Book review: The Bicycle Wheel J. Brandt

[mat h physics]

So in recent months I have been getting about 30 miles to the spoke and want to upgrade to a better rear wheel assy. After a little research this book popped up on occasion, and as an avid reader, decided to get a better understanding of build technology.
The Bicycle Wheel 3rd ed Jobst Brandt
Part 1 Theory of spoked wheels, starts by explaining how the wheel is loaded, and stands on the bottom spoke. Yes, I understand engineering and believed (before reading this) rims hang from the top spoke. For those who don't understand, READ THE BOOK!! About half way through the explaination, I was trying to justify his mis conception. By the end, I too understand why the rim stands on the bottom spoke. In short, it can be compared to biasing an electrical circuit (ie creating a sine wave in positive voltage). Yes all spokes are in tension, but when loaded the rim will have a less curved or "flat spot" on the bottom which will change the bottom spoke tension. If you choose to believe an alt means of explanation, please ref the book you have published or write a three technical pages on why your theory is better.
Here is the real world application that convinced me. Researching the proper tire pressure for my weight yielded a rear pressure of 145psi on 700x 28c (120psi for 32c, but have yet to find an suitable tire in that size) . So I ordered a 700x28 rated for 130, and don't mind a 10% over pressure. Received the tire and put it on the 24spoke rim that night, inflating it to 100psi the bicycle pump would handle. Rode to my shop where 175psi commercial compressor is avb, and proceeded to inflate to 140psi. While riding back, the rim was telling me a spoke was loose (tink, tink, tink). Using the "pluck"/tone method the spoke was isolated and tightened.
Went back to the book, and the very next section explained how the high tire pressure caused the rim to shrink due to the force created by the air pressure. This info was under "static load", the book proceeded to "dynamic loads", then into "wheel failure". Page 33 explained some points on "wheel strength". Will pick up on the next section "components, soon.
I think the misconception by the layman is that all forces must be positive, which is not the case. Tension, after all, is a measurement of negative force.

 

[Chalo]

When I first read Jobst Brandt's book in the late 1980s, much of the information was utterly new to me, and non-intuitive. Hundreds of wheel builds and thousands of wheel repairs later, I have internalized and elaborated upon the knowledge contained in the book, and I can verify that his techniques work very well as long as you use the sorts of components he assumed.

One thing that Brandt didn't anticipate was the broad adoption of very deep section rims, whose sections are stiffer radially than they are laterally. Such rims often can't be dialed up until they show signs of buckling (his method for determining practicable maximum tension), because their spoke beds will be damaged first. Fortunately, spoke tensiometers have become much more common and affordable since The Bicycle Wheel was written, and rim manufacturers sometimes provide recommendations or limits for spoke tension.

However one feels about the superficial terminology he uses to describe the way a wire wheel bears a load, Brandt's model assists the correct diagnosis and repair of spoke loosening and wheel instability. This is the remedial text for those who believe thick spokes are better than thin ones.

Chalo

 

[Drunkskunk]

Its a good read from the standpoint of learning how to diagnose trouble on a wheel. His explination of how a wheel works is confusing. No, your wheel doesn't stand on the bottom spoke. His explination is poor and confusing. he's right about the bottom spoke sharing part of the tension with the rest of the wheel. but to call it standing is a misleading term that has lead to many an argument about how spoked wheels work. You can no more stand on the bottom spoke than you can shoot pool with a rope.

JRH and LFP need to get together and write a new version of "The Bicycle Wheel."

 

[liveforphysics]

Part 1 Theory of spoked wheels, starts by explaining how the wheel is loaded, and stands on the bottom spoke. Yes, I understand engineering and believed (before reading this) rims hang from the top spoke. For those who don't understand, READ THE BOOK!! About half way through the explaination, I was trying to justify his mis conception. By the end, I too understand why the rim stands on the bottom spoke.

That is simply not the case.

If it were, a wheel like this wouldn't work, but in practice they do work, and work very well. A wheel has no meaningful component of it's strength added by compression, and a wheel with tight enough spokes under proper tension (aka, very high) should never enter a situation where tension is lost.

 

[Chalo]

What Jobst means by "standing" is that the spoke that changes in tension when a load is applied to the hub is the bottom spoke, not the top one as many people assume. The change is in the preload (so there is no compression involved), but there is not a significant increase in tension on the top spokes, so the hub isn't "hanging".

I think his terminology confuses people, but he is right about where the wheel carries loads.

Chalo

 

[liveforphysics]

I agree with everything you said there Chalo.

Seems very odd he uses the term "standing on the lower spoke", to me that implies some quantity of normal force is being applied to the spoke in a compressive manor, which it obviously isn't.

Is the author's first language not english by chance, and it's a bit of a translator befuddling?

 

[Chalo]

Jobst definitely has a Germanic name and disposition, but he's Californian, educated at Stanford. I've been lucky to discuss many things with him over the years on rec.bicycles.tech. He had a serious bike accident with major injury a couple of years back, followed by a stroke while being treated in the hospital. So he hasn't checked in at r.b.t. for a while. I understand he's still very much with us, though, both physically and mentally.

 

[mat h physics]

The author made the comparison to concrete not being able to carry a tensile load (compression only). Take the 45' strike of the empire state building, the B-25 (made of alum) was able to bust through the concrete exterior b/c there is no support on the back side (tensile force). While the engines passed through due to high density, the airframe "fell to the street unassisted".

All the spokes are effected under Poisson's ratio. But the spoke in the standing position or standing spoke will experience the cycle/change is stress the most. The static load is the natural state, the compressive load is still seen by shorting of length and expansion of the width more than any other spoke being affected.

Take a strong pair of repelling magnets (for demo purposes only they don't exist to humans) attach each to the rope with which you would like to "play pool". These magnets are so strong they pull a tension of 100 fig newton on the rope, PLAY POOL. Assuming most shoots will be less than 5 fig newton, the "rope" will work fine. Any force less than 50 fig newtons should be fine.

 

[Punx0r]

Interesting thread.

I get the description of the flat spot on the bottom of the wheel and the fluctuating tension in the spokes as the wheel turns. I get that the bottom spoke will see a reduction tension, but the OP suggests the top spoke won't see a increase in tension? That I cannot see.

Surely loading a static wheel to the point of failure would illustrate exactly what was happening?

 

[Chalo]

Interesting thread.

I get the description of the flat spot on the bottom of the wheel and the fluctuating tension in the spokes as the wheel turns. I get that the bottom spoke will see a reduction tension, but the OP suggests the top spoke won't see a increase in tension? That I cannot see.

Surely loading a static wheel to the point of failure would illustrate exactly what was happening?

Loading a wheel statically to the point of failure, if the axle didn't break first, would cause the rim at the contact patch to buckle inward just above the ground, and that in turn would taco the wheel. It's a familiar form to bicycle mechanics.

The force path is ground -> tire -> rim -> spoke -> hub -> bearing -> axle -> frame. Because the rim is somewhat elastic, other spokes away from the contact patch may see tension fluctuations up to about 10% as much as that of the spokes over the contact patch.

Chalo

 

[cal3thousand]

Yes, it wouldn't be one spoke that gains tension, but a multitude of spokes taking various amounts based on their respective location to the point of contact.

 

[liveforphysics]

Yep, as the rim deforms and stress is lessened at the spoke right above the local flat place in the rim from it's contact with the ground, the other spokes do have an increase in load, but if the spokes are stretched over a great enough distance, the rim can deform and still share that stress over a wide area, divided between perhaps a dozen spokes, so the stress to the top side is not a localized stress riser point at just the top most spoke.

If you're running spokes too thick to be stretched a sufficient distance (because they will rip through a bicycle rim), your stress load on spokes on the top side will be focused much tighter, and the loads in your wheel will be carried over just a few points in the rim as the rim deforms (which is inevitable for any rim with loads changing on it as it rolls or bumps across the ground etc).

Thin spokes stretched so tight they start to yield is the strongest wheel you're going to get using a bicycle rim. If you're using a motorcycle rim, by all means go double or triple spoke cross-section and make the accompanying doubling or tripling in spoke tension.

Also, as spokes get shorter they stretch less for a given amount of tension as well, so hubmotor wheels really get an extra bad gig for staying together. The Belville washer solution currently being tried by a few folks is the best solution I've seen to the problem.

 

[etriker]

Sit on the bike and ping the spokes. The ones on the bottom will have a lower tone and the spokes on the top will barely change in tone.

The wheel is standing on the lower spokes.

The upper spokes are not holding the added weight when you sit on the bike because they don't change tone when weight is added. The lower ones do change tone.

That is the way I read the book.

 

[Chalo]

Ian from astounding.org.uk went so far as to do some finite element modeling on tensioned wire wheels.

from http://www.astounding.org.uk/ian/wheel/:

Note that the largest increases in tension predicted by his model are on either side of the contact patch, and not at the top.

 

[WhatcomRider]

Chalo - those are decreases in tension (negative numbers) around the contact patch, not increases. That said, I think the pic illustrates the distribution of forces well - just as I would expect.

 

[Chalo]

Chalo - those are decreases in tension (negative numbers) around the contact patch, not increases. That said, I think the pic illustrates the distribution of forces well - just as I would expect.

Yes, but the largest increases are on either side of the contact patch, not opposite it. That's all II was saying. Even those are in the range of 10% the magnitude of the largest decreases, which are directly over the point of contact.

 

[WhatcomRider]

Gotcha! Sorry for the misunderstanding. I was imagining a much narrower contact patch.

 

[Punx0r]

The FEA model of the wheel is interesting (assuming I'm reading it correctly).

Clearly a wire spoked wheel is a complex thing.

It looks like the load (tension) is carried by a far greater number of spokes than I would have thought. I.e. not just the top ones. There's certainly more going on with the bottom spoke, although I still can't see how the wheel could be said to be standing on it? Perhaps it's intended as a metaphor and not literally?

I imagine if you were to cut the bottom spoke while the wheel was statically loaded not much would happen.

 

[Drunkskunk]

An FEA of a spoked wheel is a good read, and there are a bunch published. I've read a few and found a few interesting points.

*they usualy describe the bottom spokes as being in compression, However, some authors add a foot note that the term compression means a reduction in tension from the static state. The spokes are still under tension.
* the tension gradiant isn't even from top to bottom. It drops low roughly at the 1:30, 4:30 7:30 and 10:30 o'clock positions.


I think Brandt should have chosen his words better.