How many spokes should be used when building a wheelset for a specific rider weight?

[Kontact]

Originally Posted by Mark McM

Again, this is all covered in "The Bicycle Wheel" by Jobst Brandt. This book should be read by anyone who wants to claim that they are a wheel "expert".

The spokes all pull inward on the rim. All this net inward pull results in a high circumferential compresson on the rim. If there are a large number of spokes at high tension, this compression can be quite large. For example, 32 spokes each tensioned to 220 lb (100 kgf) will result in a circumferential compression force on the rim of about 1000 lb. If you double the number of spokes and keep their average tension the same, the rim will have circumferential compression of 2000 lb.

On a lightweight rim with a large number of spokes, it is very easy to tension the spokes high enough to buckle the rim in circumferential compression. For lightweight rims with many spokes, this circumferential buckling force becomes the limiting factor for spoke tension. In fact, in the "The Bicycle Wheel", Jobst Brandt presents a method for determining maximum spoke tension based on tensioning the spokes just high enough so that squeezing pairs of spokes results in minor rim buckling, and then backing off the tension.

Of course, the stronger the rim and the fewer the spokes, the greater the tension required to buckle the rim. For many modern wheels with deep, heavy rims and a reduced number of spokes, it may be virtually impossible to tension the spokes high enough to buckle the rim. In these cases, maximum spoke tension will be based on other factors.

I don't think you're getting my objection. We don't build 290 box rims with 16 spokes, and we don't build 400 gram A section rims with 48 spokes. The kinds of rims with few spokes at a "modern" tension are considerably more rigid than those old tubular rims, and the rims we build with 48 spokes are quite heavy, and could accept both few spokes or many at higher tensions.

When is it that we have to choose to lower the tension with modern rims lest they pringle? Is that not limited by the available drillings as much as the engineering of the rim.


And I've read Brandt, but I don't know if the principles he developed to explain why a 290 gram tubular needs less tension is necessarily applicable to modern rims. Not because the principle isn't true, but because the modern rims are pushing maximums in any of the configuations available. In other words, do we know that any of these modern rims we are talking about actually would exceed Brandt's formula?

[Kontact]

Originally Posted by Mark McM

While it would certainly make sense to make deep heavy rims available for small spoke counts, and shallow light rims available in large spoke counts. But in many cases, manufacturers make both their deep heavy rims and shallow light rims available in the same spoke counts. For example, the Kinlin XR200, a 380 gram, 22mm deep clincher rim is available in spoke counts of 20,24,28 & 32, whereas the Kinlin XR380 rim, a 550 gram, 38mm deep clincher rim is also available in spoke counts of 20,24,28 & 32. Do you really believe that both rims, in all the available spoke counts, should use the same tension?

Now, the 20 spoke version of the XR380 might get away with only 100 kgf tension. But it can surely take more tension, and the wheel would be even stronger due to it. I actually built a 20 spoke XR380 with 150 kgf average spoke tension, and it is holding up fine. I don't think I'd try the same tension for the 32 spoke version of the XR200.

You are talking about what I'm getting at.

The XR380 is rigid enough to not collapse due to large gaps between spoke holes on 20 hole drillings when riden, but also has the "rim coefficient" to take the compression of 32 spokes at that same spoke tension.

But it isn't offered in a 48 hole version, so we don't have to worry what happens above 32 spokes. We just have to know that the rim has enough rigidity for the minimum spokes and enough rim coefficient for the maximum, and it isn't absurd to think that one rim could have that range. Just as one heavy rim might have the range to accept 32 to 48 spokes.

The average spoke tension used today is not just about wheel strength, it also has to be at a level where the spoke holes don't crack and the hub flanges don't burst, regardless of what is happening in the rest of the wheel. So it really isn't realistic to talk about jacking up the tensions on 20 spoke wheels for overall structural reasons when the specific attachment points aren't built for it.

[Mark McM]

Originally Posted by Kontact

You are talking about what I'm getting at.

The XR380 is rigid enough to not collapse due to large gaps between spoke holes on 20 hole drillings when riden, but also has the "rim coefficient" to take the compression of 32 spokes at that same spoke tension.

Ah, but what about the other end of the product line, the 380 gram 22mm deep XR200? I think you'll agree that this rim should be built with more than 20 spokes, and 32 spokes for the rear is probably a good idea. I'm pretty sure that with 32 spokes this rim could be buckled with excessive spoke tension.

(By the way, the "buckling" of a rim isn't the same as for eccentrically loaded columns. The rim is too well braced by the spokes for that. Rim buckling is primarly from yielding under compression. Therefore, the main factors are the secion area and yield strength of the rim - the shape of the cross-section doesn't play much of a role.)

Originally Posted by Kontact

The average spoke tension used today is not just about wheel strength, it also has to be at a level where the spoke holes don't crack and the hub flanges don't burst, regardless of what is happening in the rest of the wheel. So it really isn't realistic to talk about jacking up the tensions on 20 spoke wheels for overall structural reasons when the specific attachment points aren't built for it.

Well, that's why I said that for heavier rims and fewer spokes, factors other than rim buckling limit the spoke tension.

By the way, I also believe that the role of static tension is exaggerated in regard to rims and hubs cracking. Clearly, rims don't crack and hub flanges don't "burst" purely from static tension. If they did, they'd break when the wheel was being built and stress relieved. In use, most wheel loads result in decreases in spoke tension, so some of the highest tensions the spokes ever see are during stress relieving. Other evidence that rims and and hubs don't break from momentarily overload can be found by examination of cracked components. Overloads result in localized yielding around the break, but cracked rims and hubs don't show this yielding. The cracks are caused by fatigue, which are caused by cyclic loads, not by static loads.

You might argue that high static loads decrease fatigue life, which is true. But even here the affect is exaggerated. High static loads have their greatest affect on low cycle fatigue life, and its affect decreases for high cycle fatigue life. Wheels are a case of high cycle fatigue - a wheel under goes a million load cycles in just 1,200 miles.

Instead, I believe that most cracked wheel components are a result of cyclic loads, instead of static loads. In other words, the wheel was under-designed for its dynamic loading, typically either with un-relieved stress concentrations, too few (or too thick) spokes, or with a too flexible rim.

I've been a professional wheel builder, and always used high tensions (120 - 150 kgf weren't uncommon). As far as I know, other than as a result of crashes, I think only one of my wheels ever had a cracked rim (a GL330), and only maybe 4 ever had broken spokes, and none of them had a broken hub flange. On the other hand, all wheels were well stress relieved and generally weren't underbuilt in regard to rim stiffness or spoke count.

It's interesting to note that many low spoke count "prebuilt" wheels use standard components, such as hubs and spokes, and often standard rims as well - just with fewer spokes than when the components are available separately. I know that this was certainly the case with many Campagnolo wheels. And yet, the Campagnolo technical manuals specified relatively high tensions - sometimes as high as 150-170 kgf. How is it that these components suddenly got "stronger" when they were pre-assembled in the factory?

I suspect that it is because the "recommended" maximum tensions for un-assembled are just spit-balled, or are a kind of 'catch-all' maximum that covers the worst case scenario. Similar to how many carbon fork makers all specify a maximum of 40mm of spacers, as if all steerers where the same strength, or all riders were the same weight. (Do the fork makers really think that a steerer that won't break with 250 lb. rider using a 150mm stem and 30 mm of spacers, will suddenly break when a 100 lb. rider with an 80mm stem uses 50 mm of spacers?).

Or, maybe low maximum spoke tensions are really way to dodge warranty service? (This was Mavic's standard way to deny warranties for cracked rims: "Your warranty is denied because you used too much spoke tension!" "Wait, I didn't even tell you what tension I used!" "Well, the rim broke, so the tension must have been too high!").

As a side note, a few distributors actually managed to get some 38mm deep Kinlin XR380 rims with 16 holes, so I procured one and built a front wheel. While many rim manufacturers have blanket maximum tension recommendations of 100-110 kgf, I don't think I've ever seen a pre-built 16 spoke wheel with spec.-ed tension this low. I built mine with 160 kgf.

[Kontact]

Originally Posted by Mark McM

Ah, but what about the other end of the product line, the 380 gram 22mm deep XR200? I think you'll agree that this rim should be built with more than 20 spokes, and 32 spokes for the rear is probably a good idea. I'm pretty sure that with 32 spokes this rim could be buckled with excessive spoke tension.

(By the way, the "buckling" of a rim isn't the same as for eccentrically loaded columns. The rim is too well braced by the spokes for that. Rim buckling is primarly from yielding under compression. Therefore, the main factors are the secion area and yield strength of the rim - the shape of the cross-section doesn't play much of a role.)

That's the thing - you're "pretty sure", but since you don't have the rim coefficient it is just supposition.

I don't follow what you're saying about cross section. The shape, composition and heat treatment are all factors in the yield strength of a structure, rather than the yield strength of a material alone.

By the way, I also believe that the role of static tension is exaggerated in regard to rims and hubs cracking. Clearly, rims don't crack and hub flanges don't "burst" purely from static tension. If they did, they'd break when the wheel was being built and stress relieved. In use, most wheel loads result in decreases in spoke tension, so some of the highest tensions the spokes ever see are during stress relieving. Other evidence that rims and and hubs don't break from momentarily overload can be found by examination of cracked components. Overloads result in localized yielding around the break, but cracked rims and hubs don't show this yielding. The cracks are caused by fatigue, which are caused by cyclic loads, not by static loads.

You might argue that high static loads decrease fatigue life, which is true. But even here the affect is exaggerated. High static loads have their greatest affect on low cycle fatigue life, and its affect decreases for high cycle fatigue life. Wheels are a case of high cycle fatigue - a wheel under goes a million load cycles in just 1,200 miles.

Instead, I believe that most cracked wheel components are a result of cyclic loads, instead of static loads. In other words, the wheel was under-designed for its dynamic loading, typically either with un-relieved stress concentrations, too few (or too thick) spokes, or with a too flexible rim.

I don't think anyone believes that the issue is static loads. But the cyclic loads at higher tensions, even at lower amplitude, are going to do more "work" on the components.

Additionally, the stiffer the rim the more localized the spoke hole stress.



Personally, I own two XR200 wheelsets that I built, one 24/28 and the other 20/24 (triplet rear). I've only had them three years but the 20 has stayed in true, and the 28 hasn't imploded, despite all built at the same spoke tension. We'll see, I suppose.

[bob heinatz]

Enjoyable thread. My experience is that it is more importance who builds the wheel than spoke count. A good light rim built by a professional wheel builder is the way to go for me. That also means I depend on their opinion on the build.

[Mark McM]

Originally Posted by Kontact

That's the thing - you're "pretty sure", but since you don't have the rim coefficient it is just supposition.

I don't follow what you're saying about cross section. The shape, composition and heat treatment are all factors in the yield strength of a structure, rather than the yield strength of a material alone.

As you are pointing out, there are many factors that can affect column buckling. For long slender columns, the cross section shape (as represented by the radius of gyration), the curve of the column, and the eccentricity of the load can make a big difference. On the other hand, for short, fat column shapes, yielding (deformation) is primarily a matter of area and yield strength. In other words, long slender columns bend and buckle, whereas as short fat columns just get "flattened". Since the is well braced by the spokes against radial and lateral deflection, it's yielding is less like that of a long slender column, and more like that of a short, fat column.

Of course, it's not quite as simple as that, but the primary factors in the yielding of the rim under circumferential compression are the yield strength of the material and the cross sectional area. Since the all rims for the same wheel size are approximate the same diameter, and since the density of aluminum alloys are all close to the same, the cross sectional area of the rim will be nearly proportional to its weight.

Originally Posted by Kontact

I don't think anyone believes that the issue is static loads. But the cyclic loads at higher tensions, even at lower amplitude, are going to do more "work" on the components.

That's true, but consider that: A) spokes are tensioned at well below their yield points; and B) the primary reaction of spokes is tension reduction. While a high static tension will have an affect on fatigue life, by far the largest factor remains the magnitude of the cyclic loads.

[QUOTE=Kontact;2295596]Additionally, the stiffer the rim the more localized the spoke hole stress.

Just the opposite is true. The stress in the rim hole of course will be proportional to the load on the spoke. But a stiffer rim will distribute wheel loads across more spokes, reducing the portion of the load each individual spoke must bear, thus reducing the peak spoke loads.

Originally Posted by Kontact

Personally, I own two XR200 wheelsets that I built, one 24/28 and the other 20/24 (triplet rear). I've only had them three years but the 20 has stayed in true, and the 28 hasn't imploded, despite all built at the same spoke tension. We'll see, I suppose.

Well, you didn't mention what the spoke tensions were. For a Rim Coefficient of 9 (Kgf-grams), a 380 gram rim with 28 spokes could easily operate with an average tension of 122 kgf without danger of buckling. Modern rims are made with stronger alloys than those of yesteryear. Kinlin rims are made with a particularly strong Niobium alloy, so the Rim Coefficient of these rims may be much higher than for older rims.

(Anecdotally, I once built a 32 spoke wheel with an Araya CTL-370 rims, which weighed about 375 grams. The alloy on this rims must have been particularly soft, as I couldn't get more than about 90 kgf average tension without the rim yielding during stress-relieving.)

[Kontact]

Originally Posted by Mark McM

Just the opposite is true. The stress in the rim hole of course will be proportional to the load on the spoke. But a stiffer rim will distribute wheel loads across more spokes, reducing the portion of the load each individual spoke must bear, thus reducing the peak spoke loads.

It does distribute it across the rim, but that only happens because a small area around the spoke hole is taking those stress variations rather than a whole section of rim moving.

And really, that's the 'forest for the trees' problem in this discussion - you can't just treat spoke tension as something you can add as necessary. "Good" spoke tension is whatever is sufficient (rather than optimal) for wheel strength while not overloading the localized anchor points. Because the life of wheel is limited most by the number of work cycles the spoke holes can take more than any other factor.

Well, you didn't mention what the spoke tensions were. For a Rim Coefficient of 9 (Kgf-grams), a 380 gram rim with 28 spokes could easily operate with an average tension of 122 kgf without danger of buckling. Modern rims are made with stronger alloys than those of yesteryear. Kinlin rims are made with a particularly strong Niobium alloy, so the Rim Coefficient of these rims may be much higher than for older rims.

I don't recall what tension I was using other than that is was 'typical', so let's say it was 120 kgf, right in the middle of Velocity's recommended range of 110 to 130 or right at Enve's number. Regardless, I used it across all the spokes, because I wanted spokes that would maintain very low amplitude of tension change while not overloading the spoke holes. And that seems to be the way rim manufacturers also look at the problem.

[casparwhittey]

I built mine up 32h because I don't want to cut out any of the resale market when I go to sell them on the classifieds