Folding Bikes - Why smaller wheels are better - the sequel

I was browsing through some failures on road bikes where many of the wheel failures happen when standing up to sprint.

It occurred to me that while smaller wheels are stronger, there is more. The moment (ie torque) exerted on the wheel components is smaller, too, due to the smaller diameter.

So there's a double whammy if you like - not only are the wheels stronger but under hard (or any) acceleration the stresses are lower.

Of course the bearings will wear faster due to rotating faster.

An interesting point here, but to complicate matters further what about the pros and cons of radial versus tangential spoking?
Many folding bikes have radial spokes on the front wheel (low torque loading) and tangential spokes in the rear wheel, where there is high torque on acceleration (but not on my bike!). Heavy braking will also put torque loads onto the wheel.
The angle of tangency must also be a factor and as this inceases then the spokes are longer.
What about the stretching of spokes under shock loads on rough roads and worst of all, BMX jumps.
The diameter of the spokes is yet another factor. Thin spokes will stretch more than thick ones.
I expect that there is a formula for resolving all these variables. Or is it done by trial and error?
Hey, there's a lot more to bike wheels than we thought. We take them for granted because most of the time they work so well and when you think about it, are an elegant design.

I wonder if small wheels are also potentially a bit safer?

Over here the last few years we've had more & more digi' TV channels, but the content has become awful. One current theme is accidents, police car chases etc.

Recently one clip caught my eye, that of a girl on a big wheel bike riding through pedestrian traffic lights in Cambridge. She managed to get her foot tangled in the front wheel & went over. I can't recall ever seeing that happen before. Maybe the clip is on Youtube or similar.

A couple of times in other threads, SesameCrunch has mentioned his 16 pounds Fuji bike, & I keep meaning to ask him how much of the extra speed he gets from that, he feels is attributable to the wheels & or the light weight.

With regard to spokes, whilst looking at 406 mm rims, they seem to mostly come with 36 holes, yet I see for example, some of the Downtube bikes have only 24 on the front wheel. So is there a "diminishing returns" effect over a certain quantity of spokes?

The stresses on wheels for BMX jumps must be huge. Do they have high spoke breakage rates, I wonder?

Re spokes, they work counter-intuitively. It would seem common sense that the hub 'hangs' from the top spokes, progressively less and less as you go 90degrees out. However, surprisingly what is shown by all 3 of measurement, numerical analysis and analytical analysis is that the hub 'stands' on the bottom spokes, exactly like in a wagon wheel with wooden spokes.

What in effect happens is the rim deforms inwards where it touches the ground, and the spokes in the vicinity of that deformation slacken. A large number of spokes will share the load such that each spoke sees only a small portion of that load. BMX wheels commonly come with 48 spokes to be able to take those drop hits.

406 rims come in all sorts, at least for OEM purposes. The spacing of spokes at the rim determines the load sharing. So, a small rim diameter can have less spokes to result in the same spoke spacing at the rim compared to a big rim. A 24 spoke 406 wheel is equivalent to a 36 hole 700c wheel for spoke spacing.

When the wheel load becomes so large that the bottom supporting spokes completely lose tension, the wheel is ready to collapse - having momentarily lost the properties of the tensioned structure.

Check out this unfortunate chap who is about to eat dirt: The front wheel which took the hit bottom spokes are buckling under the severe load:


http://images.velonews.com/images/news/9076.13096.f.jpg

A couple of times in other threads, SesameCrunch has mentioned his 16 pounds Fuji bike, & I keep meaning to ask him how much of the extra speed he gets from that, he feels is attributable to the wheels & or the light weight.


I notice the light weight of my 16.4lb carbon bike most when climbing hills. The extra weight makes a huge difference. I can't stay with my usual peers when I'm on any of my folders, which generally are 10 pounds heavier. However, I don't think this is attributable to wheel size - it's purely a matter of weight.

My carbon bike is also noticeably faster in acceleration than my folders. Here, it's a matter of weight and superior wheels/hubs (the 700C wheelset on the bike weighs 1500 grams and has smoooooth hubs :)). However, I do believe that simple physics dictate that, everything else being equal, smaller diameter wheels spin up faster. It's just that in real life, we hardly ever get to compare two wheelsets of different diameters with "everything else being equal".

Back to Jur's original point, though, I agree that smaller wheels will take more pounding simply due to the fact that there is less moment, and therefore, stress on the smaller diameter spokes.

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Back to Jur's original point, though, I agree that smaller wheels will take more pounding simply due to the fact that there is less moment, and therefore, stress on the smaller diameter spokes.

OK - so how come Brompton had to change their rear wheel design in the nineties to accommodate heavier 13 gauge spokes after an epidemic of breakages? It's my perception that spokes on large wheeled bikes are quite a bit finer than those 13 gauge ones.

Maybe it's about the sharper angle at the elbow and nipple. A short spoke necessarily has to exit hub or rim at a steeper angle than a longer one. Perhaps the bending moment fatigues standard gauge spokes in that scenario.

Check out this unfortunate chap who is about to eat dirt: The front wheel which took the hit bottom spokes are buckling under the severe load:


http://images.velonews.com/images/news/9076.13096.f.jpg

Looks like he snapped the stem and dropped his chain too! He must have dropped from quite a height to do that.

I can't see the attraction in losing your teeth that way.

I notice the light weight of my 16.4lb carbon bike most when climbing hills. The extra weight makes a huge difference. I can't stay with my usual peers when I'm on any of my folders, which generally are 10 pounds heavier. However, I don't think this is attributable to wheel size - it's purely a matter of weight.

My carbon bike is also noticeably faster in acceleration than my folders. Here, it's a matter of weight and superior wheels/hubs (the 700C wheelset on the bike weighs 1500 grams and has smoooooth hubs :)). However, I do believe that simple physics dictate that, everything else being equal, smaller diameter wheels spin up faster. It's just that in real life, we hardly ever get to compare two wheelsets of different diameters with "everything else being equal".

Back to Jur's original point, though, I agree that smaller wheels will take more pounding simply due to the fact that there is less moment, and therefore, stress on the smaller diameter spokes.

The thing that I don't understand is why smaller wheels aren't built lighter. Since the structure is stronger, the wheel should be made with less/lighter material until the risk of failure is equal to that of a full sized wheel. Otherwise the wheel is overbuilt.

I've been trying to understand why my Carryme feels so much more efficient than my Downtube VIIIH and I believe one of the reasons may be because it has extremely light wheels that aren't overbuilt like most 20" wheels are.

It should be obvious that, all things being equal, smaller wheels should be lighter. The strange thing is that most of the small wheels on the market aren't. People often attribute the extra weight of folders to the frame hinges, but I think that properly designed wheels should more than compensate.


OK - so how come Brompton had to change their rear wheel design in the nineties to accommodate heavier 13 gauge spokes after an epidemic of breakages? It's my perception that spokes on large wheeled bikes are quite a bit finer than those 13 gauge ones.

Maybe it's about the sharper angle at the elbow and nipple. A short spoke necessarily has to exit hub or rim at a steeper angle than a longer one. Perhaps the bending moment fatigues standard gauge spokes in that scenario.

Yes, I agree, it's probably because the hubs are too large. I bet if full sized wheels had the same ratio of hub width to wheel diameter as Bromptons that they would experience lots of spoke breakage too. Sharp angles at the elbow/nipple attack the spoke where it is weakest. On my Carryme the spokes originate from the center of the hub (which is about 1/3 the width of the hub on my Downtube). There are only three spokes on each wheel, but they are very thick and I can't ever imagine them breaking.

Also, you have to consider the fact that since Bromptons are utilitarian bikes, they get more punishment than average.

Check out this unfortunate chap who is about to eat dirt: The front wheel which took the hit bottom spokes are buckling under the severe load:


http://images.velonews.com/images/news/9076.13096.f.jpg

Ugh. This image reminds me of my mountain biking accident last year where I went endo, landed on my head and fractured my neck. Got a free helicopter ride and spent 2 nights in ER.

I'm lucky to still be here e-chatting with you guys...

Maybe it's about the sharper angle at the elbow and nipple. A short spoke necessarily has to exit hub or rim at a steeper angle than a longer one. Perhaps the bending moment fatigues standard gauge spokes in that scenario.
Disclaimer: I don't have any data other than my own experiences, and don't want to present myself as an expert on this. That said, I agree!

My observations about spoke breakage:
--When spokes break, the head comes off. Has anyone ever seen a spoke break in any other way?
--Spoke breakage is more common on wheels with a large hub flange than on small-flange hubs.
--The spokes that break are (almost?) always the ones that are the most inconvenient to replace, i.e. drive side inside spokes, the ones that have the head on the outside of the flange. The apocryphal corollary to Murphy's law ("the part that breaks will be the one that's most inconvenient to replace") is thus proven correct again; but it explains nothing.

For some reason shorter spokes are more stressed by the shock of bumps, and the inside position of the spoke concentrates the stress at one spot, right next to the head, with the result that that is where failure occurs.
That is why when I rebuilt the front wheel of my Mini with a Nexus dynamo hub, I routed all spokes to the outside. More recently I broke two spokes in the rear wheel of the same bike, so I replaced all the drive-side spokes with longer ones, all routed to the outside of the flange. The bike came with one-cross spokes; I replaced them with four-cross (!) which looks very strange: each spoke actually comes into contact with four other spokes. Each outer spoke makes a distinct bend where it crosses an inner spoke; each outer spoke makes four distinct (albeit very slight) bends. I figure each of those bends puts a little pressure on the other spoke, so the shock of a bump will be distributed among them to some degree.

(My reason for four-cross spokes, I must admit, was simple pragmatism: I discovered the broken spokes after dinner on a monday evening, and knew I couldn't get replacement spokes cut until the following Saturday; so I used what I had lying around, which turned out to be four-cross. How will it hold up? I don't know. The original spokes had about 1400 miles on them; the repaired wheel has about 100 so far. I'll keep you posted.)

Regarding spoke breakage, foremost, most folders use big bike parts. A smaller and narrower flange is needed. Most wheels need only 16-24 spokes if built properly. Oddly, Capreo hubs start at 24 spokes (up to 36) and have normal width flanges. That's silly to me. The spoke count is so high on the 36 spoke Birdy that one can barely fit a finger between the nipples on the rim.

Fortunately, the high quality Alex rims also come in 24 hole varieties. Velocity makes rims in the 28 and up range for small wheels. That's just silly.

My wheels are vastly overbuilt with 32 spokes, but I was too cheap to pay full price for 28 hole hubs and rims, neither of which were on sale.

jur,
I need convincing that a bicycle is supported by the lower spokes in compression.
Surely, a single spoke in tension will support a considerable load, but in compression it will support very little load before it buckles, in spite of the pre-tension.
Convince me please.
If I had nothing better to do, I would cut through the upper spokes from one wheel and the lower ones from the other and see which wheel collapsed first.
Perhaps I have been lucky, but I do not recall having a broken spoke in 60 years of cycling. Maybe I'm not riding fast enough.

Spokes do not always break at their heads; the Bromptons are notorious for breaking at the j-bend which has also been my experience. This wheel was also rebuilt from three-cross to two-cross to reduce the severe spoke angles of the three-cross pattern. In my experience, spoke gauge seems to have made little difference for this wheel.

In the pic above, despite any buckling, there is also no visual evidence that the wheel had, did, or will fail. Furthermore, interpretation of that pic assumes a lot. It assumes the pic was taken while the rider was riding over even terrain, that the severe buckling is not due more to the sudden shift of weight on the front wheel due to the rider's handlebars snapping, and that the tire pressure is high (such that little deformity would occur) which is not usually the case for mountain bike tires. In short, the pic of the accident does not seem to prove anything in terms of wheel strength, weight, acceleration, etc.

Small wheels are not built lighter because, as pm124 says, not many want to pay out the nose for folding bike wheelsets, therefore there is no huge market in general. In this case, it's a matter of economics, not technology.

I notice the light weight of my 16.4lb carbon bike most when climbing hills. The extra weight makes a huge difference. I can't stay with my usual peers when I'm on any of my folders, which generally are 10 pounds heavier. However, I don't think this is attributable to wheel size - it's purely a matter of weight.

My carbon bike is also noticeably faster in acceleration than my folders. Here, it's a matter of weight and superior wheels/hubs (the 700C wheelset on the bike weighs 1500 grams and has smoooooth hubs :)).

Thanks SesameCrunch, that's useful to know. Those bikes are so dear here, I'll doubt I'll get to try one! Maybe on a future trip to SF :-)

I had a gut feeling it would be the weight that was most significant. I've recently had a spell on a 30 pounds bike & when I got back on my Strida, it felt much better :-)

Also I see Moulton's are still doing well in races against 700c wheelers:

http://doocey.net/moultonbuzz/

about half way down the page "Suzuka Endurance Race",

so it does indeed look like small wheels can really hold their own :-)

That was a close one with your MTB crash! Good to see it hasn't put you off riding. I imagine your family had a worrying time!

Spokes do not always break at their heads; the Bromptons are notorious for breaking at the j-bend which has also been my experience. ...

For clarification: do you mean they break very near the head, rather than at the head?

For clarification: do you mean they break very near the head, rather than at the head?
My mistake; for some reason I mis-read your post thinking you meant the threaded end :p . But yes - one of my spokes broke near the head while the other broke at the elbow (I would consider that near the head as well) - at the same time, during the same commute. I don't remember if both spokes were right next to each other, but they were close. Both heads were still sitting in the flanges when I stopped. These were the thicker 13 ga. spokes on Brompton's 3-speed SRAM hub. I had it rebuilt using 14's.

I had a gut feeling it would be the weight that was most significant. I've recently had a spell on a 30 pounds bike & when I got back on my Strida, it felt much better :-)
Uhm, er, well.... Your gut feeling is sorta wrong.

Bike weight, particularly frame weight, is one of the least significant factors in bicycle efficiency and performance. Rider position, rider fitness, tire type, tire pressure, tire width, bike geometry, aerodynamics, gearing and stiffness are much more important. Rotating weight is more important than frame weight, which is to say it is actually a minor factor in performance. ;)

1) If you have two riders of the same physical ability, and one is on a 20 lb time trial bike and the other is on a 15 pound road bike, the TT bike will be faster (rider, bike are more aero)

2) Same two riders, one is on a 15 pound road bike and the other is on a 30 lb recumbent, on the flats the recumbent will spank the road bike, and most of that is pure aerodynamic advantage. (Climbing will be tougher, not because of weight but because the bent rider doesn't have the same leverage.)

3) On a 4% grade, 10 lbs will require an extra 8 watts or so, or 0.5 mph; that's a pretty steep grade, and a speed difference that would be overwhelmed by fat/soft tires or a wide gearing gap. On the flats, 10 lbs makes no difference in speed.

4) From the "anecdote" corner, I have two 26 lb bikes: one is a road bike, the other a cross. The road is faster than the cross -- not much, maybe 5-10% tops. Feel free to explain the discrepancy. :D

5) For your own testing: Find a nice TT loop or a big hill and stick 4 full water bottles on your bike. Do the loop and time it. Empty the water bottles: congrats, your bike is now 7 lbs lighter). Time it and compare.

Most folding bikes are set up in a hybrid or comfort geometry, have fairly wide tires, have few (if any) sizing options, are usually missing either the top tube or the downtube (thus losing some lateral stiffness). So if your folding bike is slower (or faster) than your road bike, I seriously doubt weight is the primary culprit. Unless you're doing Cat3 time trial races, weight makes almost no difference to your performance.

Don't feel bad, though. Humans held a "gut feeling" that a bowling ball and a marble would fall at different speeds for thousands of years. :D

jur,
I need convincing that a bicycle is supported by the lower spokes in compression.
Surely, a single spoke in tension will support a considerable load, but in compression it will support very little load before it buckles, in spite of the pre-tension.
Convince me please.
If I had nothing better to do, I would cut through the upper spokes from one wheel and the lower ones from the other and see which wheel collapsed first.
Perhaps I have been lucky, but I do not recall having a broken spoke in 60 years of cycling. Maybe I'm not riding fast enough.
Ah you are mistaken: the spokes in a wooden wheel are under compression (the iron tyre) but in a bicycle wheel the spokes are under tension. In both cases that is what gives the wheel its strength, enormous strength in a bicycle wheel for such puny components.

So a bicycle wheel under load still experiences the rim deflection at the ground contact area which will cause the spokes in the deflected length of rim to relax their tension somewhat. Interestingly, because the rest of the rim does not deform, the rest of the spokes do not experience increase in tension. Only the ones at the bottom change tension.

So heh, heh, you can't cut any spokes out to prove that the hub is standing on the bottom spokes because the whole structure loses its strength. But they have made measurements of spoke tension (this is easy using a spoke tensiometer) with a wheel under load.

If the wheel is loaded so heavily that the bottom spokes lose tension completely, the wheel is in danger of collapse. So a wheel with fewer spokes have to have higher spoke tension to prevent loss of tension, because each spoke is carrying a higher load.

I hope this goes some way in explanation.

My observations about spoke breakage:
--When spokes break, the head comes off. Has anyone ever seen a spoke break in any other way?
--Spoke breakage is more common on wheels with a large hub flange than on small-flange hubs.
--The spokes that break are (almost?) always the ones that are the most inconvenient to replace, i.e. drive side inside spokes, the ones that have the head on the outside of the flange. The apocryphal corollary to Murphy's law ("the part that breaks will be the one that's most inconvenient to replace") is thus proven correct again; but it explains nothing.

For some reason shorter spokes are more stressed by the shock of bumps, and the inside position of the spoke concentrates the stress at one spot, right next to the head, with the result that that is where failure occurs.
Spokes break where they get stressed the most. Usually that is at the head: As the spoke tension cycles with every wheel revolution, the elbow experiences flexing. The small amount of flexing over time will crack the material.

A spoke with an acute entry angle at the nipple has the same problem of micro-flexing, but in addition the threads constitute a weakening. So acute angle spokes sometimes fail at the start of the thread.

Regarding thicker spokes, I think I read once at Sheldon's site that butted spokes are better because the thinner section takes up most of the flexing, leaving the elbow under less stress so will last longer. Hence my choice of butted spokes for the Swift. Also, thicker ain't necessarily better because the spoke can be so strong and inflexible that the elbow gets stresses more and still fails. Thinner spokes allow more flexing in the spoke body. (This is what I recall reading. May recall wrong.)

Ah you are mistaken: the spokes in a wooden wheel are under compression (the iron tyre) but in a bicycle wheel the spokes are under tension. In both cases that is what gives the wheel its strength, enormous strength in a bicycle wheel for such puny components.

So a bicycle wheel under load still experiences the rim deflection at the ground contact area which will cause the spokes in the deflected length of rim to relax their tension somewhat. Interestingly, because the rest of the rim does not deform, the rest of the spokes do not experience increase in tension. Only the ones at the bottom change tension.

So heh, heh, you can't cut any spokes out to prove that the hub is standing on the bottom spokes because the whole structure loses its strength. But they have made measurements of spoke tension (this is easy using a spoke tensiometer) with a wheel under load.

If the wheel is loaded so heavily that the bottom spokes lose tension completely, the wheel is in danger of collapse. So a wheel with fewer spokes have to have higher spoke tension to prevent loss of tension, because each spoke is carrying a higher load.

I hope this goes some way in explanation.

I don't really see why it would be surprising or counterintuitive that a tensioned spoke would behave any differently from a compressed spoke.

All materials are under tension/compression from the time they are formed. We choose to identify the inherent tension/compression of a material as the point of zero force, but the truth is that there are molecular forces. What difference should it make whether the force of the tension/compression is provided by the molecules of the material or from an external mechanism? The distinction between applied forces and forces inherent to the material exists only in the mind of the engineer. So to me it seems perfectly intuitive that we should be able to redefine a tensioned wheel as an equivalent wheel with untensioned materials of slightly different properties.

Consider, for example, freezing a compressed sponge. If you know the sponge was compressed before freezing then you might regard it as being under compression, but if you don't know the sponge was compressed then you might regard it as uncompressed (although with different material properties). The distinction is in the eye of the beholder, but the physics is not. Therefore, the distinction cannot be a physical one and the two notions must be physically equivalent.

What I do find counterintuitive is your point about rim deformation. It seems to me that the hub should exert a force through the bottom spoke which results in a radial deformation of the rim at its contact point with the ground. The rest of the rim must deform in order to remain connected with the deformed contact point, but the shape of the rim guarantees that the forces transmitted can only be tangential. Therefore, the rest of the rim must experience a tangential deformation to accommodate the radially deformed contact point (lest the rim be severed). However, since the deformation is tangential, the spoke tension would remain unchanged for all spokes except the bottom one. Are you sure that the you don't mean to say that "the rest of the rim does not deform radially"?

Of course, I'm no expert. Just my 2c.

makeinu, this is Planet Earth. Planet Earth, this is makeinu.

You can't push a rope. That's basically what we're all talking about when it comes to spokes on a bike wheel. I'm not sure if that was you came up with or not, but I bet you get a lot of triple word scores playing Scrabble.

"the rest of the rim does not deform radially" I think you're right, and that is implicit. It also is a second order effect, I think. A wheel can be modelled by equating it to a beam hanging by spokes supported by a rigid beam above it. Pressing upwards at a point in the bottom beam will cause a local deformation and the spokes inside that deformation will lose some tension. There is an infinitesimal sideways deformation/movement of the whole lot but it can be ignored.

So a bicycle wheel under load still experiences the rim deflection at the ground contact area which will cause the spokes in the deflected length of rim to relax their tension somewhat. Interestingly, because the rest of the rim does not deform, the rest of the spokes do not experience increase in tension. Only the ones at the bottom change tension.

I'm afraid you are contradicting your earlier assertion that bike hubs stand on the bottom spokes. You are saying that the spokes are under tension - in effect they are all pulling at the hub. When the weighted wheel is deformed, the lower spokes "relax their tension". That is not the same as the hub standing on those spokes. those pokes are still pulling at the hub, just not as hard as before. In fact, you then said if the deformity is enough that the spokes completely lose tension the wheel will collapse. The reason for this is that the spokes cannot support the weight of the rider pushing down on the hub - they will bend. So by your own reasoning, the hub cannot be "standing on the bottom spokes".

I'm afraid you are contradicting your earlier assertion that bike hubs stand on the bottom spokes. You are saying that the spokes are under tension - in effect they are all pulling at the hub. When the weighted wheel is deformed, the lower spokes "relax their tension". That is not the same as the hub standing on those spokes. those pokes are still pulling at the hub, just not as hard as before. In fact, you then said if the deformity is enough that the spokes completely lose tension the wheel will collapse. The reason for this is that the spokes cannot support the weight of the rider pushing down on the hub - they will bend. So by your own reasoning, the hub cannot be "standing on the bottom spokes".The phrase "standing on the bottom spokes" was merely meant to be a helpful analogy to a spoked wooden wagon wheel to understand that it is the bottom spokes which are doing the work. Here (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000119000003000439000001&idtype=cvips&gifs=yes) is an abstract of a paper of which I have a copy; note the words
Tests show that the bottom spokes carry virtually all the load by compressive forces, which reduce the tensile prestress set up in the spokes when the wheel was made.

jur,
I need convincing that a bicycle is supported by the lower spokes in compression.
Surely, a single spoke in tension will support a considerable load, but in compression it will support very little load before it buckles, in spite of the pre-tension.
Convince me please.

The pre-tension is higher than the load. When this stops being true the wheel quickly goes out of true and fails.

You can measure that it is "standing" on the bottom spokes by measuring the tension of the spokes under load. You don't need a tensionometer for this, just ping the spokes in a well built wheel when someone is sitting on the bike. The spokes at the bottom of the wheel will play a lower tone (they have less tension) than the ones at the top.

alex

Yeah good idea! :)

Two observations.

Rim Deflection. If the rim is circular, and you hit a bump, reducing or releasing the tension on one or more spokes, the shape of the rim must change, momentarily, to something less circular. The impact must create a bit of a flat spot, where the material of the rim is under increased compression, which must result in increased tension to some of the other spokes, if not all. Perhaps that increase in tension is very small; I don't know about that. My point is only that there must be some momentary increase in tension somewhere.

And what about shock waves? You know how caramel or toffee candy is flexible; you can stretch it, bend it, compress it, and so on, but you can't fatigue it. Bend it back and forth all you want, it doesn't break. But if you hit it sharply, it shatters like glass. "Like glass" is of course key; toffee and glass have different kind of structure than metal, retaining, in their solid form, some of the properties of a liquid. So my question is: do the spokes, under tension, have anything in common with toffee? Can the shock of a sudden bump cause the sudden failure of the J-bend of a spoke that has not suffered any fatigue? It seems to me it does. A shock wave travels up the spoke without doing any damage along the way, but when it gets to the point where the spoke meets the flange, it knocks the two together violently and, sometimes, catastrophically. If the spokes are already fatigued, they will be more likely to break; but couldn't the same thing happen to a brand new spoke that has suffered no fatigue at all?

The phrase "standing on the bottom spokes" was merely meant to be a helpful analogy to a spoked wooden wagon wheel to understand that it is the bottom spokes which are doing the work. Here (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000119000003000439000001&idtype=cvips&gifs=yes) is an abstract of a paper of which I have a copy; note the words


It may sound arrogant to say this, and I will search for some scientific data to back me up, but to me that abstract shows that even engineers don't always have a basic grasp of elementary physics.

The spokes at the bottom of the wheel will play a lower tone (they have less tension) than the ones at the top.

alex

"Less tension" is not the same as load bearing. Any tension on the bottom spokes means the hub is not standing on those spokes.


In fact, they MUST remain under tension to prevent the bottom of the rim taco-ing.

Rim Deflection. If the rim is circular, and you hit a bump, reducing or releasing the tension on one or more spokes, the shape of the rim must change, momentarily, to something less circular. The impact must create a bit of a flat spot, where the material of the rim is under increased compression, which must result in increased tension to some of the other spokes, if not all. Perhaps that increase in tension is very small; I don't know about that. My point is only that there must be some momentary increase in tension somewhere.

The rim is only compressed at the contact point. Moreover, since the rim is only connected tangentially, only the tangential component of the compression can be transmitted along the rim. However, since the compression at the contact point is radial, it is not transmitted to the rest of the rim and the rest of the rim does not deform.

Of course, the rim is not perfectly thin and perfectly circular and the contact point is really a surface, so there are nonidealities, but my point is that the closer the rim is to an ideal shape, the less deformation the rim experiences away from the contact point and apparently experiment confirms that the shape of actual rims is ideal enough that the the deformation away from the contact point is negligible.


"Less tension" is not the same as load bearing. Any tension on the bottom spokes means the hub is not standing on those spokes.


In fact, they MUST remain under tension to prevent the bottom of the rim taco-ing.

No one is saying that the net forces are the same as a wagon wheel. What they are saying is that the additional force field created by loading a bicycle wheel is a scalar multiple of the additional force field created by loading a wagon wheel. Obviously these must be superimposed with the pretension forces to get the net forces. In fact, if the net forces were the same then the additional forces created by loading could not be the same.

No one is saying that the net forces are the same as a wagon wheel. What they are saying is that the additional force field created by loading a bicycle wheel is a scalar multiple of the additional force field created by loading a wagon wheel. Obviously these must be superimposed with the pretension forces to get the net forces. In fact, if the net forces were the same then the additional forces created by loading could not be the same.

What they are saying is that the hub "stands on the bottom spokes", which is a misconception. When the wheel is hanging on a wall, the bottom spokes are pulling the hub downwards with several hundred pounds force. This is counteracted by the upper spokes pulling upwards with several hundred pounds force. When a courier is trackstanding at a light, she may be pushing down on the front hub with 40 lbs force. This does not create a situtation where the lower spoke are now supporting her weight by pushing up. It creates a situation where they aren't stretched quite as tight.

...When a courier is trackstanding at a light, she may be pushing down...

I think we have a new winner of the political correctness game.

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We tension spokes because they cannot take compressive loads. Their ratio of length to width makes them way too prone to buckling. In this respect, a component will react differently to compressive and tensive loads. It is not just an esoteric naming convention by idiot engineers. It's reality. Alternating from tension to compression on a spoke does a couple things. First, since it can support very little weight in compression, it will tend to buckle and allow the rim to deflect. Second, the alternating loading makes the part much more prone to fatigue issues and it will more than likely break (depending on the loads in both directions). Even if the properly tensioned spoke next to it may see the same load fluctuation the fact that it is always held in tension makes a big difference in life.

What they are saying is that the hub "stands on the bottom spokes", which is a misconception. When the wheel is hanging on a wall, the bottom spokes are pulling the hub downwards with several hundred pounds force. This is counteracted by the upper spokes pulling upwards with several hundred pounds force. When a courier is trackstanding at a light, she may be pushing down on the front hub with 40 lbs force. This does not create a situtation where the lower spoke are now supporting her weight by pushing up. It creates a situation where they aren't stretched quite as tight.

Thanks cooker, I'm with you on this.

In the original picture shown, the force (where the tire meet the ground) has overcome the stiffness of the rim. In other words, the rim has been stressed past the point of it's ability to remember and return to it's original shape. Now there is no circular shape for the spokes to hold and the wheel must collapse.

I'm no physicist, but I understand that the wheel depends on both the tension of the spokes AND the stiffness of the rim to remain circular.

Rim Deflection. If the rim is circular, and you hit a bump, reducing or releasing the tension on one or more spokes, the shape of the rim must change, momentarily, to something less circular. The impact must create a bit of a flat spot, where the material of the rim is under increased compression, which must result in increased tension to some of the other spokes, if not all. Perhaps that increase in tension is very small; I don't know about that. My point is only that there must be some momentary increase in tension somewhere.


You don't need to hit a bump for this to take place. The increase in tension is very small though. If you have a 36 spoke wheel then the increase in tension in each spoke is about 1/35th of the decrease in tension of the bottom spoke.



And what about shock waves? You know how caramel or toffee candy is flexible; you can stretch it, bend it, compress it, and so on, but you can't fatigue it. Bend it back and forth all you want, it doesn't break. But if you hit it sharply, it shatters like glass. "Like glass" is of course key; toffee and glass have different kind of structure than metal, retaining, in their solid form, some of the properties of a liquid. So my question is: do the spokes, under tension, have anything in common with toffee? Can the shock of a sudden bump cause the sudden failure of the J-bend of a spoke that has not suffered any fatigue? It seems to me it does. A shock wave travels up the spoke without doing any damage along the way, but when it gets to the point where the spoke meets the flange, it knocks the two together violently and, sometimes, catastrophically. If the spokes are already fatigued, they will be more likely to break; but couldn't the same thing happen to a brand new spoke that has suffered no fatigue at all?

Can you describe this shock wave in a physical manner?

Brand new spokes that fail are usually a result of not stress relieving the spokes when building this wheel. This causes the spokes to go through a fatigue inducing cycle on every rotation of the wheel and kills the spokes in short order.

All of this is covered in "The Bicycle Wheel" by Jobst Brandt. Jobst is a dividing guy and you might not agree with everything that he has ever written, but the book is very good.

Can you describe this shock wave in a physical manner? What do I know? But I imagine something like what happens when you shake the end of a rope, the other end tied to a fixed point; an S-shaped curve moves from your hand toward the other end of the rope. The S-shaped curve consists of a bit of slack followed by a bit of increased tension. It moves all the way to the other end of the rope, then --depending on how it's attached at the other end, what it's attached to, etc.-- rebounds back. Of course in the case of the bicycle spoke, the curve will be very subtle, and will move very quickly.

Speaking of rebound... if a rebounding shockwave coincides with a secondary impact to the rim, something is going to break.


Brand new spokes that fail are usually a result of not stress relieving the spokes when building this wheel. This causes the spokes to go through a fatigue inducing cycle on every rotation of the wheel and kills the spokes in short order.Yes, makes sense. But is this the only way spokes break?

Again, I wonder if rebound isn't a part of this; it shouldn't be a big deal if the rim and the spokes are constantly deforming and rebounding to their original shape, as long as they rebound at the same rate. If the spokes and rim rebound at different rates, both will be under excess stress.


All of this is covered in "The Bicycle Wheel" by Jobst Brandt. Jobst is a dividing guy and you might not agree with everything that he has ever written, but the book is very good.
Thanks for the reference.

What they are saying is that the hub "stands on the bottom spokes", which is a misconception. When the wheel is hanging on a wall, the bottom spokes are pulling the hub downwards with several hundred pounds force. This is counteracted by the upper spokes pulling upwards with several hundred pounds force. When a courier is trackstanding at a light, she may be pushing down on the front hub with 40 lbs force. This does not create a situtation where the lower spoke are now supporting her weight by pushing up. It creates a situation where they aren't stretched quite as tight.

It makes no difference. When you stand on a pedestal the pedestal is not magically generating a force to push back against gravity. The force already holding the molecules of the pedestal together (in tension) is simply relaxed. When there is no more tension left holding its molecules together the pedestal crumbles.

It's the same with a bicycle wheel. The only difference is that the tension is macroscopic instead of microscopic.


We tension spokes because they cannot take compressive loads. Their ratio of length to width makes them way too prone to buckling. In this respect, a component will react differently to compressive and tensive loads. It is not just an esoteric naming convention by idiot engineers. It's reality. Alternating from tension to compression on a spoke does a couple things. First, since it can support very little weight in compression, it will tend to buckle and allow the rim to deflect. Second, the alternating loading makes the part much more prone to fatigue issues and it will more than likely break (depending on the loads in both directions). Even if the properly tensioned spoke next to it may see the same load fluctuation the fact that it is always held in tension makes a big difference in life.

Yes, it makes a big difference, but the whole point is that the difference does not change the geometric structure of the problem. The nature of the difference between tensioned and untensioned spokes is the same as the nature of the difference between spokes made of different materials. Theoretically, you could replace tensioned spokes in any wheel with untensioned spokes with different material properties and the wheel would be mechanically equivalent.

I think we have a new winner of the political correctness game.

It was a tribute to Leah and Lambchop.
http://www.dccourier.com/lambchop/
http://www.citynoise.org/article/2770/by/hool

Surely the hub 'hangs' from the rim by all the spokes at the same time. It can never 'stand' on lower spokes. In compression, they bend with a couple of pounds of force.

Surely the hub 'hangs' from the rim by all the spokes at the same time. It can never 'stand' on lower spokes. In compression, they bend with a couple of pounds of force.

Why do you assume that the load must be added to the untensioned spoke in order to be described as "standing". A tight rope walker doesn't stand on a slack rope, does he? (I know the directions of the forces are different, but the point is the same)

To me, the quality of "standing" is that the load forces are transmitted below, while the quality of "hanging" is that the load forces are transmitted above or sideways. In the case of the bicycle wheel the forces are exclusively transmitted below. Therefore, it is, in my opinion, aptly described as "standing", regardless of the fact that the bottom spoke is not under compression relative to it's "natural" state (ie sitting in the box as opposed to built into the wheel).

Indeed, there's nothing natural about it's "natural" state at all. You don't find spokes growing on trees in the wilderness. To put a spoke in a wheel, raw materials are mined, treated, machined, and finally tensioned in a wheel. Why draw a distinction at the last step? A spoke tensioned to 100 pounds is no more the same component as a spoke tensioned to 0 pounds than a spoke machined to 13 gauge is the same component as a spoke machined to 16 gauge. If you put a black box around the tensioned spoke from the nipple all the way to the head, then the black box is under compression. In other words, even in the naive sense of "standing", the load is truly "standing" on the object known as the tensioned spoke, even through the object known as theuntensioned spoke is not under compression.

even in the naive sense of "standing", the load is truly "standing" on the object known as the tensioned spoke, even through the object known as theuntensioned spoke is not under compression.
Where's Oolong when you need him?

makeinu is right - for practical purposes you can ignore the pretension in the spoke when doing analysis. The spoke and wheel don't 'care' what the spoke pretension is, as long as it doesn't go completely slack under load. That tension can be slight or huge it doesn't make the slightest difference in the end. It's relative. Like speed is relative. In the days before modern science people used to think going too fast will kill you, since they thought speed to be absolute.

You might replace the tensioned spoke tructure with a disc which can only bear axial loads, the math is essentially identical. The bottom part of the disc supports the load. And it doesn't matter how many times you insist details about the absolute spoke tension, that's in the end just semantics.

Jur,

I notice your reference earlier to a paper, so you're clearly very interested in this. You may perhaps be interested in this article:

http://steadivision.com/steadipos.htm

It doesn't mention wheels, but is interesting to read about compression & tension in another context.

I particularly like the picture of the tower on its side than can be picked up & turned.

Hmm, very interesting. Thanks for that! :)

it doesn't matter how many times you insist details about the absolute spoke tension, that's in the end just semantics.

If a lower spoke is still under tension, it is not "just semantics" to say the the hub is supported by it, it is wrong.

If I am carrying a heavily loaded bag using the two bag handles, and you help me out by taking one of the handles, so I am now carrying just half the load, by your logic I am now supported by the bag handle.

If a lower spoke is still under tension, it is not "just semantics" to say the the hub is supported by it, it is wrong.

The question "what is the best word to describe the role of the spokes in a wheel?" is a question of semantics.

Webster's Seventh New Collegiate Dictionary lists six main meanings for the verb "support", none of which specifically mentions 'compression,' though arguably that is implied in "4 a : to hold up or serve as a foundation or prop for".

To apply that definition, as literally as possible, would suggest that the spokes of a wheel serve as a series of stilts that "support" the hub one after the other... which is, as you say, wrong. But if you read over all the definitions, it's pretty clear that "support" is not the best word to describe the role of the spokes in a wheel; so we are dealing with a question of semantics after all.

The wheel functions as a unit, and the spokes are a fundamental part of it. "Fundamental" implies "part of a foundation," so... yes, the spokes "support" the bicycle. And yes, this is just semantics.

The wheel functions as a unit, and the spokes are a fundamental part of it. "Fundamental" implies "part of a foundation," so... yes, the spokes "support" the bicycle. And yes, this is just semantics.

The lower spokes do play a role in supporting a rider's weight, but not the way jur implied here (I've added the bold emphasis):

Re spokes, they work counter-intuitively. It would seem common sense that the hub 'hangs' from the top spokes, progressively less and less as you go 90degrees out. However, surprisingly what is shown by all 3 of measurement, numerical analysis and analytical analysis is that the hub 'stands' on the bottom spokes, exactly like in a wagon wheel with wooden spokes.


In a wagon wheel, the hub presses down directly on a spoke which is a rigid wooden pole. To say that a skinny, taut, diagonally mounted bicycle spoke holds the hub up "exactly" the way a rigid wooden post does, is plain wrong.


The main role the lower spokes play is due to their diagonal tension, not their vertical weight bearing capacity. They stabilize the rim so that the rim can support the bike without taco-ing.

In a wagon wheel, the hub presses down directly on a spoke which is a rigid wooden pole. To say that a skinny, taut, diagonally mounted bicycle spoke holds the hub up "exactly" the way a rigid wooden post does, is plain wrong.
I have to agree with cooker here.... mechanically speaking, compression and tension are clearly not equivalent. Tension is much stronger than compression, and can accomplish the same task with much less weight.

It's like saying that an arch bridge and a suspension bridge are "mechanically equivalent" because both are bridges. ;)

Anyway, isn't this all slightly aside the point?

I mean, the claim is: "Given the same # of spokes, smaller wheels are stronger than larger wheels."

What is it that would make a smaller rim and shorter spokes more reliable, and more capable of handling impacts, torque etc than larger wheels?

I have to agree with cooker here.... mechanically speaking, compression and tension are clearly not equivalent. Tension is much stronger than compression, and can accomplish the same task with much less weight.

It's like saying that an arch bridge and a suspension bridge are "mechanically equivalent" because both are bridges. ;)

Anyway, isn't this all slightly aside the point?

I mean, the claim is: "Given the same # of spokes, smaller wheels are stronger than larger wheels."

What is it that would make a smaller rim and shorter spokes more reliable, and more capable of handling impacts, torque etc than larger wheels?
Thanks, B.

In terms of the greater strength of smaller wheels, one obvious difference is that lateral distorting forces act with more leverage on a large wheel than on a small wheel. And in terms of handling forward acceleration, the small diameter rim has much less mass and it is closer to the axis of rotation, so the torque needed to be transmitted to the rim by the spokes, to get it spinning, is much smaller, even though the rotation speed has to be higher.

If a lower spoke is still under tension, it is not "just semantics" to say the the hub is supported by it, it is wrong.

If I am carrying a heavily loaded bag using the two bag handles, and you help me out by taking one of the handles, so I am now carrying just half the load, by your logic I am now supported by the bag handle.

The only thing wrong is your example which does not correctly apply the logic of why a tensioned spoke is like an untensioned spoke. In your example you define the assisting force to be a fixed portion of the load ("so I am now carrying just half the load"). However, the fact that the pretension of a bicycle spoke is independent of the load is the very reason it is physically and mathematically equivalent to an untensioned spoke.

If a bicycle spoke was tensioned in one micrometer segments (perhaps if made out of carbon fiber) then you wouldn't even be calling it "tensioned". What difference does it make if it's a one meter segment? Inches, meters, micrometers. The units do not matter.

Physical phenomena are related by mathematical forms. If the mathematical form is the same then the physical behavior is the same. To insist otherwise is wrong.



In a wagon wheel, the hub presses down directly on a spoke which is a rigid wooden pole. To say that a skinny, taut, diagonally mounted bicycle spoke holds the hub up "exactly" the way a rigid wooden post does, is plain wrong.

The main role the lower spokes play is due to their diagonal tension, not their vertical weight bearing capacity. They stabilize the rim so that the rim can support the bike without taco-ing.

Good point. However, it has absolutely nothing to do with tension and everything to do with spoke orientation.


I have to agree with cooker here.... mechanically speaking, compression and tension are clearly not equivalent. Tension is much stronger than compression, and can accomplish the same task with much less weight.

...for a given material. The whole point is that, mechanically speaking, a tension wheel is clearly equivalent to a compression wheel of a different material.


It's like saying that an arch bridge and a suspension bridge are "mechanically equivalent" because both are bridges. ;)

No, it's like saying a suspension bridge with cables at x pounds of external tension and y pounds of molecular tension is mechanically equivalent to a suspension bridge with cables at 0 pounds of external tension and x+y pounds of molecular tension...which is obviously true because the terms external and molecular are arbitrary semantical terms.