The wagon-wheel effect

Channel: Pixelmaniac

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A small (and very quickly made) demonstration of the famous wagon-wheel effect.

HOW DOES IT WORK?
This illusion only occurs when the rotating disc is recorded with a camera. Depending on how far each spoke travels between the camera snapshots, the movement follows. If the inner wheel has a speed lower than 288 rpm (or 4,8 revolutions/second) it will seem to rotate backwards. The camera captured 24 fps.

To calculate the speed of rotation, one's got to consider how many spokes there are and the frame rate of the camera. Imagine that a wheel has five spokes. To remain stationary, the spokes must travel a fifth of a rotation between the camera's shots. This means that the wheel rotates 0,2 r*24 fps=4,8 rps. Rotations per second is then converted to rpm: 4,8 rps*60=288 rpm. If it moves slower, the spokes "don't make it" to the position needed for the wheel to look stationary. This means that it seems to move in the direction opposite to the rotation of the wheel. The wheel seems to move in the "correct" direction if the rpm is higher than 288. But since the "stationary effect" also occurs at 576 rpm (the spokes skip two steps), increasing the rpm from 288, it accelerates, decelerates and accelerates in the opposite direction and then back to a full stop. If x=432 ((3*288)/2), it has reached its dual point. I moves clockwise and counter clockwise at the same time with equal velocity. It stops. This is the point between "decelerates and accelerates in the opposite direction". That's what you saw in the last part of the video.

So, in the video, there are two wheels with different numbers of spokes.
The rpm required for the 8-spoked wheel to be stationary is 180.
If the rpm is higher than 180, the 8-spoked wheel will move "forwards", BUT the 5-spoked wheel will move "backwards".
(About 180 rpm (less than) x (less than) 288 rpm.)

This video and wheel design can both be downloaded from Wikimedia commons:
Wheel: https://commons.wikimedia.org/wiki/File:Wagon-wheel_effect.jpg
Video: https://commons.wikimedia.org/wiki/User:Pixelmaniac_pictures#Video_miscellanea

LICENSE:
This video (footage) is in the public domain.
The music link(s) must be credited if used anywhere on Youtube and credited properly (in a manner specified by the license) if used anywhere else. Click on the link(s) to check which license applies to it (them). If a file is licensed under a CC0 or PD license, you're not required to credit it.

NOTE:
It has recently been observed that Musopen had incorrectly accepted a copyrighted recording to its library. I am sorry for this error and I advise anybody who wants to redistribute this video to remove the music. The video available on Wikimedia commons has been replaced with a version without sound.

Music:
Clair de lune by Claude Debussy.
Link:
There is no page to link to.

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