(quoted from post at 15:37:18 05/09/21) JMOR had a good explanation of the origin of the term. James Watt wanted to sell steam engines that could duplicate the working abilities of horses. As equipment at the time was built for horses on treadmills, it was typically sized in terms of how many horses were required to make it work. Hence one horse, two horse, etc. Animals were typically yoked with others of similar size, so it made no sense to have a 1.5 horse piece of machinery at the time.
The horsepower was defined as a force(lbs) x velocity(fps), which gives us the measurement of 550 ft*lbs/second. This was for pulling in a straight line. For rotary power, the definition is still the same, but the measurement is strange.
For rotary power, the measurement is torque(ft*lbs) x rotational velocity (radians/sec). RPM is a much more common unit of rotational velocity, so you have to multiply by 2*pi and divide by 60 to get the result in radians/sec. If this number works out to be 550 ft*lbs/second, you have an engine or motor that will give you 1 HP.
Applying this math to an everyday application is less than straightforward. One common mistake is to overlook the velocity component of horsepower. If you are not careful, you can reach bogus conclusions. Say a locomotive is getting ready to pull a train from a station. The coupler load is in the 10,000's of lbs, but the train hasn't moved (yet). Strictly speaking: HP = force x velocity = ZERO! Then some guys pulls up in his 400HP pickup and claims he has more horsepower than the locomotive, and therefore can pull the train. Clearly not. The locomotive could pull that truck around all day and not even know it was there.
The same trick can be done to artificially increase the horsepower rating of an engine for advertising purposes. Car manufacturers will often report their engine HP ratings at 6000 RPM. I never drive with my engine running this fast. I am typically only at 2000 RPM, so I would only get 1/3 of the claimed HP in real experience. But the math (torque x rotational velocity) gives a big, impressive number for advertising.
Then there is the matter of indicated horsepower, brake horsepower, drawbar horsepower, and actual horsepower. Indicated is the *maximum* amount an engine can produce, based on its firing pressures, bore, and stroke. The user will never see this amount. Brake horsepower is supposed to be the amount measured at the brakes, e.g. after all the internal loads & transmission losses are account for. Again, BHP as it is known, is a *maximum* number of horsepower--e.g. engine loaded almost to the point of stall.
Drawbar horsepower is as measured at the drawbar. This is similar to Watt's original definition. A spring scale is fitted between the drawbar and the wagon load, and this maximum drawing force is measured, along with the speed of the pull in ft/sec. Divide by 550 to get drawbar HP. Again, this is a *maximum* number.
Lastly, actual horsepower is what the machine is actually producing. A tractor pulling a wagon up a steep hill and loaded to the point of stall is producing close to its maximum drawbar (or indicated, or brake) horsepower. The same tractor going down hill, with brakes applied is producing ZERO horsepower, even though its engine is running. Why? Because it's not pulling anything--if anything, the wagon is pushing it. So actual horsepower is what the engine is actually producing. This will always be less than the maximum horsepower available.
The Nebraska tests typically reported drawbar pull (sometimes called tractive effort) for tractors alongside HP, as this is a more useful number than HP alone. An over-sized engine on too light a tractor will simply lose traction and spin its wheels. This is why a 30HP farm tractor can pull that 400HP pickup out of the mud with ease. Tractive effort counts more than HP in many situations. Locomotives are rated in terms of tractive effort for this reason. Rocket and jet engines are also typically rated in terms of thrust, which would be the same thing as drawbar pull if the rocket had a drawbar. All three of these are just the force part of HP, without the velocity, to avoid bogus conclusions.
Matching HP to load is also a source of confusion. It may take only 10 drawbar HP to pull an empty wagon, but 30 HP to pull it when loaded. But using a Farmall M (~33HP drawbar HP as tested) to pull the empty wagon isn't going to break it. Again, as long as the power required is less than the power available, it will work. The tractor will just burn less fuel when pulling the light load. The same thing is true when using a 5HP electric motor to run a saw that only needs 2 HP. The extra 3HP isn't wasted-- the motor just draws less current than for which it is rated. The trouble comes in as most engines produce different amounts of horsepower at different speeds--the so called speed-torque curves. Electric motors have their own curves, as do steam engines, etc. And the same thing is true for loads--pulling twice the speed is not always twice the power. This can get complicated quickly.
Then why is HP even used? A lot of it is just habit. Say a farmer with a team of horses wanted an engine that could replace two horses. But a draft animal is more than a source of power--it has hooves (traction), and can pull with enormous force at slow speeds (that velocity component), but can also break into a trot or a gallop if it has to. It would be difficult to capture all this data with several numbers, much less one number. So the horse equivalent is used, as a carry-over from the old days, although its meaning is less and less clear.
Sorry that went so long, but I wanted to make sure I was thorough. Others will likely have other information to add. In short, HP is a number. A useful number, but still just a number.
Dave
