Wagon-wheel effect

What to observe?

When this page has loaded, the neighboring demo is in "auto run” mode: the wheel rotation smoothly varies between standing still and a maximum speed of 120 rotations per minute (120 rpm, indicated at top right). The wheel rotation, however, looks quite different: it seems to slow down to standstill when the maximum speed of 120 rpm is indicated! It helps to know that the wheel is rendered with standard movie speed: 24 frames per second.

What to do

With the "thumbs” of the two vertical sliders you can set the speed, the right slider is for coarse adjustment. When you begin to adjust the speed yourself, "auto run” switches off. Now you can observe that increasing the rotation speed, starting from zero, indeed initially speeds up the wheel, but then it begins to slow down! Find the speed (≈120 rpm) where the spokes stand still (the left slider helps with fine adjustment) – but observe that the centre, and certain cute irregularities around the wheel still move. This tells you that the wheel still rotates, but because of the simulated slow movie speed of 24 frames per second the spokes seemingly stand still, and can even go backwards if you speed up! There are additional standstills at higher speeds, here you can check this around 240 rpm.

This is what you may have observed in movies (especially in Westerns with prominent spoked wagon wheels). It never occurs in direct observation under daylight (though there is a little discussion in that respect).

Comment

For this effect to occur, the display needs to be presented discontinuously – it may not be visible, but the wheel (or anything in a movie or on TV for that matter) moves in jerks. If these jerks occur fast enough (e.g. around 20 times per second) our visual system, namely its motion department, interpolates the intervening missing positions.

This interpolation relies on a "nearest neighbour” principle – thus, if the displacement of the wheel spoke from frame to frame is so large, that it is closer to the (former) next spoke than to its (former) original, our visual system assumes that the opposite motion direction. This implies, of course, that the spokes are fully identical.

Similar effects occur with stroboscopic lighting (see next page), and indeed this is used to measure the speed of rapidly rotating machinery, for instance an airplane propeller blade. Technically, the entire effect is a case of "aliasing”.

Sources

Wikipedia: Wagon-wheel effect