Why do my spokes keep breaking? - Bike wheel science.

[Yellow Saddle]

I found this the easiest to understand http://hea-www.harvard.edu/~fine/opinions/bikewheel.html
Feel free to pick it apart.

It is a nice piece but unfortunately it all falls apart in the end. The precise place where it starts to fail is the last sentence in the third last paragraph. The author understands how the wheel works, but needs to fix up his/her syntax since it only adds to the confusion.

 

[Yellow Saddle]

Interestingly at DT Swiss they say that the tension increases on the upper spokes, I think they mean the proportion of load will increase, but not the tension itself, however don't trust me, I make maps for a living, not wheels.

https://www.blog.dtswiss.com/spoke-tension/

DT Swiss makes excellent spokes but unfortunately they don't seem to have engineers on their marketing team. I don't trust DT's literature. That company doesn't understand (or perhaps they do but communicates otherwise), the purpose of butted spokes. The company even has an "extra thick spoke" in its catalogue billed as stronger than the others. That smacks of ignorance.

 

[Ajax Bay]

I found this the easiest to understand http://hea-www.harvard.edu/~fine/opinions/bikewheel.html
Feel free to pick it apart.

Thank you for finding that which I recommend to others to read.
These sections bear commentary:
1) "What's interesting is what happens to the wheel when a load is applied (someone gets on the bike). If you measure the tension in all the spokes, only those spokes in the bottom of the wheel change tension significantly - the tension decreases. In other words, the bottom spokes become more loose, all the other spokes remain unchanged."
I'd prefer the description "the bottom spokes reduce in tension, all the other spokes remain unchanged" as "more loose" to me implies they were "loose" in the first place, but this may be a translation/ntic issue between Oxford and Harvard.
As an aside, "all the other spokes remain unchanged" is not strictly true because the tension in the spokes near the horizontal actually increase slightly (ie above the static tension) to hold the wheel together which would otherwise oval (slightly).
2) "In mathematical terms it is possible to describe the bottom spokes as being in compression. The have less tension than they had before, so if you count the starting (pre-tensioned) state as the zero state, you have put them "in compression". The reason they can support this compression is that the spoke has been pre-tensioned."
That's rather like shifting the area of the graph which has the bottom spokes in compression up from zero (force) to 1000N, on the 'force' axis. "In mathematical terms maybe; but not in real terms (and noone (here) has suggested that the bottom spokes are "in compression".
3) Otherwise @Yellow Saddle thought this let down the piece:
"Only the upper spokes are actually pulling upwards on the hub. This is why I still say, without any doubt, that the hub hangs from the upper spokes. Oddly this does not contradict the following statement, that the lower spokes play the most dynamic role in supporting the load."
3a) "Only the upper spokes are actually pulling upwards on the hub." Basically true.
3b) "This is why I still say, without any doubt, that the hub hangs from the upper spokes." I don't think "hanging" and "standing" are useful terms to use (and their use seems to provoke unnecessary angst without adding clarity).
3c) "Oddly this does not contradict the following statement, that the lower spokes play the most dynamic role in supporting the load." If by "dynamic" [characterized by constant change, activity, or progress] the author means that the lower spoke tensions vary most from the unweighted state then fine, but it's an unusual use of "dynamic" because all spokes in a rolling wheel are 'dynamic' and when considering a static loaded wheel model the spoke tensions are 'static' with different magnitude - again it seems to me the author is seeking to throw a bone to the (standing) dogs.

 

[Milkfloat]

Thank you for finding that which I recommend to others to read.

Ooops sorry!

 

[Ajax Bay]

Then, a suggestion. When calculating the reduction in tension at the bottom spokes, we leave out the angular component from the spokes arriving radially. This suggestion is for two reasons.
. . . .
[model] a central spoke arriving plumb with the road and two other spokes, either side of it, arriving at X angle. Only these three spokes share the load
. . . .
We're not after exact numbers here, just broad concepts.
2) Should you still insist on eliminating the cosine error . . . Let's ignore that simply because it does not change the concept.

Ajax Bay: "I seek to persuade YS that the upper spokes, albeit at no more tension than when the wheel is unloaded, provide the surplus force (via the hub) needed to support the load exerted by the fork. Disregarding the spokes other than the top 2 and the bottom 2, this surplus is the force (on the hub) up from the two upper spokes minus the pull down of the two lower spokes."
This seems to be the crux of you differing from me, because, taking into account the exceptions I've suggested above, our models are the same.
What I don't get is "surplus force". Can you show it on the force diagram? I just don't get it.

Our models are essentially the same and lets accept/adopt your 3 lower spokes of relevance at the bottom model, disregarding all but the upper spokes and the lower spokes (3 + 3). Note that I'm content with the model but do not agree with "only these three spokes share the load" (because the albeit reduced tension in the 3 lower spokes is pulling the hub down and not "shar[ing] the load").
The "surplus force" - perhaps an unwise phrase in a 'balanced' system - which I sought to explain is the vertical force that the hub needs to exert on the fork to keep the bike 'up' balancing the gravitational force (40+% of the rider plus bike weight) on the (front) wheel.
The wheel as a structure is 'in compression' load acting down and the ground's 'normal' force acting up. Vector summing (with respect to forces on the hub) the tension in all 6 spokes and "leave out the angular [think you mean horizontal] component from the spokes arriving radially [meaning non-vertically]" there needs to be a 'surplus' vertical force component to resist the fork pushing down.

Forces acting on the fork dropouts
I Fork
I
v
^
I
I Hub

Forces acting on the hub
Upper spokes (all 1000N say)
^
I
I
Iooooooooooooooo^
IoooooooooooooooI
OooHuboooooooooI (500N) Resultant force
I
v
Lower spokes (900/700/900N say)

Notes (agreeing that you/"we're not after exact numbers here"): 16 spoke wheel. 22.5 degrees between each spoke, cos 22.5 is 0.93
Vertical force from 3 upper spokes is 1000 + 2x1000cos 22.5 = 2860N
'Surplus' force required to support load = 500N
Downwards force exerted on hub by the 3 lower spokes = 2860-500=2380N
2380=Tv + 2TLcos22.5 [Tv is tension in vertical spoke, and TL is tension in the two spokes either side of vertical.]
Estimate Tv = 740N and TL = 880N
So as this (model front) wheel rolls, the spoke tension cycle between (slightly over) 1000N (when horizontal) through 880N down to 740N and back up.
The more spokes in a wheel the less reduction (%) the lowest spoke experiences. Will the magnitude of the cyclical range of tensile force in a spoke be related to fatique life? Probably (intuitively), but I don't know.
The spokes fatique and eventually, when @hobo gives that last push, the rear wheel spoke that happens to be weakest parts. On my ride last week each of my spokes (36 spoke front wheel) went through this cycle (1000N to >800N) over 100,000 times. Last year the spokes in my front wheel which I built it in Jan 18, completed this cycle over 5 million times. I used the original spokes from the fubarred wheel (rim) so I estimate these spokes have completed 20 million cycles with me aboard (plus no idea how many with the first owner on board). Pleased to say no front spokes broken yet.

 

[Yellow Saddle]

Our models are essentially the same and lets accept/adopt your 3 lower spokes of relevance at the bottom model, disregarding all but the upper spokes and the lower spokes (3 + 3).

Great.

Note that I'm content with the model but do not agree with "only these three spokes share the load" (because the albeit reduced tension in the 3 lower spokes is pulling the hub down and not "shar[ing] the load").
The "surplus force" - perhaps an unwise phrase in a 'balanced' system - which I sought to explain is the vertical force that the hub needs to exert on the fork to keep the bike 'up' balancing the gravitational force (40+% of the rider plus bike weight) on the (front) wheel.

That's not what your diagram shows. Can you show the above in a diagram please.

The wheel as a structure is 'in compression' load acting down and the ground's 'normal' force acting up. Vector summing (with respect to forces on the hub) the tension in all 6 spokes and "leave out the angular [think you mean horizontal] component from the spokes arriving radially [meaning non-vertically]" there needs to be a 'surplus' vertical force component to resist the fork pushing down.

That's where I think you go wrong. Please try and show that in a force diagram. I can't get my head around your ASCII diagram.


I'm going to resist the distraction about metal fatigue. That's for another day. Let's stick to the forces on a static, loaded wheel for now.

 

[Pale Rider]

Apart from comedy physics, has anyone answered the OP?

It's worth replacing a single broken spoke, but if you get a series it's full wheel rebuild time with all new spokes.

That may - or may not - be cheaper/dearer than a new factory built wheel.

Shimano wheels are excellent for someone who just wants the bike to work.

 

[Salar]

@Yellow Saddle and @Ajax Bay

I generally agree with your assumptions, funnily enough when you were preparing your diagrams I scribbled one out with the same concept.

The spokes are always in tension.

It reminds me slightly of cross bracing in buildings, guy ropes etc where only one member takes all the force in tension and the other member is redundant.

However my practical mind keeps trying to tell me the upper three spokes take a tensile load of axle load /3 + spoke tension

 

[Ajax Bay]

That's not what your diagram [assume the image in AB post 2 pages back] shows. Can you show the above in a diagram please.

Sorry - I've done my best by diagram and text. Hopefully it will be clearer to others.

That's [there needs to be a 'surplus' vertical force component to resist the fork pushing down?] where I think you go wrong. Please try and show that in a force diagram. I can't get my head around your ASCII diagram.

I have revised the 'ASCII' diagram which might now make more sense to you - it seeks first to look at the forces on the fork dropout and then the forces on the hub, and illustrate that the upper spokes 'pull' upwards more than the the lower spokes 'pull' downwards, and that the magnitude of the difference is equal to the weight borne by the wheel.

I'm going to resist the distraction about metal fatigue.

I thought that might pique your interest, though clearly, as a distraction technique, it failed.

 

[Salar]

and illustrate that the upper spokes 'pull' upwards more than the the lower spokes 'pull' downwards, and that the magnitude of the difference is equal to the weight borne by the wheel.

Don't you mean the upper spokes take more tension and the lower spokes take less tension?

 

[Ajax Bay]

Anything I should be looking for before just replacing another spoke? is it easy to do for a fairly hands off cyclist who usually uses lbs for much more than puncture or minor tweaks? Should I look at new wheel?

Apart from comedy physics, has anyone answered the OP?
It's worth replacing a single broken spoke, but if you get a series it's full wheel rebuild time with all new spokes.
That may - or may not - be cheaper/dearer than a new factory built wheel.

I think the OP's questions were answered on Page 1 - perhaps worth scanning (regret I cannot see your contribution). Your summary is fair but some TMN awards maybe in order -is @Tinyminewt around?
https://www.cyclechat.net/threads/you-know-youre-not-in-london-when.223290/post-4942781
Except this question "is it easy to do for a fairly hands off cyclist who usually uses lbs for much more than puncture or minor tweaks?" My answer: Within expressed OP's skill/inclination parameters - 'No'. First one needs to learn to true a wheel with a spoke key. Then move on to replacing a spoke, and bear in mind that right hand spoke on the rear will require temporary cassette removal and getting the right length spoke.

 

[Ajax Bay]

Don't you mean the upper spokes take more tension and the lower spokes take less tension?

No I didn't mean or (I think) said the first bit, but 'yes' to the latter part.
So I said: "the upper spokes 'pull' upwards more than the the lower spokes 'pull' downwards" (on the hub).
As the spokes in a loaded wheel move up to the top they revert to their normal static unloaded tension. When spokes are horizontal they are in slightly greater tension than at the top (to stop the wheel's rim going oval from the force exerted on it by the ground). As the spoke goes lower the tension reduces (see my suggestions attempting to quantify that in the adopted model above). The delta (resolved vertical force) between the upper and lower spokes is equal to the wheel's load.

 

[Salty seadog]

Much as I am fascinated by these sort of discussions and can get my head around the arguments on either side my only contribution would be....

X+Y=Z.

I'm glad we have some great engineering minds on here, I've learned a lot over the years and am eternally grateful.

anyway, X+Y=Z, lest we forget.

 

[Yellow Saddle]

No I didn't mean or (I think) said the first bit, but 'yes' to the latter part.
When spokes are horizontal they are in slightly greater tension than at the top (to stop the wheel's rim going oval from the force exerted on it by the ground).

I have a problem with the use of "oval". That implies that the top part of the rim receives a downward force as if someone is sitting on the wheel. That's not the case. The change of shape is there for reasons I've described above, but the topmost point of the wheel remains exactly the same distance from the hub when the wheel is loaded.
Most people's assumption that the hub hangs from the spokes implies that the topmost point of the wheel remains static in space.

 

[Yellow Saddle]

Sorry - I've done my best by diagram and text. Hopefully it will be clearer to others.

.

Your diagram shows exactly my model, yet you still bring in this concept of surplus vertical forces. There are none. The road pushes up at 500N and the fork/hub pushes down at 500N. To bring in surplus vertical forces the system is out of balance. It is a pity that you can't indicate them on your force diagram.