"A double butted spoke is like 3 springs in series. Maybe this is the key difference?"

Yes, that's right, it's like three springs in series. A straight gauge spoke is three springs in series too, it's just that they are all the same. In either case if you apply the same load to the three springs in series, the elongation of the two outer springs is the same -- Hooke's law. If the middle spring is springier, it will elongate more and the total elongation will be more, but the end springs will behave the same.

What we're not considering, and which I don't have the tools to consider or understand, is how the rim behaves when there are butted spokes as opposed to straight gauge spokes. Is the deformation still confined to essentially the same section of the rim or is the deformation significantly more extensive with butted spokes.

So you are assigning a greater significance to the 4 spokes at the bottom of the rim meerly because they undergo the most dramatic change? Even though it is more of an effect than a cause?
so If those 4 spokes on the bottom of the rim dont give up thier tension, the acceleration, or load + the added tension of the spokes would most likely cause the rim to fail?

from Danos description of what happens to the rim the spokes in the rest of the rim limit its amount of expansion since double butted spokes stretch more than nonbutted the contact patch for non butted spokes should be smaller due to this arrested expansion,no?

When you pull on a spoke, it elongates in accordance with the stress-strain relationship of the material that it is made out of. The parameter which ties stress(think of this as tension) to strain (think of this as elongation or compression) is called Young's modulus, or the modulus of elasticiity. So, for a stainless DT spoke, the modulus is a constant. The variables that tie stress to strain are the cross sectional area (pi r^2) and the length of the section you are considering. So, if you are looking at a particular length of 14 gauge spoke from the hub out, the only thing that controls how much it stretches or contracts is how much the tension changes. The length is the same, the area is the same, and the modudlus is the same, so for a given tension change, the length change is the same. If the rate that tension changes is small with respect to the speed of sound in the material, you can consider the tension in an element like a spoke to be constant. That's the case in a bicycle wheel. So, when you pull on a spoke from the ends, tension is constant everywhere within the spoke -- either in the fat sections or the skinny middle section.

Back to the fat section near the hub of the butted spoke: when you pull on that spoke with a force of 100 units, the fat section will lengthen by the same amount that the same length section of a straight gauge spoke will elongate. Just because the middle section stretches more in a butted spoke doesn't change the behavior of the unbutted portion -- if the tension change is the same.

I'm leaning towards the rim not behaving any differently, assuming equal spoke count and tension. I think the section properties of the rim exclusively dictates how the load is spread to the spokes. But that's just my hunch.

I don't know the answer to that question. Well, I know it a little -- I believe that it must be at least a little bit smaller with straight gauge spokes, but I don't know if it's enough to make a difference. In the other thread it was stated that the number of spoke crossings does not have a significant effect on the performance of the wheel. I think that's probably true, based on the graph that was presented. Is the effect of butted spokes of the same order or is it much more significant? I don't know.

That's my hunch too. But, let's not get into what that means. We need to kill this thing soon.

I'm done! :thumb:

so the entire spoke stretches together just at different rates. the narrow section doesnt stretch first to a certain degree then the thicker portion begins after tension reaches a certain point. it all happens at the same time.

Edit; Never mind,
That's the case in a bicycle wheel. So, when you pull on a spoke from the ends, tension is constant everywhere within the spoke -- either in the fat sections or the skinny middle section.

Yes, that's right. If tension changes very quickly you can have resonance or tension waves or something and that analysis is much more complicated. The general rule that I have heard is that if stress changes slowly with respect to the speed of sound in the material that stress should be considered constant. Sound is waves of stress -- at least rap music is.

more like distress, at least thats what it causes me. Thanks for the tutorial. Both of you and dano from the other thread. most enlightening.

I think it's distributed based on the relative stiffnesses of the rim and the spokes. So either a stiffer rim or thinner spokes would result in the spoke load being more broadly distributed (being distributed among more spokes).

I'm really surprised this topic is even being debated.

S. Kalyanasundaram, et. al. "Finite element analysis and optimization of composite wheelchair wheels" Composite Structures Volume 75, Issues 1-4, September 2006, Pages 393-399
DOI link: 10.1016/j.compstruct.2006.04.011

Read it. It does a far better job of explaining rim reflection, spoke orientation,optimization, etc in reference to both normal and static loading than anyone has in either thread.
This topic has been studied and discussed ad nauseum in my field.

stifness of the rim. The contact patch on the bottom of the rim is not bound by the spokes, but wheather the amount the rest of the rim is allowed to expand controls the size of the contact patch .

Anyone interested in the math behind FE wheel analysis should read this paper:

D. D. Mariappan, et, al. "An efficient algorithm for solving spoked wheels" Advances in Engineering Software
Volume 34, Issue 1, 1 January 2003, Pages 25-30
DOI Link: 10.1016/S0965-9978(02)00093-5

Its a little bit outdated because a 174 element model is trivial by today standards where we routinely solve 600k fe models in 2-3hrs, but it is still an excellent article.

I read it. It doesn't.

They specifically modeled the hub & rim as a shell element and spokes as a beam element. That is exactly how a rear wheel is modeled within the industry. To my knowledge every manufacturer that employs FE analysis into their development cycle uses this model. We lease our excess HPC compute time to contractors doing this exact type of development work. First static load analysis, then normal load analysis.

I'll see if I cant pull up another article that does a better job of explaining the torsional effect on the wheel. I thought the article was crystal clear even though the premise was wheelchair optimization.

Sure, their FEM was valid; I just didn't see where they clearly explained how the spokes and rim work together. More specifically, I was hoping to see a discussion of whether thinner spokes redistributed the load more effectively, resulting in better fatigue life.

Here is a much better article:
Henri P. Gavin "Bicycle-Wheel Spoke Patterns and Spoke Fatigue", Journal of Engineering Mechanics, Vol. 122, No. 8, August 1996, pp. 736-742
DOI Link: 10.1061/(ASCE)0733-9399(1996)122:8(736)

Anyone that doesnt have access to a journal database: http://www.duke.edu/~hpgavin/papers/...heel-Paper.pdf

Its missing a few figures. But in a nutshell his lab used the vishay 120 ohm strain gauges that we all use. Its not clearly explain in the article, but when measuring negative strain...that is compression. positive strain = tension. Several lace patterns, and spoke thickness were used.

Fig 11 does a nice job of showing tension/compression throughout the rotation...and I suspect the results are not what most on here expected. Compression (or in this case the release of tension from steady state) angle is very small...<40 degrees while tension is distributed over 320 degrees.

An interesting article. Fig ure 11 is very similar to another figure posted in the other recent thread on this topic. I didn't find anything in the article surprising -- basically it says that a bicycle wheel works real well and lasts a long time.

There are only two load paths through which the rider's weight can get to the ground: the rim and the spokes. If the wheel "hangs" from the rim then that load has to get to the ground somehow. Either it gets to the ground via the spokes (by decreasing the tensile load on the bottom spokes) or it gets to the ground via the rim, or some combination. This test shows that the primary load path is via the spokes.

Actually you meant if the hub hangs from the spokes...... but it really doesnt the hub is suspended by the tension in the spokes. And yes I get what is meant by decreasing the tensile load on the bottom spokes and how the rim contributes to this whole thing. It is a balancing act, everything working together. So I guess I think its the combination of the parts. I get that the four bottom spokes giving up some of their tension is important but on the other hand the deformation of the bottom of the rim is also just as important. Without this deformation the tension in the bottom spokes remains high, add that to the load and from what I can gather the rim stands a good chance of collapse.

And truthfully there are 36 (dependant on the amount of spokes) paths but all lead to the rim. the debate was about weather this path went up or down. But I get what you mean and I believe I see it.

This is an interesting and frustrating thread to read. Interested parties might want to read the other thread too. After 5 pages of back and forth I can guarantee you that the following is in fact a correct statement and is how the wheels work:

Anybody interested in the way things actually work should go back and read Ian's article. Pay particular attention to "superposition of stresses". A long, thin element such as a spoke will buckle if it ends up in compression. BUT if a wheel is built properly it starts out with a large amount of tension in the spokes. Apply the load from a big rider like me and the stress in some spokes increases while the stress in other spokes decreases. As long as the FINAL stress in the spokes does not become compression, the spokes will not buckle. This is the principle of superposition of stress.

If you had big fat spokes like the size of chainstays, you wouldn't worry about them buckling and we could better accept that stresses in the lower spokes would hold up the rider's weight. We think the spokes in reality are so thin that they will buckle but they don't because they normally stay in tension the whole time. Now if you have a wheel that is improperly tensioned, or you put more load on it than the normal rider does by hitting something, then the spokes at the point of contact try to sustain a lot more compression, which overcomes their initial pretension. NOW they have actually achieved compression, which they cannot handle, so they buckle and the wheel taco's.

It is valid to analyze the wheel using the applied load at the hub, and calculate tension in some spokes and compression in other spokes. Then take the separate analysis of the stresses in the components due to tensioning the wheel during building, and now ADD the stresses of the two analysis cases together. The result of the addition will be the final stresses in the components. This is superposition of stresses.

I posted an explanation in the other thread of why double butted spokes behave differently. It isn't a big difference, actually a small percentage, but it gives you that percentage of advantage.

As far as how the loads distribute differently if you have butted spokes- go back to Ian's article and read the part about 'indeterminate" systems. This means that the system of rim plus spokes determines the results, meaning the actual properties of the rim and the actual properties of the spokes. If you change the rim stiffness or change the spoke stiffness, the results will be different. Someone asked what would happen with an infinitely stiff rim. There would be no localized deflection at the bottom of the rim so the load would spread to more spokes at the bottom. Taking a normal rim and reducing the stiffness of the spokes by reducing the diameter of the center section will have a similar effect of spreading the load to more spokes.

Anybody still with me?
Let me relate a little structure that my previous boss designed at one time in the past. Within a building the architect wanted to have a pedestrian bridge going across an atrium. He wanted the structure to be very thin visually, so thin that it wouldn't work with a normal structure. So my boss designed the bridge with some upwards curve to it (camber), then he added some thin rods from the middle of the bridge down to a foundation below and tightened the rods until it pulled the bridge down to a flat shape. He ended up with a thin bridge like the architect wanted but still stiff enough to support people without deflecting or vibrating, due to the TENSION rod below. (Starting to sound like part of a bicycle wheel?) In operation as people walked across the bridge the bridge would want to deflect a little bit but the center of the bridge would push down on the thin rods below and they would push up on the bridge in the center to keep it from deflecting very much. Thin rods pushing up on the bridge? This is "superposition of stress". The bridge pushes down on the thin rods, the rods began life with tension, as long as they still maintain some tension then they will push up on the bridge and not buckle. (If you ever put enough people on the bridge to completely overcome the original tension in the rods then all bets are off!)

(Now I'm tired.)

Imagine 1 spoke at the top of the wheel and one at the bottom, wheel unloaded

Tension is equal hub is central. Tension is sustained by opposing spoke forces
Add load to hub
Tension in lower spoke reduces due to rim deflection
top spoke tension remains all but the same.
Internal forces now out of ballance because lower spokes are slacker than they started
tension in top spoke now created by 2 component forces, remaining tension in lower spoke plus tension created by extenal load which allows forces to ballance again.

Conclusions:
1. The original rim deflection was not caused by release of spoke tension, that would cause opposite deflection. Rim deflection caused loss of spoke tension

2. The largest change in tension is experienced by bottom spokes as they become less loaded and less critical to the wheel forces ballancing.

3. Tension in the top spoke of a loaded wheel contains a component force of the applied load.

4. Because of conclusion 3, the load path for applied loads is from hub to top spoke to rim to ground. This load path caused the original rim deflection.

5. conclusion 2 is just an interesting fact and should not lead to claims that the bottom spokes are most critical to the stability of a loaded wheel (they are not, they are the least loaded spokes in the wheel)

6. Last but not least, conclusion 3 demonstrates that it is perfectly acceptable to state that the hub hangs from the upper spokes and makes a BS of previous claims in this thread that the load path I have described here is "more than 100% wrong"

7. I'm off to release the tension in my bottom spokes now, because i think it will make my bike a lot lighter because they wont be pulling my hubs down anymore