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It has been a busy last week (27th June - 3 July) and have not got as much work done as one would like.

I have started to work on calculating the final statistics for a car. Such as 0-100 km/h times (0-62 mph). In fact the acceleration times is first thing I have set myself to work out (and are still in the midst of writing the calculations for). So first question first, What actually makes the car accelerate? The force of the tyres pushing against the ground and using Newton's second law F=ma and a bit of jiggery pokery we can work out how fast a car would accelerate with a given force and known mass (a=f/m). That's all great, but how do you get the force at the edge of the wheels?

Well, we need to calculate the wheel torque, which is why torque matters. Torque is measured as force at a distance from a pivot, in Newtons Meters (Nm) or Foot-pounds (ft-lb). Once we have the wheel torque we can divide it by the wheel's radius and calculate the force at the edge of the tyre.

Example:

Torque / Radius = Force

4000 Nm / 0.3 m = 13333.3 N

Force / Mass = Acceleration

13333.3 N / 1000 kg = 13.3 m/s^2 (1.35g)

So torque does matter! But only at the wheels. The job of the gearbox and differential is to multiply the crank torque. If the gearing reduces crank RPM to wheel RPM by 9x you also get 9x the torque at the wheels. If we have 2 engines, a low revving but 'torquey' V8, and a high revving 'torqueless' L4 that both produce peak power of 200kW at differing RPM.

V8: 2000 RPM - 200kW - 954.88 Nm

L4: 8000 RPM - 200kW - 238.72 Nm

We can work out the torque from these figures, as power is just a function of torque by RPM.

Lets work out how fast our wheels would be turning at 100 km/h. It takes the wheel above with radius 0.3m, 530 revolutions to cover a km. At 100 km/h we would be covering 1.66 km a minute. Then calculate a gear ratio to allow us to have peak power at 100 km/h:

WheelRPM = 1.66 * 530 = 883.3 or call it 900

So what gearing would we need:

V8: 2000/900 = 2.22 (Reduce Crank rpm by 2.22)

L4: 8000/900 = 8.88 (Reduce Crank rpm by 8.88)

Which would give us wheel torque of:

V8: 954.88 Nm * 2.22 = 2119 Nm

L4: 238.72 Nm * 8.88 = 2119 Nm

So there we have it it, torque doesn't matter. If both engines produce the same power, and have correct gearing they will produce the same torque at the wheels. Of course the consistency of the torque curve through the rev range matters. The other thing I like about this is how and why higher speeds take longer to accelerate. I never really thought about it before, it is not just the build up for air resistance upon the car, but also as the gears get longer the engine torque is being multiplied by a smaller amount (longer gearing) and so the output force is smaller, and as acceleration is force/mass a small force gives a smaller acceleration. A quick bit maths shows this:

Again calculate what the perfect ratio would be for peak power at 200Km/h:

200 km/h = 3.33 km per minute

WheelRPM = 3.33 * 530 = 1766.6 again all it 1800

V8: 2000/1800 = 1.11

V8: 954.88 Nm * 1.11 = 1061 Nm

Wheel Force at 100 Km/h:

Torque / Radius = Force

2119 Nm / 0.3 = 7063 N

Wheel Force at 200 Km/h:

Torque / Radius = Force

1061 Nm / 0.3 = 3536 N

Acceleration:

100Km/h: 7063 N / 1000 kg = 7 m/s^2 (0.713g)

200Km/h: 3536 N / 1000 kg = 3.5 m/s^2 (0.356g)

So without even taking into account air resistance, the car is now accelerating at half the pace.

So now you can see how fun my general days are, and this doesn't get into weight transfer, tyre friction coefficients and all of that fun stuff. Back to work I go!