Jobst Brandt and how wheels hold load
08-20-16, 09:33 AM
#126
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Correct, (my brain fart) you need tight enough to be in the elastic range, which is why you need to pre-tension it. Increasing won't make it less or more springy. The point to focus on is that regardless of the initial tension, you will have an increase in tension where the spoke works against the rim deformation. That's what causes tension, you're trying to stretch the spoke.
Sorry for the digression from prathmann and rpenmanparker who no doubt have a handle on it. Sometimes people need to take a step back and look at the whole picture, and it isn't as complicated conceptually as one might imagine.
Sorry for the digression from prathmann and rpenmanparker who no doubt have a handle on it. Sometimes people need to take a step back and look at the whole picture, and it isn't as complicated conceptually as one might imagine.
08-20-16, 10:13 AM
#128
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How do things change when an inflated tire is added to the system?
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08-20-16, 10:40 AM
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Tyre pressure compresses the rim from all the sides, equally. It is not high enough to really compress the metal, so it doesn't affect spoke tension a lot. It should decrease all the spokes tension equally.
08-20-16, 10:43 AM
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Does an inflated tire change the amount of rim deformation ?
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"When I hear another express an opinion, which is not mine, I say to myself, He has a right to his opinion, as I to mine; why should I question it. His error does me no injury, and shall I become a Don Quixot to bring all men by force of argument, to one opinion? If a fact be misstated, it is probable he is gratified by a belief of it, and I have no right to deprive him of the gratification."
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08-20-16, 12:49 PM
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08-20-16, 12:50 PM
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Yes, it is common to observe that wheels with inflated tire have lower spoke tension than the bare wheels on the order of 5%. That must come from very slight compression of the rim toward the hub.
08-20-16, 12:53 PM
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It's entirely possible for the tension elements in a pre-stressed structure to lose energy when a load is added.
Think of a cement block that you've drilled a hole through. You now insert a steel rod through this vertical hole and attach some plates to it resting on the outside surfaces of the block. Now screw down those plates so the cement block is compressed and you have tension energy in the steel rod. If you now place a weight on top of this structure, the tension in the rod is reduced and the energy stored in it is also reduced.
Think of a cement block that you've drilled a hole through. You now insert a steel rod through this vertical hole and attach some plates to it resting on the outside surfaces of the block. Now screw down those plates so the cement block is compressed and you have tension energy in the steel rod. If you now place a weight on top of this structure, the tension in the rod is reduced and the energy stored in it is also reduced.
08-20-16, 12:54 PM
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Likely the rim also deforms at the top as the hub is pushed down by the vertical load from above. That is why the top spokes increase in tension, the hub is pushed away from the top of the rim and toward the bottom of the rim. As I said before, the wheel ovalizes with the long axis horizontal. But the hub is no longer centered vertically in the wheel. It is closer to the bottom of the rim than the top. This would be consistent with the increased top spoke tension and decreased bottom spoke tension.
08-20-16, 12:55 PM
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No. Because I know that the total energy of the wheel is increased. I can even calculate it (just integrate force over deflection).
08-20-16, 01:06 PM
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Likely the rim also deforms at the top as the hub is pushed down by the vertical load from above. That is why the top spokes increase in tension, the hub is pushed away from the top of the rim and toward the bottom of the rim. As I said before, the wheel ovalizes with the long axis horizontal. But the hub is no longer centered vertically in the wheel. It is closer to the bottom of the rim than the top. This would be consistent with the increased top spoke tension and decreased bottom spoke tension.
08-20-16, 01:06 PM
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Easier said than done. Do you have the function for the behavior of the rim, i.e deflection at every point on the rim when the weight is applied? Or the data for a specific case?
08-20-16, 01:09 PM
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But you apply the load, see how much closer the axle is to the ground and get the energy from that.
08-20-16, 01:22 PM
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Anyone who has built a wheel using a TM might be familiar with this behavior.
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08-20-16, 01:34 PM
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Yes radial wheel flexibility will complicate this, but I doubt by all that much since the wheel is so stiff.
Now keep in mind that in this perfectly stiff rim case, only the hub moves and that is downward. Of course we are not accounting for tires. When the load is removed, the hub springs back up. If there is an energy increase under load, it is hard to see how. The tension in the top spokes and vertical component of the top-wards side spokes would have to increase more than the tension in the bottom spokes and bottom-wards side spokes decreases. But it is hard to see how of all the spokes have the same spring constant (tensile modulus), because the downward motion of the hub increases the length of the top spokes until the weight is supported just the same as it decreases the length of the bottom spokes.
In effect adding a weight to the bike is the same as loosening the top spokes and tightening the bottom spokes thereby moving the hub down. I can see how that would be energy neutral.
Last edited by rpenmanparker; 08-20-16 at 01:38 PM.
08-20-16, 01:38 PM
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Read my treatment just posted. The added load is just the same as tightening spokes and loosening the opposite ones. Energy neutral.
08-20-16, 01:39 PM
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08-20-16, 01:40 PM
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Why? In the limiting case of a perfectly rigid rim, the hub is pushed down by the weight on the dropouts. That reduces tension on the lower spokes and increases it on the upper spokes more or less equally. The magnitude of the tension change is directly related to the vertical component of the angle of the spokes. Greatest at the top and bottom and decreasing as you go around. If we talk about the spoke angle from the vertical, then the ratio of tension change of each spoke to the vertical spokes is the cosine of the angle.
Yes radial wheel flexibility will complicate this, but I doubt by all that much since the wheel is so stiff.
Now keep in mind that in this perfectly stiff rim case, only the hub moves and that is downward. Of course we are not accounting for tires. When the load is removed, the hub springs back up. If there is an energy increase under load, it is hard to see how. The tension in the top spokes and vertical component of the top-wards side spokes would have to increase more than the tension in the bottom spokes and bottom-wards side spokes decreases. But it is hard to see how of all the spokes have the same spring constant (tensile modulus), because the downward motion of the hub increases the length of the top spokes until the weight is supported just the same as it decreases the length of the bottom spokes.
In effect adding a weight to the bike is the same as tightening the top spokes and loosening the bottom spokes thereby moving the hub down. I can see how that would be energy neutral.
Yes radial wheel flexibility will complicate this, but I doubt by all that much since the wheel is so stiff.
Now keep in mind that in this perfectly stiff rim case, only the hub moves and that is downward. Of course we are not accounting for tires. When the load is removed, the hub springs back up. If there is an energy increase under load, it is hard to see how. The tension in the top spokes and vertical component of the top-wards side spokes would have to increase more than the tension in the bottom spokes and bottom-wards side spokes decreases. But it is hard to see how of all the spokes have the same spring constant (tensile modulus), because the downward motion of the hub increases the length of the top spokes until the weight is supported just the same as it decreases the length of the bottom spokes.
In effect adding a weight to the bike is the same as tightening the top spokes and loosening the bottom spokes thereby moving the hub down. I can see how that would be energy neutral.
Say both spokes pull with force of 100 N. Bottom one pulls the hub down with 100 N, while the upper one pulls it up with the same 100 N - so it stays in place.
Now put 50 N load on the dropouts, pushing the hub down.
The lower spoke will have it's tension reduced by 50 N. The upper one will have 100 N - 50 N from the lost tension in the lower spoke + 50 N from the load applied - leaving it with 100 N load/tension.
Is there a flaw in this logic?
08-20-16, 01:43 PM
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08-20-16, 01:49 PM
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Putting this another way, do this thought experiment. Hang a weight on a spring. Hook another spring underneath the weight so that the two springs are pulling on the weight up and down. Different weights will equilibrate at different heights, but no matter what weight you use, there is no change in energy so long as the springs aren't bottomed out. Is there? Yes weight is moving up and down and force and motion define change in energy, but the opposite is taking place inside the springs. Unless I am mistaken that is a simplified model of the wheel question we are discussing.
Last edited by rpenmanparker; 08-20-16 at 01:54 PM.
08-20-16, 01:51 PM
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In case a wheel is perfectly straight, kept only by one top and one bottom spoke.
Say both spokes pull with force of 100 N. Bottom one pulls the hub down with 100 N, while the upper one pulls it up with the same 100 N - so it stays in place.
Now put 50 N load on the dropouts, pushing the hub down.
The lower spoke will have it's tension reduced by 50 N. The upper one will have 100 N - 50 N from the lost tension in the lower spoke + 50 N from the load applied - leaving it with 100 N load/tension.
Is there a flaw in this logic?
Say both spokes pull with force of 100 N. Bottom one pulls the hub down with 100 N, while the upper one pulls it up with the same 100 N - so it stays in place.
Now put 50 N load on the dropouts, pushing the hub down.
The lower spoke will have it's tension reduced by 50 N. The upper one will have 100 N - 50 N from the lost tension in the lower spoke + 50 N from the load applied - leaving it with 100 N load/tension.
Is there a flaw in this logic?
08-20-16, 01:53 PM
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The spoke/rim/hub system is more complicated to understand. If you do the proper finite element analysis of it you'll find that a few spokes (those at the bottom) lose a lot of energy while some others gain a tiny amount, but the sum of all the spoke tension energy does decrease.
08-20-16, 01:53 PM
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