Why do my spokes keep breaking? - Bike wheel science.

[Ajax Bay]

I have a problem with the use of "oval". That implies that the top part of the rim receives a downward force as if someone is sitting on the wheel. That's not the case. The change of shape is there for reasons I've described above, but the topmost point of the wheel remains exactly the same distance from the hub when the wheel is loaded.
Most people's assumption that the hub hangs from the spokes implies that the topmost point of the wheel remains static in space.

OK, perhaps I should not have used 'oval' but "sometimes I have to simplify in order to keep my audience, and there's no slight intended to my audience."
There is no additional downwards force on the upper section of a loaded wheel's rim (additional, that is, to the forceful but not increased tension of the upper spokes pulling downwards on the rim). The "topmost point of the wheel [rim] remains" the same distance from the hub as the rim is in an unloaded wheel. I've already said that (imo) the use of 'hang' and 'stand' doesn't help one understand the dynamics.

 

[Ajax Bay]

Your diagram shows exactly my model, yet you still bring in this concept of surplus vertical forces. There are none. The road pushes up at 500N and the fork/hub pushes down at 500N. To bring in surplus vertical forces the system is out of balance. It is a pity that you can't indicate them on your force diagram.

If one considers the system as a whole, there are no unbalanced forces (static wheel - Newton init).
But considering just the wheel, its load bearing function is to accept the normal force from the ground and transmit it via spokes and rim through the hub to the fork (which is applying the downwards load on the wheel). Forces acting on the hub from within the wheel have to result in that vertical upwards force - and that resultant upwards force is the difference in tension, resolved vertically, between the upper spokes (normal tension) and the lower spokes (reduced tension).
There - that's 3+ lines without using the 's' word.
Load = Upper spoke tensions (resolved and summed) minus lower spoke tensions (resolved and summed).

 

[Yellow Saddle]

OK, perhaps I should not have used 'oval' but "sometimes I have to simplify in order to keep my audience, and there's no slight intended to my audience."
There is no additional downwards force on the upper section of a loaded wheel's rim (additional, that is, to the forceful but not increased tension of the upper spokes pulling downwards on the rim). The "topmost point of the wheel [rim] remains" the same distance from the hub as the rim is in an unloaded wheel. I've already said that (imo) the use of 'hang' and 'stand' doesn't help one understand the dynamics.

If one considers the system as a whole, there are no unbalanced forces (static wheel - Newton init).
But considering just the wheel, its load bearing function is to accept the normal force from the ground and transmit it via spokes and rim through the hub to the fork (which is applying the downwards load on the wheel). Forces acting on the hub from within the wheel have to result in that vertical upwards force - and that resultant upwards force is the difference in tension, resolved vertically, between the upper spokes (normal tension) and the lower spokes (reduced tension).
There - that's 3+ lines without using the 's' word.
Load = Upper spoke tensions (resolved and summed) minus lower spoke tensions (resolved and summed).

OK, I get it. Your end result is exactly the same as mine, via exactly the same mechanism, but you don't like to use the term "standing".

That's your choice but your diversion is a helluva mouthful.

 

[Milkfloat]

In my over simplistic mind - I see a way to visualise that a wheel does not hang is turn a wheel on its side and squeeze the wheel at the rim and the hub, the spoke tension may reduce slightly but nothing is hanging. That is probably nonsense, but it keeps me happy.

 

[Yellow Saddle]

In my over simplistic mind - I see a way to visualise that a wheel does not hang is turn a wheel on its side and squeeze the wheel at the rim and the hub, the spoke tension may reduce slightly but nothing is hanging. That is probably nonsense, but it keeps me happy.

No, that's not nonsense. That's exactly the type of thinking required to figure out what's happening. Even, get up on a ladder and squeeze the wheel against the ceiling (holding onto the axle of course).

 

[Milkfloat]

No, that's not nonsense. That's exactly the type of thinking required to figure out what's happening. Even, get up on a ladder and squeeze the wheel against the ceiling (holding onto the axle of course).

I guess even a stopped clock is right twice a day. The ceiling explanation is far better than mine, although I don't need a ladder and therefore a helmet

 

[Ajax Bay]

you don't like to use the term "standing".

S is for 'surplus'!

 

[Yellow Saddle]

S is for 'surplus'!

Surplus is for budgets, in which case there is none.

 

[overmind]

I guess even a stopped clock is right twice a day. The ceiling explanation is far better than mine, although I don't need a ladder and therefore a helmet

Agreed the ceiling analogy helped me understand also.

 

[roubaixtuesday]

I was contemplating this on my cycle home, and have a thought experiment to offer which may clarify things.

Or may not, naturally!

The rim is considered infinitely stiff in the following.

Three steps:

1. Consider a wheel with a single spoke. The spoke must be vertically upwards from the hub. A weight, W is applied at the hub. The tension in the spoke is W; the infinitely stiff rim transmits the force to the ground where there is a reaction force W. All the weight is supported in extra tension in the spoke.

2. Now, consider a wheel with two spokes. These spokes are infinitely stiff, so do not elongate under load. They have a pre load tension, P, which obviously must be equal in both spokes. The spokes are vertical, and the load W is applied at the hub. We simply add the solution to (1): the upper spoke has tension (P+W) and the lower spoke has tension P.

This brings our first conclusion: In the absence of elasticity, all the weight is supported by increased tension in the upper spokes.

3. We now allow the spokes to be elastic. Both spokes must deform by the same amount as they form a straight line, and the rim is infinitely stiff. The tension in the lower spoke must reduce, as its length reduces. We will call this elasticity reduction E. The tension in the upper spoke must also reduce by the same amount, to keep the overall hub forces in balance.

The upper spoke now has a tension of (P+W-E)

The lower spoke has a tension of (P-E)

This leads to our second conclusion: allowing for elasticity, tension in upper spokes will increase, and tension in lower spokes will decrease. The amount of each depends on the elasticity of the spokes.

I hypothesize that these, whilst proved only for a two spoke stiff rimmed wheel, hold generally for a wheel with many spokes and an elastic rim. I don't propose to do the maths to prove it!

Criticism of above most welcome.

 

[Ming the Merciless]

Well a single spoke pointing downwards has nothing but air underneath it and in the absence of spoke pointing upwards to counteract the forces, there is nothing to stop that spoke moving downwards towards the road. Remember the spoke is not supported from below by the rim, it does not sit on the rim, it just passes through a hole and will quite happily fall out on its own. It is only constricted from moving towards the hub by the nipple, there is no such constraint or constriction moving the other way

 

[roubaixtuesday]

Well a single spoke pointing downwards has nothing but air underneath it and in the absence of spoke pointing upwards to counteract the forces, there is nothing to stop that spoke moving downwards towards the road. Remember the spoke is not supported from below by the rim, it does not sit on the rim, it just passes through a hole and will quite happily fall out on its own. It is only constricted from moving towards the hub by the nipple, there is no such constraint or constriction moving the other way

In the thought experiment, the wheel is static. For the first part, with a single spoke, it points upward. When a second spoke is added, that one points downward.

This is the simplest way I can think you allow the problem to be broken down into its key elements.

 

[Ming the Merciless]

In the thought experiment, the wheel is static. For the first part, with a single spoke, it points upward. When a second spoke is added, that one points downward.

This is the simplest way I can think you allow the problem to be broken down into its key elements.

Ah ok so the single spoke pointed upward supports the hub (below) on its own, then you add a downward pointing spoke. Bit like what you will see in the real world if you build a wheel.

 

[roubaixtuesday]

Ah ok so the single spoke pointed upward supports the hub (below) on its own, then you add a downward pointing spoke. Bit like what you will see in the real world if you build a wheel.

Yup.

 

[Ming the Merciless]

Yup.

Chandelier is a good way of thinking of it.