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I assume that most of the weight of the bicycle is taken by spokes in tension, but there must also be a contribution from spokes in compression. Any idea of percentages?

2 Answers2

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For conventional wheels (32 spoke), the answer is 0% compression, 100% tension. This is why it is possible to have spokes that are no more than wires - in fact, bicycle wheels are called "wire wheels" (see the wiki article)

What is clear from that article:

  • spokes are under tension, and provide "suspension" of the load from the top rim (see for example this article by Tom Fine)
  • spokes are offset tangentially to be able to transfer torque (acceleration and braking)

With that said, there is this interesting paper that shows that the greatest strain (change in stress) occurs in the spokes closest to the point of contact. This is in fact because the wheel deforms most readily at that point - if you think about it, the spokes pull more or less evenly on most of the top half of the rim, but at the bottom the force of the ground is not distributed. As a result, there is local distortion and this causes the bottom facing spokes to slacken. At no point do the support a significant load in compression, and I can prove that.

The buckling load of a straight rod is given by

$$F = \frac{\pi^2EI}{(KL)^2}$$

Where $E$ = Young's modulus (195 GPa), $I$ = second moment of area ($\frac14 \pi r^2$), $K$ = "effective length factor" (~ 0.7 when one end is fixed and the other pinned - that describes spokes fairly well) and $L$ is the length (35 cm). Putting in these numbers, we find

$$F = 25 N$$

So a single spoke can support about 25 N before buckling. But before you get close, the tensile force gets sufficiently greater that it will carry the wheel. So while it is conceivable that a spoke (at the bottom of the wheel, where it touches the ground) is in compression, it will not support the weight of the bike.

See also problem #1 in this problem set from MIT OpenCourseWare

UPDATE

Let's put it differently. Assume that the spokes are under some pre-tension. When the axle is loaded, it stretches the top spokes and shrinks the bottom spokes. Before the bottom spokes could carry any weight in compression, the top ones must double their tension. This means that the net force on the axle would be equal to half the total tension in all the spokes (the vertical vector gives me a 50% contribution, and otherwise the contribution of the top spokes doubles while that of the bottom spokes disappears).

The typical tension in a spoke is set to at least 80 kg (800 N) according to this article which looks like it knows what it is talking about. Again, using 195 GPa and 2 mm diameter for the spokes, that would result in a strain of

$$\frac{800}{\pi\cdot 0.001^2 \cdot 195\cdot 10^9~0.0013}$$

That is equivalent to a 350 mm spoke stretching about 0.5 mm, which sounds about right. But if that is so, then you would need a force of about 16*800 = 12,800 N before the spokes start to buckle.

In other words - they stay in tension as long as the wheel remains round. And if, as the above-linked article measured, the rim distorts slightly at the contact point, then those spokes may lose tension; but they will not carry the load.

All bets are off, of course, when you go to "solid" spokes (like the 3-spoke designs you see on some fancy bikes). This answer is purely for wire spokes.

Floris
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Without getting into the complex mathematics and physics involved, let me suggest that this description, in laymen's terms, may explain and make clear what is happening when the wheel rotates:

At any given moment, the top spokes are under the greatest tension, with the bike "hanging" from the hub. These spokes are acting to "pull" the top of the rim downward, because of the weight of the bike as it hangs from the hub.

The horizontal spokes are also under tension, keeping the rim from collapsing outward under the weight of the bike "pulling" the top top of the rim downward.

The lower spokes are under the least tension, and doing the least amount of work holding the bike up.

  1. As the wheel rotates, the tension on any given spoke changes, depending on on its position. For example, the highest spoke is doing most of the work, and under the greatest tension holding the bike up.

  2. Its tension gradually changes (probably lessens) as it moves toward a horizontal positions, where, along with its opposite partner, keeps the rim from collapsing.

  3. It tension coninues to lessen as it moves to its lowest position, where it is under its lowest tenion, and likely doing its least work.

  4. Its tension gradually increases while moving to a horizontal position, where it works with its opposite, as in #2.

  5. Tension increases to it greatest level when the spoke reaches its highest point, where the cycle repeats itself.

AAR@prodigy.net

A Rossi
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