## Monday, 16 August 2010

### Torque and Power

When discussing performance or simulations of vehicles, the concepts of torque and power usually come up and often get confused. Our goal in writing a simulation is to get the vehicle to behave exactly like the real vehicle, in order to do this it is vital to understand the concepts of torque and power from the engine (these concepts apply to all type of rotary engines, including electric motors).

I'm not going to give a detailed description of what torque and power are generally, you can look up on wikipedia for that, what I am going to do is explain how it relates to engines in vehicles.

A vehicle is generally something that generates torque (an engine) connected to wheels through one or more gear ratios (gear box and differential). To calculate the forward force on the vehicle from the engine you multiply the torque generated by the engine by the total gear ratio, and then divide by the radius of the tyres. That's it.

As you can see there are two things that can vary here (without changing wheels!), the gear ratio and the amount of torque the engine generates. The gear ratio simply depends on which gear you have selected, and the torque the engine is generating mainly depends on how far you have the pedal pressed and how many RPMs the engine is turning at.

You can look up the "torque curve" for common engines, that will tell you the maximum torque the engine can generate at each RPM. You can also look in the spec sheets of cars to find the gear ratios of each gear, and also of the differential (often called "final drive").

Here's a quick example:

Let's assume going 50 km/hr in 3rd gear, we want to know if we floor it how quickly will the car accelerate.

Firstly we have to work out the RPM of the engine, we need this to find out how much torque the engine is capable of generating. In my car 50 km/hr means the wheels are rotating at 420 rpm (it will depend on the size of your tyres). Also my "final drive" ratio is 2.563 and the 3rd gear ratio is 1.804. This means the engine will be turning at 1941 rpm. I now look up on the torque curve for my engine (often included in the car brochures) and it shows that at 1941 rpm the engine can generate about 325 Nm of torque.

Once we know that figure, we can then work back along the drivetrain to the wheels, multiplying the torque by each gear ratio. I end up with about 1500 Nm of torque at the wheels in this case. Dividing by the radius of the tyre gives a forward force of 4775 N. I can then use that in my physics engine to accelerate the car (it works out at about 0.3g acceleration, which certainly seems realistic to me).

You might have noticed I haven't mentioned power at all yet. That's deliberate because power has no uesful function in the above calculations. Power is easily calculated as the torque multiplied by the rotation, so after going through a gear ratio (where rotation is reduced, and torque is increased) the power remains constant (ignoring any losses).

However when discussing engines you don't want to always carry around a chart with you, so this is where power is a useful quantity. Let's compare 3 engines, a small passenger diesel that can generate 300 Nm up to about 3500 RPM, a sporty petrol/gas engine than can generate 300 Nm up to about 7500 RPM, and a Formula 1 racing car that also can generate about 300 Nm up to 18000 RPM. The engine in all three cars can generate a maximum of 300 Nm, but the performance is vastly different. This is purely because of the engine speed that the torque can be generated at. In the Formula 1 car we can use a gear ratio about 5x higher than the small diesel car to get a decent speed, but this also means in the Formula 1 car the engine torque is multiplied up 5x more. So instead of having 1500 Nm of torque at the wheels like in the example above, we might have 7500 Nm - even though the engine is generating exactly the same amount of torque.

To quantify this we simply use the term power, the Formula 1 engine has much more power than the small passenger diesel. When people say that engines with higher torque are better at load-pulling etc, it's really wrong unless you look at the gear ratios used in the application (ie the car or truck). Remember, the forward force *at the tyres* depends on the engine torque and the gear ratio.

#### 1 comment:

1. Cool stuff! Tks!