Why The Wheels of A Car May Appear to Rotate In Reverse – In Real Life


The Sunday Nation


09 October 2005


A few weeks ago, we looked at the optical illusion where the wheels of a car appear to be rotating in reverse in a motion picture. Now Charles Maina (who started the discussion) wants to know at what speed (in kilometres per hour) this effect is seen. He protests: “You promised to explain it on ‘another day’. That day may never come!”

As explained, since movies are recorded at 24 frames per second, the wheels of the car appear to move in reverse if they are making between 12 and 24 rotations per second. To find out the corresponding speed in km/h, we need to determine the total revolutions made in one hour and multiply that number by the circumference of the tyre; thus:

There are 3,600 seconds in one hour. Therefore, at 12 rotations per second, the wheels make 3,600x24 = 43,200 rotations in one hour. The diameter of the wheels of a regular family saloon with 175-60x14 tyres is 56.6 centimetres, thus the circumference is 178cm.Therefore, in one hour, the car will move 178x43,200cm = 7,689,600cm = 7.7km along the road. That is, the car moving at 7.7km/h.

A similar analysis using 24 rotations per second yields a speed of 15.4km/h. Therefore, when the car in a movie is between 7.7km/h and 15.4km/h, its wheels will appear to be rotating in the reverse direction. From 15.4 to 23.1km/h the tyres will rotate in the forward but after that, they will again reverse until 30.8km/h is reached.

But Peter Munyao adds: “…this illusion is also observed in real life. I have seen it in the streets of Nairobi especially in the evenings. How do you explain that?”

Actually, Peter, you can only see the illusion in the evening, at night or early in the morning when the streetlights are on.

The reason is that the electricity supplied by Kenya Power and Lighting oscillates to and fro – that is, it moves “forward”, stops and then “reverses” – 50 times every second. Now streetlights are fitted with fluorescent lamps. This type of bulb is very sensitive to fluctuations in the flow of electricity.

When the current stops, even for a very short time, they go off. So, when supplied with KPLC’s oscillating electricity, the fluorescent bulbs will go on when the current flows “forward”; then off when it stops; and on again when it moves in “reverse”. Since the back and forth cycle is repeated 50 times per second, the lamps flicker 100 times every second.

Now, when you view a wheel illuminated by this flickering bulb, you see it only when the bulb is on. Therefore, it will appear to move in reverse when it is rotating at between 50 and 100 rotations per second. At what speed does this happen? I leave that for you to work out.

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