How come the wheels of a moving car appear to rotate backward sometimes?

Dear Cecil:

Two questions. First, does it bug you when people write you questions on bar napkins, like I am? Second, as we leave a stoplight in our cars and look at the wheels of the car next to us, we notice that when the RPMs reach a certain point we get the optical illusion of reverse rotation. What causes this?

Cecil replies:

After 17 years of mystery mail, J.R., believe me, the only letters that bug me are the ones that smell, bubble, or tick. I’ll tell you one thing, though — if you notice the reverse-rotation phenomenon looking out your window, you’re a lot more pixilated than I thought. Reverse rotation usually only shows up when you’re watching a movie.

Basically what you’re seeing is a strobe (i.e., stop-action) effect. A movie camera operates at 24 frames per second. If a wheel is turning at some multiple of 24 revolutions per second, the spokes will be in the exact same position every time the shutter opens. Ergo, the wheel will appear to be motionless (though possibly blurred) when the movie is played back. If the wheel now begins to slow down slightly, it doesn’t get a chance to rotate all the way around to its original position before the shutter opens again. Therefore it appears to be rotating backward.

Don’t get it? Then try the following demonstration, courtesy of Rainbows, Curve Balls & Other Wonders of the Natural World Explained by science writer Ira Flatow. Get a hand eggbeater. While rotating the handle, look at a TV picture through the eggbeater’s blades. (For best results, point the eggbeater at the TV and look through the blades the long way.) When you get to 30 revolutions per second, the speed at which a TV picture flashes, the blades will appear to be motionless. Slow down slightly and the blades appear to rotate backward. Fun for the whole family.

Incidentally, this is one of the few times you’ll see reverse rotation outside the movies. People tell me they’ve noticed it on other occasions in real life as well, but they can never recall the circumstances. I’ll concede it’s a possibility, but absent some mechanism for flickering or blinking, it’s damned unlikely. If you want to dispute the issue, therefore, be prepared to dish up some facts.

Facts au jus

Dear Cecil:

You were skeptical that J.R. could see the stroboscopic illusion of reverse rotation while looking out of his car at the wheels of other cars. You said this illusion is usually only visible in movies. Actually, there’s nothing surprising about what he saw if the cars were illuminated by artificial lighting rather than sunlight. When powered by alternating current, gas discharge lamps (which include neon, mercury vapor, sodium vapor and fluorescent tubes) flicker at twice the frequency of the power line (i.e., 120 times per second on a standard 60 cycle line). In each cycle of current the power peaks twice (once with positive voltage and once with negative) and twice goes to zero, and the light output varies accordingly.

Though 120 flickers per second is too fast for us to perceive directly, such lamps can produce stroboscopic effects. Mercury and sodium vapor lamps are widely used for street lighting, and under such lights J.R. could easily have seen what he said he saw. The effect may be less intense under fluorescent lights because the fluorescence does not die away completely between each half-cycle, but you may be able to see it if you play with a variable-speed fan lit only by fluorescent light. (I’ve often seen the effect with centrifuges in fluorescently-lit labs.) Incandescent bulbs have very little flicker because the filament doesn’t cool off much in 1/120th of a second.

“Fluorescently-lit labs”? Such language. Nonetheless, Cecil is prepared to concede you’re right, not because you’re a PhD — hey, we all God’s chillun roun’ here — but because he and Mrs. Adams spent a hair-raising hour driving like maniacs on the expressways trying to find out if the phenomenon in question actually occurs. Alas (for me), it does.

To tell you the truth, Mrs. Adams raised the possibility of reverse rotation being caused by flickering street lights prior to the publication of the original column. But I blithely dismissed the idea on the grounds that what most people think is reverse rotation is really just reflections off the hubcaps from passing street lights. Indeed, having done the research, I remain convinced that nine times out of ten that’s what they are seeing. The tenth time, though, no question they’re observing a genuine strobe effect.

For best results, check out a car with dark cutouts (bolt holes, whatever) spaced around the rim of the hubcaps — that way you won’t be deceived by reflections. On a car with wheels 22 inches in diameter and having eight cutouts per wheel, the cutouts will appear stationary at 59 MPH. If the car slows down slightly, the cutouts will appear to rotate slowly backward.

Incidentally, I got a dozen letters on this topic in a single mail. You guys are such wankers. At the Straight Dope, however, we don’t let mere ego get in the way of the facts.

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