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The Bicycle Wheel by Jobst BrandtEdit

At the end of this article there is a reference to a well-known book by Jobst Brandt and a statement that "it contains several serious factual engineering and math errors". I am aware that there is some controversy about aspects of Brandt's book but I feel it is not appropriate to make an assertion like this without either expanding on it to give one or more examples (however briefly)or provide a link to a text that explains those errors.Chrisrustsheffield (talk) 20:20, 16 December 2010 (UTC) As there has been no response to my comment above I've removed the statement referred to and replaced it with a more balanced one indicating that there is some controversy about Brandt's work.Chrisrustsheffield (talk) 23:08, 9 March 2011 (UTC)

That statement has come back. The "factual engineering" error are not errors. It follows quite simply from force balance that the spokes support the hub as rigid columns: F=MA, and since in a bicycle wheel acceleration is negligible in the force balance, and zero for a stationary bike wheel supporting weight, we see that the forces sum to zero (or essentially zero). With a tensioned wheel, spokes are pulling the rim inward. This is resisted by the induced outward pull of the rim. It's the same as if you pressed your finger on a rim. The rim responds by elastically deflecting a very small amount, and pushing back on your finger to maintain force balance. Thus, in an unloaded wheel, the spokes are all tensioned, and the rim is pulling outwards. Now, if the rim is supporting a load at the bottom, the rim deflects inwards at the bottom. In other words, the rim's outward pull is reduced. This reduced outward pull is counteracted by the reduced inward pull of the bottom spokes as the spokes have their tension reduced by the inward deflection of the rim. The tension in the top spokes does not change, because the downward force on the hub counteracts the reduced spoke tension of the bottom spokes.
Therefore, the spokes do indeed support the rim as rigid columns. There are some controversial things in Jobst's book, but how prestressed structures work ain't one of them. — Preceding unsigned comment added by (talk) 23:38, 13 February 2012 (UTC)
That is preposterous. Observe the joints at each spoke end. The only mechanism to load a bicycle spoke is in tension. Also, explain how bicycle wheels with flexible fiber spokes work. — Preceding unsigned comment added by (talk) 00:59, 26 February 2012 (UTC)
Yes, saying that "the spokes do indeed support the rim as rigid columns" for common bicycle wheels is preposterous. As John Forester explains here, when you are on your bicycle your weight is supported by the downward pull of the spokes on the hubs; it's just that the downward pull is less than it would have been had you not been on the bike, less than the original tension built into the wheel. The spokes remain in tension, but the tension of a few at the bottom is reduced. -AndrewDressel (talk) 19:30, 26 February 2012 (UTC)

You all obviously don't understand the concept of prestressed structures. If you would actually read what I wrote I never claimed the spokes at the bottom aren't under tension. The bottom spokes support the load as rigid columns because they are prestressed. That's what the term means. It's the same as how you can have prestressed concrete spans work under tension. Concrete is the opposite case of a wire spoke. It works under compression, but not tension. By itself, it can't be used as a horizontal beam, like small bridges, because there is tension at the bottom of beams. To use concrete under tension, it is cast around tensioned steel bars, and then the tension is released when the concrete cures, transferring the tension of the steel beam into the concrete. Thus prestresses the concrete, putting it under compression. Then, the beam can handle tensile stresses, as the total normal stress is just the compressive stress - the normal stress. If that's positive, the beam is still under net compression, and everything is fine and dandy. It's the same with bicycle wheels. As long as the tension is greater than the compression, it's under net tension, and the spoke can support the rim. When the compression exceeds tension, the spoke detensions, and does not support the rim and is subject to more fatigue. This is how prestressed structures work, if you want to argue with me about it I'd appreciate it if you got an understanding of basic continuum mechanics and basic engineering.

On an unloaded wheel, the spokes are all under tension. Upon loading, the tension on the bottom spokes is reduced by the action of the rim deflecting inward. This load is balanced by the downward force that the hub exerts. The tension in the top spokes is unchanged, because the reduced downward pull of the bottom spokes is made up for by the increased downward pull of the hub. The top spoke's tension is completely unchanged. — Preceding unsigned comment added by (talk) 02:02, 3 March 2012 (UTC)


< The last cross is normally "interlaced" by wrapping the spoke around the one from the other side of the flange. >

Why is this done? What is lost by not doing it? (talk) 02:02, 11 August 2011 (UTC)

This forces the two spokes to "bend" past each other a slight amount. When two spokes are equally tensioned, each one bends the same amount. If instead you imagine one highly tensioned spoke and one untensioned spoke, the untensioned spoke will bend much more, while the highly tensioned one will hardly bend at all.
When a wheel is loaded, the bottom most spoke will see its tension reduced the most. Because it is "crossed" with another spoke from the other side of the flange, its takes up some of the bend from the other spoke. The bottom spoke's angle at the bend increases, which requires the spoke to elongate, increasing its tension. The more highly tensioned spoke kind of gives some of its tension to the bottom spoke.
This decreases the cyclic loading/unloading that the spokes receive, which helps keep the spokes from breaking due to metal fatigue (by far the most common reason spokes break). — Preceding unsigned comment added by (talk) 23:57, 13 February 2012 (UTC)
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