they?.
Thanks,Ray.

[Anders Troberg]

While not actually knowing anything about this, my guess would be that the rest of the spokes give support by stopping the rim from deforming. If only the top spoke where there, the rim would get bent into an oval, which is usually not the preferred shape. All the spokes work together to make sure the wheel stays round and the hub stays centered, but the main weight is probably carried by the top spokes.

It may very well be that the flexibility in the rim can transfer some of the force into the other spokes as it tries to bend out of shape, much like the bow string can create a force straight backwards, even though it is attached to the ends of the bow. Think of it as the bow being the upper part of the rim, the point of the string where you put the arrow is the hub and the string is the spokes.

[El-Kablooey]

The hub in the center is being pulled equally in all directions. It is kind of just suspended, I see what you are saying about the weight being on the top 90 degrees of spokes, but with the wheel spinning the top spokes are always changing very quickly.

[Bruno Ogorelec]

All the spokes are under load because the rim transfers the force by trying to deform under load. When a load pushes downwards on the top of the rim, the rim tries to deform. The effort is transferred to the entire circumference of the rim and thus exerts force on all the spokes. The difference is that the direction of the loading differs, depending on position. For instance, the upright spokes are being compressed while the side spokes are being pulled apart. In practice, as the wheel rolls, each spoke is subject to a quick cyclic change of compression and pull.

[El-Kablooey]

good explananation!

[WebPilot]

For instance, the upright spokes are being compressed while the side spokes are being pulled apart.

If one has ever laced a spoked wheel, you know "a spoke in compression"
is an impossibility. You insert the hooked end of the spoke thru the hub
(the part where the axle goes), and attach the other end (which is
threaded) to the wheel with a nipple. This nipple makes only surface "contact" with the wheel (or rim), thus it is capable of exerting a force in
only one direction.

If the hub were to get closer to the rim, the tension in the spoke would reduce to zero and the spoke may "loosen". The spoke load would not go into compression.


-fde

[Anders Troberg]

Well, I still believe that the key lies in the deformation of the rim. I doubt the bottom spokes takes any load, but just about every other spoke does as they stop the wheel from going oval. This tendency to go oval transfers the load around the wheel, somewhat like a keystone bridge.

As a side note, there is a style of Swedish folk music that has been described as riding a bike with an oval wheel, and the further north in Sweden you get, the more oval the wheel get. I doubt this has anything to do with spokes, though. (If there are any Swedish readers here, think of a bike with an oval wheel while humming "Hej tomtegubbar slå i glasen".)

[larry cottrill]

For instance, the upright spokes are being compressed while the side spokes are being pulled apart.

If one has ever laced a spoked wheel, you know "a spoke in compression"
is an impossibility. You insert the hooked end of the spoke thru the hub
(the part where the axle goes), and attach the other end (which is
threaded) to the wheel with a nipple. This nipple makes only surface "contact" with the wheel (or rim), thus it is capable of exerting a force in
only one direction.

If the hub were to get closer to the rim, the tension in the spoke would reduce to zero and the spoke may "loosen". The spoke load would not go into compression.

Bruno, Forrest is correct here. In actuality, the nipples never leave the rim, though - the tension and number of the spokes is such that even those at the bottom maintain some tension - it is just briefly lessened by their passing through the bottom region.

Spokes can loosen quickly if the nipples are not "set" in the rim. To set the spoke nipples, you get all the spokes tight, then you go around the rim a few degrees at a time "squeezing" it between your gut and the ground with all/most of your weight on it. This forces the sides out, "setting" the spoke nipples in the side regions. After you've been all the way around, then and only then can you complete the final tightening of the spokes. You will be surprised to find a few spokes that seem slightly "slack" after setting the nipples, especially if you happen to be using a brand-new rim.

L Cottrill

[Bruno Ogorelec]

The spoke load would not go into compression.

Corect, Forrest & Larry. I just forgot we were talking about the actual angled criss-crossing spokes on wire wheels. Those do not go into compression. (I should know; I've busted quite a few.) I was talking about fixed radial spokes. Sorry for the confusion.

[Mike Kirney]

Consider this:

The rim is a rigid hoop, but stresses left over from the manufacturing process combined with imperfections in the material mean that it will not lay straight and true unless held in position by numerous balanced forces. When the wheel is laying on its side, all the spokes should be in equal tension (as applied by tightneing the nipples), pulling on the rim and on the hub and keeping everything lined up just so. When the wheel is in use (standing vertically and carrying the mass of the rider), the hub actually hangs from the top spokes (which, aside from carrying the pre-applied tension load are now also hanging from the rim by their nipples {ouch!}), and the bottom spokes are not compressed at all because they are hanging off the hub and their nipples are pulling upwards on the rim, so they are still in tension. The rim deforms a tiny bit in use but nowhere near enough to affect the tension of the spokes. At any given time, about 2/3 of the spokes are serving simply to keep the rim round and true (pulling upwards and inwards), and only about 1/3 or 1/4 actually transfer any gravitational force (from axle to rim via spokes). The weight of the cyclist is transferred to the axle through the handlebars and bike forks, so the force of gravity actually makes a U-turn at the axle. The bottom spokes cannot carry any weight because they would not compress, rather they would slip from their holes and puncture the inner tube. This can happen in a poorly-tensioned wheel or if a nipple breaks or loosens off from vibration.

The forces acting on the rear wheel are somewhat more complex because there is also torque coming from the freewheel via the chain, chainwheels, crankarms pedals, etc.. In a cross-spoke pattern, drive torque counters the tension placed on the spoke by the tightening of the nipple, so that several spokes will slacken off completely but temporiarily as the rear wheel travels through its revolution. This is bad for the wheel and wastes energy. This can be remedied by lacing the one side of the wheel radially.

Having worked as bicycle messenger for 7 years, I have spent countless hours of my life staring at the front wheel of my bike, in all positions both at rest and in motion. That is how I know that that is how it works!

[cudabean]

This subject has been beaten to death here. Well almost. The thing I would add is a bicycle wheel is not completely in tension. There is some compression, but none is in the spokes. The compression I'm refering to is the rim. I would bet that a thin flat flimsy rim (like a barrel hoop) would readily buckle if loaded with spoke tensors. But bicycle wheels are not like barrel hoops, they are more like I-beams for the tubed style wheel or like box-spars in the sew-up style rims.

Marlin

[WebPilot]

-fde

[larry cottrill]

Mike K -

As always, you are a good observer. However, you are incorrect in a couple of assumptions:

The rim is a rigid hoop ...

This is simply not possible. If it were true, it would be impossible to use your weight to 'set the spokes' in the manner I have already described, and that definitely works. Of course, the section of the rim is designed to make the rim as nearly rigid as possible, but it doesn't come close to being a deflectionless structure. Even a space truss many feet deep deflects measurably under its intended load; there's no way a hoop with a fancy cross-section is going to do better than that.

The rim deforms a tiny bit in use but nowhere near enough to affect the tension of the spokes.

Not so. The spokes are high strength steel or, nowadays usually, stainless. The modulus of elasticity is so high that it would only take a hundred-thousandth of an inch to significantly gain or relax tension. Obviously, you would not observe a reduction in tension unless it were reduced to zero (slack spokes), which doesn't happen unless a spoke is not tightened correctly in the first place.

Respectfully submitted,

L Cottrill

[Anders Troberg]

Not only that, I think that the fact that the rim can deform somewhat actually helps distribute the load between more spokes.

Something like this:

It takes some force to deform the rim to an oval shape. This force comes from the weight of the biker. Since the rim doesn't deform (noticeably), this force has to be handled by a counter force somewhere, namely as tension in the spokes where the radius would increase.

I'm pretty sure that the rim would deform if only the top spokes where in place, in fact it would probably go more or less flat. Whatever way you look at it, that deforming force can only come from the weight of the rider and can only be absorbed by the spokes at the side quarters of the wheel. In other words, they carry some of the weight.

The bottom spokes are probably more or less useless, though, at least until the wheel starts turning...

Not being a bicycle expert, I would still feel sure enough to venture a guess that the fancy shape of the rim profile is indeed to stop it from deforming, but its primary function is probably to give sideways stability, to stop the rim from deforming sideways.

[larry cottrill]

Anders -

I think that's pretty much what Forrest's posted diagram above is showing, though it's impossible for me to read it. Note that some of the spoke force acts to keep the rim 'true' and centered as well, since alternate spokes run to opposite sides of the hub.

The bicycle wheel (curved rim notwithstanding) functions as a space truss with a high degree of indeterminacy, variable loading and a pre-stress (the tightness of the spokes). Almost an engineering marvel, really.

L Cottrill