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

[Yellow Saddle]

"There is a compressive force between road and bike." Like the compressive force in the sole of a worn shoe. Difference is that the wheel is a structure so saying that "there is a compressive force between road and bike" lacks meaning/utility.

I'm not sure what worn shoe or structure has to do with it. I don't get your argument here at all.

"The only spokes that interact to transmit that net downward force are the ones in the load affected zone, i.e the two or three right at the bottom." Depends what you want "interact" to mean. I agree that they're the ones in which tension reduces most, which means they pull down on the hub less than when the wheel is unloaded.

Interact means that they act in a way to support the load. That way is to reduce in tension. None of the other spokes have anything to do with the load, they do exactly what they do as when the wheel is unloaded.

"The other radial forces in the other spokes play no role in transmitting the bike's weight down to the road. None."
Sorry, I have difficulty with that. The hub is 'hanging' on the spokes above it and the upwards force it has to exert on the fork drop outs is because the lower spokes have reduced the amount they are pulling down.

No the hub does not hang on the top spokes. That implies an increase in tension, which doesn't happen. An analogy is to look at a car wheel and tyre. Only the bottom squashes down, the top doesn't somehow become fatter/elongate because the rim is hanging on it.

To get your head around it, remove your front wheel and hold it by the axle, vertically, with two hands, each one side of the wheel. Push the wheel down on the floor by the axle. Now imagine your "hanging" hub. Now, pick up the wheel, turn it horizontally and do the same as before, but push against a wall. What happened to the "hanging" hub.

To prove this experimentally, find two friends to help you. Sit on the bike and have one friend hold you upright. Have the other pluck the bottom spoke and listen to the tone. Unload the bike and listen again. Now sit again and pluck the top spoke. Unload and pluck again. You'll notice that the top tone never changes but the bottom one goes down in frequency when the bike is loaded.

The lower spokes just experience a cyclical lower tension - the force exerted on a lower spoke by the rim lessens and results in a lower tensile force. This means that the resultant force (the result of all the spokes pulling on the hub at various tensions) on the hub is up (ie operates vertically upwards through the drop outs and is equal to the weight on the wheel).

Please rephrase, I can't comprehend.

I think we agree what happens but I think your use of certain terms (like compression, compressive and 'stands') clouds rather than provides the clarity needed for "a better understanding of this complex but fascinating topic".

That's not my problem. I've explained my meaning of those terms and so far no-one has come up with more appropriate ones. Those are exactly the same terms used in the literature on the topic and accepted by those who understand the concept.

 

[Ming the Merciless]

Of the course the tension of the spokes various as the wheel turns. It is nonsense to suggest only when spokes are at the bottom do they change tension. To suggest that the upwards facing spokes play no role in supporting the weight of bike and rider is absurd.

 

[Yellow Saddle]

Of the course the tension of the spokes various as the wheel turns. It is nonsense to suggest only when spokes are at the bottom do they change tension. To suggest that the upwards facing spokes play no role in supporting the weight of bike and rider is absurd.

We ignore the fact that the wheel turns because the only effect that it has is that it alternates the spokes where things happen. A static wheel is an accurate and easy model to work with.

You seem to have a different model for load support. Please feel free to modify my diagram and put figures to what you think happens to the tension.

 

[Ming the Merciless]

Well for a start a spike pokes through a hole in the rim and the only thing beyond that is rim tape and a tyre or tube. Neither of which provide support. The spoke does not connect with a so,I'd surface to help it provide load support against a force pushing it towards the tyre.

 

[Ajax Bay]

Thank you for the force diagram, @Yellow Saddle , spookily like the one I sketched on paper before being diverted to children taxiing and supper etc. I will attempt to transfer mine to an electronic medium (my application consultant came home ill from school, so ill he even agreed to leave his phone in my care while he went to recuperate in bed (I can see the 'too ill to go to school' card being prepared)).
I went for a load of 500N (eg a 50kg wt load - typical load on a front wheel) and an individual spoke tension at 1000N (a figure I know you have quoted before) except the 2 lower spokes (of 8) at less tension. Resolving vertically each of those two spokes drop to a tension of 730N.
TL = 1/2 (500/cos(22.5deg))
Given up on 'Paint'. Here's a photo:

Of the course the tension of the spokes various as the wheel turns. It is nonsense to suggest only when spokes are at the bottom do they change tension. To suggest that the upwards facing spokes play no role in supporting the weight of bike and rider is absurd.

I think we all agree that the tension of each spoke varies as the wheel turns. But for the force analysis it's sufficient to consider a static loaded wheel. I seek to persuade YS that the upper spokes, albeit at no more tension than when the wheel is unloaded, provide the surplus force (via the hub) needed to support the load exerted by the fork. Disregarding the spokes other than the top 2 and the bottom 2, this surplus is the force (on the hub) up from the two upper spokes minus the pull down of the two lower spokes.

 

[FishFright]

I've always thought that the bike 'hangs' from the spokes above the hubs rather than sits on top of the spokes below the hubs.

 

[Ming the Merciless]

The lower spokes in the diagram do not contact the road. Nor do the support the hub above. The only thing stopping the hub moving downwards under the force exerted are the spokes that point upwards which will be under different tensions depending on their angle. If you removed the upper spokes in a static load position the lower spokes would just push through their spoke holes and puncture the inner tube as there is very little to resist the weight of rider and bike weight.

 

[Ming the Merciless]

Maybe you should do some research before diving in with the same mistakes which have been made dozens of times before, on this forum. You have not provided a model or a coherent argument.

Yes I have. Pay attention the tension in the spokes is pulling the hub towards the rim in every case. The hub does not move (much) towards any particular part of the rim because it is countered by the tension in the rest of the spokes. The hub does not sit supported on the lower spokes nearest the road surface. Those spokes are not resisting the downward force due to gravity, they have nothing to push against other than rim tape, and that does not offer much resistance compared to the forces in place. It is the spokes pointing upwards that are providing the upwards forces resisting the hub moving downwards under the force of gravity.

 

[hobo]

What about the forces involved from the drive side of the rear wheel being applied by the rotational force from the
chain onto the hub?

 

[hobo]

Every time iv broke a spoke its been when i have been applying force on to the pedals.
So the torque force breaks the spoke.

 

[Yellow Saddle]

What about the forces involved from the drive side of the rear wheel being applied by the rotational force from the
chain onto the hub?

Those are particularly interesting.

My art above can't be referenced because driving wheels have to be cross-spoked and that one is radially-spoked.

Nevertheless on a rear wheel where the hub is stiff enough to transmit torque to the side opposite the sprockets, it works like this.
Every second spoke increases in tension and the others decrease in tension. If the tension and reduction were to be exaggerated, then the wheel can be visualised as daisey-shaped. That's because there are "pushing" and "pulling" spokes in such a wheel. The average tension does not change at all, but the tension in individual spokes change by an equivalent positive and negative amount.

 

[Yellow Saddle]

I think we all agree that the tension of each spoke varies as the wheel turns. and...But for the force analysis it's sufficient to consider a static loaded wheel.

Yes, for now I'm going to ignore the side-chatter that regurgitates stuff we've said before. This includes rotation, spokes lifting off the spoke bed etc. Anyone who wants to understand that or think they've just invented it, can go back in the record and read up on it.

Then, a suggestion. When calculating the reduction in tension at the bottom spokes, we leave out the angular component from the spokes arriving radially. This suggestion is for two reasons.
1) There are paired, parallel spokes in a cross-laced wheel. Typically such as the two spokes either side of the valve and at equal, opposite ends of the wheel. For such a real-world wheel the cosine component for those would have to be disregarded and the adjacent angular spokes then compensated with another angle. We then end up with a different model for each position of the wheel.
I suggest we treat the LAZ by having a central spoke arriving plumb with the road and two other spokes, either side of it, arriving at X angle. Only these three spokes share the load and we don't attempt to calculate the adjacent spokes' actual share other that attributing an arbritary figure to it. For instance, Central takes 30, the two adjacent ones each take 10, making up a total of 50.

We're not after exact numbers here, just broad concepts.

2) Should you still insist on eliminating the cosine error, then you'd have to know the angle, which is not the same in the load affected zone as it is elsewhere. That's because, as soon as the wheel is loaded, an arc in the circle is converted to a cord, without affecting the length of the arch. In other words, the wheel is deformed by flattening at the bottom and opening up elsewhere. Let's ignore that simply because it does not change the concept.

Then:

I seek to persuade YS that the upper spokes, albeit at no more tension than when the wheel is unloaded, provide the surplus force (via the hub) needed to support the load exerted by the fork. Disregarding the spokes other than the top 2 and the bottom 2, this surplus is the force (on the hub) up from the two upper spokes minus the pull down of the two lower spokes.

This seems to be the crux of you differing from me, because, taking into account the exceptions I've suggested above, our models are the same.

What I don't get is "surplus force". Can you show it on the force diagram? I just don't get it.

 

[Milkfloat]

I found this the easiest to understand http://hea-www.harvard.edu/~fine/opinions/bikewheel.html
Feel free to pick it apart.

 

[Ajax Bay]

What about the forces involved from the drive side of the rear wheel being applied by the rotational force from the
chain onto the hub?

https://www.cyclechat.net/threads/broken-spokes-when-to-give-up-on-a-wheel.173282/#post-3500342

 

[Milkfloat]

Interestingly at DT Swiss they say that the tension increases on the upper spokes, I think they mean the proportion of load will increase, but not the tension itself, however don't trust me, I make maps for a living, not wheels.

https://www.blog.dtswiss.com/spoke-tension/