Wagon wheel

Simulator

Why the wheel turns backwards

A camera does not see motion. It takes still pictures at a fixed rate and leaves your eye to join them up. When something repeats faster than the camera samples it, the joined-up version can be slower than the truth, stopped, or running the wrong way.

• Temporal aliasing

  Sampling anything that repeats, at a rate close to its own, produces a slow false rhythm. It is the same effect that makes two slightly different musical notes beat against each other, moved into time rather than pitch.

• Spokes, not wheels

  The camera cannot tell one spoke from the next, so what matters is the spoke rate: wheel turns per second multiplied by the number of spokes. A twelve-spoke wheel aliases at a third of the speed of a four-spoke one.

• Frozen

  When the spoke rate lands exactly on the frame rate, every frame catches a spoke in the same place and the wheel appears to stop while the vehicle keeps moving. Multiples do it too: twice, three times, any whole number.

• Backwards

  Just below a multiple of the frame rate, each spoke falls a little short of where the last one was, so the pattern creeps backwards. Just above, it creeps forward instead, far slower than the wheel is really turning.

• Shutter angle changes how clearly you see it

  Aliasing comes from the frame rate, not the shutter, so a narrow shutter does not cause it. It does sharpen each spoke, which makes the false motion obvious. A wide shutter blurs the spokes into a disc and hides it.

• It is not only wheels

  Helicopter rotors, fans, propellers, strobe-lit dancers and the spokes of a bicycle all do it. Film has shown backwards wagon wheels since the silent era, which is where the name comes from.

• What to do about it

  Nothing in camera will remove it, because it is in the sampling. Change the frame rate, change the shutter angle to blur it, change the speed of the thing itself, or frame it so the wheel is small and soft.