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While off-roading on a bicycle during a rainy season, it seems inevitable that blotches of mud would stain the back of my shirt at the end of the day. I am not sure the physics behind this.

I am going forward at a speed that is directly related to the rotational speed of the wheel in contact with the ground. The mud is picked up by the wheel and given a spin. But in order for the mud "projectile" to reach my back, it would need to be travelling faster than me in the forward direction.

How is this possible?

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The centre of your wheels are travelling at the same speed as you. However the top of the wheel must be moving forward faster than this in order for the wheel to be rotating.

If you do the sums you can see that whilst the point of the wheel in contact with the ground is momentarily stationary (unless you are skidding), the top of the wheel is moving forward at twice the speed of the centre of the wheel and you.

If it helps conceptually, imagine filming your wheel using a camera that is mounted on a rod sticking out horizontally from the wheel axle. From that frame of reference the centre of the wheel appears stationary, but the top of the wheel must move forward whilst the bottom of the wheel (with the ground) moves backward with an equal but opposite velocity.

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  • $\begingroup$ There is also the effect pictured in this answer:physics.stackexchange.com/questions/51373/… $\endgroup$ – Martin Argerami Jan 31 '15 at 14:26
  • $\begingroup$ @MartinArgerami That's an interesting thought. I would have thought liquid mud would be a bit too heavy to be affected by turbulence in the air, but I could be wrong. $\endgroup$ – Rob Jeffries Jan 31 '15 at 15:34
  • $\begingroup$ Not sure about the bicycle, because the water already has the speed given to it by the wheel. But on my minivan, the back door definitely gets muddy. $\endgroup$ – Martin Argerami Jan 31 '15 at 15:58
  • $\begingroup$ Thanks, I do get the picture now. But it won't be coming from mud leaving the top of the wheel but somewhere in between the top and the centre since it needs to travel upwards as well as forward to reach my back. $\endgroup$ – Question Overflow Feb 1 '15 at 2:05
  • $\begingroup$ @QuestionOverflow Yes, I'm sure that is the case. $\endgroup$ – Rob Jeffries Feb 1 '15 at 8:37

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