Brian Blades

What Is Motorcycle Horsepower?—From The Archives

What it really is and how it got saddled (pun intended) with such a name

From the May 2010 issue of Cycle World

Horsepower. What a magical word those 10 letters constitute. Riders constantly talk about it, hot-rodders relentlessly pursue more of it, manufacturers and performance-equipment suppliers brag about it, magazines write endlessly about it. To motorheads all around the world, horsepower is a big, big deal.

Obviously. But the question is, just exactly what is it?

The real answer is that horsepower isn’t anything tangible, like height, width or depth; it’s merely someone’s fabricated method of measuring the rate of work an engine can perform.

That someone was 18th-century Scottish engineer and inventor James Watt. Among his many other accomplishments, Watt pioneered the development of usable steam engines, which gave rise to the need for a way of measuring the amount of work those engines could perform over a given period of time. No such values had been established back then because no practical engines were yet in use. So, Watt set out to find a way of helping the public understand the potential of those newfangled devices.

Because most people of that era were very familiar with the work a horse could do, Watt decided to compare steam engines to horses. Through a series of less-than-scientific tests in which he had dray horses move loads of coal, Watt concluded that the average horse could lift 550 pounds one foot in one second or 33,000 pounds 1 foot in 1 minute. He deemed that rate of work one horsepower; and ever since, horsepower has remained the standard by which we measure the output not just of steam engines but those of the internal-combustion variety, as well.

So, let’s see…we’re talking about a one-man, non-scientific test involving horses and loads of coal? Sounds pretty makeshift for a global power standard that has endured for more than two centuries. Nevertheless, that is the origin of the term.

mathematics of force and torque illustration
The simple mathematics of force and torque: If a mechanic applies 50 pounds of pressure on a wrench one foot from the nut (50 x 1=50) or 25 pounds of pressure two feet from the nut (25 x 2=50), he is exerting 50 foot-pounds of torque on the nut in either case. If the torque causes rotation, the result is called work.Illustration by Jim Hatch

But it still doesn't explain what power—regardless of whether it's called horsepower, oxenpower or puppydogpower—really is. To do that, we have to start with force, using an example that motorcycle enthusiasts should be familiar with: a mechanic using a wrench to turn a nut. If the wrench is one foot long and the mechanic puts 50 pounds of pressure on the very end of the wrench, he is exerting 50 foot-pounds of force. If the wrench is two feet long and he puts only 25 pounds of pressure on it, he still is exerting 50 foot-pounds of force at the nut.

There are several different kinds of force, but the kind that tries to cause rotation—such as exerted by the mechanic and his wrench on a bolt or nut—is called torque.

Torque does not necessarily have to cause movement. If our hypothetical bolt needed 100 ft.-lb. of torque to move, the mechanic could apply that 50 ft.-lb. until he died of starvation without causing the bolt to turn one little bit. But as soon as the bolt moves—no matter how far or how much torque is required—the mechanic will have accomplished work, which is a measure of force exerted over a distance.

So far, so good. But how long did it take the mechanic to do that work? If it took him 5 seconds to rotate the bolt one full turn, he performed work at three times the rate than if it had taken him 15 seconds. And the measure of that rate of work is called power. Power is calculated by multiplying the force applied by the distance covered and then dividing by the time required. You could use that formula (Power = Force x Distance ÷ Time) to determine the power the mechanic generated when rotating the bolt one full turn.

crankshaft and piston action illustration
What goes on in an engine is much like the mechanic turning a nut with a wrench. The pressure of combustion above the piston tries to push the piston and the connecting rod downward to make the crankshaft rotate. The pressure of combustion is analogous to the force applied by the mechanic, and the throw of the crankshaft is like the length of the mechanic’s wrench.Illustration by Jim Hatch

Okay, but how does this wrench-and-bolt scenario relate to the power output of a motorcycle? Quite directly. Engine torque is generated by combustion pressure above the piston pushing downward, through a connecting rod, to a crankpin at the outer end of the throw of the crankshaft. That pressure acts just like a mechanic pushing on a wrench, but instead of rotating a bolt, it rotates the crankshaft. The total distance the crankshaft turns is determined by the number of revolutions it makes, and the time required for it to make those revolutions is measured in minutes—rpm, in other words.

Thus, to calculate the engine’s power (not horsepower; just power, period), we refer back to our wrench-turning-the-bolt equation: Force times Distance divided by Time. We take the torque output of the engine (force) and multiply it by the distance covered while it is being generated, then divide by the time required to do it (“rpm,” as you will soon see, includes both the distance and the time). The result is the power output at that engine speed.

Now, it would seem that to make such a calculation, you would need to know the stroke of the crankshaft, since the circumference of the circle the crankpin scribes during each revolution determines the total distance the crankpin travels in one minute. But have you noticed that none of the horsepower and torque figures you’ve ever seen include the engines’ stroke dimensions?

That’s because they don’t have to. Torque figures (at least here in the U.S.) are expressed in foot-pounds, which means they assume a lever distance (on an engine, this is the crankshaft throw, which is one-half of its stroke) of one foot. The circumference of a circle is calculated by multiplying its diameter (twice the radius) by Pi (3.14). So, for the purpose of power calculations, the distance traveled during each revolution of any engine always is 6.28 feet (3.14 x 2).

Confused? Don’t be; all this will become clear in a minute.

Let’s use as an example an engine that makes 90 foot-pounds of torque at 5000 rpm. If you multiply 90 (the torque) by 6.28 (the distance, in feet, the crankpin travels during each revolution) and then multiply by 5000 (the number of revolutions in one minute), you get 2,826,000. In other words, the engine has a power rating of 2,826,000 ft.-lb. of work per minute.

All right, but that’s just plain power; what about horsepower? Well, James Watt’s formula states that one horsepower is 33,000 foot-pounds per minute; so, if you divide the engine’s power rating, 2,826,000, by one horsepower, which is 33,000, you get 85.64, and that is the amount of horsepower our hypothetical engine makes at 5000 rpm.

But wait—there’s an easier way. With the method just described, you always have to multiply the rpm by 6.28 and then divide the resultant power number by 33,000. Because that requirement never changes, you can use a constant—a mathematical shortcut—to calculate horsepower more quickly. That constant is 5252, determined by dividing 33,000 by 6.28. (Actually, an engineer would carry Pi out to many more decimal places, perhaps as far as 3.14159265, which would yield 6.2831853 when multiplied by 2; but for simplicity, we’ve rounded it off to 3.14.)

So, to calculate horsepower, you just multiply the torque by the rpm at which it is generated and divide by 5252. Using our same torque output of 90 foot-pounds at 5000 rpm, multiply 90 by 5000 and divide by 5252; you get 85.68, the amount of horsepower the engine makes at that rpm. (The tiny difference between this figure, 85.68, and the previous one, 85.64, is the result of rounding off Pi in those two different methods of calculating horsepower.)

If you know any engine’s torque output at any given rpm, you can calculate its horsepower at that rpm by using this formula. Conversely, if you know its horsepower output at any given rpm, you can calculate its torque at that same engine speed: just multiply the horsepower by 5252 and divide by the rpm. So, using the numbers in our previous example, multiply the horsepower, 85.68, by 5252, then divide by the rpm, which is 5000; you get 90, the amount of torque the engine makes at 5000 rpm. It’s all just a matter of simple math.

Now that we know what torque and horsepower are, what do they mean in practical terms? A number of things. For starters, since torque is a force that can be measured, and horsepower is a calculation based on that measurement, the two are inexorably and mathematically tied together. As a result, the only ways you can increase an engine’s horsepower are either to increase the amount of torque it produces at any given rpm or increase the rpm at which it produces any given amount of torque. And that’s it! There is no black magic, no secret tuner’s tricks that work around that principle, no exceptions; it’s simple, everyday, grade-school math.

applying torque to a nut illustration
When you exert force on a wrench, you are applying torque to the nut or bolt you’re attempting to tighten or loosen, but no work is accomplished until that fastener actually moves.Illustration by Jim Hatch

Engines of different designs—or even like engines that are in unlike states of tune—can develop very different torque and horsepower curves. It’s not uncommon for two engines to produce the very same peak horsepower or peak torque values yet have completely different torque curves and powerbands.

As an example, suppose you have a Harley-Davidson with a modified 100-inch V-Twin engine that makes 111 ft.-lb. of torque at its peak power rpm of 5200. Using the formula for calculating horsepower that we discussed a few paragraphs ago, multiply the torque (111) by the rpm (5200), divide by 5252, and you get 109.9 horsepower, which we'll round off to 110.

Now let's look at a 2009 Kawasaki ZX-6R, a 600cc sportbike with a four-cylinder engine that's extremely high-revving compared with the Harley's low-rpm V-Twin. At its horsepower peak, the Kawasaki only makes 41.6 ft.-lb. of torque, but that peak occurs at 13,890 rpm. So, multiplying 41.6 by 13,890 and dividing by 5252, we get 110 peak horsepower, the same amount as with the Harley. By the way, these are not trumped-up, imaginary examples; they are numbers pulled right off the dyno charts for a modified 100-cubic-inch Twin Cam 88 Harley owned by a friend of the magazine and a stock 2009 ZX-6R that we tested.

How is this possible? Again, it’s just simple math. Even though at its horsepower peak, the Harley makes 2.67 times more torque than the ZX-6R (111 ft.-lb. divided by 41.6 ft.-lb. equals 2.67), the Kawasaki makes its peak-power torque 2.67 times more often during each minute (13,890 rpm divided by 5200 rpm equals 2.67). The end result in both cases is 110 horsepower. Again, it’s just math.

Even though both bikes make the very same amount of peak horsepower, their actual performance out in the real world couldn’t be more different. The big-inch Harley accelerates hard at low-rpm top-gear cruising speeds and pulls consistently until it nears its moderately low redline; by comparison, the smaller-displacement Kawasaki has weak low-end and midrange acceleration but comes on like gangbusters at higher rpm. At cruising and around-town speeds, the much-heavier Harley will smoke the lighter Kawasaki unless the smaller bike is downshifted several times; but when allowed to accelerate at full throttle in the upper one-third of its rpm range, the 600cc Kawasaki will leave the 1639cc Harley for dead. For all practical purposes, these two are like night and day.

horsepower dyno chart comparison
Both of these motorcycles make the very same amount of peak horsepower, but they do it in dramatically different ways. The 1639cc (100-cubic-inch) Harley produces a huge amount of torque at comparatively low rpm, while the 600cc (36.5-cubic-inch) Kawasaki makes a much smaller amount of torque but at extremely high rpm. The end result is exactly the same peak horsepower for both, but there are no similarities whatsoever in the way the two bikes feel or behave when being ridden.Cycle World

Obviously, then, peak horsepower is not the answer if what you want are shift-free cruising, right-now power and strong acceleration in normal riding conditions. In fact, the only time peak horsepower means much is when the engine is operating at full throttle right at or near its peak power rpm. But rarely do we—or can we—ride streetbikes like that, so peak horsepower generally is not what we should be so intent on obtaining. When you’re riding at reasonably normal road speeds and rpm, the height, width and shape of the torque curve are what you should be most concerned with.

And let’s not forget that, through simple math, the shape of the torque curve always dictates the shape of the horsepower curve. Flat torque curves and wide powerbands make for great street motors; steep torque curves and narrow powerbands are usually best suited for racing.

So, when someone brags about how much peak horsepower his bike made on a dyno, that doesn’t necessarily mean he has the ideal motor package. If your bike makes a bit less peak horsepower but has a broader, flatter torque curve, you still could likely open a big can of whoop-ass on him just about anywhere but on a racetrack.

This is why discussions about torque and horsepower can be very misleading if you don’t understand what those terms actually mean. Just be thankful, though, that James Watt knew how to get his hands on a few good horses; otherwise, we all might find ourselves standing around our favorite hangouts bragging about our bikes’ Dutchwindmillpower. That doesn’t quite roll off the tongue as easily as “horsepower,” does it?