Two Guys Rally

Engine performance: Torque and Horsepower
[ April 8th, 2008 ] By: Mark Ozimek Posted in » Technical Articles

Time and time again, I see people all over arguing the endless debate in engine design: Torque vs Horsepower, and which one is better. Although I am aware that ending this debate is impossible, and trying to do so would be quite insane, I wish to share what the engineer in me thinks matters most.

A quick crash course in physics for those who are not familiar with the topic. There is a very simple relationship between acceleration, mass and Force: F=m*a. Bear with me here, we have a lot of fun material to cover.

For cars, the force that causes the car to accelerate and decelerate (braking!) is generated by the tires and the ground. There is a torque at the wheels that causes the wheels to rotate. The fricton between the tire and the ground converts this torque into a force. This force is equal to the torque applied to the wheels divided by the radius of the wheel, with this radius measured from the center to the tire’s contact surface with the ground. This is assuming that the tire is not slipping. If it is slipping, then the force is dependant upon a lot of other things, like the surface conditions, friction coefficient, how fast the surface of the tire is sliding across the ground, temperature, and a few others.

With our intentions of rally racing, we obviously want the most acceleration possible to get out of slow corners quickly, while still having a fairly fast top speed for the straighter sections of the course. We can rewrite the relationship given above to be a = F/m, which implies that either increasing the Force or decreasing the mass will improve the acceleration of the car. The mass would simply be the mass of the car, more commonly refered to as the weight. I won’t get into how this affects acceleration yet, since this is an article on the engine, not weight reduction.

Now since more force determines acceleration, and the force increases with more torque, you’re most likely thinking: “AHA! So torque really does detemine the acceleration of the vehicle”. You are correct to think this, but there is a catch: it’s the torque at the wheels that matters. Taking it a step further, it is the engine torque and overall gear ratio that determines the torque at the wheels. This may seem obvious, but this is why acceleration is greater in 1st gear than a higher gear, such as 2nd or 4th. The gear ratio is much higher in lower gears, causing the torque that the engine generates to be multiplied by a factor of 8-15 in first down to around 1.5-3 in fifth gear, depending on the gearbox setup.

The consequence of this is that the output rpm from the transmission is much lower in the lower gears, so it is difficult to reach high speeds in low gears unless you’re using an F1 engine that hits the rev limiter at 19,000rpm. So now we have three factors to consider, the torque the engine is creating, the gear that the car is in, and the engine speed, to determine the acceleration of the car and the speed that it is traveling at.

So where does horsepower come into play? It’s quite simple actually. Using the imperial system, horsepower, torque and engine rpm can be related very simply: HP = (torque * rpm) / 5252. That bottom number is just the combination of factors used in unit conversion, since HP is a measure of power (who would have thought?!) which is an amount of work done per unit time. As a visual representation of the relationship between these three things, consider two power sources that I will use in an example later: One that puts out a constant amount of power, and one that puts out a constant amount of torque.

Realistically, an engine’s power and torque curves will look more like this, for a well configured turbocharged engine:

Work and torque are the same thing, in a twisted sense. Work is measured by a force applied over a certain distance. Pounds is a force and a foot is distance. Say you pressed on a block with 200 lbs of force over a distance of one foot. You just did 200 ft-lb of work.

To convert it into power, the time it took to do this amount of work is needed. Let’s assume that you’re a strong guy, and managed to do 200 ft-lb of work in just a half second. This means that you generated 400 ft-lb/s of power. Way back in the day, it was decided that there are 550 ft-lb/s of power in one horsepower. This means that you just generated 0.72hp when you moved that object in a half second.

To clarify power further, consider two different power sources, a turbocharged gasoline engine and an electric motor. The gasoline engine puts out a constant amount of torque through a broad rpm range (not really, but go with it for simplification of the explanation), while an electric engine puts out a pretty constant amount of horsepower, but has a very high RPM limit. To achieve the same range in speed, the turbocharged gasoline engine needs a gearbox to vary the ratio between the engine speed and wheel speed. The electric motor does not need this gearbox, as it has lots of torque at 0 rpm and can spin much faster. The electric motor will have a pretty smooth acceleration curve. The most acceleration will be seen when starting from a stop, due to the high torque at low rpm. As speed increases, the accleration tapers off because the motor creates a constant power; at high rpm, the torque is very low. On the other hand, the gasoline engine will produce an acceleration curve that looks like a step function. It generates a consistent amount of torque through the usable rpm range. As a result the acceleration in each gear is roughly constant while speeding up. When the driver shifts to a higher gear as the speed increases, the amount of torque to the wheels drops, thus decreasing the acceleration of the car.

How does all this fancy unit conversion relate to the rally car? Well, while the torque gets multiplied and changed along with the rpm through the transmission’s gear ratios, the power stays the same, minus some losses through friction, regardless of the gear. This power that the engine puts out can be directly equated to the power put into accelerating the car, overcoming the various drag forces, moving the entire car up and down hills, and so forth. This is where I introduce another equation, one that relates Energy with mass and velocity: E = (1/2)*m*v²

To avoid getting into calculus and integrating power with respect to time, just keep in mind that energy can be thought of as the total amount of power that has been applied to the system, which in this case, is the car. The more power the engine generates, the faster the velocity changes. The change in velocity is measured as… dundunDUN! The acceleration! However, note that the velocity term is squared. As the speed increases, the engine needs to create more and more power to maintain the same accleration. This should sound pretty familiar to something we found when calculating the acceleration with the torque: higher gears let you go faster, but decrease the amount of acceleration. There is no getting around this. So now we have two relatively simple ways of finding the acceleration of a car at any given moment:

1. The torque at the wheels, found by multiplying the engine torque and gear ratio.
2. The power output of the engine and the velocity of the car.

So in the end, what is it that really does matter? To such a difficult question, I find it neccessary to give a cryptic answer: it depends on what you’re trying to do! In a perfect world, engines would have infinite amounts of torque and power, and the acceleration would be limited by the friction coefficient of the tires. Unfortunately this isn’t the case, so we must settle on a compromise between power and torque. With common engine technology, the camshaft profile and timing has the largest easily changed effect on where the engine’s peak torque is in the rpm band. Due to this limitation, engines usually focus on low end, midrange or high end torque. The low end stuff is great for getting moving, especially if you’re moving a lot of weight. Good midrange torque makes for a very drivable car in almost all circumstances. High end torque translates to the most horsepower, which is good if you want to go really fast all the time, though it usually comes with the cost of reduced acceleration. One way to avoid this compromise is to use variable valve timing, but this is out of the scope of this article.

For high speed racing, like F1, having as much power as possible is what wins races. This can be seen by the design philosophy of the engines: Astronomical rev limits to get the most amount of power out of an engine that can develop limited amounts of torque. It’s not every day that you see normally aspirated 2.4L V8’s putting out 700-800hp. They can do that thanks to the rpm that the design allows. Remember that hp = torque * rpm / 5252. We can solve for torque in this case to find that at the rev limit, the F1 engines are making around 200 ft-lbs of torque. This is still very impressive for the displacement, but not nearly as high as the power output. Conversely, engines with a very low rpm limit, like diesel engines, must generate massive amounts of torque to make any reasonable amount of power.

For rally racing, having as much acceleration as possible available to you at any moment is imperative. As such, we want an engine that has a very broad torque and power curve with good responsiveness. Gobs of torque down low, without sacrificing the top end is ideal for maximum performance in the varied conditions that rally cars encounter. As such, compromises are usually made to focus on midrange torque, which will still offer decent low end and top end power. This is the design path we will follow when we start doing engine modifications to our car.