Is Horsepower the whole story?

[Bill_C]

Well, torque and horsepower would be equal at 5252 RPM...if the units of torque were ft-lbs. This means that 1 horsepower would produce 1 ft-lb of torque at a rotational speed of 5252 rpm. Or 100 hp would produce 100 ft-lbs of torque at the 5252 rpm.

If the units of torque were inch-lbs, then they'd be equal at 63024 RPM. 1 hp produces 1 in-lb of torque at 62024 rpm.

And if instead of horsepower we were using kilowatts, the number is something else. And something else if torque were Newton-meters.

It's a constant--but it's dependent on the units being used, so that's why I sometimes call it a conversion factor. (The 5252 can be derived, I've done it, but it's late and I've got a migraine so I don't feel like getting out my textbooks)

 

[ShenandoahJoe]

... and now I know why my tachometer has a mark indicating the RPMs I should use to run an attachment on the PTO.

 

[ModMech]

Well, torque and horsepower would be equal at 5252 RPM...if the units of torque were ft-lbs. This means that 1 horsepower would produce 1 ft-lb of torque at a rotational speed of 5252 rpm. Or 100 hp would produce 100 ft-lbs of torque at the 5252 rpm.

Correct, at 5252 RPM HP = Tq, period.

If the units of torque were inch-lbs, then they'd be equal at 63024 RPM. 1 hp produces 1 in-lb of torque at 62024 rpm.

Um., no.

If the units of Tq were "In-lbs", 1 HP @ 5252 RPM = 12 lb-in (instead of 1 lb-ft). Changing the units of measure does not change the RPM at which Tq and HP are equal. Ergs, dyns, Watts, N-M, it doesn't matter, HP = Tq at 5252 RPM.

 

[Bill_C]

I'm not sure why or how you are disputing this.

First, let's assume we are discussing a theoretical constant-horsepower motor. It's rated 1 hp from 1 rpm to 100,000 rpm for example.

If torque is specified in inch-lbs, as it often is for fractional horsepower motors such as servo motors and stepper motors, then the formula is merely converted by multiplying the 5252 by 12. The curves then cross at 63000 rpm. This formula is just as common, and just as valid, as the formula using 5252. At 63000 rpm, the theoretical 1HP motor produces 1 inch-lb of torque. At 63000 rpm, if we want to use different units, the same 1 hp motor produces 1/12 ft-lbs of torque. This is indisputable.

Torque is always "equal" to Hp times a constant for a given RPM. The constant merely changes depending on the units. I can shift the curves anywhere I want merely by changing the units. There is nothing magic with respect to the 5252 rpm.

From the old physics books: Torque equals Force times Distance, or T=FxD

Work equals Torque times delta Theta, where Theta is the angular displacement in Radians. Power is the work done in a unit of time, which means Power=W/t. Substituting backwards, this equates to P=Tw where w is the angular velocity, in radians per sec for example. We can convert radians/sec back to RPM using the appropriate conversion factors. Then we decide whether torque will be in ft-lbs or inch-lbs or n-m, plug in the appropriate conversion factors...and we arive at 5252 for the constant. Or 63024. Or whatever, it depends on the units.

 

[SPYDERLK]

Yay Bill C. :thumbsup:
larry

 

[Typhoon]

I always had trouble understanding torque vs. hp, until I read this little exerpt in a physics book, and it cleared it up to me. Just remember this...... A windmill (the great big wooden ones that they used back in the day to mill flour, etc) exerts approximately 5 horsepower, with about 1,200 foot pounds of torque!!!!

 

[rphinney]

Gary has it right. The lawnmower engines advertise "maximum output" horsepower numbers. If you look at the output curves the engine suppliers put out there will be 2: "maximum output" and "recommended maximum output". The recommended maximum output will typically be much less. If you tried to mow at maximum output you wouldn't be mowing for long.