Wagon Wheels: Newsletter Challenge (03/22/05)

Two possible answers: 1. They are rewinding a taped movie 2. The images are made up of discrete frames. As such, the frames are not syncronized with rotations and the images will, particularly in relatively slow rotating wheels, have a lead that is long enough to show more than a 180 deg change. Hence the rotation will appear backwards merely because subsequent frames show >180 deg positions.

Films shot with a typical motion picture camera expose one frame every 24th of a second... Let's take a simple wheel with only 1 spoke. The wagon is going left to right so the wheel goes clockwise. In frame 1 the spoke is at the noon position. If the wagon only travels enough of a distance to put the spoke at the 11 o'clock position on frame 2, 10 o'clock on frame three and et cetera, then the wheel will appear to be going backwards. Adjusting the shutter on the camera can minimize or maximize this effect, as can longer focal length lenses. Quickly panning the camera (which means left to right movement on a tripod head) with a long lens can introduce the "picket fence effect." An object will jump from position A to position C without a B position in-between. Cheers! Steve.

Films shot with a typical motion picture camera expose one frame every 24th of a second... Let's take a simple wheel with only 1 spoke. The wagon is going left to right so the wheel goes clockwise. In frame 1 the spoke is at the noon position. If the wagon only travels enough of a distance to put the spoke at the 11 o'clock position on frame 2, 10 o'clock on frame three and et cetera, then the wheel will appear to be going backwards. Adjusting the shutter on the camera can minimize or maximize this effect, as can longer focal length lenses. Quickly panning the camera (which means left to right movement on a tripod head) with a long lens can introduce the "picket fence effect." An object will jump from position A to position C without a B position in-between. Cheers! Steve.

As reported in the 03/29 edition of Specs & Techs from GlobalSpec:

This is due to an effect known as aliasing, whereby the frame rate is not fast enough to capture the correct direction of rotation. Each frame (1/24 second apart in most American movies) is captured when the wheel has gone approximately 7/8 of the way around. This results in the wheel appearing to have traveled backwards 1/8 of a turn in each successive frame. This is an important concept in data acquisition, for which the Nyquist theorem states that the data sampling frequency (in this case, the movie frame rate) must be at least twice the acquired signal frequency (i.e. the stagecoach wheel rotation) for meaningful data.

one word : aliasing. QED

How to explain to kids?

Get a variable frequency strobe light and show them while you explain it.
Let them play with it. They'll figure it out.