# What’s the difference between power and torque?

Here is another great pub debate; does your car accelerate most at peak torque or peak power?
Right then, if you think you know the answer then tell me why its that way.
If you really do know then this article will teach you nothing but you can nonetheless spend a few moments reading it and then write in explaining where I went wrong and complaining about my grammar.

First concept to grapple with is that power and torque are NOT two independent things, they both are in fact different ways of looking at the same thing – the output of the engine. In engineering we use each one depending on what calculation we are doing.

Torque is the twisting effort on your shaft (oo er misses) expressed in foot pounds or Newton meters (Nm). But this isn’t the whole story. I am sure you have had to undo a really tight bolt at sometime, you know the scene, there you are heaving at the spanner, the veins on your neck bulging but the bolt not budging, just sitting there taunting you. So you stop heaving and simply stand on the end of the spanner. Now here, if you weighed 180lbs and the spanner was a foot long and you had all your weight bearing down on the end of the spanner, then the torque at the bolt is 180lbsft. Which is a lot of torque. But in this example the bolt is not moving, no progress is being made, nothing is getting done.

So if we want to measure what work has actually been achieved, then we need to factor in movement too, and that’s where power comes in; power is literally torque (the twisting force) times speed (how fast its spinning) and it’s a proper measure of the ‘work done’.

If you get your car tested on a rolling road, you get presented with a graph showing engine power plotted against engine speed. The way the machine measures this is by measuring the force produced at the wheel as it tries to turn a big brake (hence ‘brake horse power’). Then, knowing how big the wheel is, it is simple to calculate the torque at the wheel. To get the power curve, this torque value is multiplied by the speed that the wheel is spinning at. Easy

If you like using traditional units then at a given rpm the power (in bhp) is torque (in lbft) times speed (in RPM) and then divided by 5252, that number is there just to make the units add up. It also means that at 5252 RPM, the torque in lbft will be the same as power in bhp – top trivia.

Well that’s all very nice but how does it relate to a car? Well, put simply the torque figure is useful when calculating acceleration, because the harder the engine twists the drive shafts and the driven wheels, the more force is transmitted through the tyres and the harder you accelerate (acceleration is equal to the drive force divided by the car’s mass). Its all about the force pushing things along.
Power is more useful when working out things like top speed, because at a given speed there is a rate of work being done moving the air out of the way and overcoming mechanical losses. It’s all about how fast things get done.

So in each gear you will get the hardest acceleration at the engines peak torque speed. If you want to test the theory, put the car in a lowish gear, maybe 3rd and floor the loud pedal (obviously on a private test track), you will get the highest acceleration when the torque is highest, then as the revs climb further past that point the rate of acceleration slowly drops, although you will be going quite fast by then and the perception of speed might make it feel like its accelerating harder than it actually is so it’s best to try this with a dataloger.

If you thought that was too hard then stop reading now, but if you want to know more read on.

It gets a little more complicated when using the two values together, for instance if you wanted to work out how hard a car will accelerate when its already doing 100mph you could use the drag value to work out the power needed to shift air out the way, deduct this value from the engine power at that speed to find how much power is left over to accelerate the car. Take this power figure and divide by rotational speed to get torque and thus find the force at the wheel available to accelerate the cars mass.

So you can work this out for your own car, take the torque of the engine in Nm, times it by the gear ratio and then by the dif ratio and you have the torque at the wheel.
You can now work out the force delivered to the road in Newtons by dividing this torque by the radius of the wheel in meters.
Now you can divide this by the mass of your car in Kg and you get the acceleration at that point, in m/s/s.
By the way, one m/s is about 2mph. So 10m/s is about 20mph. And 10m/s/s is about 20mph per second, which is 1 g, or how fast you accelerate due to gravity if you fall out of a tree.
My dear old Jag has about 450Nm of torque at 3000rpm, on a good day. First gear is 2.48:1 so the torque in first is up to 1116Nm but the speed is down to 1210 rpm at the prop shaft. Then the diff is 3.54:1 so the wheel torque is 3950Nm at a speed of 341rpm.
At this point some might point out that there are two driven wheels, well an open diff would split the torque evenly giving half to each wheel, my LSD buggers this about a bit but the two wheel torques always add up.
The radius of my race wheel/tyre is about 0.3m. So at 3950Nm results in 3950/0.3 = 13168 N of force in total. If I use a smaller wheel I get more acceleration but at a lower road speed.
My car weighs about 1700kg with me in it (which is a lot) and so the acceleration at this speed is 13168/1700 = 7.7m/s/s or about 15mph per second, or 0.75g.
Which as luck would have it is nearly correct. In reality the vehicle acceleration is slower than this because not only am I accelerating the mass of the car, but also I am accelerating the spin of the engine crank, gears, propshaft, diff, half shafts and wheels. Even if I put the car up on jacks and floored the throttle with the wheels in the air, it would take a short while to accelerate all those rotating masses up to speed. This is why light weight flywheels can improve acceleration.
You can see from all this that as the engine speed rises past the peak torque engine speed and the torque starts slowly dropping, that the acceleration will ease in proportion.
The next fly in the ointment is drag. Not all the engines effort goes into accelerating the vehicle mass and spinning up the rotating inertias. Effort also goes into simply moving the air out of the way as the car passes through it, but that’s a whole different blog post.
And also the tyres take some effort as they are bent flat at the contact patch and then spring back.

Anyway, I hope that gives you a flavour of what power and torque mean.