I posted this a year ago but it came up in a thread so

A dyno measures Torque, torque is easy a moment arm 1 foot long with a 1-pound weight is 1 pound-foot, increase the weight or moment arm length and increase the torque.

HP is 33,000 foot-pounds of work in one minute or 550 foot-pounds per second

To get from torque to horsepower, you need the "per second" term. You get that by multiplying the torque by the engine speed.
But engine speed is normally referred to in revolutions per minute (RPM). Since we want a "per second," we need to convert RPMs to "something per second." The seconds are easy -- we just divide by 60 to get from minutes to seconds. Now what we need is a dimensionless unit for revolutions: a radian. A radian is actually a ratio of the length of an arc divided by the length of a radius, so the units of length cancel out and you're left with a dimensionless measure.
You can think of a revolution as a measurement of an angle. One revolution is 360 degrees of a circle. Since the circumference of a circle is (2 x pi x radius), there are 2-pi radians in a revolution. To convert revolutions per minute to radians per second, you multiply RPM by (2-pi/60), which equals 0.10472 radians per second. This gives us the "per second" we need to calculate horsepower.
Let's put this all together. We need to get to horsepower, which is 550 foot-pounds per second, using torque (pound-feet) and engine speed (RPM). If we divide the 550 foot-pounds by the 0.10472 radians per second (engine speed), we get 550/0.10472, which equals 5,252.
So if you multiply torque (in pound-feet) by engine speed (in RPM) and divide the product by 5,252, RPM is converted to "radians per second" and you can get from torque to horsepower -- from "pound-feet" to "foot-pounds per second."

See more than you ever cared to know.

Why two different things James Watt wanted to know how much work his coal mining ponies were doing. He also said 1 hp is 746 watts (yes like his name) and 1 hp for 1 hour is 2545 BTU. OK I'll stop now

 

Why does a diesel make say 550 ft pounds of torque at 2200 rpm, and only 200 hp at 3500 rpm, if horsepower is torqueXrpm=HP ??? A gas motor makes it hp at a higher rpm, but a diesel makes more torque at a lower rpm, I don't get it, esplain Lucy,,,, Ken

 

HP= torquexrpm/5252

a PSD makes 500ft/lb torque at 2500 rpm then it is making 238 hp at that same rpm.

a gas motor makes 400lb/ft torque at 2500RPM then it is making 190hp there. Noe what happens is the PSD can not rev any more but the Gas will. Torque will drop but hp will rise due to rpm. so at 6000 rpm the gas is making say 300 lb/ft it will make 342hp.


That is why both are given, it helps paing a picture of the performance. If a 500lb/ft motor makes 200 hp than you know It does not rev. Now peak torque and hp #'s are not in the same place. you know with out needing rpm figures that this motor will not rev.
then you see a 200lb/ft and 500hp you know right away you will need to rev this beast to the moon.
In the end when given torque hp and the rpms they peak at you can right away develope a picture of the motor.

 

The higher the RPM at which an engine can make torque the more horsepower it will have. The formula is slightly different than what you have listed.

Formula:

torque x RPM / 5252 = HP

Example:

550 ftlb x 2200 RPM / 5252 = 230.39 HP

375 ftlb x 7000 RPM / 5252 = 499.81 HP

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Engines typically see a drop in torque as RPM's pass a certian level. But even though the torque is lower, the RPM's are higher. So when you put the figures in the equasion they are making more horsepower even though they are making less torque.

Example:

300 ftlb x 3000 RPM / 5252 = 171.36 HP

250 ftlb x 4000 RPM / 5252 = 190.40 HP

 

Daimon 1054, Thanks for your explanation. I have asked other gear heads I know how HP and torque relate and before long I determine they know less than me. Ok, the math makes sense but could you ( or anyone else) share with us the key parameters for a torque or hp engine. Do high compression and big displacement or long piston stokes lead to high torque (tractor engines) and do small pistons or short strokes lead to high rpm high HP engines with very little low rpm torque (Honda S2000). Is it that simple? I know there are many other variables such as inline vs V engines, valve trains(sp) and piston head designs but what are the top (two or three) design parameters/variables for a gas engine and diesel engine.

I have to add an empirical example that makes me wonder. Cebbies v8s seem to have higher hp than Fords for similar displacement engines and a lot of people buy simply for advertised hp. Fords V8s seem to have a flatter torque curve (and more usable) than chebbie. So what is it in the design that causes that? Then there is the Hemi v8 with 345hp, more than my v10 but my v10 has more torque almost at 1800rpm or so that the hemi ever develops........

 

first hp= torque x rpm / 5252 = torque x RPM / 5252 = HP
yeah I know it's confusing but they are the same.

Longer the stroke the slower the motor will rev that is one reason why a diesel prodeces so much torque but the piston speed starts to really get out of hand with speed so it just can not rev. A short stroke motor is a reving motor. Higher compression means you can squeeze the fule harder and when it burns you get more of the energy that is stored within.
That is very basic. but pretty much hold true from F1 to NASCAR.

Now you are about to get into a real can of worms, valve timing has everything to do with how much air and fuel get into the motor. Chevey wants to sell trucks on HP eventhough any truck owner knows torque is what you want. But chevy is not after working trucks so they tune their motors to rev a little more.

Ford want a usable power so they went to an overhead cam designe, what thet does is allow them to place the valves on opposite sides of the cylinder and the plug in the center. That means air gets in smoother and since the ignition point is near the center and not on the side the flame front has less distance to travle. The Hemi head is almost the excat same thing but the use push rods to move them.
How do you get the best of both worlds, you do what Ford is doing on the new 3 valve 5.4. Variable valve timing, so you get a torque cam and an HP cam in the same motor. That way you get a big smooth torque curve. OK that is about as simple as I can go and still make sence.

Now a diesel makes so much torque because there is no throttle body so when the piston goes down you get an unresticted flow of air and fill the cylinder compleetly, then the right amount of fuel is injected in for the RPM. Also a diesel can run very very lean and still ignite so that is why the better fule mileage at lower RPM but if you start to spin a diesel you would end up using pretty much the same fule as a gas.

OK lastly look at a motorcycle motors. a 1000cc 4 cylinder motor in a crotch rocket has a short stroke and will rev to 11,000 rom or so but it only makes about 60 lb/ft.
Now a V-twin in the Harley (hopped up)vein woud have a long stroke it will not rev past 5500 rpm but it will make say 90lb/ft but would not crack 80hp.
now which do you want? for speed? no doubt the 4 banger for daily usefulness the twin.