Why The Wheels of A Car May Appear to Rotate In Reverse – In Real Life
By MUNGAI KIHANYA
The Sunday Nation
Nairobi,
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
17560x14 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.
