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Torque and Horsepower

by Nick Jenkins

This isn't an article about how to make your Miata faster (there goes half the audience). This is an article about horsepower, what it does, how it's measured, and how it differs from torque.

We all learn two things about horsepower early on: 1) It makes a car move, and 2) more is better. We also learn relative numbersó100 horsepower is pokey, 200 is pretty fast, and 500 will shake your teeth loose. From this we can interpolate the in-between numbers, so we can anticipate the difference between, say, 90 hp at the rear wheels in a tired 1.6L Miata, and 160 hp from a fresh Rebello 1.8.

But what is horsepower, exactly? In scientific terms, it's a unit of power equal to about 760 watts. Power is a measure of the relationship between three things: force, distance, and time. Before we can discuss power, though, we first need to do some work.

Work

Pushing an object over some distance takes work, both in the colloquial sense and scientific sense. Work is a scientific term for force times distance (f*d). It takes exactly twice as much work to push an object 20 feet as it does to push it ten feet, using the same pushing force. Similarly, it takes twice as much work to push an object ten feet with 50 pounds of force as it does to push the object ten feet with 100 pounds of force. Work is something that can be precisely measured and calculated.

Power

If I'm pushing a heavy sofa, I can either take my time (preferred) or rush the job. Regardless how fast I do it, though, the amount of work I do will be the same, because I'm pushing with the same force over the same distance. Yet somehow it doesn't seem that way. I'm a lot more tired when I push it faster. Part of this is due to the fact that I had to push harder to get the sofa to move faster, so I actually did do a little more work. But that wasn't all of it, just the initial push. It still feels harder to push the sofa faster. Why is that?

This is where power comes in. Power is the scientific term for work divided by time (f*d/t). If I push the sofa faster, I'm doing the same amount of work, but exerting more power. So it's harder. The reverse of this is also true. The more power I have, the faster I can push the sofa. You can see how this translates directly to your Miata. More about this in a moment.

Torque

How hard can your Miata push? This is where torque comes in. Torque is force applied in a circular motion. Pistons in the engine push down with a lot of force on the crankshaft, and the crankshaft transmits that force as torque by spinning. Before we see how this plays out, let's take a look at force in a straight line.

Newton came up with the first scientific description of force. He reasoned that objects moving in a straight line would continue in the same direction and speed forever, and objects at rest would remain at rest forever, unless acted upon by an outside force (like air, the ground, or a 500hp V8). He figured out a way to calculate the amount of force needed to speed up (accelerate) an object, and the calculation couldn't have been simpler. Force, he determined, was equal to mass times acceleration (f=m*a). Twice the force, twice the acceleration. Half the mass, twice the acceleration. It's all good. The results are completely linear, and completely applicable to your Miata.

In British or SAE units, force is measured in pounds. In the metric system, it's measured in Newtons, in honor of Sir Isaac. (A Newton is more than a pound, but to find out exactly how much more, I'd have to look it up, and that's not going to happen right now).
Force varies based on the distance from the center of torque  

torque
                     force
Because torque is applied in a circular motion, i.e. around a point, the pounds (or Newtons) of force produced is a function of how far you are from that central pointócloser in, more force, farther away, less force. Because of this variability we have to express values of torque in foot-pounds (or Newton-meters), which is the amount of force one foot (or one meter) from the center. If we attach a large wheel to an engine that produces 100 foot-pounds of torque, the force generated one foot from the center of the wheel will be 100 pounds. The force generated two feet from the center will be only 50 pounds, and the force at 6 inches will be 200 pounds.

The arrangements of wheels and gears on a Miata are a little more complicated than that, but it's still easy to calculate the force produced where the rubber meets the road. Gears increase or decrease the force of torque the same as moving in or out on a driven wheel. Fourth gear has around a 1:1 ratio, so we'll start with that. Differential gears use a ratio close to 4:1, which is like moving in on the wheel from one foot to 3 inches. So torque at the rear wheels in fourth gear is about four times what the engine produces, or around 400 foot-pounds. Since the rear wheels have a 1-foot radius, or thereabouts, the "push" by the rear tires in fourth gear is around 400 pounds. The push would be less with larger wheels, and more with smaller ones.

Shifting down increases the gear ratio, increasing the push at the rear. This is why the car accelerates faster in first than it does in fourth or fifth. If first gear gives you a 3:1 advantage over fourth (I'm guessing here), even a high-mileage NA can put out about 1200 pounds at the rear wheels (at least briefly), which translates to about .5G of acceleration. Changing the differential ratio will affect acceleration in all gears. A 3.9 diff will decrease overall acceleration, and a 4.3 will increase it, with the trade-off that you'll hit the rev limiter sooner and have to shift more.

Horsepower

If acceleration is all about torque, why do we need horsepower? Marketing, of course, but beyond that, speed is ultimately dependent on power, since more power means we can perform work (force over a distance) faster. A car is doing a lot of work even when it's not accelerating, mostly to overcome air resistance (drag). Obviously more horsepower is needed at higher speeds, because drag is greater.

If torque (force) over a distance produces work, and horsepower increases as the work is done faster, then it follows that for a fixed amount of torque, a car produces more horsepower the faster it goes. This is entirely correct, and it would seem that horsepower should go on increasing forever, and the top speed of any car should be unlimited.

But the amount of torque an engine produces is not constant. It varies with engine speed. How much it varies depends on the engine design. The usual design trade-off is between an engine that produces a decent amount of torque over a wide range of RPMs, and one that produces a lot of torque over a more narrow RPM band. Ultimately torque is limited by the size (displacement) of the engine, so often smaller engines tend toward the high-torque/narrow-band design, and larger engines toward moderate torque over a wider band.

Oddly, we usually think of wider-band engines as more "torquey", even though the engine designers purposely sacrificed some torque for a wider RPM range. The reason a lower-torque engine can feel faster is that the torque extends down to the lower RPMs, where we spend most of our time (unless we're driving an old NA, in which case we live above 4000 RPMs, where all the torque is).

The change in torque with engine speed can be displayed on a graph. The line that's produced is a curve that starts
Typical Miata torque curve

torque
                     curve
at around 1000-1500 RPMS, where only a moderate amount of torque is produced, then rises over the next 1000-2000 RPMs, stays fairly flat for another couple of thousand RPMs, then falls off after 4000-5000 RPMs, dropping back by about half or more at redline. This torque curve will have a peak somewhere in the near-flat range, usually between 3000 and 4000 RPMs in a high-performance street engine. It's the torque peak number that's advertized in car literature, and it's always given along with the RPM where the peak occurs, for example 120 ft-lbs @ 3500RPM.

The longer and flatter the middle part of the torque curve, the better. You can stay in one gear longer, and the car feels more powerful because more torque is on tap at lower RPMs. The torque curve for 1.8 liter VVT engines in later Miatas is very respectable, with decent torque as low as 2000 RPMs. Keep in mind that torque at any engine speed is also dependent on how much gas you give it, and all published torque and horsepower figures are at WOT.

Since we know how much force is generated at the rear wheels in a particular gear at a given speed, we know how much work is being
Horsepower curve

horsepower
                     curve
done and how fast it's being done. So we can calculate the horsepower produced at that speed. Because it's based on torque, it's going to vary with engine speed, but since it increases with the speed of the car, its curve continues to climb well past peak torque. In fact, horsepower would keep climbing to redline and beyond, were it not for the fact that torque drops off so much in the higher RPMs, which consequently reduces the force at the rear wheels and the amount of work being done.

Most engines are designed so that the horsepower curve peaks just below redline. It's the peak value that's advertized. Like torque, horsepower figures are usually published along with the RPM where the peak occurs, although we don't really care about that so long as the horsepower number is big enough.

Using this knowledge, we can come up with two basic ways to increase horsepower. The first is obvious: increase torque. You can do that several ways, by increasing the size or efficiency of the engine, or adding a turbo or supercharger. The second is to move the torque peak farther up the RPM range. Torque curves are a function of several variables, but the most significant is valve timing.

Peak torque occurs when the valves are opening and closing at a rate that maximizes pressure changes in the cylinders. Above and below the peak, pressure changes aren't as great because the valves aren't opening at quite the right time. The reasons for this are somewhat complex and would take another full article to cover even briefly, but it has to do with the speed at which pressure changes propagate, which is roughly the speed of sound, a speed that doesn't change a lot no matter how fast the engine is spinning.

Opening the valves sooner and closing them later moves the optimum valve rate to a higher engine speed. Valve opening and closing is controlled by the camshafts, and replacing them with longer-duration "race" cams is a tried-and-true method for increasing horsepower. The downside is the engine is now less-efficient at lower RPMs, which means less torque produced at those lower RPMs. The engine may not feel as fast unless you keep the RPMs up all the time.

For this reason, variable valve timing (VVT) in the later 1.8 liter engines is a huge advantage. In a non-VVT car, the rate that valves open and close is completely dependent on engine speed. In a VVT car, the rate doesn't change as much with engine speed, so torque stays near its peak value over a wider RPM range.

Shifting

If we want to maximize acceleration, we should be able to use the torque graph to pick our optimum shift points. Shifting up, we lose about a third of our RPMs. If we shift at 4500, for instance, we'll end up in the next gear at about 3000 RPMs. Looking strictly at the torque curve, shifts at 5000 that drop the engine to 3500 will keep us in the fat part of the torque band, so 5000 RPMs would seem to be a pretty optimal shift point. But that's not quite right, for a couple of reasons.

The first reason is that along with the decrease in RPMs, the next higher gear produces about a third less force at the rear wheels from the same amount of torque, because of the change in gear ratio. So it pays to stay in the lower gear longer even though the torque is dropping off. For example, let's say we shift at 5000 RPMs, where torque is 90 foot-pounds, and we end up at 3500, where torque is also 90. We've actually skipped right over the torque peak, 100 @ 4000 RPMs, but we never drop below 90. If the overall gear ratio (transmission + differential) before the shift is 5:1 and the ratio after is 4:1, the force at the rear wheels before the shift would be 450 pounds (90*5), and the force after would be 360 pounds (90*4), a big drop.

Now let's say we wait until 6000 RPMs to shift, even though the torque falls off to 80 foot-pounds. The force at the rear wheels before the shift would drop to 400 pounds (80*5), but the force after the shift will jump to 400 pounds (100*4). The car will not only accelerate faster, but it'll also feel much stronger after the shift. The precise optimal gear shift RPM depends on the exact torque numbers, but it'll almost always work out that it's better to end a shift at or near the peak of the torque curve, rather than trying to stay close to the middle before and after the shift.

The second reason we can't rely strictly on torque curves for optimizing acceleration is that besides accelerating, the car is also doing a lot of work to overcome wind resistance (drag). So we have to consider the horsepower curve as well, especially as speeds increase. Because horsepower doesn't peak until about 6500 RPMs, we can actually wait until then to shift, or even later since horsepower will fall off quite a bit after the shift, as the engine RPMs drop.

It works out that the optimal shift point in a stock Miata that's trying to maximize acceleration is somewhere between 6500 and 7000 RPMs. The 2-3 shift, where speed (and drag) is lower, can be executed closer to the 6500 number, while the 3-4 shift can be made closer to 7000 RPMs. In no case does it ever help to shift above 7000 RPMs in a stock Miata, regardless what your racing instructor may tell you.

Top Speed

We've seen how horsepower increases as the speed of the car increases, as long as the torque remains constant. We've also seen that torque falls off at higher engine speeds, which means horsepower can't go on increasing forever. But what if we shift up to the next gear? We're going faster, doing more work, and we're back in the fat part of the torque curve. Shouldn't we be making more power?

Not quite. Engine torque is the same in any gear, and so is horsepower. Your speed may increase after a shift, but the force at the rear wheels is reduced by the new gear ratio, so the amount of work being done only increases a little bit. In any gear, you'll reach a speed where the engine is at maximum horsepower. At that speed, if the force generated at the rear tires is greater than the wind resistance (and all other forms of drag), you won't be using all of the available horsepower and you'll continue to accelerate.

When you shift up, the force at the rear wheels will be reduced, and at the same time drag will continue to increase. With rear wheel force going down and drag going up, you eventually reach a point where drag becomes equal to the force at the rear wheels, and you stop accelerating. You're using all the available horsepower to overcome drag. You have nothing left to accelerate with.

To maximize top speed, the gear ratiosóparticularly the differential gearsóneed to chosen so that you reach this equilibrium point when the engine is at or near peak horsepower. If the diff gear ratio is too high, you may not be able to reach peak horsepower in high gear, and your top speed will be lower. If your diff ratio is too low, you might sail past the horsepower peak at an even lower speed, with the same result. Some cars are designed that way, with top speed redline-limited. In a car like that you run out of gears and RPMs with power to spare. Mazda didn't do that with the Miata. A stock Miata is power-limited just below peak horsepower, around 6000-6500 RPMs (depending on the year), and it won't redline in top gear.

What have we learned?

It seems that torque is more important than horsepower in terms of acceleration, and horsepower is simply a number calculated from the amount of torque produced. Yet it's always the horsepower numbers that impress us. I think there's a historical reason for this. In the early days of the automobile, acceleration wasn't such a big deal. You didn't stop as often. But horsepower determined your top speed, and that's what determined how long your journey took. Horsepower was everything. A car's horsepower was always it's selling point, and in all these years, we've never changed that view.

Nowadays, of course, we can't drive at top speed very often, but we do get to accelerate a lot. So when we say we want our Miata to have more power, what we're really asking for is more torque. On a track car things would be different. More horsepower would equate to higher top speeds and faster lap times, and we could get away with a peaky engine that had no torque below 4000 RPMs, but gobs of horsepower all the way up to the rev limiter.

But for a daily driver, when you're comparing performance, you should look beyond the advertized horsepower. Horsepower will give you bragging rights, but the torque numbers will give you a better idea of how much fun the car will be to drive.