A Speedometer Is Only Accurate If Correct Tyres Are Fitted

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

17 April 2005

In last week’s article I stated that if you fit big tyres on a small car, it would move faster than the speed indicated on the speedometer. Many readers have requested for a detailed proof of this, so here we go…

I also stated that the speedometer shows the speed of a vehicle and not the rate of rotation of the wheels. Thus a bus and a car moving at 80km/h will cover equal distances in equal times – none is faster than the other. This appears to be the source of the apparent contradiction. To understand it, we need to look at the working principle of a speedometer.

The Speedo cable is connected to the output shaft of the gearbox. Thus, strictly speaking, the speedometer measures the rate of rotation of this rod. However, the vehicle designer calibrates the display so that it shows the speed of the vehicle when the car is fitted with the recommended size of wheels – and when the tyres are in good contact with the road.

If a car is lifted off the ground and put in gear, the wheels will rotate and the speedometer will show some speed – but obviously, the vehicle will not be moving! This is what the “Michuki Compliance Inspectors” do when checking that a Matatu’s speed governor is doing its job.

So what would happen if you fitted your car with the wheels that are larger than the recommended size?

The diameter of the wheels of a car is about half a metre – 50cm. Thus the circumference (the length along the outer surface) is about 157cm (50 multiplied by 3.14). So, when the wheels make one complete rotation, the car moves only 157cm on the road. The next question is; how many rotations do the wheels make if the car moves one kilometre? One kilometre is equal to 100,000cm, thus the answer is 100,000 divided by 157, which equals 637 rotations.

Therefore when the car travels for 80km, the wheels will make 637 x 80 = 50,960 rotations. Thus when the speedometer indicates, 80km/h the tyres are making 50,960 rotations per hour (=849rpm). What if we fitted bus wheels on the car?

Obviously, the relationship between speedometer reading and the number of wheel rotations per hour does not change when the tyres are changed. When the Speedo shows 80km/h, the wheels will be making the same 50,960 rotations per hour. Now, the diameter of the wheels of a bus is about 75cm, therefore their circumference is about 236cm.

50,960 rotations of a tyre whose circumference is 236cm translate to about 12,000,000cm = 120km. Thus the true speed of the car will be 120km/h even though the speedometer reads 80km/h.

Obviously, it is not practical to fit bus wheels on a car, however, this example explains the effect quite well. The important thing to remember is that the speedometer is only accurate if the vehicle is fitted with the size of tyres recommended by the manufacturer.