Arrow of time
Arrow of time

TIL: How do bicycles (and cars) turn?

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It occured to me while driving a car that the act of turning direction is actually non-trivial. Reducing the case …

It occured to me while driving a car that the act of turning direction is actually non-trivial. Reducing the case to a bicycle, consider this:

  • You are pedaling your bike, and driving in the forward direction (of course). You now have certain speed and acceleration vectors pointing in front of you.
  • You stop pedaling, and decide to turn left, 90 degrees to your current direction. You turn the wheel.
  • Depending on the angle of the wheel and your speed, sooner or later you find yourself driving in a direction 90 degrees to the left, while still not pedaling.
  • You now have speed + acceleration vectors wose directions are basically completely different from the previous ones (they are perpendicular), and do so without any outside force giving you the push in the new direction. A speed vector going north suddely becomes a speed vector going west, and there is no outside force pushing you to the west.

This is trivially generalized to the case when you do pedal during the turn, and to cars.

So, what happened? Generally, by conservation of momentum (and Newton's first law), you were moving in one direction, and should continue to move in that direction until:

  1. An equal and opposite force stops you
  2. A force pushes you in another direction (e.g. to the west)

I had a hunch before entering my apartment, and a quick googling session confirmed it. It's actually fascinating and at the same time very simple (as an idea) and very complex (at its most low-level details).

The tires do the work, all by themselves, of changing your direction, i.e. your speed vector. Here's how (assuming you're turning gently enough and not skidding):

  1. On a bike, you turn your steering wheel to the left, and this causes your front wheel to turn to the left.
  2. Consider what happens in the exact place where the front tire is in contact with the ground: the first few layers of rubber (etc.) molecules are in a friction contact with the ground, they're not losing this contact without a great force.
  3. However, the tire has turned, and since the bike still has a speed vector pointing north, this stretches the tire in the north direction, trying to break the tire apart (or deform it).
  4. The elastic bonds between rubber molecules between the first few layers (which are in contact with the ground), are pulling the deeper layers to them, trying to keep the tire in its original shape. There are two components of this pull: a part of the miniature forces between those molecules are combining to create a large new speed vector in the direction perpendicular to the old one, and another part of the forces are counter-acting the previous speed vector which pointed to the north.
  5. The bike is turning, driven by the forces between the tire molecules which are trying to keep the tire in its shape.

This is why it's important to have quality tires.

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