# B Spray from bike wheels

1. Nov 20, 2016

### Simon Lorimer

Do different sized bicycle wheel spray differently?

I was asked this question recently and have got myself confused with an answer. To expand on the question a little, when riding through mud at the same speed, which would spray the mud further, a 26 inch wheel or a 29 inch wheel? My thought are that, at the same speed, the smaller wheel will send the mud further because it will have turned through a greater angle before becoming unstuck from the tire, and so be projected at a greater angle. Does this seem reasonable? Are there other factors which should be taken into account? Does the mud leave each wheel at the same speed?

Hope my question is clear! Thanks in advance

Simon

2. Nov 20, 2016

### Simon Bridge

Welcome to PF;
The basic pattern will be much the same for wheels that differ only by diameter.
The amount of mud flung will depend on the rate that mud is picked up by the wheel.
Larger diameter wheels will pick up more mud (because more of the rim is in the mud at once).
Smaller wheels have higher angular speed for the same bike speed... rim speed is the same as the bike speed.
I would expect that the mud will unstick a bit like how water drips - so, same time for same sort of mud - so small wheels turn by bigger angle.
However, too large an angle and the range gets smaller ... the sweet spot is around 45deg. So I'd say that sometimes the bigger wheel flings mud farther - depends on the mud.

However - this is something that can be easily tested.
Sounds like a good project for a science class or a science fair right?

3. Nov 20, 2016

### Cutter Ketch

ok, there will be a lot of caveats about tread patterns and such. Let's assume everything is as similar as possible except for the tire diameter.

The tangential velocity is the same as the bicycle speed and so the same in both cases. The centripetal force required to keep the mud on the tire is

m v^2 / r

So it requires only 80% as much force to hold the mud on the 29" wheel. So, it holds on longer. But, of course it takes 12% longer to get to the same angle past vertical with the larger tire.

That's where I got stuck. What determines how long the mud hangs on? The best I could do was the analogy of a water drop forming at a faucet. The rate of formation is directly proportional to the force (usually gravity). So that would suggest the mud will hang on 25% longer on the large wheel. The lower force beats the slower angular rate and the mud releases at a higher angle on the larger tire.

That last bit is a stretch, but I think the actual dynamics are probably pretty dense.

4. Nov 21, 2016

### Simon Lorimer

Thanks - I hadn't thought about the larger wheel picking up more mud - an interesting extra variable!

In the end I think you are right that trials would be the way to go. This could get messy.

Simon

5. Nov 21, 2016

### Simon Lorimer

Thanks for the reply. The water drop analogy is useful. Does the 25% longer for the large tire come from the lower centripetal force on the tire? It looks like it is necessary to make some assumptions about the behavior of the stuff on the tire

Simon

6. Nov 21, 2016

### Cutter Ketch

Yes, from the lower centripetal force.

7. Nov 21, 2016

### Simon Bridge

$mv^2/r$ is the net centripetal force needed to keep the mud moving with the tyre.
If the net force holding the mud to the tyre is less than this, then it will not follow the tyre around.

8. Nov 21, 2016

### Cutter Ketch

But it does! That's the maddening part. If it were a simple question enough stick or not enough stick it either wouldn't be picked up in the first place or it wouldn't have later come loose.

Clearly the mud/water went on the tire in a configuration that can hold with sufficient centripetal force, but rearranged under the force to a configuration that couldn't. The change in configuration requires time and energy and some nontrivial fluid dynamics. The only analogy I could think of was the water droplet where surface tension won't allow the water droplet to come loose until it has flowed and rearranged into a drop with more weight than the necked down surface tension can support.

9. Nov 21, 2016

### Simon Bridge

... Maybe I am not being clear: I think we agree here. technically the part of the mud sticking to the rubber stays behind - it is the internal cohesion of the mud blob we are considering here. That is what most people are thinking of when they talk about mud sticking to stuff (witness post #1: the mud flies off the wheel - yet the wheel is still muddy...) How well the mud holds to the wheel, in this sense, will change over a short time.

ie. You can pick up a lump of mud on the end of a stick and watch as it falls off. The stick is still muddy.

The thing to realise is that centripetal force is a resultant force, not an applied force.

10. Nov 21, 2016

### CWatters

In the above "V" is the velocity relative to the axel? But if our wheel is rolling isnt it the velocity relative to the contact point with the ground that matters? Isn't that the point at which mud at the top of the wheel is revolving around?

11. Nov 21, 2016

### Cutter Ketch

Oops. Yes. Dang. Back to the drawing board.

12. Nov 21, 2016

### Simon Bridge

I think this is a neat project for an investigation at school level.
I wonder if it has been formally investigated - probably.

13. Dec 1, 2016

### Simon Lorimer

This is the closest I can find. I think this suggests that the important thing is the way that the water (in this case) breaks up as it leaves the wheel as is suggested by people above, though the details of I am a little less clear on. I need to admit that I haven't read the whole thing!

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