 |
 |
Wagon Wheel Illusion
Name: Robert M.
Status: other
Age: 50s
Location: N/A
Country: N/A
Date: 5/28/2003
Question:
Please explain the phenomena where propeller blades or wagon-wheel spokes appear to
change direction of revolution when the rpm is changed or varied.....is it just my eye's inability
to "track" the speed of the blurred objects?
Replies:
Robert,
What you describe ordinarily does not happen if you are viewing the rotating object under a continuous
light source like the sun. However, if the primary illumination source is flickering on and off -- like
that of a fluorescent light or a stroboscope lamp -- the position of the rapidly rotating wheel is
alternately illuminated by very fast pulses of light. If those pulses are synchronized so that each
occurs when the wheel is in exactly the same position (for example, once per revolution), the spokes
will appear to be stationary. If the pulses occur slightly faster or slower than the rotation speed,
the wheel is illuminated earlier or later than it was in the first condition. If earlier, the wheel
appears to turn backward; if later, the wheel appears to turn forward.
There is a bit more to this explanation because the flash rate does not necessarily have to exactly
match the rotation rate for the object to appear stationary. If the flash rate is a fraction or a
multiple of the rotation rate, the object can also appear to be motionless.
The same principle applies when a movie camera and projector are used. The shutter of the camera and
projector affect the apparent rotation rate observed. The movie effect is most pronounced when the
"stagecoach wheels" are slowing down.
If the flash rate is adjustable (as it is with a stroboscope) one can view rapidly rotating objects
in a manner that makes them appear to be standing still. That is the principle of the timing light
used to set the firing interval of and engine.
Regards,
ProfHoff 677
Your eye's ability to "track" (this is between about 1/15th and 1/40th of a second depending upon the
individual) is only part of the phenomenon. Another part is the eye's image retention, which is about
1/10th to one second or so -- this is the effect of "seeing" the image of a flash after you close your
eyes. If the flash is colored you will "see" the color turn into its complementary color, e.g. red to
green. The major part is the "strobe" effect.
For simplicity consider a two-blade propeller -- the blades 180 degrees apart. Now suppose you have a
flash gun that flashes a 1/1000 sec. light pulse, and you have a controller that lets it flash from 0
pulses per second to as fast as you need, say 500 flashes per second. You are in a dark room so that
you cannot see the blade except when the flash gun fires. Suppose you start with the blade in a
vertical position and it is not rotating. You just see the blade in the vertical position, whether or
not the flashes occur 1 time per second or 500 times per second. Now suppose you start the blade
rotating at some number of "rpm's" and you match those "rpm's" with the frequency of the flash. When
the blade is rotating at exactly the speed where the top position is superimposed with the position of
the bottom half, it will appear to you that the blade has not moved, because you cannot "see" that the
top and the bottom parts of the blade have exchanged places. That first occurs when the flash frequency
is exactly 1/2
the number of "rpm's" of the blade's rotation. The same thing will happen when the flash frequency is
at intervals: 1/2, 2/2, 3/2, 4/2, ... and so on. If the flash frequency is a little slower than the
blade's "rpm's" the blade will have advanced just slightly more than superposition, and the blade
will appear to be moving "forward". On the other hand, if the flash frequency is a little faster than
the blade's "rpm's" the blade will not quite have caught up to the image position where the blade
image appears superimposed, and the
blade image will appear to be moving in a direction opposite that of the blade's rotation (i.e.
backwards). Of course, if the blade has more "spokes", superposition will occur at smaller and
different intervals of the blade's "rpm's".
There is a related phenomenon that happens when you look through two sheets of window screen that are
tipped with respect to one another. Then you see alternating lighter and darker lines whose separation
depends upon the viewing angle and the mesh of the screens.
Vince Calder
Click here to return to the General Topics Archives
| |
Update: February 2012
|
|
