Bicycle Mechanics - Mechanics of the tensioned load-bearing wheel

I remember reading in Jobst Brandt's "The Bicycle Wheel" that the tensioned (bicycle) wheel supports a load by standing on the bottom spoke, which loses part of its tension force in proportion to the load. Unfortunately, I couldn't remember all the details of it when trying to relate it to my friend, who thought the load was supported by "hanging" the hub off the rim and increasing the tension on the top spokes. Could anyone explain it to me better?

No, it doesn't hang from the top spokes, but from ALL of the ones not on the bottom. So let's say you have 100kg tension on all the spokes on a 32-hole rim. And there's 4 on the bottom that's unloaded from your weight. The round rim becomes a D-shape with the flat spot on the bottom. These four spokes lose their tension due to the rim getting closer to the hub. However, since the rim has a fixed circumference, the round part of the D has to expand in order to keep the same circumference (it's like pushing on one side of an inflated balloon, it expands on all the other sides evenly). This expansion on the rounded upper part increases the spoke-tension by an even amount on ALL the unloaded spokes.

You can figure it out mathematically:

50-kg load on wheel
50kg/4 = 12.5kg tension unloaded on 4 spokes at the bottom (87.5kg tension)
50kg/28 = 1.79kg tension increased for remaining 28-spokes above contact area (101.79kg tension)

Of course, it's not so simple because spokes undergo tension-changes linaerly, not all at once. So the tension-decrease increases slightly as it nears the bottom and only fully at the very bottom. So the above scenario might have more tension relieved on the two at the very bottom and less on the two on the sides of those. But total tension-relieved is still the same total as the load.

Basically it's a buoyancy equation where the load is redistributed evenly. Whatever tension is relieved off the bottom must be taken up the others.

I had thought that while the bottom spokes support the load, the increase in tension in the other spokes can be attributed only to the maintenance of equilibrium and not to the load, thus the bottom spokes would remain (for argument's sake, as the tension changes are caused by outside forces) the only spokes subject to outside forces (which is the load), while the changes in tension for the other spokes are made by the forces already existing in the tensioned wheel. Yes/no?

the increase in tension in the other spokes can be attributed only to the maintenance of equilibrium and not to the load, thus the bottom spokes would remain (for argument's sake, as the tension changes are caused by outside forces) the only spokes subject to outside forcesIt's one and the same. What's "equilibrium" in this case? It's dealing with the extra forces from the load.

Look at the directions of load. Draw a picture of a wheel and put a down-arrow at the hub. Then an up-arrow at the ground that balances the load. You can consider that the "outside force" of the weight-load actually starts at the hub "inside" the wheel. The result is that the hub and ground squeezes the spokes at the bottom together, thus relieving their tension.

Tension and buoyancy can be difficult to grasp as it deals with distribution in a fluid-like manner. A wheel can be considered a suspension-bridge that's wrapped up around itself. If you push up underneath a suspension-bridge, the cables above it are actually relieved of their tension right?

So it's actually the RIM that experiences the outside forces. The RIM then changes shape in response to load which causes the tension to change on ALL the spokes. In Jobst's book, he draws an exaggerated picture somewhere that shows the D-shaped rim. Compare the distance from the rim to the hub in the flattened D-part at the bottom versus the rounded parts above. So there is existing tension, which is what carries the load and that load is redistributed evenly.

It's like a care tyre. The flattened part at the bottom squeezes up and reduces the volume at the bottom of the wheel. This increases the existing 32psi of pressure to say... 33psi. This extra 1psi is distributed ALL the way around the upper parts of the tyre. Basically the sidewall cords of a car-tyre loses tension, you can see that where it bulges out sideways, and all the remaining cords above take up that extra 1psi. You don't see a corresponding bulge above a tyre that corresponds to the bottom compression because the extra load is distributed evenly around the upper part of the tyre.

Buy the book and read it? :innocent:

There's actually a very easy experiment you can do to demonstrate that the weight is supported by a loss in tension of the bottom spokes rather than an increase in tension on the top spokes.

First, we should establish that spoke tension can be qualitatively measured by the tone the spoke produces when plucked. The plucking is best done to the middle of the supported ends. Higher tone equals higher tension, and vice-versa. We do not need to know what the exact tension is, only to establish that there is an increase or a loss of tension.

Next, pluck the top and bottom spokes of an unladen wheel to establish a baseline tension/tone. Then get someone to apply a load to the wheel. Now, pluck the top and bottom spokes again. You should observe that the bottom spokes produce a lower-than-baseline tone but none of the top spokes offers any change in tone. On a very strong wheel (e.g., properly tensioned 36-spoked 559 wheel), you may need to apply a surprising amount of load to hear any effect.

Have fun! :thumb:

There's actually a very easy experiment you can do to demonstrate that the weight is supported by a loss in tension of the bottom spokes rather than an increase in tension on the top spokes.It's actually one and the same. The total loss of tension MUST be accompanied by an equivalent increase in tension. The only difference is that there's a lot fewer spokes losing tension than the ones increasing in tension. So you can easily measure the tension-loss in the 2-4 spokes at the bottom, but the much smaller increase in ALL of there 28-32 upper spokes is not as noticeable.

But if you're comparing the 2 bottom spokes ONLY to the 2 top spokes, then yes, you'll see A LOT of loss in tension without much tension-increase on the top 2.

I went looking around the interweb and found this to support me:
http://www.astounding.org.uk/ian/wheel/

It has some finite element analyses near the bottom, which I found helpful, as well as this for his conclusion: "I conclude that it is perfectly reasonable to say that the hub stands on the lower spokes, and that it does not hang from the upper spokes. It is also wrong to say that the force distributes all around the rim and all the spokes contribute to holding up the hub - over a third of the spokes have an effect that pulls the hub down!"


Mr. Fly - I actually remembered and performed that demonstration to my friend, but he remained unfortunately obstinate in his conceptions of the wheel.

So I happened to have a copy of "The Bicycle Wheel" on my coffee table, the chapter which actually covers this is a bit too long to quote, but I think y'all are talking around each other. The spokes on the top of the wheel actually do not change that much in tension, the D shape is caused by the detensioning of the lower spokes, wires under tension (spokes) behave like solid columns under load until all of the tension is used up. This means that you can assume that the tensioned spoke supports the hub the same as say a stick or a cement pillar would. So if a spoke is tensioned to 1000 lbF you can apply 1000 lbs of force downwards on the spoke before it again behaves as a wire as opposed to a solid column. The other spokes are necessary to maintain the tensioned equilibrium in the wheel and will change tensions slightly to maintain equilibrium, but the greatest tension change on the loaded wheel will be to the bottom spokes which are supporting the hub like solid columns.

The thing is, forces on a spoke is always in tension and the bottom spokes lose tension under load. That is, they experience lower amounts of force when load is applied. Columns experience an increase in force when they have load applied.

And you're right, the upper spokes do not change tension as much as the few at the bottom, but they DO increase in tension when load is applied at the bottom; just a lot less because it's distributed. Another way to look at this is to consider that total-tension on the rim must remain constant.

You are right about columns... but in a statics analysis you can substitute a tensioned wire for a column. A tensioned wire loosing tension will behave exactly like a rigid column increasing in compression up until the point where all of the tension is used up.

But if you see a decrease in the tesile load of spokes along the contact patch area this is due to a decease in their length.

A fair way to look at a wheel is as an array of springs. Spokes are not totally rigid. They act like very high rate springs. Similarly the rim is flexible as well so you can consider it as a series of compression springs with very high rates that join the ends of the spokes with act as very high rate tesion springs. So if you reduce the tension loads of the spokes in the vicinity of the contact patch then you have reduced their length by a very small amount. But that means you have just moved the rim compared to hub in a way that places a higher tensile load on the spokes on the upper side of the wheel via the flexing of the rims "ring of compression springs". And since with something as flexible as a spoke the load can only be carried by an increase in tension then it's still fair to say that the bike and rider hangs from the upper half of the rim and upper spokes since that is where the tesion gain takes place.

While I agree that you can look at tensioned spokes as a column until the tension dissapears this is a rather twisted and convoluted way of looking at tension loads in a wheel. It also suggests that the spokes pointed in directions other than straight up or straight down do nothing to support the wheel. But since we are talking about a situation where a far more accurate model is a series of very high rate springs constrained in a locked and balanced manner I really don't think the column model has much validity in the study of how a wheel carries its load.

What's the point of talking about spokes as springs just to say that the hub hangs from the rim? Spokes are not springs, and while they are susceptible to lateral deflection, they do behave as a rigid structure under compressive forces, given that their tension is greater than the compressive load. There is a very simple aural test you can perform to confirm that the bottom spokes are the load-bearing ones, mentioned earlier by Mr. Fly. Pluck the bottom and top spokes to establish a baseline sound (make sure that the spokes you choose are on the same side, ie drive/non-drive), then, applying a compressive force to the wheel via the seat, pluck the top and bottom spokes again. The lower sound you will hear in the bottom spoke indicates that it is supporting the compressive load by compromising part of its tension; the lack of change in tone you will hear in the top spoke indicates that it is not bearing a load. You might say in response that there is no aural change detected because the force is distributed over the top third of the wheel, but seeing as that is only 10.66 spokes out of 32 that would be supporting the hanging load you should be able to hear a change if that were the case. If that test isn't enough for you, examine the site I posted earlier (http://www.astounding.org.uk/ian/wheel/), where you can find finite analyses of the forces on a loaded wheel which are fairly damning to the case of "hanging" a load.

The column model is not only neither twisted nor convoluted but also exceedingly more accurate than the "high rate springs" model, and while it is true that every spoke changes in tension under load to maintain equilibrium within the wheel, it is only the bottom spokes that support the load. Try it for yourself - I am confident that your findings will match my own.

If I am coming off as rude at all, I sincerely apologize and wish my comments to be taken in only the most humble and positive way; this thread has the subtle beginnings of a flame war.

I remember reading in Jobst Brandt's "The Bicycle Wheel" that the tensioned (bicycle) wheel supports a load by standing on the bottom spoke, which loses part of its tension force in proportion to the load.

The term "standing on the bottom spoke[s]" is very misleading, especially when followed by "which lose part of their tension". It's not like a conestoga wagon wheel where the axle is compressing the lower spokes. In a bike wheel the spokes are all very tight and pulling the rim towards the hub. When the wheel is carrying a load, the bottom spokes are still under tension, but slightly less. They aren't being compressed.

Let's say God has my left arm and is pulling me up to Heaven, and the Devil has my right foot and is pulling me down to Hell. They're evenly balanced and I am stuck in the middle. Then somebody hands me the weight of my sins, and that makes me heavier. That should help the Devil pull me down, but being lazy, he relaxes a bit, and doesn't pull as hard, and I don't move. God's workload doesn't change. Would you say the Devil is now supporting the weight of my sins by not pulling down as hard? After all, God didn't have to pull any harder when that weight was added. It was the Devil who made the adjustment.

That's what Brandt is saying about the bottom spokes. They are supporting the weight of the rider by not pulling down as hard as before. The upper spokes don't have to increase their tension (more than a trivial amount) to accomodate the load.

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BC and cooker's got it down. Replace "spokes" with "strings" or "rubber bands" and the wheel will still operate exactly the same way. You can even lace up the wheel with a continuous line like a tennis-racquet and it would still work due to TENSION.

....If I am coming off as rude at all, I sincerely apologize and wish my comments to be taken in only the most humble and positive way; this thread has the subtle beginnings of a flame war.

Not taken that way at all. Debate can be described as "a friendly arugument". As long as the exchange is polite and we can all go and have a beer at the end of it and leave as friends it's all good..... :thumb:

From a purely mathematical point I'll accept the analysis described in that page. In fact it's an interesting and informative page from that aspect.

The real issue seems to be the author going to a considerable effort to bring sematics into the issue and bend how he describes the summation of the forces to support his "standing on the lower spokes" concept.

He brings in the definition of "standing" at one point and talks all around it and finally moves on leaving the reader with some vague impression that it applies to how a hub is supported by standing on the lower spokes. But our hub is only "standing" on the ground as much as a car is "standing" when supported by a suspension bridge. The road way is hanging from cables which are then supported by the end columns. Similarly our hub is hanging from the rim which then stands on the ground. But in both cases the hub loads and the car on the bridge are hanging from some element which then is used to transfer the loads to the ground by standing on it. The rim and tire in our case and the column in the bridge's.

He brings up the issue of static tension in the spokes of the wheel and then dismisses this because the forces all balance. But we can't just dismiss the spokes preload. It's there and it's fundemental to how the wheel supports loads. We all talk about how spokes only fail when the tension drops close to zero and the metal has to move and work. So it is equally biased to dismiss the static spoke preload here as well. Yet this dismissal sets the stage for the descriptions to follow later in his conclusions.

Yes his analysis shows a marked reduction in tensile loading of the contact area spokes. But to call it compressive is inaccurate. There is still tensile loads in the lower spokes, just less of it. But he set up the stage earlier by bringing up the preload tensions of the wheel and then dismissing them by saying they were balanced. But the wheel still knows the preloads are there and will see the changes in spoke tensions not as compression but as a reduction in tension. Semantics used again perhaps but it seems to be key to the idea of "standing on the lower spokes".

The point remains that you can't "push a rope". The author has worked in a very nice circumlocution to support his idea of standing on the lower spokes versus hanging from the upper spokes. Yes the change in values in the majority of the spokes that undergo an increase may not seem all that grand but the point is that spokes can only support a load when tension is added and are less able to support a load when the tension is reduced. And the spokes with the increased tensions are along the sides and upper half of the wheel and those are the ones that support the load.

Getting back to the plucking or light tapping of the spokes to indicate how all this plays out.... Sure, the lower spokes along the contact point are seeing the most reduction in tension and so you'll hear a marked tone decrease. Meanwhile the increase in the upper spokes that are supporting the shift in tensions is not noticable only because our ears and brain can't differentiate the small change in tone that each individual spoke sees. But it is there just as shown by the table in the analysis.

Which all brings it back to the reality that the hub and load hangs from the upper spokes and the only "standing" going on is in the rim that is used to transfer the loads from the upper half of the rim to the ground just as the suspension bridge columns transfer the cable loads to the ground.


Anyway, that's my take on the matter. Make of it what you will.

Let's say God has my left arm and is pulling me up to Heaven, and the Devil has my right foot and is pulling me down to Hell. They're evenly balanced and I am stuck in the middle. Then somebody hands me the weight of my sins, and that makes me heavier. That should help the Devil pull me down, but being lazy, he relaxes a bit, and doesn't pull as hard, and I don't move. God's workload doesn't change. Would you say the Devil is now supporting the weight of my sins by not pulling down as hard? After all, God didn't have to pull any harder when that weight was added. It was the Devil who made the adjustment.

That's what Brandt is saying about the bottom spokes. They are supporting the weight of the rider by not pulling down as hard as before. The upper spokes don't have to increase their tension (more than a trivial amount) to accomodate the load.

.Souls, sins and spokes!! Hahahahahhaahh.... :) :lol:

...That's what Brandt is saying about the bottom spokes. They are supporting the weight of the rider by not pulling down as hard as before. The upper spokes don't have to increase their tension (more than a trivial amount) to accomodate the load.

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If the part in red is from Brandt's book (I confess I have not read it or plan on getting it any time soon) then he has unfortunetly helped set the stage for this misconception. The upper spokes may only see a small change but with so many of them sharing the load this small change adds up.

A single thread is easily snapped on its own but when woven into a belt it can support massive loads.

If the part in red is from Brandt's book (I confess I have not read it or plan on getting it any time soon) then he has unfortunetly helped set the stage for this misconception. The upper spokes may only see a small change but with so many of them sharing the load this small change adds up.
Ah, but it adds up to much less than the weight of the rider on the fork. Before the rider got on, the upper spokes were pulling up to counteract the downward pull of the lower spokes. Now, the upper spokes are pulling up to counteract the weight of the rider and the downward pull of the lower spokes. However, the lower spokes aren't pulling down as hard. Their relaxation almost equals the weight added by the rider, so the upper spokes hardly experience a change in tension when a rider puts weight on the fork. That's the point Brandt is making. Just as God didn't have to pull harder when my sins were added, because the Devil stopped pulling down so hard, so the upper spokes don't have to work much harder to carry my weight, because the lower spokes are slacker and don't pull down as hard.

You can't just add up the upper spokes that are in direct opposition with the lower spokes. The rim acts like an arch to distribute the forces and all the spokes on the upper and even some of the ones in the lower side all come into play sharing and constraining the various loads in the system. The true model of forces is far more complex then what is shown on that website.

Some of the changes are directly due to the supporting of the weight and show up at the axle of the hub to support the outside load that started it all and some are locked into the wheel due to deformation loads. This second aspect is why the spokes just outside the deformation in the wheel diagram and table are shown as pulling outwards and downwards. They are reacting to the local teeter totter like levering bend in the rim that is induced by the localized rim deformation in the model. This actually makes those spokes see more tension even though they are on the lower side of the wheel. But that increase cancels out part of the decrease in the "compressed" spokes nearby so the total value for the reduced tension spokes needs to take that into account.

The true model of forces is far more complex then what is shown on that website.

Ah, then tell us, what is the One True Model of forces in a loaded wheel? I fail to see how that diagram is wrong, given that it's on a computer program with inputs for spoke tensions and load weights. It's not just a drawing with of a wheel with a flat spot. Look at the table below it, there are the output tension values.

As for the postulation that, under the hanging model, the distribution of forces among the top spokes would be too small to notice: first, I think we can agree on a wheel with 32 spokes, and further agree that .5 to .66 of those spokes would be supporting a hanging force on the hub (the spokes below the half line would be opposing the top spokes' effort, and the ones on the half line would be perpendicular to our vector and thus not supporting). I will say .66 of the spokes, because that makes more sense. That gives us 10.66 of the spokes that would support a hanging load. If the load was 100kg, then each spoke would be under ~10kg of additional force (completely discounting that the most vertical spokes would be under much more force). I fail to see how that would not be reflected in the finite analyses I linked, where deflections were multiplied x100, or even in an auditory response test. In my experience with wheelbuilding, tensiometers, and truing by sound, which is admittedly not extensive but certainly sufficient, you can tell a difference in sound for at least a change of 5kg.

Finally, I'd like to make a semanticism in the terminology of forces on the bottom spokes. In this case, because the tension force exceeds the compressive force, it is correct to say that it is "in compression" while not "compressed," because it experiences a compressive force but not to failure.

For me - this is a great thread. Personally - I thumbed through the Brandt book, and when he appeared to describe spokes acting like columns and supporting compressive loads, put it down and bought Schraner. Now I understand more of what he was trying to say (but still don't think it he expressed himself clearly)

I think the problem with the "hang" vs "supported" perspectives is that they are both trying to oversimplify what is happening and are poor terms to boot, since they seem to mean different things to different people.

To the "hang" crowd - a spoke can not "support" any axial force like a column, since that involves compressive forces and the slender characteristic of a spoke means that it will fail in buckeling long before it carries any appreciable compression. Since the only element in compression is the rim, the hub is therefore hanging from the spokes.

To the "not hanging" or "supporting" crowd - I'm guessing that they note on the finite element chart, that some of the spokes below the hub actually gain tension when the wheel is loaded, and would appear to be pulling down on the hub. The hub therefore can not be "hanging" from the spokes.

Both sides are right as far as their perspectives go. The lower spokes are not carrying anything in the traditional sense of the word. Reducing the tension forces carried by a tension member, does not somehow turn it into a compresson member capable of supporting an axiel load. And yet - to say a hub is "hanging" when some of the spokes that increase under load are pointing down at a 45% angle (or more) doesn't seem quite right either.

So where does that leave us ? Where we started - with the simple explanation that DannoXYZ provided and which was confirmed by Ian's bicycle wheel analysis of a 36 spoked wheel. An unloaded bicycle wheel starts out with all spokes in equal tension and the rim as a perfect circle. When the wheel is loaded through the hub, the rim deforms slightly at the bottom causing the lowest 15% or so of the spokes to loose tension, and the other 85% see an increase in tension due to restraining the hub from deforming into an oval.

Then somebody hands me the weight of my sins, and that makes me heavier. That should help the Devil pull me down, but being lazy, he relaxes a bit, and doesn't pull as hard, and I don't move. .

I hate to break it to you - but the only reason the Devil isn't pullng as hard, is that the weight of your sins has moved you closer to hell.;) (remember - the rim has flattened out at the bottom. This strain at the rim decreased the distance from hub to bottom of rim and reduced the tension in the bottom most spokes)

I hate to break it to you - but the only reason the Devil isn't pullng as hard, is that the weight of your sins has moved you closer to hell.;)
Drat!
But at least I'm not perceptibly farther from God :)

The guy in the website even says that he simplified things to make it easier to analyze. In the page where he explains the development of the model used he says what to analyse and what to skip is a bit of an art. But as for the data that is presented in the table I have not said I have any beef with that.

My only real beef is with the human analysis portion of the data. Some aspects of the results are ignored, twisted or glossed over to further the idea of this "standing on the lower spokes".

Just one such example of an area that wasn't really explained fully is the increase in tension in spokes near the bending points of the rim. A bicycle wheel is a locked system and that you can't look at any increase or decrease in any single or even a limited group of spokes in isolation. The whole wheel contributes to the job with various forces between spokes fighting each other and balancing out a lot of the tension changes in any individual or small group of spokes. Sort of like pushing your hands together super hard and then using your isometrically tensioned arms to reach out and move an object. It doesn't take much to move the object but the total forces involved in the balanced pressures between your arms and the amount needed to move the object are FAR higher than the amount needed to move the object. But the outside world only sees the effort needed to move the object and the locked isometric forces in your opposing arms are hidden other than to your arms.

A full blown analysis of this would result in a hugely complex vector diagram or a ream of higher math equations. But I don't see any reference made to such a study of the findings. Instead the spoke loadings are only commented on in isolation or in small groupings. It's things like this that indicates to me that there's more to this model and data analysis that isn't being mentioned.

But in the end it really is about not agreeing with the semantical idea of standing on the lower spokes.

Instead I see it as the upper spokes have to take up the slack from the lower contact patch spokes that are no longer doing their job due to being under reduced tension. My own semantics? Perhaps. And in the end the whole idea of standing on or hanging from seems to come down to a case of semantics.

Lets take a non wheel example to illustrate the point. A platform is attached to a crane lift line. A steady line from directly below is tensioned to hold the platform from swaying. There's a lot of tension in both the upper and lower lines. A man steps onto the platform.....

The concept of "standing on the lower spokes" would suggest that the man is being supported by a decrease in the lower steady line tension.

The "hanging from the upper spokes" suggests that the increase in tension in the line to the end of the crane boom is holding up the man.

If I was the man on the platform I think I'd be happy that the line to the crane boom was there.....

Using this compressive concept may be an interesting way to study the forces involved from a mathematical standpoint and certainly I ran across many similar examples of "relative observation point" convieniences when I studied physics in university. But those cases all recognised that it was a convienience for the sake of making the calculations easier rather than a real world reality. This whole standing on the lower spokes seems like such a convienience run amok to me.

Does anyone here have any idea of how much of the load bearing forces are carried from the bottom of the wheel to the top by the rim. It would appear that the bicycle wheel is a classic monocoque construction with large parts of the forces being supported by the "skin" or in this case the rim. The spokes are there to keep the rim from crushing.

For the rim to collapse, deformation inward by part of the rim will cause (prior to the point of failure) an attempted expansion outward of other parts of the rim. The spokes prevent this expansion and thus the inward compression also.

Spokes work under tension.........not compression.

And in the end the whole idea of standing on or hanging from seems to come down to a case of semantics.

This whole standing on the lower spokes seems like such a convienience run amok to me.

Agreed and agreed and agree with everything you'e said........ however - not to dismiss the standing on the spokes crowd too lightly - the crane is holding a platform attached to a lift line. The steady line is affixed to a giant concrete slab on the ground and held in place by a turnbuckle tightened to produce 150 lbs of tension on it. A 150 pound man now steps onto the platform. The crane will not experience an additional load of the entire 150 lbs. Do you agree ? Is this signigicant with respect to the construction and behavior of a bicycle wheel ? and if so, how should it be described ? ( I think thats what Brandt and the "standing on the spokes" crowd are concerned with)

.....the crane is holding a platform attached to a lift line. The steady line is affixed to a giant concrete slab on the ground and held in place by a turnbuckle tightened to produce 150 lbs of tension on it. A 150 pound man now steps onto the platform. The crane will not experience an additional load of the entire 150 lbs. Do you agree ? Is this signigicant with respect to the construction and behavior of a bicycle wheel ? and if so, how should it be described ? ( I think thats what Brandt and the "standing on the spokes" crowd are concerned with)

Quite right. If the upper cable can stretch to some degree then yes the upper cable may only see a fraction of the man's weight or not seen ANY load increas if it can stretch to where the lower cable goes slack. The lower tension being replaced by the man's weight.

But which of the cables can you remove and not have the man and platform fall to the ground? That would seem to be central to this whole concept of which provides the support.

Let's take our wheel to the same extreme but useable for case of demonstration zero load example. The rider's weight matches perfectly the preload in the spokes along the center of the contact patch. As they reach zero tension you can remove them just as you could remove the lower steady line. So if the spokes don't need to be there to hold the rider up then which are doing the work? Obviously things get messy if you try to roll the wheel with that many missing spokes but that's part of the fun, right? :D

I agree that the study and concept is an interesting and unique way to look at the loading involved but it just went over the top when it started attributing lifting powers to spokes losing tension. That very loss of tension is what lets the other spokes hold up the load. The interesting part being that it can do it with increases in tensions that don't seem to add up because some of the riders weight is carried by the preload thanks to the de-tensioning of the lower spokes.

While I know that some tempers have maybe come to a simmer over this (mine included :D) it's been a great debate and made me think a lot about all this. And I'll take stuff like this over a crossword puzzle any day of the week. Well done to one and all and I trust we can still all get together for that E-beer at the E-pub regardless of our deeply held final beliefs on the matter.

. And I'll take stuff like this over a crossword puzzle any day of the week. Well done to one and all and I trust we can still all get together for that E-beer at the E-pub regardless of our deeply held final beliefs on the matter.

Sounds good I'll E-buy the first round.

The concept of something being suported by spokes does not work for me either,but the point of showing how the crane does not experience an appreciable increase in load, despite the application of an external force was to get everyone thinking about the effect of preloading the rim in compression. If we stick to the simple hanging from the spokes theory, the starting tension of the spokes shouldn't make any difference in the wheel behavior. But we all know from experience that the higher, the initial tension (short of buckeling the rim or failure at the spoke holes) the more durable the wheel. I haven't thought it through, about how to explain it - and in my opinion neither has Brandt - but I think thats what they are trying to do. Just something to chew on besides a crossword puzzel:)

I remember reading in Jobst Brandt's "The Bicycle Wheel" that the tensioned (bicycle) wheel supports a load by standing on the bottom spoke,

That's mainly down to semantics, and everyday use don't quite match strict engineering use. The reason for this seemingly illogical statement is that if you were to stick a tensiometer on each spoke and roll a loaded wheel around you'd see that the the spoke that sees the biggest change is the one between the hub and the ground.
So if that's where the biggest change is then naturally that must be where most of the "work" is being done.

Equally true is that a spoke can't take much load in compression, so of course the wheel isn't really standing on the spoke. But the load for the other spokes is so well distributed that the proportional change is much smaller than for the bottom spoke. And with no change there's no work being done, hence no "hanging" from the top spokes.

Ah, then tell us, what is the One True Model of forces in a loaded wheel? I fail to see how that diagram is wrong, given that it's on a computer program with inputs for spoke tensions and load weights. It's not just a drawing with of a wheel with a flat spot. Look at the table below it, there are the output tension values.The main problem with the analysis on that website you posted is that the model is not set up correctly to begin with, and the resultant data is incorrect. A second mistake is in not using experimental measured data to confirm the model. If he had used a tensiometer on the spokes and actually measured the tension-changes, he'll find that it doesn't match his analysis.

The first problem of the incorrect model comes in assuming that the forces on the upper-spokes comes from the hub, it actually doesn't, it comes from the upper part of the RIM. He assumes the rim is some super-elastic structure that doesn't deform all around and that's incorrect. The rim is actually super-ridid structure that refuses to deform easily and transmits forces all around. The sequence of events is kinda like Cooker's god/devil analogy, but it's not static.

The first event that happens is load pushes down on the hub. This then pushes the bottom of the rim and flattens it. HOWEVER, the next step is where the guy went wrong, he assumes that the rim ONLY deforms at the contact patch. In reality however, the RIM must maintain a fixed circumference. The shorter distance of the bottom flattened section has to go somewhere; it goes to expanding the entire top of the rim that's not in contact with the road. This expansion of the upper-section then goes to increasing the tension on ALL of the upper-spokes. The picture should really look like the right side where the rim maintains the same circumference by expanding the section not in contact with the ground to compensate for the shorter flattened section:

http://i42.photobucket.com/albums/e346/DannoXYZ/Cycling/WheelCompression.gif

Another way to see this is with the difference in distance between the hub and the spoke-nipples. Obviously the spoke-tension will change with deformation in the shape of the rim and the closer the rim is to the hub, the lower the spoke-tension. The change in the rim's shape changes the spoke-tension and vice-versa. If the spoke-tension really changed like the way he modeled, the rim would take on a flower-shaped pattern with some sections expanding more than others:

http://i42.photobucket.com/albums/e346/DannoXYZ/Cycling/WheelShape.gif

The main problem is he's modeling movement of the hub as if it doesn't affect the shape of the rim at all. And he models it as if each spoke acts independently without affecting the rim's shape or its neighboring spokes. When in reality, it's actually the rim re-acting to load and deforming which then results in changes in tension of ALL the spokes. Since the upper-part of the rim expands evenly, the increase in tension on the upper-spokes increase evenly as well; and by a miniscule amount due to having so many more of them than the few at the bottom.

You can test this yourself with a balloon. Hold it up in front of your face with one hand in front and one hand in back of the balloon. This way, you can see pretty much all around the outside circumference. Then push it down onto a table and you'll see that the upper part not in contact with the table will expand evenly.

The main problem with the analysis on that website you posted is that the model is not set up correctly to begin with, and the resultant data is incorrect. A second mistake is in not using experimental measured data to confirm the model. If he had used a tensiometer on the spokes and actually measured the tension-changes, he'll find that it doesn't match his analysis.

The first problem of the incorrect model comes in assuming that the forces on the upper-spokes comes from the hub, it actually doesn't, it comes from the upper part of the RIM. He assumes the rim is some super-elastic structure that doesn't deform all around and that's incorrect. The rim is actually super-ridid structure that refuses to deform easily and transmits forces all around. The sequence of events is kinda like Cooker's god/devil analogy, but it's not static.

The first event that happens is load pushes down on the hub. This then pushes the bottom of the rim and flattens it. HOWEVER, the next step is where the guy went wrong, he assumes that the rim ONLY deforms at the contact patch. In reality however, the RIM must maintain a fixed circumference. The shorter distance of the bottom flattened section has to go somewhere; it goes to expanding the entire top of the rim that's not in contact with the road. This expansion of the upper-section then goes to increasing the tension on ALL of the upper-spokes. The picture should really look like the right side where the rim maintains the same circumference by expanding the section not in contact with the ground to compensate for the shorter flattened section:

http://i42.photobucket.com/albums/e346/DannoXYZ/Cycling/WheelCompression.gif

Another way to see this is with the difference in distance between the hub and the spoke-nipples. Obviously the spoke-tension will change with deformation in the shape of the rim and the closer the rim is to the hub, the lower the spoke-tension. The change in the rim's shape changes the spoke-tension and vice-versa. If the spoke-tension really changed like the way he modeled, the rim would take on a flower-shaped pattern with some sections expanding more than others:

http://i42.photobucket.com/albums/e346/DannoXYZ/Cycling/WheelShape.gif

The main problem is he's modeling movement of the hub as if it doesn't affect the shape of the rim at all. And he models it as if each spoke acts independently without affecting the rim's shape or its neighboring spokes. When in reality, it's actually the rim re-acting to load and deforming which then results in changes in tension of ALL the spokes. Since the upper-part of the rim expands evenly, the increase in tension on the upper-spokes increase evenly as well; and by a miniscule amount due to having so many more of them than the few at the bottom.

You can test this yourself with a balloon. Hold it up in front of your face with one hand in front and one hand in back of the balloon. This way, you can see pretty much all around the outside circumference. Then push it down onto a table and you'll see that the upper part not in contact with the table will expand evenly.

I call BS on this. Have you run your finite element analysis prpgram to come up with those pictures? That was what Ian did. He didn't assume any particular deformation in the rim, nor did he assume an extremely flexible rim. He just wrote a mathematical model of a wheel, applied a reasonable load, and let his FE program determine how the wheel works. The assumptions he made about rim flexiblity look pretty good, and finite element analysis is a generally accepted method for analyzing flexible structures.
How did you develop your model of how a wheel works? Did you actually calculate anything, or is it just based on your opinion? By your model, it appears that the circumference of the wheel INCREASES as load is added. How does that work?
BTW your statement to the effect that the rim expands outward was confirmed by the FE analysis. The only difference is that the outward expansion is uneven and very small compared to the inward bending at the bottom.


em

I think that Dano has done a pretty good job in pictographically representing what is happening to the rim during the proposed deflection. Given that the picture has to be an exageration for us to actualy visualize what is happening, there may appear to be an increase in diameter that really isn't there.

Given that the rim doesn't actually get much longer or shorter then the area between the round rim and the deflected rim at the point visualized as deflected is counterbalanced by the area between the round and deflected rim over the rest of the view.

What is not clear to me in the FE examination of the wheel in the article we are looking at are the compressive forces in the rim (I think, neither the bending or angular forces specified in the model) In other words, all of those forces represented as the sum of spoke forces must be conuterbalanced by compressive forces in the rim.

In simplified form, the spoke tension is attempting to collapse the rim inward and the compressive forces acting in a tangent around the rim + some relatively small forces opposed to the bending inward of the rim at any given spoke are keeping the rim round.

I do not see these tangential forces represented in the FE model but I do see them in Danno's pictographic model of the inward deflection creating an outward pressure on the rest of the rim. This is what I was implying in the earlier post to this thread when I spoke of monocoque construction. I believe that there are relatively large forces traveling around the outside (relatively) of the rim that are not accounted for in the spoke and rim bending model.

I think that Dano has done a pretty good job in pictographically representing what is happening to the rim during the proposed deflection. Given that the picture has to be an exageration for us to actualy visualize what is happening, there may appear to be an increase in diameter that really isn't there.

Given that the rim doesn't actually get much longer or shorter then the area between the round rim and the deflected rim at the point visualized as deflected is counterbalanced by the area between the round and deflected rim over the rest of the view.

What is not clear to me in the FE examination of the wheel in the article we are looking at are the compressive forces in the rim (I think, neither the bending or angular forces specified in the model) In other words, all of those forces represented as the sum of spoke forces must be conuterbalanced by compressive forces in the rim.

In simplified form, the spoke tension is attempting to collapse the rim inward and the compressive forces acting in a tangent around the rim + some relatively small forces opposed to the bending inward of the rim at any given spoke are keeping the rim round.

I do not see these tangential forces represented in the FE model but I do see them in Danno's pictographic model of the inward deflection creating an outward pressure on the rest of the rim. This is what I was implying in the earlier post to this thread when I spoke of monocoque construction. I believe that there are relatively large forces traveling around the outside (relatively) of the rim that are not accounted for in the spoke and rim bending model.
The difference is that the finite element analysis calculates changes in tension in each spoke, while Danno assumed that each spoke changes equally. There is no reason to make that assumption. The FE analysis shows the the big changes in tension, and therefore the greatest movement of the rim from its original position, occur near the bottom. The FE analysis takes into account the bending forces in the rim (you know that because Ian estimated the bending strength of the rim) and there is also another analysis on Ian 's website that models the internal bending and shear forces in the rim. Compression in the rim is straight forward up to the point the strength of the rim is exceeded, but that doesn't seem to be much of an issue with bicycle wheels.
I wish I had an FE program. I'm getting ready to build new wheels and I'd really like to be able to estimate the loss in strength if I build with less than 32 spokes.

em

I call BS on this. Have you run your finite element analysis prpgram to come up with those pictures? That was what Ian did. He didn't assume any particular deformation in the rim, nor did he assume an extremely flexible rim. He just wrote a mathematical model of a wheel, applied a reasonable load, and let his FE program determine how the wheel works. The assumptions he made about rim flexiblity look pretty good, and finite element analysis is a generally accepted method for analyzing flexible structures.
How did you develop your model of how a wheel works? Did you actually calculate anything, or is it just based on your opinion? By your model, it appears that the circumference of the wheel INCREASES as load is added. How does that work?
BTW your statement to the effect that the rim expands outward was confirmed by the FE analysis. The only difference is that the outward expansion is uneven and very small compared to the inward bending at the bottom.


emYou can't run an FE analysis on an incorrect model. Take a look at his model here: http://www.astounding.org.uk/ian/wheel/build_wheel. He slides the wheel into wedges and duplicates it. The problem is each wedge is independent and doesn't push on the next. He assumes that the spoke attaches to a fixed point that doesn't move. Then he moves the HUB and measures the change in spoke tension. But that's backwards. He needs to model the rim first and transmit forces circumferentially around the rim and THEN measure the change in spoke-tension based upon changes in the shape of the rim.

If you want to set up a more accurate model, I've got Solidworks w/FEA option that you can try out. The main catch here is that the model MUST reflect empirical measured data. And it's so much simpler to pull out a tensiometer and measure actual spoke-tension changes. That data is real-world and it doesn't match what his model predicts.

Danno
You are confusing different things. First, the program you referred to is only a program to work out the geometry of the wheel for different spoke patterns. It's nit a finite element analysis. Second, whether the rim moves when you apply a load at the hub, or the hub moves and the rim stays put, is a frame of reference problem, and has no effect on the results. I haven't seen his FE program, but he has estimated the bending strength of the rim section, so i assume that is included. Finally, with the relatively low changes in tension among most of the spokes, you will not be able to prove or disprove much about the model by measuring with commonly available instruments, beyond the fact that most of th eload is carried by reduction in tension in a few spokes.

em

Damn! There's some smart fuggers in this forum!

Let's say he did include a lot of what has been discussed already. That's fine, let's accept the data from the FE program. But it's pretty easy to see from all the posts here and factors brought up that he hasn't analyzed the outcome and presented it in an integrated way. All his conclusions are based around isolated factors or small groups of factors instead of bringing in the obviously interrelated aspects and looking at how the tensions all around the wheel all work together and what forces induce the changes. That's where we lose a lot of the value of the FE results because we don't then bring it out as a full wheel analysis like it should be where various spoke groups aid or counter each other and why.

Please don't take all this to mean that the FE results are garbage. They are far from that. Even if not quite all the factors are in there it provides some fascinating numbers to look at and ponder. It's the lack of a really meaningful follow through that is lacking.

But it's pretty easy to see from all the posts here and factors brought up that he hasn't analyzed the outcome and presented it in an integrated way. All his conclusions are based around isolated factors or small groups of factors instead of bringing in the obviously interrelated aspects and looking at how the tensions all around the wheel all work together and what forces induce the changes. That's where we lose a lot of the value of the FE results because we don't then bring it out as a full wheel analysis like it should be where various spoke groups aid or counter each other and why.

i don't get it. Ian has the change in tension in every spoke, and the change in shear stress and bend stress in the rim. If you add back the pre-load, you essentially have all the stresses in the spokes and in the rim, except for the local stresses related to the spoke attachments and the stress related to tire pressure (which should be a constant as well).
what else do you believe he is missing?

em

I'm getting ready to build new wheels and I'd really like to be able to estimate the loss in strength if I build with less than 32 spokes.

This may constitute a new thread entirely, but from what I've heard the stiffness of newer low-spoke rims largely makes up for the low spoke count, but no FE analyses to back that up here, sorry. My own personal, underexperienced, probably underinformed advice would be to stay above 24/28 spoke count front/back, but that's just what I would be comfortable with building myself.

.....what else do you believe he is missing?

em

He did fine in the first part. Where he failed was in not fully and open mindedly analyzing the FE program results and offering a more overall and integrated interpretation of those spoke tensions and how it all adds up from a full wheel persective. Instead he chose to use isolated parts of the results to further his viewpoint of hubs standing on reduced tension spokes while misinterpreting or ignoring the rest of the results in whatever way suited his goal. For example he points out that spokes adjacent to the reduced tension spokes are showing higher than normal tension and that tension is pointing down. Well.. yeah... the rim is distorting so the spokes at the point where the rim is trying to push outwards the hardest are responding. This has nothing to do with holding up the load and is only a local force that is locked into the internal web of balanced forces. However this isn't brought out in the conclusions at all. Instead he stops at the observations of tension changes in the lower spokes and a few linked observations in the spokes around the affected area. There's nothing else about how all this affects the rest of the wheel.

He did fine in the first part. Where he failed was in not fully and open mindedly analyzing the FE program results and offering a more overall and integrated interpretation of those spoke tensions and how it all adds up from a full wheel persective. Instead he chose to use isolated parts of the results to further his viewpoint of hubs standing on reduced tension spokes while misinterpreting or ignoring the rest of the results in whatever way suited his goal. For example he points out that spokes adjacent to the reduced tension spokes are showing higher than normal tension and that tension is pointing down. Well.. yeah... the rim is distorting so the spokes at the point where the rim is trying to push outwards the hardest are responding. This has nothing to do with holding up the load and is only a local force that is locked into the internal web of balanced forces. However this isn't brought out in the conclusions at all. Instead he stops at the observations of tension changes in the lower spokes and a few linked observations in the spokes around the affected area. There's nothing else about how all this affects the rest of the wheel.

He identified all the changes in tension in all the spokes, confirmed that the only large changes in tension are decreases at the bottom. He can vary the number of spokes, the rim section and load. That's enough to determine the optimum size and number of spokes, and the preload, for any particular rim.
What he didn't do was apply torque loads or side loads, which are the cause of important failure modes. I don't see any reason why he couldn't do that.
The weakness is that he assumed how the load was applied to the rim. He could confirm the model by measuring the tension change in a few spokes. Most of the tension changes are below the threshold that can be measured, even with the best instruments, but the large changes could be measured.
What else do you need to know to design a wheel? What's misleading? What did he misinterpret? If he didn't discuss every element you want to discuss, you could ask him. Just remember that you normally need to pay someone to do that kind of work
What's your better method of determining the loads, or selecting components to match the load?

em

What are the compression changes in the rim that correspond to the changes in spoke tension? These would not be the bending forces on the rim but rather, those that are following a vector around the rim. Several of us have mentioned these forces in posts above.

What are the compression changes in the rim that correspond to the changes in spoke tension? These would not be the bending forces on the rim but rather, those that are following a vector around the rim. Several of us have mentioned these forces in posts above.
That's a good point. Over loading the rim in compression will cause the wheel to taco. Compression is easy to calculate. You just resolve all the force vectors acting on the rim, add all the parallel components in any direction, and divided by 2. It's easier to visualize than to describe, but I have no graphics capability here.
From that FEA, it looks like the compression on the rim increases by half the load, or 500 Nt for a 1000 Nt load. The compression due to preload is equal to one half the number of spokes, times the tension, divided by pi.

em

This may constitute a new thread entirely, but from what I've heard the stiffness of newer low-spoke rims largely makes up for the low spoke count, but no FE analyses to back that up here, sorry. My own personal, underexperienced, probably underinformed advice would be to stay above 24/28 spoke count front/back, but that's just what I would be comfortable with building myself.
I'm a heavy guy, so it makes me nervous to ride a 24 spoke wheel. Using a stiffer, deep section rim definitely makes fewer spokes possible, but I'm concerned that the deep section is not much stiffer laterally, and that could lead to a folding failure. I also don't understand if it's reasonable to use fewer spokes on the rear wheel. The total possible load under braking on the front wheel is much greater then possible load on the rear wheel, and the lateral load on the front wheel is probably greater as well. Maybe the rear wheel needs more spokes because half of them are undertensioned, but I'd like to see some real analysis of that.

em

So....if your sitting there on your bike and I run up and cut all the spokes above the hubs center line you wont fall over?

OK, gents,

Say you have a 2-spoke wheel, with a spoke above the hub and one below, each tensioned with 100 Kg pulling on the hub, and a rigid rim. Then you apply a 50 Kg weight to the hub. I submit that the spoke above now has 150 Kg of tension and the spoke below has 50 Kg of tension. So is the weight "standing" on the lower spoke or "hanging" from the upper spoke? The answer is both- the sum of the spoke tension is constant over the whole wheel. If you assume that the rim is less rigid but the circumference is fixed, the sum is distributed less symmetrically, but the sum is still fixed and the top spokes take some extra tension and the bottom ones are relieved of some tension. If you allow that the rim can change circumference, well, then you used a rubber rim strip instead of a rim, and I wouldn't ride on that wheel if I were you...

Here's my two cents, a priori:

There must be a specific load such that the bottom spoke has zero stress, but still does not buckle. Thus the bottom spokes, under human-like loads, take little or no load at all; it's like they become dead weight.

In general, the majority of the load (and reaction force) is carried by the spokes roughly situated in the top semicircle, with the greatest tension increase in the top spokes. They should roughly correspond to the tension relief in the bottom spokes, but Danny's geometrical construction shows that to be exactly precise, the top spokes do not compensate for all of the stress loss and the stress distribution is rather much more distributed.

This assumes, with a convenient angular position, that the left and right wheel halves are symmetric, which is not the case under braking and acceleration.

Thirty-six spokes should have a sufficient number of elements/nodes to represent a mostly solid wheel with the interior under tension (not unlike tempered glass) for FE analysis under SAP or Solidworks. If at a later time, I can provide some input with graphics.

In general, the majority of the load (and reaction force) is carried by the spokes roughly situated in the top semicircle, with the greatest tension increase in the top spokes. They should roughly correspond to the tension relief in the bottom spokes

No, the upper spokes don't have to increase tension to correspond to the loss of tension in the lower spokes. They have to increase tension by an amount equal to (the loss of tension in the lower spokes)-(the weight of the rider on the hub).

So if the weight added is 50 kg, and the combined loss of tension in the lower spokes is (guesstimating) 45 kg, the combined increase in tension in the upper spokes is 5 kg.


OK, gents,

Say you have a 2-spoke wheel, with a spoke above the hub and one below, each tensioned with 100 Kg pulling on the hub, and a rigid rim. Then you apply a 50 Kg weight to the hub. I submit that the spoke above now has 150 Kg of tension and the spoke below has 50 Kg of tension.


I can't give you exact numbers but you're certainly wrong. The up and down tension on the hub have to be equal. The force is more likely something like along the lines I guesstimated above: 105 kg on the upper spoke and 55 on the lower spoke.


So....if your sitting there on your bike and I run up and cut all the spokes above the hubs center line you wont fall over?

Yes I will. This is why Brandt's quote as reported is so misleading. He allegedly states the weighted hub "stands" on the lower spokes. That's either engineer talk or (dare I suggest?) troll talk.

In plain language, his point is that when you add a rider's weight to the hub, you don't see much increase in tension in the upper spokes, but you do see a marked reduction in tension in the lower spokes.

Folks,
Read the entire thread. FEA is an engineering modeling tool. You can use it to say that you're standing on a spoke but if you examine the argument you wouldn't build a wheel that way (with the upper spokes tight and the bottom spokes loose). He used semantics, FEA and an arbitrary arrangement of spoke tensioning to present an interesting idea. We have all proved that we've been entertained.

2-3 engineers here have made some very good efforts at presenting the true picture but as you can see with all their mathematics, modeling and measurements they don't know 100%. But they have a pretty good idea. This is proven by the excellent bicycles that these engineering concepts have given us today.