Everywhere you turn, people and manufacturers are making horsepower claims for their cars or products. Unfortunately, most people do not really understand the theory and history behind the horsepower rating system. In this short article, I would like to explain a little of the history, and use analogies to help the reader to better visualize the concepts. Understanding how the formula for horsepower works may help you sort through the jungle of performance information out there. The math behind calculating horsepower is extremely simple, but let’s start with a brief history.
In the middle 1800’s, America and the rest of the world for that matter, was going through a period called the Industrial Revolution. Because of the growing use of the steam engine, industry no longer needed to be located next to a river for power and horses were no longer the only means for transporting goods and people. However, no one had a “ruler” for measuring the power of a steam engine or any power-producing device. If you needed a power supply to run your sugar cane press, what size steam engine would you need? Experience may tell you that a team of 4 horses would probably drive the press, but what size steam engine would suffice?
Without doubt, you have heard of a unit of electrical power called a Watt. Named after James Watt, he also defined a system for rating power producing devices.
Watt started with the definition of WORK, which is FORCE multiplied by DISTANCE. If you pushed a 100-pound box a distance of 1 foot, you have done 100 pound-feet of work. If you pick up that same box 1 foot off the floor, you have done the same amount of work. What James Watt really wanted to define though, was the POWER that an engine could produce. POWER is defined as WORK / TIME. If it took you one minute to push that 100 pound box one foot then the power you expended was 100 pound feet per minute. If it took you two minutes then you did 50 pound-feet per minute of work. Get it?
In our example of the sugar cane press, you may have come to the conclusion that the obvious answer is a four horsepower engine. This must have been obvious to James Watt also; because what he did was to try and define how much power a horse could produce. We don’t know if the horse he had in mind was a Shetland pony or a mighty Clydesdale, but nevertheless, the number he came up with for one HORSEPOWER is 33000 pound-feet per minute or 550 pound-feet per second. So what James Watt figured was that a typical horse could pull or lift 550 pounds one foot in one second.
We now have a definition for horsepower. Just like we know that 12 inches equals one foot, we know that 33000 pound-feet per minute equals one horsepower. Horsepower would be hard to measure on an engine directly, so we must use a little math to find some quantity that we can measure and convert it to horsepower. That quantity is TORQUE. TORQUE is defined as a twisting about a point caused by a force on a lever arm. For example, a one-pound weight at the end of a 1-foot long wrench applies a torque of 1 foot-pound on a bolt or nut. Note that WORK and TORQUE have the same units and foot-pound equals pound-foot.
Now, let’s imagine that you get an exercise bicycle. You know, one of those with the big wheel in front and a strap running around the outside of that wheel that can be tightened to make it harder to pedal. Now let’s say that you adjust the strap tension so that the wheel is difficult to turn. Now get a wrench and a spring scale. Attach one end of the wrench to the center of the bicycle wheel and attach the scale to the other end of the wrench. Suppose that it takes a 50-pound pull at the end of the wrench to turn the wheel. If the wrench is one foot long, it requires 50 foot-pounds of torque. Now start turning the wheel with the wrench as fast as you can. Suppose you can turn the wheel 55 times in one minute. (I’ll bet you can’t!) How much horsepower are you producing?
This is actually pretty easy. To figure horsepower, we need to know work per unit time. Earlier, we established work as:
Work=Force x Distance
and Distance for our example = 2 x Pi x wrench length
Since we are moving in a circle, 2xPi x radius (wrench length) is the distance around a circle. (Remember that Pi = about 3.1416) We have already pointed out that power is Power=Work/Time
So our equation looks like this:
2 x Pi x wrench length x Force x rpm= power we expended.
Since this will give us foot-pound per minute, we can divide the answer by 33000 foot-pounds per minute and get the horsepower. But before we start plugging in numbers, note that
wrench length x Force = Torque.
Replacing that into the equation has:
2xPi x Torque x rpm/ 33000= horsepower. (Pi= 3.1416)
Simplifying the equation yields:
Torque x rpm/5252= Horsepower
This equation is the one that most people recognize. Plugging in the numbers from our exercise bicycle example:
Torque = 50 foot-pounds
Rpm = 55 rev/minute
50x55/5252=0.524 hp!!!
To turn that bicycle wheel 55 times in one minute, you produced over ½ horsepower. Most trained athletes can only produce a little more than ¼ horsepower for any extended length of time. So my example might not have been the most realistic, but you get the picture.
A dynamometer can only measure torque and rpm, but can use this formula to calculate horsepower. Also note, that by definition, at 5252 rpm horsepower equals torque. So be very skeptical of someone’s horsepower and torque chart if the curves don’t cross at or very close to 5252 rpm.
In the next article, we will play around with this formula some more and use it to compare different engines. The results might surprise you! F/M
HOW MUCH HORSEPOWER DO I NEED?
HORSEPOWER TO ET CONVERSION CHART
The following chart shows how much total engine horsepower (i.e. “at the flyhweel”) is need to run a particular ET at a given weight. Keep in mind this is under optimal conditions (traction, shifting, etc.) and assumes that your are utilizing every bit of power.
In reality very few cars run 100% of their optimum. Wheelspin, slow shifting, clutch slippage, and other factors “bleed off” the usable horsepower. Figure on adding as much as 10% to the power numbers below (or add a few tenths to the ET) to get a real world estimate.
ET (seconds) VEHICLE WEIGHT *(pounds)
2600 2800 3000 3200 3400 3600 3800 4000
15.0 152 164 176 187 199 211 223 234
14.5 169 182 194 207 220 233 246 259
14.0 187 202 216 230 245 259 274 288
13.5 209 225 241 257 273 289 305 321
13.0 234 252 270 288 306 324 342 360
12.5 263 283 304 324 344 364 385 405
12.0 297 320 343 366 389 412 435 458
11.5 338 364 390 416 442 468 494 520
11.0 386 416 445 475 505 535 564 594
10.5 444 478 512 546 580 615 649 683
10.0 514 553 593 632 672 712 751 791
9.5 599 645 692 738 784 830 876 922
9.0 705 759 813 868 922 976 1,030 1,084
8.5 837 901 965 1,030 1,094 1,159 1,223 1,287
8.0 1,004 1,081 1,158 1,235 1,312 1,390 1,467 1,544
*fully loaded with driver, fuel, etc.
