Finding the relationship between speed of a car and rate of rotation of its tyres

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

08 September 2024

After reading last week’s article, Peter Mwaniki asked me how he can work out how fast the wheels of his car rotate at a given speed. Before showing the calculation, I must reiterate something: the belief that vehicles with large wheels move faster than those with small ones when the two are going at the same speed is completely and totally not true. It is actually utter nonsense!

With that out of the way, to work out the rate of rotation (not speed of rotation) of a car’s wheels, we need to know their diameter. I asked Peter about his car but he did not respond in time. Still, there are two ways of finding out: simply measuring them or working it out from the size of the tyre.

 My car’s tyres are labelled 195/65R15. This means that the width of the tread (the part that touches the ground is 195mm and the side wall is 65 per cent of that width. The last number is the rim diameter in inches.

You can try and work out the diameter from that information, but I chose to simply measure it. It is 62cm. This works out to a circumference of about 195cm. Therefore, for every rotation of the tyres, my car moves over a distance of 195cm. Note that this figure of “195” is not from the “195” in the size! It is just a coincidence.

When I am doing, say, 90km/h, how many rotations do the tyres make every minute (RPM)? First, we convert this peed from km/h to km per minute (km/min). This comes to 1.5km per minute; or 1,500m per minute; or 150,000cm per minute.

Since the circumference is 195cm, it is easy to work out the number of rotations required to cover a distance of 150,000cm. It is simply 150,000/195, which is about 769. Therefore, the rate of rotation is 769RPM. But please note that this is for my car, not yours – unless yours has the same size of tyres as mine!

My neighbour has a bigger car than mine. Its tyres are 255/55R19. I measured the diameter and found it to be 72cm. Doing similar working as above reveals that, when she is driving at 90km/h, her tyres rotate at 662RPM.

Clearly (and obviously), the bigger the wheels, the slower the rate of rotation required to reach a given speed. A trivial question arises: when driving forward, which direction do the tyres rotate?