Folding Bikes - Common misconceptions about wheels and bike engineering

I've really enjoyed some of the links that have been put n this thread. I had to print out Jur's PDF (Burgoyne & Dilmaghanian) because it was sideways and upside down. My laptop was getting dizzy I think as I swapped it from one side to another. The article was excellent though once I got it printed and collated.

Is it theoretically possible to replace the spokes with pretensioned strings?Yes; in fact you can buy these emergency spokes made from Kevlar cords.


Also, can a spoke carry significant compression before it buckles or does it basically behave like a string?No; the compression it can handle is only that amount which causes it to lose tension. Immediately after that it will buckle.

So here's the thing to understand: A string under tension is no different in behaviour from a stiff rod. Let's say that a mass is suspended by a system of an elastic band running vertically up, and a string which is running vertically down and kept under tension by the elastic. You can in effect push the mass up by pushing up on the string, always assuming the string is always under at least some tension. As you push up, the string tension will decrease, and because it has some elastic component, it therefore must become slightly shorter. It is not incorrect to say the string is compressing (from its "unpushed" state, that is).

Same for spokes made from wire - as long as the spoke remains in tension, it is correct to speak of compression of such a spoke (from its rest tension) and therefore to make the next logical step to say that in effect, the hub is standing on said spokes. If you ignore the pretension, then this is easy to accept. And ignoring pretension is perfectly valid - pretension turns wires into stiff rods.

However, for a tensioned member, being "compressed" because it has lost some tension does not mean that it is carrying the lost elastic load by compression.

If that was the case, you would be able to tie one end of an elastic down, attach a mass to the other end, stretch it up and let go and then when the stretched elastic "compresses", when the distance compressed x spring constant equals the weight of the mass, it will stand straight up.

Ok, I'm still trying to get my head around this so I started doing though experiments. What if you take a strung archery bow and then push the ends together? The tension in the string will decrease. Now, does the decrease in tension mean the string is taking load in compression or is the bending of the bow carrying the load?Hmmm... you are stretching me here...

The string by itself can't take any load, but strung to a bow, you can (theoretically at least) perform a length measurement on the string before and while pushing the ends together. You can also measure the string's Young's Modulus (ie the elastic strength), and multiplying the change in length (ie compression) from pushing the bow ends together with the string's Young's Modulus, you get force. So you can calculate the amount of force from that.

F = deltaL * K

But if you are asking what is actually transmitting the force, then that must be the bow. The string is incapable of that.

Well, Jur. My thinking is the lower part of the wheel rim is acting as an arch with local beam action as well and the rim carries the load. This would produce deflections in the rim which would reduce the spoke tensions in that area.

People who can't deal with the concept of preload...

Preloading the spokes will add lateral stability/stiffness to the wheel and increase the fatigue life of the spokes. However, it does not make them into compression resisting members.

Here is another paper on bike wheels: http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf

OK, but the ones on the bottom get shorter, right? Just ignore the word compression, since all the spokes remain in tension.


Preloading the spokes will add lateral stability/stiffness to the wheel and increase the fatigue life of the spokes. However, it does not make them into compression resisting members.

Is it theoretically possible to replace the spokes with pretensioned strings?

Also, can a spoke carry significant compression before it buckles or does it basically behave like a string?

Kam

People have actually built solid wheels and rode them quite long distances with only these kevlar string spokes.
http://www.peterwhitecycles.com/fiberfix.htm

I haven't ridden a wheel made only of these, but have ridden one with two of these spokes about 300km and it worked great.

People have actually built solid wheels and rode them quite long distances with only these kevlar string spokes.
http://www.peterwhitecycles.com/fiberfix.htm

I haven't ridden a wheel made only of these, but have ridden one with two of these spokes about 300km and it worked great.

What a clever idea that Kevlar spoke is -oops - I meant Aramid. Spokes are only wires of course - even though they aren't as flexible as some.

I used to work for a boss who was terrible at explaining things... if I didn't understand what he meant, he would explain it again in the same words, just a lot louder... same with having a debate with him... he would just repeat the same argument louder and louder... at about the 3rd rendition it would become laced with the f-word...

So, I have explained for all I'm worth in this thread... the only option open to me now is to repeat it, a bit louder... :P

I think you are mistaken on a number of points...

1. The analysis is only for relatively small loads. The numbers show that - they are in newtons - so a load of 100kg. No slamming into the ground here.

2. The tensions at 4 and 8o'clock are small beer - not "snapping" tensions at all. They may be for you gross distortion scenario, I don't know, but not for the analysis in the OP. The numbers are merely 3-4kg of weight hanging from a spoke - almost infinitely far from "snapping" tension.

The diagram that closely resembles the data you are talking about is actually Figure C2 and not Figure C3.

As mentioned, Fig 2 depicts a wheel loading whereby pre-tension on ALL spokes is always present but uneven to some degree (therefore non-snapping tensions); Fig 3 is when the wheel is overloaded to the point of rim deformation, whereby the bottom spokes can loose all pre-tension momentarily during extreme applications...

http://i156.photobucket.com/albums/t24/Rollopics/big-jump.jpg


3. Spokes do not snap from excessive tension. For that they are too ductile. No, they snap from metal fatigue due to thousands of times of small bendings to and fro at the spoke elbow as the tension relaxes a bit when the spokes go through BDC. This develops metal fatigue - micro cracks which propagate and eventually the spoke hangs by a thread, so to speak, then only a small amount of excess elbow flexing will make it go, such as when you hit a bump. For a spoke to snap from tension like you are thinking of, it will rip the nipple thread right out before it pulls a neck and finally gives. You can safely put that scenario completely away from you.

I do understand the effects of metal fatigue at the J-bend causing eventual failure purely from pre-tension fluctuations as the wheel rolls along the ground. The test numerical data in the article shows once again that the worst pre-tension fluctuations actually occur between the 4 and 8 o'clock positions, as the spoke tensions are at their highest on either side of the bottom spokes where the pre-tension reading is at it's lowest. In a rolling wheel, it is likely that the bottom area of the rim would treat each passing spoke to a tension spike, a sudden drop of tension, followed by another tension spike... like a micro bull whip crack. It makes sense to keep a wheel adequately tensioned in order to minimize this pre-tension fluctuation.

However, metal fatigue over time at the J-bend isn't the only premise for spoke failure if you take into account various forms of cycling other than road. The J-bend is a natural stress-riser on its own even with a brand new spoke, and correctly installed nipple threads are unlikely to rip before the bend fails when overloaded. For slam landings, where rim deflection is so severe that the bottom spokes loose all pre-tension, the test data (although the results are not for this specifically) does show where the tension spikes are located. Figure C3 is the logical amplified progression of Figure C2. Its the only information I have at the moment that remotely makes sense as to why and where a spoke would snap at the same moment of impact, and if not... would result in a flat-spot on the rim instead.

It would be cool to see a slow-motion video camera and an oversized hydraulic robotic swingarm, slamming various wheels onto a concrete floor to provide further study on the nature of spoke and rim failures from simulated jump landing loads and it's relationship to whether the hub hangs from the spokes above it, or is held up by the spokes underneath it. In the meantime, this is where my thinking is at the moment...

Cheers
Pocko



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Ok, I'm still trying to get my head around this so I started doing though experiments. What if you take a strung archery bow and then push the ends together? The tension in the string will decrease. Now, does the decrease in tension mean the string is taking load in compression or is the bending of the bow carrying the load?

A better way would be to find a plastic "hula hoop" for your experiment Use string as spokes and tie them to the hoop starting with Figure A1 and progress from there one figure at a time. But don't push the hoop from the top like you mentioned about the archery bow, you have to push down from the central point. Use a wooden handle in the middle so that you don't hurt your hands when you push down on it, so always tie the strings centrally to that. Have fun.

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