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### 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Wed Jan 16, 2019 3:35 am
Here's something for you (fellow) wheel nerds to digest.

Reinventing the Wheel: Stress Analysis, Stability, and Optimization of the Bicycle Wheel.

https://github.com/dashdotrobot/phd-the ... s_v1.0.pdf

I have to say I like this part. None of this "reduction of tension is the same as compression" nonsense I read from keyboard commandos sometimes.
It is often erroneously assumed that the lateral stiffness is different in the left and right directions on
such a wheel. Damon Rinard demonstrated that the stiffness is indistinguishable [70], but it should also be
clear from a theoretical perspective because the stiffness is the instantaneous slope of the load-displacement
curve and the spokes on each side give the same stiffness in tension as in compression" (or more precisely,
loss of tension) 19

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Wed Jan 16, 2019 5:58 am
Looks very interesting. Thank you!

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Wed Jan 16, 2019 5:58 am

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Wed Jan 16, 2019 9:20 am
Nice.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Wed Jan 16, 2019 9:26 am
On p58 he finds that stiffness actually decreases at high spoke tensions. Interesting.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Wed Jan 16, 2019 3:52 pm
^ makes sense to me. If tensions are really high, it takes more deflection at the rim before the near side goes slack. But I doubt the difference is significant. And it's always more important to ensure that tensions are high enough to prevent any spoke going slack from load.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Wed Jan 16, 2019 4:01 pm
Yes there are a lot of interesting things in there. For instance, the stiffness of the dished rear wheel is the same on both sides which supports what bm0p700f has been saying.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Wed Jan 16, 2019 10:07 pm
I'll have a read. If I had been into bikes when I tried doing. PhD I might have done the same thing.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Thu Jan 17, 2019 1:08 am
One should remember when building with a tubeless rim once the tubeless tyre is fitted there is a big tension drop so high tension is needed. I need to compare a tubeless tyre to a tubed tyre really.
Normally for tubekes ready wgerls I tension the D's rear to 1250n with kinlin rims using washers. Once an IRC tubeless tyre is fitted the tension drops to 1000n. I had not realised that increases lateral stiff was. The mechanism for this is not clear to me. rim compression is not a satisfactory explanation to my mind.

This also mean with 2:1 lacing spoke tension can be lower. 1100N rear should be enough.

Interesting so far. I'd like to buy this guy a pint.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Thu Jan 17, 2019 1:34 am
If you place your thumb on a rear wheel and push equally, one side usually moves further than the other.

On a front it doesn't.

Is that for some other reason then?

Nice light read by the way

Haven't looked at it in detail obviously but my first thought goes to how a maybe a carbon rim can continue to deliver lateral strength before reaching this buckling state that is mentioned.

I wonder what was the goldilock tension for his alloy wheel before seeing a decrease in strength. Can't find it.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Thu Jan 17, 2019 3:05 pm
Lateral stiffness is the same both sides so long a spoke tension is maintained. Think about one side cant have a different stiffnes other wise it would mean the left side and right side are not coupled (i,e joined) they are joined though so when you push the rim you are see the combined lateral stiffness regardles of which side you are pushing.
Lateral stiffnes left + lateral stiffness right = total and that does not change when pushing from the left/right. You cant decouple each side either.

Logic is falwed because of the murky explanation you have used.

Goldilocks tension is different for each rim. it depends on the buckling tension. Also peak stiffnes is for (presumably drive side tensions of under 500N. That is unusable though as NDS spokes would go slack for all riders. Therefore normal tensions of 1200N drive side seem to be needed to avaoid spoke going slack. According to these results that means your wheel is less stiff but it wil hold together. As I pointed out 2:! laced wheels and non dished wheels can use lower tensions. We knew that anyway but did not realise that lateral wheel stiffness improves. The tyre drops tension anyway.

So nothing changes with regard to wheel building. phd seems to confirm our best practices. Still not clear why lateralstiffne decreases with spoke tension.

an anyone here code? An app to use acoustics to determine lateral and radial stiffness of the rims.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Thu Jan 17, 2019 4:30 pm

alcatraz wrote:If you place your thumb on a rear wheel and push equally, one side usually moves further than the other.
On top of what bm0p7000f already said, a short layman's explanation - remember when you are pushing the rim sideways, you are pushing and pulling on the spokes attached to that particular spot on the rim, and the same push transitions 180 degrees around the rim to other corresponding spokes (as a simplified example). So although force is exerted only to one side, the whole wheel is built to carry load together and always resists as a system.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Thu Jan 17, 2019 4:34 pm
Page 91-92 figure 5.2 and 5.3 note that for .7Tc-.8Tc the lateral stiffness is 40N/mm while the radial stiffness is 3500N/mm. The lateral stiffness is so much lower that it would be stupid to sacrifice any lateral stiffness to lower the radial stiffness in the name of "compliance" - which is what Stans did on it's Mk3 series of mountain rims.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Thu Jan 17, 2019 11:58 pm
The thesis talks about stress relieving. It fails to mention the main effect. It talk about relieving stress but when you grasp pairs of spokes and squeeze you get a tension drop ok no the wheel. The spokes have bedded in to the hub and have stretched. I get this on straight pull hubs and j bend hubs. When building. Wheel I will start "stress relieving" once spokes are up to 700N. Each time I added a round of tension follows a round " stress relieving". The tension drop can be significant -200N initially. Essentially the effective spoke length is shorter by bedding in and the spoke gets longer by stretching.

Once the wheel is at full tension, true and found the final round of squeezing is done and then the test wheel placed on the end cap and push down. It should still be just as true afterwards. If its not, then the spokes have not been grasped hard enough. It seems the stress relieving is really bedding in a stretching the spokes. Wheels go out of true when ridden if the spokes stretch and bed into the hub further.

That's how I see it. That were reading this done of the explanation get a bit wooly. It does not change the results though.

Also he had a hub with variable spacing but I can't see where he has teased out the effect of bracing angles on lateral and radial stiffness. It might be buried in the maths. I can't see it Gough. Can any one.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Fri Jan 18, 2019 1:46 am
Are you on your phone? The syntax errors are getting unreadable.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Fri Jan 18, 2019 11:23 am
bm0p700f wrote:
Thu Jan 17, 2019 3:05 pm
Still not clear why lateralstiffne decreases with spoke tension.
They way I understood it is that with high tension, the wheel gets closer to the "Taco" state.

Regarding symmetrical stiffness, I doubt this has to be symmetrical: Imagine a wheel with the NDS flange really far out and the DS flange under the spoke holes - it obviously will be less stiff if you push the DS towards the NDS.

### Re: 137 page PhD Thesis on the Bicycle Wheel by Matthew Ford, Dec 2018

Posted: Fri Jan 18, 2019 11:23 am