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Old 11-28-07, 11:19 PM   #1
jur
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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.
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Old 11-29-07, 02:16 AM   #2
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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.
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Old 11-29-07, 03:27 AM   #3
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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?
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Old 11-29-07, 03:58 AM   #4
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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.
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Old 11-29-07, 04:05 AM   #5
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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:


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Old 11-29-07, 07:07 AM   #6
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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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Old 11-29-07, 07:59 AM   #7
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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.
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Old 11-29-07, 08:06 AM   #8
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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:


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.
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Old 11-29-07, 08:06 AM   #9
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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.

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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.

Last edited by makeinu; 11-29-07 at 08:22 AM.
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Old 11-29-07, 08:38 AM   #10
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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:


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...
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Old 11-29-07, 08:57 AM   #11
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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.)
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Old 11-29-07, 09:31 AM   #12
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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.
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Old 11-29-07, 10:11 AM   #13
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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.
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Old 11-29-07, 11:14 AM   #14
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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.

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Old 11-29-07, 11:24 AM   #15
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Originally Posted by SesameCrunch View Post
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!
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Old 11-29-07, 01:21 PM   #16
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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?
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Old 11-29-07, 03:54 PM   #17
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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 . 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.
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Old 11-29-07, 04:16 PM   #18
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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.

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.
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Old 11-29-07, 04:22 PM   #19
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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.
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Old 11-29-07, 04:55 PM   #20
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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.)
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Old 11-29-07, 09:20 PM   #21
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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.

Last edited by makeinu; 11-29-07 at 09:28 PM.
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Old 11-29-07, 09:32 PM   #22
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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.
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Old 11-29-07, 09:41 PM   #23
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Originally Posted by makeinu
"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.
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Old 11-29-07, 09:50 PM   #24
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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".
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Old 11-29-07, 10:32 PM   #25
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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 is an abstract of a paper of which I have a copy; note the words
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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.
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