Thread for the wheel builders (warning: contains maths)
I'm sure we all know that when building a 700c wheel the limiting factor is the maximum tension the rim can withstand (if you disagree with this statement then there's not much point reading the rest of this thread).
So I was re-reading Roger Musson's excellent E-book today and I saw that he says:
Now I had always been led to believe that more spokes means a stronger wheel but if the overall tension has to remain the same then the individual spokes (particularly the non-drive side of a dished rear wheel) will have a lower tension and therefore higher risk of coming loose via the nipples unscrewing themselves, won't they?
As an example, let's assume we have two identical rims (same model, same manufacturer) apart from one difference - the number of spoke holes. Rim one has 32 holes and rim two has 40.
Now we know that both can withstand the same overall tension, but the one with 40 holes will distribute this tension over more spokes, so each spoke will have a lower tension in that wheel.
If we assume that our 32 spoke wheel is "perfect" when drive-side tensions are at 1250N per spoke and non-drive-side tensions are 750N per spoke then we get the following:
Total drive-side tension = 20,000N (16 spokes x 1250N per spoke)
Total non-drive-side tension = 12,000 (16 spokes x 750N per spoke)
Total overall tension = 32,000N (20,000 + 12,000)
Split = 62.5% of overall tension on drive side and 37.5% of overall tension on non-drive-side.
So we're going to keep the total overall tension the same for the 40 spoke wheel and for the sake of simplicity let's assume the split also stays the same, so...
Drive-side tension of 40 spoke wheel = 1000N per spoke (20,000N / 20 spokes)
Non-drive-side tension of 40 spoke wheel = 600N (12,000N / 20 spokes)
Now that figure of 600N per spoke seems very low to me and it would set alarm bells ringing in my head that the nipples were going to unscrew themselves, or have I made a mistake? Is there something to do with the overall tension that will counteract the drop in per-spoke tension? If so then what am I missing?
Also, when we contact rim manufacturers (as I know some of us here do) to ask them the maximum tension a particular rim can withstand, they typically reply with a per spoke tension, for example Mavic usually say 900N, Rigida say between 800N and 1000N (for the Sputnik) and DRC are happy to go up to 1200N for the ST19 rim.
However, surely what they should be telling us is the maximum overall tension the rim can withstand, rather than the 'per spoke' tension, then we can account for the split/dishing with different hubs.
I'll be building my second wheel soon and it's going to be 40 spokes but I'm a little concerned about the 'per spoke' tension on the non-drive side being low enough to allow the nipples to work loose. And I don't want to use thread lock or self-locking nipples because I've had trouble in the past when it comes to re-truing wheels later.
So I was re-reading Roger Musson's excellent E-book today and I saw that he says:
For the same rim, the spokes in a 32 spoke wheel will be tighter than those in a 36 because the total tension in the wheel will still be the same but distributed over less spokes in the 32 spoke one and hence they are tighter.
Now I had always been led to believe that more spokes means a stronger wheel but if the overall tension has to remain the same then the individual spokes (particularly the non-drive side of a dished rear wheel) will have a lower tension and therefore higher risk of coming loose via the nipples unscrewing themselves, won't they?
As an example, let's assume we have two identical rims (same model, same manufacturer) apart from one difference - the number of spoke holes. Rim one has 32 holes and rim two has 40.
Now we know that both can withstand the same overall tension, but the one with 40 holes will distribute this tension over more spokes, so each spoke will have a lower tension in that wheel.
If we assume that our 32 spoke wheel is "perfect" when drive-side tensions are at 1250N per spoke and non-drive-side tensions are 750N per spoke then we get the following:
Total drive-side tension = 20,000N (16 spokes x 1250N per spoke)
Total non-drive-side tension = 12,000 (16 spokes x 750N per spoke)
Total overall tension = 32,000N (20,000 + 12,000)
Split = 62.5% of overall tension on drive side and 37.5% of overall tension on non-drive-side.
So we're going to keep the total overall tension the same for the 40 spoke wheel and for the sake of simplicity let's assume the split also stays the same, so...
Drive-side tension of 40 spoke wheel = 1000N per spoke (20,000N / 20 spokes)
Non-drive-side tension of 40 spoke wheel = 600N (12,000N / 20 spokes)
Now that figure of 600N per spoke seems very low to me and it would set alarm bells ringing in my head that the nipples were going to unscrew themselves, or have I made a mistake? Is there something to do with the overall tension that will counteract the drop in per-spoke tension? If so then what am I missing?
Also, when we contact rim manufacturers (as I know some of us here do) to ask them the maximum tension a particular rim can withstand, they typically reply with a per spoke tension, for example Mavic usually say 900N, Rigida say between 800N and 1000N (for the Sputnik) and DRC are happy to go up to 1200N for the ST19 rim.
However, surely what they should be telling us is the maximum overall tension the rim can withstand, rather than the 'per spoke' tension, then we can account for the split/dishing with different hubs.
I'll be building my second wheel soon and it's going to be 40 spokes but I'm a little concerned about the 'per spoke' tension on the non-drive side being low enough to allow the nipples to work loose. And I don't want to use thread lock or self-locking nipples because I've had trouble in the past when it comes to re-truing wheels later.
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Comments
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1: you are assuming that Roger Musson knows what he is talking about
2: I would imagine that the individual tension is important because each spoke afects the area around it - but to pull a circle apart with even torque would be extremely difficult
3: does it matter0 -
I think you're worrying too much. IME the more spokes, the easier the build. You can get the spokes to the same tension as if it was 36 or 32 spoke. The rim won't implode.
have a nice cup of tea while you're building it, and put some music on. Enjoy it.0 -
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Caveat - I'm not a wheel builder but I am an engineer.
I think gundersen has it right and Musson is ambiguous at best...
The per spoke limit is a consequence of the local stress limit around the holes. I.e. pull too hard on the spoke and the eye fails due to local stress concentration around the hole.
The "overall tension" limit you talk about isn't really a practical limit. The hoop stress (for that is what the spoke tension causes) is never going to cause rim failure before the eyelets fail. Not only is it very strong in compression, but the failure mode of a rim in compression will be buckling, and more spokes (i.e. less rim area that is not braced sidewards) will prevent this..
Romans and arches and all that!
Basically, just build your wheel nice and tight without going overboard and you'll be alright.0
