Why Do Car Wheels Rotate The Wrong Way In A Movie?

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

11 September 2005

Charles Maina has made an interesting observation: when a car is accelerating in a movie or on TV, the wheels appear to slow down, stop and then rotate in the reverse direction. He wants to know, “Why does this happen? Are my eyes doing tricks on me?”

To understand this phenomenon, we begin by looking at how a motion picture is created. The camera takes very many pictures in succession and these are recorded a length of film or on a magnetic tape. When watching the movie, the pictures are replayed at the same rate that they were recorded. If the rate is high enough, an illusion of smooth motion will be created. Movies are recoded at 24 pictures (or frames) per second (fps) and TV at 30fps.

Suppose the wheels of the car are making one complete rotation every second, then in a movie recorded at 24fps, each successive frame will capture a 15 degrees advancement of the wheel. This is simply 360 degrees (full circle) divided by 24 – because there are 24 pictures in every second.

As the car accelerates, the rate of rotation of the wheels increases. When it reaches 12 rotations per second, the camera will capture two frames in every rotation. That is, between any two frames, the wheels will have made half a turn. When replayed, the tyres will appear to be vibrating back and forth.

Suppose now that the car accelerates further and the wheels now make, say 18 rotations per second in a clockwise direction. From one frame to the next, the wheels will make three quarters of a rotation. When the film is replayed, the first picture will show the wheel at, say, the 12 o’clock position.

In the second frame the wheel will have rotated three quarters of a circle to the 9 o’clock position. The third shot will have the wheel at 6 o’clock and so on. That is, it will appear as if it rotating anticlockwise – from 12 to 9 to 6…

When the car accelerates to 24 rotations of the wheel per second, every frame of the movie will capture the wheel at the same position. That is, it appears to be stationary. At a slightly faster speed, the wheels will appear to be rotating slower than then car.

This apparent reversing of the tyres occurs when the wheels rotate at 12 to 24 cycles per second (for movies). After 24 it disappears and repeats again between 36 and 48 rotations per second and so on.

In the case of television where the pictures are take at 30fps, the first reversal occurs between 15 and 30 rotations per second, then from 45 to 60 and so on. But at which speed (in kilometres per hour) does this illusion occur? Well, that is a story for another day.