Some people say you get maximum acceleration at any speed with the engine at peak power, and some people say it’s peak torque from the engine that delivers the maximum possible acceleration.
As hypotheticals go – I can see they’ve both got merit. But they can’t both be right. So let us unleash some righteous jihad on bullshit using the hi-tech miracle of physics.
First I want to be very clear what I mean by ‘maximum acceleration’. Obviously cars operate through a great many speeds, and the maximum possible acceleration obviously varies with speed. You typically get higher accelerations at lower speeds.
What I’m talking about is taking a snapshot in time, with the car at some arbitrary speed – and then working out how to get the maximum acceleration out of the car at that speed. I’m going to use 75 km/h here (that’s about 45 mph) – but you can use any particular speed – the actual amount of acceleration possible will change, but the revs you need to achieve it will not.
Acceleration depends on only two things: the mass of the car, which is generally pretty constant, and the accelerative force the driveline is capable of applying. That’s Newton’s second law of motion.
And of course you need to subtract any resistances the car is battling against – like rolling resistance of the tyres, and aerodynamic drag, which is hugely speed dependent.
There’s also gravity, which helps if you’re running downhill, and hurts if you’re slogging uphill.
Three things come out of your engine: Power, torque and revs. Power is conceptually complicated, because you can’t see or touch it, but it doesn’t have to be. Power equals torque times revs. It’s that simple – but you have to get the units right.
I’ve done a whole video on this but in brief, you balance everything up by getting the units right. It’s easy. Kilowatts equals Newton-metres times rpm divided by 9549. If you work in imperial units in your neck of the woods, horsepower equals lb-ft times rpm divided by 5252.
I chose the i30 SR as a demonstrator of sorts here for a reason. Because 75 km/h is real interesting in the i30 – first gear is a non-starter, obviously, because the engine would be revving at over 10,000 revs. Good luck with that. But you could easily be in second, third, fourth, fifth, sixth or even seventh at 75 kays an hour.
If you’re in second, the engine’s at 6000rpm making its peak of 150 kilowatts. But third to seventh is interesting. In third, you’re at 4100 revs, and in seventh you’re at 1600 – so the engine’s making its peak torque in all gears above third. 265 Nm. Because the SR makes peak torque from 1500 to 4500rpm.
So – here’s the bottom line: Engine at peak power at 75 kilometres per hour delivers 620 kilograms of tractive effort – thrust, if you like). Engine at peak torque (at 4500rpm) delivers 520 kilos of thrust, and engine still pumping out peak torque, but at the lower limit of 1500rpm this time, delivers only 170 kilos of thrust.
This correlates pretty neatly with the experience of driving the car. Get to 75 in manual mode, upshift to seventh, floor the throttle. It’s just bogging down all over town. Downshift to second, repeat the experiment: big difference.
So you can very clearly see that, provided you can find the right gear, maximum acceleration at any particular speed can only ever occur when the engine makes peak power – because peak power at the engine delivers peak torque at the driving wheels. Every time.