You have seen it in countless car advertisements and well-polished movies / programmes about cars: As the car is accelerating, the shiny metal alloy wheels seem to slow down, and briefly turn backwards, before becoming a big blurry mess again.

But how? How? And how come have you never seen that happen in real life before? And why does the article-writer insist on using braindead rhetorical questions instead of just getting on with the blasted article?

Anyway, this effect is known as the 'wagon wheel effect', or 'temporal aliasing'

You can see it in many different circumstances, where something rotates. Take this fantastic example:

Why?

Imagine a 3-spoked alloy wheel. The wheel is symmetrical, which is quite important. Now, imagine that you are looking at the wheel as it is fixed on a car, rolling along at high speed. You won't be able to even tell how many spokes the wheel has, as it is all a blur. If you were to take a picture of the car with a very short shutter time (1/1000 of a second usually does it), and look at the image, you can see and count the spokes, because you will have frozen the motion.

When working in film or television, you aren't actually capturing the motion, you are capturing a series of still frames. In the case of television, 29.9 frames per second (let's call it 30 fps, for the sake of simplicity). That means that if your camera happens to take a picture every time the wheel has turned a 1/3rd, 2/3 or full revolution (because the axis of symmetry is every 1/3rd of the wheel. A 4-spoked wheel would require 1/4th of a rotation etc), it would appear that the alloy wheel is standing still, while the tyre is whizzing along, pulling the car with it.

If your camera's shutter aligns perfectly with a rotation that can be devided by 1/(the number of spokes), the wheel appears to stand still. If there is an offset, it appears to turn slowly forward or backward, depending on the timing difference.

How?

The easiest way to capture the effect on film is to accelerate slowly - that way, your car's alloys will definitely align with the camera's shutter time, and you will get the slowly-forward-to-still-to-slowly-backward motion. You could also let the car roll, so its deceleration causes the same effect.

A more advanced way to do it, is to use mathematics. You will need to find out how long the circumference of the wheel is, and how many spokes the wheel has.

If a wheel has a circumference of 2 meters (that would be normal for a regular saloon car, I believe. Corrections welcome), it will do a full revolution every 2 meters travelled. On a 3-spoked alloy, the wheel crosses the axis of symmetry every 2/3 meters. When filming with a camera that shoots 30 images per second, that means that you will want the car to be travelling 2/3 meters every 1/30 second, or a multiple thereof. In other words: at 20 meters per second, or 72 km/h (45 mph)

The formula:

Required speed = (circumference / number of spokes) / (fps)-1

Why never in Real Life™?

Actually, it is possible to see this phenomenon in real life. If you look at a car through the safety barrier (guard rail) between two directions of traffic, you might be lucky. If it is dark, and the streetlights flicker (they normally do, at either 50 Hz or 60 Hz, depending on the electrical system of the country you are in), you might also see the effect. In full daylight and with unobscured view, however, it is a theoretical impossibility.

A different example

Now that you know how it works for cars, you should also be able to explain how this awesome video works:

stunning bass-string shot from urbanscreen on Vimeo.

I'll give you a hint: The strings on a double bass vibrate somewhere in the region of 40Hz - 180Hz or so, and the camera this was shot with (the Canon 5D MarkII) shoots video at 30 fps or so...

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