Backward spinning wheels-an illusion
![[© Copyright Jeff Adams] Wagon wheels](wagon-wheel.jpg) Q:
I can grasp that wagon wheels, which turn in the direction of the vehicle's motion, appear to reverse their direction
as the vehicle accelerates. It's just an optical illusion, right? But why, as the vehicle continues to accelerate, does the
direction appear to change again, and then maybe again? el-rey
A: I assume you're talking about wheels turning in TV movies. Wagon wheels appear to turn backwards or forwards due to a
strobe effect. It's an optical illusion, of course; the wheels don't really reverse direction.
[© Copyright Jeff Adams] Wagon wheels
The movie is a series of still pictures that flash on and off 24 times every second. That's plenty fast enough for your brain to
think the motion is continuous because your eyes can't see the separate frames. No finite sampling rate, however, is fast enough
to capture the true continuous motion.
The wagon wheels can even appear stationary: Suppose the movie camera snaps a frame and the wheel turns just enough in the
1/24th of a second before the camera snaps the next frame so that the next spoke has rotated into the position of the first spoke.
Then the camera snaps another frame. The second frame looks identical to the first frame even though the individual spokes are
in different positions because all the spokes look alike and they line up with the first-frame positions. At this wagon speed, the
wheel doesn't seem to be turning at all in the movie.
If the wheel turns a little faster than this, the spokes seem to slowly move forward. That's because the second spoke, going a little fast, went by the position of
the first spoke by the time the camera snapped the second frame. If the wheel turns a little slower, then the spokes appear to move slowly backwards.
Thus, wagon wheels can appear to move backwards, then forwards as the wagon picks up speed. If the wagon slows down, the wheels can seem to change
direction again and go backwards. It all depends on how fast the camera snaps frames relative to the wagon wheel speed.
(Answered by April Holladay, science correspondent, October 17, 2001)
Further Surfing:
U of Southampton, UK: Sampling and aliasing
U of North Carolina: Analysis of wagon-wheel movement
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