Why do the wheels on a stagecoach sometimes appear to be going backwards when traveling forwards?

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pferde IS RIGHT. It is called the strobe effect. It will not work in natural sunlight, which is continuous,but it will work on film or in artificial light. For instance, lets say you have a spoked wheel on a car or a wagon. If you could get it to spin clockwise at exactly 60 revolutions per minute under artificial electric light that is generated by the power company at exactly 60 cycles per second, then the same spoke will be in exactly the same position every time the light hits it, and the wheel will look like it is not spinning at all when it actually is. If the wheel is spinning slightly faster than 60 revolutions per minute it will look like it is spinning clockwise very slowly even though it is going very fast. If it is spinning at slightly less than 60 rpm then it will look like it is spinning slowly backward when we know it is spinning forward very fast. Remember, light from artificial light sources is not continuous, but actually blinks 60 times per second, which is much too fast for our eyes to see, so it looks like a continuous stream of light, but it is actually blinking like a strobe light. Only when spinning objects are in the light do we get the strange effect of them spinning backward when they are in fact spinning forward. Lets say you have a strobe light and you set it at 1 blink every 2 seconds. If your friend stands in one spot and spins around in a clockwise direction once every two seconds, and every time the strobe flashes you see his face, it looks like he is not spinning at all. But if he spins slightly slower than the strobe is flashing, it will give the effect that he is turning in the opposite direction. This is why people dancing under strobe lights look like robots. The movements look sudden and jerky and people seem to change positions instantaneously when in fact they are moving rather smoothly. Our eyes cant see them moving in between flashes. The same holds true for the wagon wheel. If the rpm of the wheel doesn't match the cycles of the strobe or the frames per second of the film, it may look like it is spinning backward when we all know it is moving forward.

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Our eyes don't focus quck enough to see it go all the way around. So when the wheel gets to a resonance or close to one. Our eyes will try to sync with the spokes but it will appear to be going backwards.

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It sometimes looks that way on TV because the framerate (number of frames shown per second) doesn't always exactly match with the rate at which the wheel is turning. If the framerate and the wheel revolution rate was exactly the same, the wheel would appear to be still. It's an optical illusion.

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This happens only when watching a movie (on tv or in the theater), not in real life. It has to do with the fact that a movie is really a series of frames/pictures, projected in really fast sequence. At a specific speed, the frames of the movie will be taken at exactly the interval that it takes for the wheel's spokes to come out in the exact same position... so it'll seem as if they're stopped... or at a slightly different speed they'll appear to go backwards.

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Optical illusion due to limitations in our eyesight. Try watching different wheels on cars on the highway(carefully tho) and then blink your eyes while watching. It will seem as if you can see the wheels stop if just for a brief second. Another illusion.
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