How Does the Design of a Spoked Wheel Affect Its Physical Properties?

[Little Mac]

Hello. I've come across a physics curiosity while reading the Tao-te Ching. Chapter 11 begins by stating (Robert G. Henricks translation)...

"Thirty spokes unite in one hub;
It is precisely where there is nothing, that we find the usefulness of the wheel."

At first, I thought this was completely wrong. Surely, a solid-wheel would be stronger and more useful than a ring with spokes. But later, the idea came to me that this wheel with spokes might in fact be able to support more weight. I've never seen a solid wheel on a cart, or a bicycle, or anything. Also, there's just some intuition that tells me that this type of wheel will be stronger.

Does anyone know if this is really true, and if so, what are the principles of physics behind it?

 

[TuviaDaCat]

nope... it isnt.

full solid metal wheels whould be stronger, but not effective to its weight and cost.
while a ring is enough to hold certain weights...

also, it is connected to stregth of materials...
almost all metalic parts are hollow, street lights poles for example...
the thiner the ring is, and the bigger diameter, the ligher, and the less expansive it would be.

it would be irrelavent to explain it here, because a forum is not a good replacment for books, yet ill tell u that the thing is, that if u make a filled shape, the inner mass of the part would be less strained than the outer parts(not exact, but ussuly this way...), and when a part breaks, it happens in the most strained point, so that most of the metal is partly wasted...
but in a ring shaped part, the strain would be about the same...

 

[Integral]

That is quite a leap, from that passage, to a comparison of solid vs spoked wheels. I think you are reading to much, or perhaps the wrong things, into it.

Of course solid wheels are stronger the spoked wheels. The difference is the amount of work required to turn them. A solid wheel requires a greater force to turn, so if speed is main concern a spoked wheel will go faster for the same force. The extra strength of a solid wheel is usually not needed, while minimizing the force required to move a load is always nice.

 

[eep]

I think the point of the passage is that the holes in the wheel which you use to attach it to a cart or whatever are what makes it useful. can't really do much with a solid wheel. the same passage i believe states that the hollow of a cup is what makes it useful.

 

[HallsofIvy]

Have you noticed that in modern racing bicycles, the rear wheel is solid?

 

[Little Mac]

That is quite a leap, from that passage, to a comparison of solid vs spoked wheels. I think you are reading to much, or perhaps the wrong things, into it.

Yes, I'm very aware that this is not the main point of this passage. The Tao-te Ching is not an ancient guide to physics or mechanical engineering, but of philosophy. I just thought it might be interesting to to probe what literal truth was in this particular passage.

Thanks for the input everyone. It sounds like we came up with two possible areas of usefullness, speed and material savings (since the center of the wheel wasn't required to provide support for the strain).

I think the point of the passage is that the holes in the wheel which you use to attach it to a cart or whatever are what makes it useful. can't really do much with a solid wheel. the same passage i believe states that the hollow of a cup is what makes it useful.

This seems quite possible, as the translation leaves the first line with the idea of the center hub of the wheel rather than the space between the spokes. But I guess I'll never know until I learn ancient Chinese. And yes, this chapter also includes the statement that the usefulness of a vessel or a room is related to the empty space within them.

Thanks again.

 

[Gokul43201]

Lao Tse was only trying to make a philosophical point. Any enginnering insights drawn from them are most likely coincidental.

 

[TuviaDaCat]

Have you noticed that in modern racing bicycles, the rear wheel is solid?

yea, but is plasctic, and the metal pokes are still intact...

 

[Hootenanny]

Have you noticed that in modern racing bicycles, the rear wheel is solid?

I hate to be pedantic, but only in time trial or indoor bikes are the rear wheels solid. For longer stages, strong gusts of wind can lead to the bike becoming unstable.

 

[Little Mac]

Lao Tse was only trying to make a philosophical point. Any enginnering insights drawn from them are most likely coincidental.

As I've already mentioned, I'm aware that this is a work of philosophy, not physics. I don't believe it offers any enginnering insight.

In this case, however, I would argue that the author's understanding of physics is important to the meaning of the chapter. In this chapter, he states that the empty space in a wheel, a vessel, and a room defines its usefulness. Likewise, a person should cultivate such "empty space" within themselves, and so forth. Why the author felt the empty space within a wheel is useful is, therefore, not trivial.

Generally, I think readers link the example of the wheel together with that of the vessel and room, for which the usefulness of the empty space within them is easy to grasp. However, the wheel is a very different case, and it is not so clear why the empty space within it is useful. It could have been a misconception of the author, but it could also be a product of a unique understanding of how a wheel works and what was important in the function of a wheel.

As such, it's also an interesting point concerning the author of the text, of whom we know nothing. This might suggest what practical knowledge he did or didn't have.

 

[quark]

Chances of these kind of analogies coming into picture just by coincidence or without the real knowledge may also be less. Fritzof Capra's "Tao of Physics" shows parallels between physics and many things written in eastern philosophical books.

 

[Farsight]

As eep says, it's the hole in the hub that's important. Where the axle goes. Not the gaps between the spokes.

A hole is quite interesting, actually. It's a thing that isn't a thing.

 

[leright]

Well, if you look at this from an engineering standpoint (which you shouldn't...understanding mechanics of rotating bodies is not a pre-req for humanities...) the spoked wheel certainly has a lower moment of inertia than the solid wheel, which means that for a given TORQUE there is a higher angular acceleration in the spoked wheel than in the solid wheel.

The moment of inertia for a rotating point mass is the product of the mass and the square of the distance between the point and the axis of rotation. For continuous bodies such as disks and spoked wheels the total moment of inertia can be found using integration. You can divide the body up into differential mass elements, find the moments of inertia due to each differential element and these differential moments of inertia. The result will most certainly be that the spoked wheel has a lower moment of inertia.