waterlaz

This is a simplified model but it is actually perfect to show my point. If you have two preloaded springs pulling in different directions and you apply some force to the system (say you are pulling down) the energy increases.

Bike Gremlin

+1

Well explained.

prathmann

Total energy of the wheel does not equal the sum of the spoke tension energies.

rpenmanparker 

By definition tension means force pulling on the ends of an object. Isn't the 50 N weight pulling on the top spoke?

Bike Gremlin

The error of this analogy is that lower spring is not pulling with less force when more weight is applied.

rpenmanparker 

No, because you relieve potential energy inside the lower spring...assuming you are pulling down. You are exerting energy, but the spring has less.

Bike Gremlin

50 N is pushing the hub down, reducing the tension of the bottom spoke by the same amount. So while the 50 N form the weight does increase tension of the upper spoke, the bottom one is pushing by 50 N less force - so the tension of the upper spoke remains the same.

At the same time, similar thing happens in the hub with preloaded bearings.

That's why it all works so nicely and lasts long. That is also one of the reasons why, when spokes (or bearings) come loose - damage quickly happens.


Tyre and rim do not have this "luxury", so they get all the beating directly, and without any relief (of course, the whole wheel, including the rim, does enjoy some relief from tyre flex working as a shock absorber).

rpenmanparker 

The lower spoke doesn't lose any tension until the hub moves down. That is like relieving the pull on a spring. And when the hub moves, the upper spoke increases in tension by 50 N. The upper increases to 150 as the lower decreases to 50.

BillyD

I could easily settle this, seeing as how I stayed at a Holiday Inn last night, but you guys are having fun kicking this around so why should I rain on the parade.

waterlaz

I assume that the rim is very flexible but incompressible (this is very close to what happens in classical low profile rims). That way it can not store any energy.
If you apply the same logic to your example with concrete then the concrete does not deform with extra load and the tension of the steel rod does not change.

waterlaz

I am referring exactly to your spring example. One spring will lose energy but the other spring will get slightly more energy.

rpenmanparker 

No, the lower spoke cannot lose tension (nipple unchanged) unless it shortens. It shortens in response to the hub moving down. When the hub moves down, the upper spoke must lengthen to allow it. That can only occur when it is under higher tension. Modulus X elongation = stress or load. Higher elongation means higher load (tension). If the hub goes down, the tension in the upper spoke must go up, and the tension in the lower spoke must go down.

This is really ironclad.

waterlaz

It pretty much does.

Bike Gremlin

Rim slightly deforms at the lowest part. That allows for the lower spoke to loose some tension.

In addition to that - if the lower spoke looses tension by amount of X N, the upper spoke gets 100 N + 50 N (load) - X N (the amount of lost tension from the lower spoke).

The X is dangerously close to the load applied.

rpenmanparker 

Please don't get offended, but lose is spelled with only one o. I figured that if this were going to continue for a while, I could either mention it or go crazy.

We were ignoring deformation. If you consider deformation, you have to consider that the top of the rim flattens too.

Bike Gremlin

No problems.

Still, with a perfectly rigid rim, there remains the amount of lowered tension of the lower spoke, that is deducted from the 50 N increase. How much is it? Probably about 50 N.

rpenmanparker 

But it is added back on the upper spoke. Why do you keep ignoring that? Otherwise the two spokes wouldn't meet each other...with the hub between them of course. You are double dipping the reduction of tension in the lower spoke, saying the lower spoke has reduced tension, AND you have to subtract it from the upper spoke as well. You can't consider it twice.

Bike Gremlin

Back to the beginning.

100 N each spoke. OK?

50 N load.

If the lower spoke looses tension with that load, the upper spoke gains tension: 100 N minus lost tension of the lower spoke, plus the added 50 N load. That results in less than 150 N. Exactly 100 N.

rpenmanparker 

I think I was wrong! I wasn't considering the total forces on each side had to be the same. Some serious simultaneous equations needed. Let me work on it.

prathmann

We could just as well hypothesize that the spokes are flexible but unstretchable and therefore can not store any energy. But I thought the idea was to consider the situation with real materials in the real world.

Concrete is not easily compressed, but if a preload is applied using the steel rod and a weight (wt. < preload) is then applied on top of it the result is that the tension in the rod is reduced because of the weight.

A paper giving an FEA of bicycle wheels was already presented at:
https://www.ewp.rpi.edu/hartford/~ern...inalReport.pdf
As expected it shows large reductions in tension of a few spokes at the bottom of the wheel and much smaller increases in other spokes. There's a table with the forces on p. 17 and you could calculate the corresponding stored energies. But just glancing at the table makes it clear that the sum of the spoke stored energies went down when the load was applied.

waterlaz

If concrete does not compress then the tension in the rod will not decrease.

prathmann

As I said before, I thought we were interested in real materials in the real world - not some fictitious material. I said that concrete doesn't compress easily - not that there is no compression at all.

If you want to dispute the FEA studies of rim loading that have been done, then you need to either show exactly where their errors are or do your own study that supports your claim. In the latter case we'd then need to examine both yours and the previous ones to see where they differ and which one should be trusted. Just repeating the claim based on energy conservation when it's clear that the spokes by themselves do not constitute a closed and isolated system is not convincing.

waterlaz

Then I don't understand why you keep pushing the experiment with concrete. You say that the rod loses energy. Well I say that it goes to concrete. Then you say that concrete doesn't compress easily. Well if it doesn't compress then the rod doesn't lose tension and doesn't lose energy. If compresses just a bit well then the concrete block will take just a bit of energy and the rod will lose only a bit.

So I don't understand your point very much. I've said that a couple of times that some parts of the system can lose energy. It's the system as a whole that can't. Either be it a rod with the concrete block or spokes with a rim.
Whether the rim can store much energy is another question.

And I'm not disputing the FEA studies. In fact I've seen it as such that supports my claims. It does look like the total energy of spokes decreases so the rim plays greater role than I thought. I'll have to think about it.

prathmann

Sounds like we're in complete agreement then.

Brian Ratliff

Waterlaz is correct. You can calculate the amount of energy stored in the wheel just by noting the force applied to the hub and measuring the vertical movement of the hub in response to that force. Energy is force times distance. This stored energy has to be stored somewhere in the wheel; it is stored by the rim seeing more compressive forces. But you don't have to calculate the exact storage distribution to know the total amount of energy that was stored.

Like a powermeter. you don't need to measure all the places where power is dissipated (aero loss, elevation gain, rolling friction, etc.) to calculate the power out of your legs. You can simply measure the force and deflection of a load component and calculate power directly. Same calculation as above, in fact.