TORQUE & HORSEPOWER

One of the most confusing (and frequently contentious) questions in the automotive realm is the difference between horsepower and torque. You may have heard any number of pithy expressions, like “horsepower sells cars, but torque wins races,” or fans of big-engine muscle cars complaining that 200-horsepower four-cylinder engines are “gutless.” Surprisingly few of the worthies who throw around comments like that, though, are actually able to define the difference. What IS the difference between horsepower and torque, and what effect do they have on how a car performs?

UNDERSTANDING TORQUE

If you stayed awake through high school physics, you may dimly recall that torque istwisting force — that is, a force that tries to cause an object to rotate around a particular axis. For example, if you turn a doorknob or spin a roulette wheel, you are applying torque to it.

If we were in physics class, we’d say that torque is the cross product of the vector of the force applied and the distance vector. The force vector is the direction in which you’re applying force. The distance vector is (at its simplest) the distance between the point where you’re applying the force and the axis of rotation. For example, imagine you are using a wrench to turn a bolt. In that case, the center of the bolt is the axis of rotation. If the wrench is one foot long and you apply ten pounds of force to the end of it, you are applying 10 pounds-feet of torque to the bolt. If the wrench was two feet long and you applied ten pounds of force at its end, you’d be applying 20 pounds-feet of torque.

What is engine torque? As you probably know, an internal combustion engine works by burning air and fuel. The energy of that combustion moves one or more pistons (or rotors), which act on the engine’s crankshaft, causing it to rotate. In a car, the rotation of the crankshaft turns the gears in the transmission, which turn the wheels. An engine’s torque is the amount of twisting force the pistons (or rotors) can exert on the crankshaft.

UNDERSTANDING HORSEPOWER

Now, what is horsepower? Again recalling that long-ago physics class, power is workperformed over time. Mechanical work represents force exerted over distance — for example, moving a 10-pound weight a distance of one foot represents 10 foot-pounds of work. Power is the rate at which that work is performed. One mechanical horsepowerrepresents the ability to do 550 foot-pounds of work per second, or 33,000 foot-pounds of work per minute. (One metric horsepower represents a rate of 75 kilogram-meters per second; a metric horsepower is about 735 watts, whereas a mechanical horsepower is equivalent to about 746 watts.)

The brighter students among us may have noticed the similarity between the units for work — foot-pounds (ft-lb) — and the units for torque — pounds-feet (lb-ft). In fact, the units are the same; the only reason they’re written differently is to avoid confusion. For an engine with a rotating crankshaft, then, one horsepower is equivalent to exerting 550 pounds-feet of torque per second.

Remember that torque is a twisting force; that means that if applying torque to an object will tend to cause the object to rotate, rather than move in a straight line. Therefore, if torque produces any work, we have to measure how much rotation it imparts (angular speed), rather than how far it cause the object to move. Angular speed is usually expressed in terms of radians per second or radians per minute (one radian is 180 degrees divided by π, or about 57.3 degrees), but since we usually measure engine speed in terms of revolutions per minute (rpm), it’s more useful to think of it that way. One revolution is 360 degrees, which is equal to 2π radians. If 1 horsepower equals 33,000 lb-ft of work per minute, then we can calculate an engine’s power based on its torque (in lb-ft) and its engine speed (in rpm):

Power (hp) = Torque (lb-ft) x 2π x Rotational Speed (rpm) / 33,000

or

Power (hp) = Torque (lb-ft) x Rotational Speed / 5,252.113

For example, if an engine produces 200 lb-ft of torque at 4,000 rpm, it has 152.3 horsepower (200 x 4,000 / 5,252.113) at that speed.

The upshot: Horsepower depends on torque and engine speed. If your engine produces more torque, it also makes more power; if you run the engine at a higher speed, it also makes more power. It is entirely possible for engine A to make more power than engine B, even if engine B makes more torque — engine A must simply rev higher to make up for its torque deficiency.

TORQUE AND POWER CURVES

Engines used for stationary applications (generators, for example) or in aircraft spend most of their lives running at a constant engine speed. As a result, they produce their full, rated horsepower most of the time. Engines used in cars, trucks, or motorcycles operate over a broad range of engine speeds, from a few hundred rpm at idle to 10,000 rpm or more at redline. Since horsepower depends in part on engine speed, the amount of power the engine produces varies quite a bit at different points in its rev range. Engineers describe the relationship between an engine’s power and rpm as the power curve.

If an engine produced its maximum torque at all engine speeds, the power curve would be a straight line: that is, increasing rpm by 50% would also increase horsepower by 50% (as long as it didn’t rev the engine beyond its redline, which risks serious mechanical failure). That is true of electric motors, but it isn’t true of internal combustion engines. We will discuss the reasons for this in more detail in a future article, but for now, we’ll just say that an engine’s torque output also varies with engine speed.

All internal combustion engines produce their maximum torque at one particular engine speed; this is called the torque peak. Above or below the torque peak, the engine produces somewhat less torque than that maximum value. Just as an engine has a power curve describing how much power the engine produces at different points in its rev range, the engine also has a torque curve, describing how much torque it generates at different speeds. The engine’s design determines at what speed the engine’s torque peak occurs, as well as the shape of the torque curve. If an engine produces a fairly constant level of torque throughout its rev range, its torque curve is said to be flat. Electric motors, which usually produce close to their full torque output from zero rpm all the way to their maximum safe operating speed, have extremely flat torque curves. (Contrary to popular belief, the shape of the torque curve is not directly related to how much torque the engine produces. Two engines can have very similarly shaped torque curves, even if one has far more maximum torque than the other does. Again, we will look more at the factors that determine the shape of the torque curve in a future installment.)

An engine can be tuned to produce its maximum torque at the low end of its rev range, in the mid-range, or at high rpm. Modern engine designers have various tricks available to “flatten” the torque curve of an engine (that is, to keep engine torque close to its maximum through a broad range of engine speeds), but any given engine will be notably stronger in one range than in others.

Since power is a function of torque and rpm, the shape of the torque curve also determines the shape of the power curve. The horsepower curve will always peak later than the torque curve, but if the engine’s torque curve is strongest at low rpm, the power peak will also be relatively low. If the torque peak is at high rpm, horsepower will also peak at lofty engine speeds.

If you’ve ever driven a car with a tachometer, you’ve probably noticed that the engine spends much of its time at speeds well under 4,000 rpm. Since the horsepower peak of almost every modern engine is higher than 4,000 rpm, that means the engine rarely has a chance to develop its rated maximum power. Therefore, in normal driving, the shape of the torque curve is often more important than maximum power.

THE REAL WORLD (SORT OF)

To see how this works in practice, let’s consider a couple of real engines: Ford’s 4.0 L “Cologne” V6 (which powered the Ford Ranger and Explorer for many years) and Volkswagen’s turbocharged, four-cylinder 1.8T engine (used in several different configurations in a wide range of Volkswagen and Audi models).

The Ford Cologne V6 was an engine of venerable design dating back to the early 1960s. The 4.0 L (245 cu. in.) version was intended for truck use, so it was tuned for strong low-end torque. Its peak torque was 220 lb-ft at only 2,400 rpm; maximum horsepower was 160 at a modest 4,200 rpm.

Volkswagen’s 1.8T was a more modern and far more technically sophisticated engine with dual overhead camshafts, five valves per cylinder, and an intercooled turbocharger.Turbocharged engines tend to be “peaky,” putting out more power at high rpm, but Volkswagen designed it to have as flat a torque curve as possible. In fact, Volkswagen claimed that the engine produced its full maximum torque from 1,950 rpm to 5,000 rpm. VW offered it in several states of tune, but the one we’ll use for our discussion is the version found in later Mk 4 Golfs, Jetta/Bora sedans, and the SEAT León, which had 180 horsepower @ 5,500 rpm and 173 lb-ft of torque.

The best way to judge an engine’s torque curve is to hook it up to a dynamometer and see exactly how much torque it actually puts out at various rpm. We aren’t in a position to do that, but we can make some educated guesses about the torque curves for both engines based on their rated torque and horsepower peaks.

As we mentioned above, the Ford engine’s rated torque peak is at 2,400 rpm. Using the equation we derived earlier, we can calculate its power output at that speed: 101 horsepower (220 lb-ft x 2,400 rpm / 5,252). The V6′s horsepower peak comes at 4,200 rpm. Using the same equation, we calculate that it has 200 lb-ft of torque at that speed (160 hp x 5,252 / 4,200 rpm). We can see from those numbers that between 2,400 and 4,200 rpm, the engine probably produces between 200 and 220 lb-ft of torque.

What about at higher speeds? We know that the engine never produces more than 160 horsepower. Even if it still produced 160 horsepower at 5,000 rpm (which is unlikely), torque would have dropped to 168 lb-ft at that speed. If it produced 140 horsepower at 5,000 rpm, that would mean that its torque output was down to 147 lb-ft. In short, the Ford engine’s torque and power both start dropping off very rapidly after the 4,200-rpm horsepower peak — the V6 was designed for low-end grunt, not high-rpm power.

What about the Volkswagen engine? The 1.8T’s peak torque begins at 1,950 rpm. At that speed, it’s making only 64 hp (173 lb-ft x 1,950 rpm / 5,252). By 2,400 rpm (the Ford’s torque peak), the VW engine’s horsepower has risen to 79. At 4,200 rpm, the 1.8T has risen to 138 hp, still well behind the Ford. The VW’s power doesn’t start to exceed that of the Ford engine until after the Ford hits its peak power. When the VW hits its peak horsepower at 5,500 rpm, torque is still about 172 lb-ft — torque has tapered off, but only very slightly. That means the engine continues to make useful power even past its power peak; its redline is 6,500 rpm, which it doesn’t have much trouble reaching.

These torque and horsepower curves are estimates based on published power and torque figures, but they illustrate the difference between the engines. Note that even though the VW’s torque curve (light green) is far flatter than the Ford’s, the Ford’s is higher over much of the rev range.

What does this mean in practical terms? Even though the VW’s torque curve is very flat, it has significantly less torque than the Ford until well over 4,200 rpm, which means that the 1.8T also has less power at lower speeds. It ultimately produces more power than the Ford engine, but not until over 5,000 rpm.

Imagine that we installed these engines in two otherwise identical cars, with the same transmissions, same gearing, and identical weight. We would discover the following:

• In normal, street driving, the car with the Ford engine would almost always be quicker than the VW-powered car. That shouldn’t be surprising — the Ford’s greater torque gives it almost 30% more power than the VW engine at low rpm, even if the VW is stronger at higher speeds.
• In a drag race over a standing quarter mile or standing kilometer, the Ford-powered car would take an early lead and would stay ahead until both cars were well down the strip. The 1.8T car would begin to catch up as it hit higher engine speeds and it would eventually pull ahead. It would win by a narrow margin and its trap speed (its speed at the finish line) would be slightly higher than the Ford-powered car’s.
• In a road race or on a big NASCAR-style oval track, the VW-powered car would be ahead most of the time. As long as both cars were driven flat out, the VW engine’s greater horsepower would be more important than the Ford’s low-speed torque. The only place the Ford-powered car would have an advantage would be in slow corners, where its higher torque would again give it more power than the VW engine.

This assumes everything else is equal, which in the real world isn’t necessarily the case. For example, we could help the VW-engined car by changing its gear ratios so that the engine is always running at higher rpm. This would give it more power in low-speed driving, although it would also mean more engine noise, greater fuel consumption, and somewhat higher engine wear.