Horsepower & Torque

Explaining the Fundamental Measures of Engine Performance in Plain English

By Joe Pettit

This is the first installment of a new series in Sport Truck devoted to bringing new enthusiasts up to speed on technical issues that tend to get distorted in the translation from engineers to our enthusiast readership. The present installment is a good case in point. We all use horsepower and torque, and for the most part we believe we know what these terms mean. But how accurate is that belief? What is the difference between a foot-pound and a pound-foot? And what does a foot-pound have to do with horsepower? We'll examine and explain this and other technical concepts in this series in easy to understand terms.

In addition, we'll include real world, useful applications of this information. For example, as we explain in our current offering, there are specific areas of an engine you can alter to increase the power and force output of an internal combustion engine. Once you're aware of those, then you can make educated changes to your engine combination that will actually give you the desired result. We hope you find the information entertaining, informative, and useful.

to understand horsepower and torque, we need first to understand a few concepts used in developing the units of horsepower and torque. These are the concepts of mass, force, work, power, and, yes, torque.

Mass: Mass is essentially the measure of how much matter is in an object. To find the mass of an object, you can divide its weight by the force of gravity or multiply its mass by the force of gravity to get its weight. Now that we've introduced the concept of force in order to explain mass, it's time to explore the concept of force.

Force: Just as we used force to help define mass, we'll use mass to help define force. We already discussed the relationship of weight to mass as the application of the force of gravity to a mass. There are two points of interest about the force of gravity that will help us understand both mass and force. First, the force of gravity pulls you toward the center of the Earth, and second, that force is proportional to your mass. The more matter you contain, the greater the force of Earth's gravity on you. In other words, the more massive you are, the more you weigh, at least when you're near a monstrously larger mass such as a planet or a moon.

Weight is a measure of the force of gravity. Another way of looking at it is that force causes acceleration. When you put an object on a scale, it applies a force to the springs in the scale compressing them. The amount of compression is an indication of the force exerted on the mass.

These observations are so obvious that their importance were overlooked for millennia until Isaac Newton formulated these relationships into his Second Law of gravity, from where the concepts of horsepower and torque come from, as well as much of the mechanics that govern the performance of your machine. Newton's Second Law states that the acceleration (A) of an object is directly proportional to the force (F) applied, and inversely proportional to the object's mass (M). In other words, the more force applied to an object, the greater the rate of acceleration. Also, the more massive an object the lower the rate of acceleration. Newton's Second Law is best known as an equation: F = MA, or force equals mass times acceleration.

The foot-pound, or ft-lb (distance times force), is the unit of work (it's also the unit of energy because work and energy are very similar) in the English gravitational system of measurement that we use. It is the work done by a force of 1 pound applied through a distance of 1 foot. So if you lift a 1-pound weight 1 foot, you've done 1 foot-pound worth of work. If you lift 2 pounds 2 feet, you've done 4 ft-lb of work.

The term foot-pound also designates units of torque. As a convenience, engineers typically reverse the order of the torque unit to pound-foot in order to distinguish it from the work unit. The order, foot-pounds or pounds-foot, doesn't matter because the terms are multiplied (2x1=1x2) and therefore equivalent.

Horsepower is a term invented by the engineer James Watt. In his capacity as an engineer in England, he needed a way to calculate the power available from horses for work. His measurements determined that, on average, one horse exerted a 180-pound force on a 12-foot lever attached to a capstan that it walked around. The distance around the circle (circumference) was a little more than 75 feet, and the horse made 2.4 revolutions per minute for a speed of about 181 feet per minute. Multiplying the 180-pound force exerted by the horse by the distance traveled in one minute gave him 32,580 ft-lb per minute, which he then rounded up to 33,000 foot-pounds of work in one minute to be his measure of 1 hp.

To help you get your head around this, think of it this way: According to Jimmy Watt, one horse can do 33,000 foot-pounds of work every minute. That means a horse generating 1 hp can raise 330 pounds 100 feet in one minute, 33 pounds 1,000 feet in one minute, or 1,000 pounds 33 feet in one minute. It doesn't matter what combination of feet and pounds; as long as the product equals 33,000 foot-pounds in one minute you have 1 hp. You can even express horsepower in ft-lb/second by dividing each term by the 60 seconds in the minute. When you do that you find that 1 hp equals 550 ft-lb/second. It's in this form that horsepower is most conveniently calculated from engine torque.

As described in the equation above, engines generate horsepower by the pressure in the combustion chamber acting on the piston top to force it down the bore in order to make the crankshaft spin. This generates a torque force that allows work to be done at a rate dependent on the engine's speed and the magnitude of the torque.

Looking deeper into the formula for horsepower, we find there are four variables that contribute to the power generation in an internal combustion engine. They are:

The following equation explains and shows the relationship of how these variables influence horsepower output of a four-stroke internal combustion engine:

Here's a quick explanation of the relationship of the values of this formula. MEP is the theoretical mean effective pressure acting on the piston top through its stroke. Notice that cylinder pressure is divided by the work of 1 hp (33,000 ft-lb). These are the force units. Cubic inch displacement (CID) reflects piston top area and the crankshaft's stroke length, which is divided by 12 to convert the value to feet. And finally, the number of power strokes per minute for a four-stroke engine is the term RPM/2 because the cylinder fires every other revolution.

This equation predicts theoretical horsepower, not brake horsepower. It does not account for the frictional power losses of the engine. When you measure on an engine dyno, you measure the net power output of the engine after all losses. The reason it's good to know the math and physical reasoning behind power generation is that it shows you exactly where to make changes to improve the performance of your engine. If you work with the equation, you'll see that to increase power output you have to increase one of these variables. In other words, you have to increase the mean effective pressure in the cylinders, the stroke, the bore size, or the engine speed.

The most common approach is to increase cylinder pressure in order to increases torque output. To do this you need to add more air and fuel to the combustion chamber and ignite it. That's why tuned intake manifolds, superchargers, turbochargers, and nitrous systems work and part of the reason free-flowing intakes and exhausts work as well. Another popular way to obtain more horsepower is to build a bigger engine. The same cylinder pressure acting on a larger piston surface or through a longer stroke will make more power. And finally, you can choose components that will allow your engine to spin very quickly, producing more power strokes per minute in order to increase power. This approach requires tuning the intake and exhaust flow capability to be tuned so the cylinders have enough fuel and air to generate adequate torque at high engine speeds and tends to reduce torque and power at lower engine speeds.

Torque is a force that we measure through the distance of a lever arm. But four-stroke internal combustion engines have to spin to make torque and, more importantly, they have to spin in order to do any work, moving your rig down the road for example. The equation that describes the relationship of force at the flywheel, engine speed, and work expressed as horsepower follows:

What is of interest is the conversion factor 5252. We reach that number when we divide Watt's 33,000 ft-lb/minute of work by the distance that the end of a 1-foot lever arm travels in one revolution of the engine, which happens to be 6.2831 feet. When we divide 33,000 ft-lb/minute of work by the distance of our lever arm for measuring a force (torque), we're beginning to convert force into power. To define power you need a time unit. The time unit is supplied when we factor in the engine speed in revolutions per minute (rpm). This is how the equations that describe horsepower and torque convert the constant force at the end of a 1-foot lever arm (lb-ft of torque) into a measure of how fast work is done (horsepower).

They were generated in a PC Dyno using stock heads and camshaft. 355 4.030 x 3.480 393ftlbs@3000rpm 303hp@4800rpm 377 4.155 x 3.480 413ftlbs@3000rpm 305hp@4800rpm 383 4.030 x 3.750 425ftlbs@2000rpm 301hp@4200rpm 406 4.155 x 3.750 452ftlbs@2000rpm 301hp@4000rpm Higher performance cam and heads. 355 358ftlbs@4500 361hp@6000 (340@5000) 377 375ftlbs@4500 364hp@5500 383 376ftlbs@3500 361hp@5000 406 391ftlbs@4000 363hp@5500 What is really clear from looking at these number is more cubic inches make more power Here is the biggest small block I build 434 408ftlbs@4000 360hp@5000 You will see a bigger bore makes more horsepower and a longer stroke makes more torque. The differences are small but can be increased with further up grades. Going from a 355 to 383 added 28cid 32ftlbs & 0hp on a stock motor and 18ftlbs & 0hp on a big cam/head combo The 377 added 22cid 20ftlbs & 2hp and 17ftlbs & 3hp In the real world we make a little more power than these numbers because the camshafts and heads are better than those in the computer simulation dyno. But you will see the increasing the bore size increased horsepower where as stroke increased torque. The reason 377s are used in sprint cars are a maximum cid rule, and higher RPM motors make more horsepower, and these cars operate at higher RPMs. Using a 383 would not be taking advantage of the stronger torque because the engine would be revving too fast, and as a result not making enough torque or horsepower. To exaggerate the bore/stroker torque/horsepower relationship look at this motor 330cid 4.185 x 3.00 372ftlbs@3500 307@5000 stock 497ftlbs@6000 640@8500 everything thrown at it 377 with everything 540ftlbs@5500 630@8000 From this illustration you can see that short stroke motor likes RPM and the extra RPM makes more HP not Torque.