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That you see more change in tension in the bottom few spokes is irrelevant to the explanation of how the wheel supports a bike. My professional experience is th

That you see more change in tension in the bottom few spokes is irrelevant to the explanation of how the wheel supports a bike. My professional experience is this area (preload of structures, beard turning grey) and I had to think a bit to gain confidence in my thinking and explanations. I'm not replying to prove you are wrong, I am an expert in this field and I am enjoying trying to elaborate on my reply. I understand that there is significant change (reduction in tension) in only a few spokes, but there _must_ also be a corresponding increase in tension to other spokes to keep equilibrium. Not distributed equally but absolutely distributed in a way that keeps equilibrium of forces within the wheel. It's distributed among many more spokes because that's how structures work. The rim's stiffness determines how this happens. A mechanical engineer designing a wheel knows that the wheel fails as soon as the bottom spokes have zero tension and fail by buckling. And the analysis works if you assume no buckling, ignore most of the spokes and just check the "red areas" in FEM or hand calculations and make sure the compression forces are less than the design preload. But this doesn't mean that in the physical world, the bottom spokes are "pushing up the bike". It's just a convenience of the problem. So let's simplify things. Imagine if there was only one spoke on the top and one spoke on the bottom, and the wheel is locked from rotating. Consider each spoke is a tension spring in tension, because they are. They can provide a tension force but are almost as useless as a string in compression (indeed, one of my comments linked to a new type of spoke that is literally a string). Each spoke is installed by tightening it to stretch it slightly and make a preload according to Hooke's law. Each spoke is tightened to get about 1000N of tension preload[1]. Note here that it's impossible to do this exercise with only one spoke, at least two spokes are required to tension them. State 1: The bike and wheel are held off the ground, and the wheel has negligible mass so each spoke has 1000N of tension. State 2: A person gets on the bike, resulting in a 500N force at the bottom of the wheel. This is roughly correct for a 100kg person, if front and rear wheel are loaded equally. The bottom spoke will compress and have a resulting 500N of tension preload. The top spoke will stretch and have a resulting 1500N of tension preload. Both spokes are still in tension and _pulling_ the hub to the wheel. But clearly the top spoke is stretched more than State 1 and the bottom spoke is stretch less than state 1. More stretch of a spring = more force, but less stretch of a spring = less force. How can it be said that the bottom spoke is holding the wheel up if basic physics says it is providing less force than before? State 3: leave the top spoke and cut the bottom spoke. The top spoke's preload goes to zero and the top spoke will actually have its tension reduced from 1500N to 500N. State 4: leave the bottom spoke and cut the top spoke. The bottom spoke's preload goes to zero and the bottom spoke will experience 500N in compression, immediately buckle and the rider will fall. [1]https://www.parktool.com/en-us/blog/repair-help/wheel-tension-measurement https://www.parktool.com/en-us/blog/repair-help/wheel-tensio...

ndsipa_pomu 3y ago
I disagree with your analysis of State 2. There's a 500N force from the ground pushing up on the rim. The bottom spoke will thus have a 500N reduction in tension which balances and results in no movement of the hub. The top spoke doesn't change in tension as it's still balancing the 1000N of the bottom spoke and rim forces. State 3 is a different scenario and in that instance, the hub is hanging from the rim. I don't see how it helps with the comparison as that's nothing to do with a wire wheel. In reality, you'd expect to see the rim buckle as the forces are now being applied purely at the top rather than opposed spokes distributing the 1000N between top and bottom. I agree with state 4, but again, that's a different system and doesn't help clarify what's happening. From this article: https://www.cyclist.co.uk/in-depth/the-science-behind-spokes https://www.cyclist.co.uk/in-depth/the-science-behind-spokes > While it’s easy to believe a bicycle spoke would simply collapse under the weight of bike and rider, he goes on to explain that the tension created in a spoke during the wheel building process (called ‘pre-tension’) is what allows the lower spokes to bear the load without buckling, as they would if there was no pre-tension. ‘Every spoke on the unloaded wheel has a tension of the order of 100lb [445N]. When the axle is pressed towards the ground with a force of 100lb, the only significant effect on spoke tensions is to reduce those directly below the hub – typically, one reduces to about 50lb and spokes to each side of that one reduce to about 75lb. This is exactly what one would see with solid wooden spokes like an old wagon wheel – the bottom one would carry 50lb and those to either side of it would carry 25lb. The difference with wire spoked wheels is that a wire spoke cannot carry a compression load – it will collapse. So all spokes are ingeniously pre-tensioned. A wire cannot carry a compression load of 50lb, except when it already carries a tension load exceeding that. > ‘Of course a bike wheel will collapse if the upper or horizontal spokes are removed,’ Papadopoulos adds. ‘But that is essentially because the altered structure has a very different load path, and furthermore is unable to supply the required pre-tension. We can’t use that collapse to conclude that the typical wheel carries load through the upper spokes.’
- johnwalkr 3y ago
  If you make a free body diagram and check the sum of vertical forces you’ll find that you cannot change the tension in one spoke without a corresponding equal (in total) reaction in others. I reduced it down to two spokes so that this becomes trivial to do.

ndsipa_pomu 3y ago

I disagree with your analysis of State 2. There's a 500N force from the ground pushing up on the rim. The bottom spoke will thus have a 500N reduction in tension which balances and results in no movement of the hub. The top spoke doesn't change in tension as it's still balancing the 1000N of the bottom spoke and rim forces. State 3 is a different scenario and in that instance, the hub is hanging from the rim. I don't see how it helps with the comparison as that's nothing to do with a wire wheel. In reality, you'd expect to see the rim buckle as the forces are now being applied purely at the top rather than opposed spokes distributing the 1000N between top and bottom. I agree with state 4, but again, that's a different system and doesn't help clarify what's happening. From this article: https://www.cyclist.co.uk/in-depth/the-science-behind-spokes https://www.cyclist.co.uk/in-depth/the-science-behind-spokes > While it’s easy to believe a bicycle spoke would simply collapse under the weight of bike and rider, he goes on to explain that the tension created in a spoke during the wheel building process (called ‘pre-tension’) is what allows the lower spokes to bear the load without buckling, as they would if there was no pre-tension. ‘Every spoke on the unloaded wheel has a tension of the order of 100lb [445N]. When the axle is pressed towards the ground with a force of 100lb, the only significant effect on spoke tensions is to reduce those directly below the hub – typically, one reduces to about 50lb and spokes to each side of that one reduce to about 75lb. This is exactly what one would see with solid wooden spokes like an old wagon wheel – the bottom one would carry 50lb and those to either side of it would carry 25lb. The difference with wire spoked wheels is that a wire spoke cannot carry a compression load – it will collapse. So all spokes are ingeniously pre-tensioned. A wire cannot carry a compression load of 50lb, except when it already carries a tension load exceeding that. > ‘Of course a bike wheel will collapse if the upper or horizontal spokes are removed,’ Papadopoulos adds. ‘But that is essentially because the altered structure has a very different load path, and furthermore is unable to supply the required pre-tension. We can’t use that collapse to conclude that the typical wheel carries load through the upper spokes.’

johnwalkr 3y ago
If you make a free body diagram and check the sum of vertical forces you’ll find that you cannot change the tension in one spoke without a corresponding equal (in total) reaction in others. I reduced it down to two spokes so that this becomes trivial to do.