Tuesday, March 21, 2006

bicycle wheels part 1

Today I started building up the rear wheel for the maruishi in the garage. I have it all laced up, and have just started tensioning it. Before I explain what all that means, let's talk about how a wheel works. I'm not talking about rolling. You already know that a wheel rolls. But a wheel does something else. It supports a heck of a lot of weight in proportion to its own weight.

My wheel - hub, axle, rim, and spokes (no tire or innertube on it), weighs just a hair over a kilogram. When it's finished (if I build it right), it should be able to support around 200 kilograms of radial force - force applied to the axle and pointing straight down. How is this possible?

A lot of people think that bicycle wheels support the weight of the rider because the hub hangs by the spokes from the top of the rim. In other words, they think that when you sit on your bike, the tension in the spokes at the top of the wheels increases (which is to say, the spokes at the top of wheel stretch), and that force is then transmitted around the circumference of the rim to the ground. Well, that's not the way it works.

How does it really work? In fact, the hub "stands" on the bottom spokes! That is, the bottom spokes get shorter which transmits the force of the rider directly through to the ground. A bicycle wheel actually works just like an olde-fashioned wagon wheel with wooden spokes. Don't buy the explanation? You can verify it for yourself. The easy way to verify it is by having someone straddle their bike and hold onto the handle bars. Then, pluck one of the bottom spokes with your fingernail. It will make a sound of a certain pitch, just like a guitar string would. Now, have your friend press down on the handle bars as hard as possible. Pluck the same spoke. The pitch will have gotten lower. You can use this same method to find out if the tension of any of the other spokes changes. You'll find that a few spokes at the bottom of the wheel change, but the ones at the top and the sides stay the same. If you don't believe that, ask yourself the following
question: If you had an un-laced rim (i.e. no spokes in it), would you expect to be able to sit on top of the rim without bending it? I wouldn't! Well, the rim would have to be that strong if it were to support your weight from the top.

Maybe you still have some doubts. How is it that the spokes can support weight pressing down on top of them? If you take a spoke by itself, and try to stand on it, it will bend immediately. The answer is pre-tension. (which is different than 'pretension', something I'm exhibiting by trying to add something new to the internet on the subject of the bicycle wheel). When you finish building a wheel, there's a lot of tension in the spokes - that is, each spoke is pulling outward on the hub, and inward on the rim. Then, when you put weight on the wheel, the tension of the spokes at the bottom of the wheel decreases slightly.

In other words, with no weight on the wheel, the spokes at all points of the wheel might be pulling the rim in towards the hub with 20 Newtons of force. When you put weight on the wheel, the spokes at the bottom of the hub decrease in tension, while the spokes at the top retain the same tension. So then you have, say, 10 Newtons at the bottom wheels and 20 at the top. This means that the hub is being pulled up towards the top of the rim harder than it is being pulled down towards the bottom of the rim, and so the rim can support as much weight as it takes to restore balance to the forces acting on the rim.

That's hard to conceptualize. People who have taken (and understood) a physics class have it beaten in to them to look at things this way, but most people find this counter-intuitive.

Here's another way to understand it. Suppose you and your friend are playing tug of war. You have a rope with a red flag in the middle of it, and you are pulling on the rope exactly as hard as your friend is. This means that the red flag in the middle of the rope doesn't move at all. Now, your other friend Manfred comes up behind you and starts to to push on your back. You're still pulling just as hard on the rope, but suddenly you start to move forward, and so does the red flag. But if
Manfred's sister, Uma, comes along and grabs the flag and starts pulling it back toward you with the right amount of force, then the flag will stop moving again. At this point, the tension betweeen the flag and your friend is the same as it was before, while the tension between you and the flag has decreased (because Manfred is pushing on your back). Well, substitute Manfred for the ground, and Uma for the weight of the rider - a bicycle wheel works the same way.

There are a lot of other forces that a bicycle wheel can support besides radial force. For instance, when you pedal, the spokes transmit the twisting force (the torque) on the hub to the rim, which makes the wheel turn, which makes you go. I'll write about how that works next time.

Lastly, if you want to build your own wheel, see http://sheldonbrown.com/wheelbuild.html


At 7:21 PM, Blogger ark said...

There's nothing supporting the spokes at the bottom. The spokes and nipples go right through the rim. In an untensioned wheel the spokes stick out of the rim so they can't possibly 'stand on the lower spokes'.

I call shenanigans on your explanation.

At 8:14 AM, Blogger emtel said...

Did you try my experiment, testing the pitch of the bottom spoke as you put more weight on it?

What's supporting the spokes at the bottom is pretension. As the tension in the bottoms spokes decreases, a net upward force on the hub results. Yes, the nipple still pulls upward on the rim (or it would puncture your inner tube, as you say), but it is pulling up less hard the more weight you put on the wheel. The top spokes, meanwhile, have a relatively static load in relation to the load at the hub.

It's partly a semantic dispute - you might object that a decrease in tension is not the same as an increase in compression. But the important point is, the bottom spokes are the ones that react to dynamic loads.

By the way, this isn't just my explanation.


* http://www.astounding.org.uk/ian/wheel/
* http://www.digest.net/alfa/archive/v9/msg08302.htm
* "The Bicycle Wheel", Brandt
* "Bicycling Science", Wilson

At 2:16 PM, Blogger ark said...

"a decrease in tension is not the same as an increase in compression."

that's the key phrase that made it more clear to me, thanks for explaining further.


Post a Comment

<< Home