Wheels appearnig to rotate backwards on film

Can anyone offer an explanation as to why wheels on cars, wagons, etc. appear to be spinning backwards (and rather slowly) on film? I cannot figure out what optical illusion is going on here.

It is the shutter speed that gets you. During the time that the shutter is closed, the wheel makes almost one complete revolution (or one and almost one, or two and almost one, etc.) Each new frame shows the wheel at a point where it is almost back to the same rotational position it was in in the previous frame. This gives the appearance of the wheel turning backwards.

The closer the “almost” is to the position in the last frame, the slower the wheel seems to turn.

By the way, this effect shows up in everyday life too, not just in movies. I often notice it on the freeway at night, caused by the steetlights flickering 120 times a second.

In engineering-speak, this effect is called “aliasing.” You’re sampling something at a rate that’s not fast enough to catch its true speed. If you don’t, you’ll see effects at a rate that’s the difference of the two frequencies.

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Here is Cecil’s column on this

And here is the most recent Comments on Cecil’s Columns thread on this topic.

Mort’s pretty much got it, except that the wheel doesn’t have to go almost completely around between each frame. It only has to rotate enough so that one spoke rotates almost to the position of the neighboring spoke between each frame. The wheel then looks almost exactly like it did in the first frame, but the new spoke will be shifted a little clockwise or or CCW from the old spoke. We interpret that shift as motion of the original spoke.

Actually, because of multiple spokes, the wheel need not make almost a complete revolution.

For example, a wheel could be just short of half a revolution (say 49%). So the spoke that was at the bottom of the first frame would be almost at the top in the next frame.

If you have a wagon wheel with 10 spokes, you would get the effect if the wheel had revolved 9%, 19%, 29%, … 99% of the way around. The more spokes the wheel has, the greater the chance you have of the effect.

[This is based on the assumtion of uniformity in the spokes]

with spoked wheels, the wheel need only turn a fraction of a rotation (that fraction being 1/[number of spokes]) between consecutive frames.


[hijack quiz]
Well, I once saw the effect in braod daylight. Can any of you guys figure out how this might have occured?
[/hijack quiz]

My guess is that it has to do with the angle of sunlight. The spokes probably reflected sunlight only when it was at a certain location, so even though the wheel was spinning, the spokes appear stationary. As the car moved, this position changes, so it could appear to spin backwards slowly.

You often see this effect on helicopter rotors and propeller blades. The propellers may be spinning too fast to see, but you see two “blades” which are the angles at which the blades reflect sunlight.

A similar effect happens when you see a TV image of another TV or computer monitor. The scan lines on the second TV don’t match up with the camera’s shutter, so the image appears to flicker.

Good one, scr4. I due to drive through Camp Pendleton here in a few minutes, so I’ll keep my eyes peeled.

But the effect I saw was of wheels rotating backwards in sunlight.

sorry to spoil your glory scr4, but cecil already mentioned that in his column…

I thought he did, but I can’t find the article. Have you got the URL? The one dqa posted only talks about the aliasing effect.

Gran Turismo 3: A-spec actually accounts for this. You can see it in the game or during replays. How badass is that?

Might that not just be a side-effect of the frame rate and that the wheels are modelled in enough detail to have spokes?

Mangetout, I hope that you are referring to my post, or else I’m gonna sound like a real jackhole. But “frame rate” and “modeling” makes me think “video game”, so here goes.

GT3 runs at a smooth 60fps. And not only are the wheel spokes intricately detailed, but you can even choose from several dozen different styles of them.

So if the game properly models the wheel rotation, the backwards-spinning effect will be a side effect. It’s impressive that the game has much detail, but it’s not like someone said “wheels usually look like they turn backwards, so let’s simulate that effect in our game.”

It’s that the game is simulating (aspects of) the real world accurately enough for emergent phenomena to be duplicated.

Similarly, I played around with a few 3d modelling programs a while back; some of these accurately model refraction in transparent objects (and let you set the refractive index) - so I created an opaque tube object and a few transparent lens-shaped obejcts and made a working virtual telescope.