brain teaser

The spokes of a unicyclist’s wheel are tensioned to 125kg.
What is the tension in the spokes when the unicyclist, who weighs 75kg, sits on the saddle?

Good Luck!

Which spoke?

Oh no not another wheel puzzle!

hi mike

ahh, i’ll leave the desicion to you!
whilst trying not to give away the solution - it doesn’t make a great deal of difference.

did you see my reply to your J27 post?
any info?


I think the answer would be something like:


very nice mathematics

but i’m looking for something much simpler

Is it 125kg?

I’ll guess:

The average spoke tension will be 125kg. If your weight presses down on the bottom spoke, loosening its tension, it is pulling down on the upper spoke, increasing its tension correspondingly. Assume that the horiz spokes are less affected at that moment.

So, if you could measure each spoke’s tension during this episode, add them all together and then divide (lets assume 36 spks/hub) by 36, the average would be 125.

125kg is correct

the simple answer is…

the load in the spokes does not change until the imposed load exceeds the preload- so as the unicyclist weighs less than the preload the spokes remain tensioned to 125kg.

thanks to the engineer magazine from which this is adapted.


Re: 125kg is correct

I had a feeling that was the case, but I can’t say I understand it.

Anyone feel like explaining this?


I’ll explain. He is wrong. What’s the resulting net force on the rim if they do? Zero. So according to what he said, you apply a net force to the hub of the wheel and there is no net force on the rim. Am I understanding correctly? If that is true then we can all fly.

No, it’s not the force that’s being talked about, it’s the amount of tension in the spokes. there’ll still be a downwards force on the rim applied by the spokes, it’s just that this won’t change the tension of the spokes cos they’re already loaded to more than the amount of tension which would be produced by the weight, so nothing much happens to them.

I think.

You might be able to ping the spokes of a loaded and unloaded wheel to verify this, ping spokes, lean on seat ping spokes, no change in noise.


How does one “tension” spokes in kilograms? WHere in the universe does one “weigh” 75 kilograms?

gimp, I like your approach, but I think you have jacked some things around. First, I think you have some problems with TN check that some. I don’t see why you neglect that second term in the summation. Also, you seemed to be on the right track with the sum of the forces equalling the rider’s weight, but then your final result is a constant increase in each spoke’s tension? This shouldn’t be. Also, you have 36 spokes and two equations. You may use a symmetry boundary condition to perhaps get 18 spoke tensions to solve for. So you have 18 unknowns that you solve with two equations?

Harper, you tension in kilograms with a special spoke tool from tark prool. The company that makes tools out of antimatter. Oh yes, and you have to divide the kilogram readout by the number of seconds you took to tighten the spoke and by the number of seconds it takes you to taco your new wheel. And multiply by the length of your hair. This should work out nicely.

This is why my spokes are so tense! And I’m so calm.

Joe. I am considering the spokes as two force members. I think this is reasonable. That being the case. I guess I don’t understand the difference between force and tension. What is it exactly? Aside from tension being scaler and force being vector.

is it not different because the spoke is effectively a spring rather than a solid rod. Kind of like bolts -

Although this is doing my head in thinking about it, so I might be talking rubbish.

by the way Harper, why aren’t you a member yet?

That is WAY cool. I’m waiting for a nomination otherwise I would be too self-concsious.

Yes, you are exactly right. The spoke tensions are forces imparted on the rim. Therefore if you apply a force to the hub by sitting (which you are doing) and there is a reaction force on the rim (which there obviously must be) then this force, tension, whatever name you want to call it is transmitted by the spokes. Therefore the spoke tensions cannot possibly remain unchanged. They don’t, and they can’t. Nobody here argued that the change is small. Everyone said there is no change. And that is exactly wrong. Consider this: If you apply a force to the hub, how does that force get to the rim if it may not be transmitted through the spokes? Please don’t reply with things like pretension. We already agree that tension is force so the load in the spoke is a load in the spoke. Pretension does this and our weight on the hub does this. Whether you hear it with plucking or not makes no difference. If you add weight then the tensions change.