Calculating HP

Discussion in 'Math' started by Dynamic_Thom, Aug 7, 2015.

1. Dynamic_Thom Thread Starter New Member

Jul 16, 2015
7
0
So in the formula for calculating Torque in an ac motor

T = 5252 HP/rpm

Can anybody describe to me where the 5252 comes from, I have been trying to figure it out.

Thanks

2. ericgibbs Senior Member

Jan 29, 2010
2,499
380
Dynamic_Thom and MrAl like this.
3. Papabravo Expert

Feb 24, 2006
10,135
1,786
The answer to this type of question is always the same. It is a constant of proportionality designed to make the units on both sides of the equals sign agree. In all the algebraic equalities that you will ever see, besides all the ones that you won't, both the numbers and the units must agree

4. WBahn Moderator

Mar 31, 2012
17,715
4,786
First off, as is so often the case, the equation as given is meaningless without a crystal ball.

If you divide HP by rpm you get a torque that has perfectly valid, if inconvenient, units. The purpose of the 5252 is to scale that torque to more convenient units, but since no units are given you have to guess at what the final units of torque are. Are they ft·lb? oz·in? N·m? Engineering is not about guessing! That's how airliners run out of fuel in midflight and multibillion dollar space probes get slammed into planets.

Power = work per unit time
Work is force through a distance
Torque is force applied with a lever arm to create a turning moment

So image you have a wheel of radius R with a rope affixed to it and wrapped around it. A force, or tension, F, is applied to this rope in order to turn the wheel. The amount of work down by this force is F multiplied by the amount that the rope unwinds off the wheel, which is 2piR for each revolution of the wheel. Hence the work done per revolution is

The power is this amount of work divided by how long it takes to happen

P = (work done per revolution)/(time to complete one revolution)

If t is the amount of time to complete one revolution, then the speed of rotation is

S = 1/t => t = 1/S

The torque is just the force multiplied by the moment arm, so

T = R·F

T = (P/S) (1 rev/ 2pi radians)

This is all you need. Now you just need to multiply by one using appropriate units.

If you want P in HP and T in ft·lb, and S in rpm, then

T = (P/S) (1 rev/ 2pi radians) {[550 ft·lb/s]/[1 HP]} {[1 rpm]/[1 rev / 1 min]} {[60 s]/[1 min]}

Note that each term in curly braces is simply equal to one.

Multiplying this all out and we have

T = (P/S) [ 5252 ft·lb·rpm/HP ]

The key point is to recognize that the term in square brackets is identically equal to one (rounding aside). If you use P with units of HP and S with units of rpm, then the units that survive are ft.lb, which are A unit of torque, but not the ONLY units of torque.

Papabravo likes this.
5. Papabravo Expert

Feb 24, 2006
10,135
1,786
My point was that this same detailed analysis method can be applied to any and all problems that show up with one or more mysterious constants of proportionality.

The very first question you should always ask is: "what are the units of Torque", as defined or implied by this formula.

It is fortunate that even if you don't know the answer to that question there is a small finite set of high probability choices you can choose from to see if one of them fits.

6. shortbus AAC Fanatic!

Sep 30, 2009
4,000
1,512
Learned something in this thread. Didn't know the "5252" also applies to electric motors too. It also is the cross over RPM of an internal combustion engine, where the torque and horsepower on a dynamometer graph are the same.

7. WBahn Moderator

Mar 31, 2012
17,715
4,786
What does it mean for torque and horsepower to be the same?

This is like saying that someone's age is the same as their height. It's meaningless.

8. Wendy Moderator

Mar 24, 2008
20,764
2,534
Seems like they correlate to me. A motor in a car produces a torque, which translates into HP.

9. shortbus AAC Fanatic!

Sep 30, 2009
4,000
1,512
But it's not. The Hp and torque is the same number at or very close to 5252RPM,but is usually rounded off to 5200RPM on dyno charts. Before that the torque number is higher than the HP number. After that the HP number gets higher and the torque drops.

An electric motor or steam engine is different. The torque is highest at starting and drops as RPM increases.

Last edited: Aug 8, 2015
10. WBahn Moderator

Mar 31, 2012
17,715
4,786
Again, what does it mean for horsepower and torque to "be the same number"?

At 5252 rpm, something that is producing 1000 hp of power will be producing 1000 ft·lb of torque.

So what?

That same motor at that same speed is also producing 746 kW of power and 1356 N·m of torque.

So, again, what does it mean for the horsepower and torque to "be the same number"?

You have many different units of power and many different units of torque. Pick any pair and you will have some speed at which the numerical value of the power, in that power unit, is equal to the numerical value of the torque, in that torque unit.

So what?

Pick a speed and I can device a power unit and a torque unit that will be numerically equal at that speed.

The notion of the power being equal to the torque is fundamentally meaningless.

11. ericgibbs Senior Member

Jan 29, 2010
2,499
380
I understand what 'shortbus' is simply saying, is that the Power and Torque plots intersect at that value.

shortbus likes this.
12. boatsman Senior Member

Jan 17, 2008
165
382
Very ambiguous headline. I thought at first it was someone getting a dig at Hypatia's Protege.

13. WBahn Moderator

Mar 31, 2012
17,715
4,786
No, they don't. Saying that they intersect is saying that they are equal at that point and they aren't. All that is happening is that they are being numerically scaled to create this superficial impression.

Horsepower and torque are two different things and any claim that they are ever equal is meaningless.

Plot those exact same curves except use newton-meters for torque and watts for power? Do they still intersect at 5252 rpm? No? If not, then what is magical about this 5252 rpm?

14. ericgibbs Senior Member

Jan 29, 2010
2,499
380
I did not use the word 'equal', nor am I suggesting that they are equal, I said the lines intersect.

15. WBahn Moderator

Mar 31, 2012
17,715
4,786
Okay, so what does it mean when lines intersect?

16. ericgibbs Senior Member

Jan 29, 2010
2,499
380
You obviously know the answer, but this is the definition I consider as correct.
Lines that have one and only one point in common are known as intersecting lines.

ie: one point in common, which the posted plot shows at 5252.
I have assigned no more significance to that point other than its the intersection point of the two plot lines.

Without wishing to sound adversarial, why are you making such an issue of this minor point.

E

shortbus likes this.
17. WBahn Moderator

Mar 31, 2012
17,715
4,786
So lines that have two or more points in common do not intersect?

As for why I keep asking what the meaning supposedly is, it's because I think that shortbus is ascribing meaning where none exists. The notion that the horsepower number and the torque number are the same at 5252 rpm is nonsensical and has exactly as much significance as saying that someone's age is the same as their height if they happen to be 36 months old and 36 inches tall.

18. Wendy Moderator

Mar 24, 2008
20,764
2,534
I'm still trying to wrap my head around what the difference is. Most motors product rotary energy, which can be expressed as a torque value. Through the entire gear chain it is rotary in nature. Even the tires are producing torque, it is translated to linear motion where the rubber meets the road. So how is torque not equivalent to HP?

19. ericgibbs Senior Member

Jan 29, 2010
2,499
380
Obviously they do, I thought you would know that, are you saying they don't.?

I agree.

'shortbus' post was ambiguous regarding saying the two values are the same, you corrected him, but in your post #13 you quoted my post
I understand what 'shortbus' is simply saying, is that the Power and Torque plots intersect at that value.
Which I still consider is what he was actually meant.

EDIT:
Corrected quotes

shortbus likes this.
20. WBahn Moderator

Mar 31, 2012
17,715
4,786
Torque is a twisting force, for lack of a better description. If you take a 2 ft wrench and apply 10 lb of force to the end of it, you are applying 20 ft-lb of torque to the nut (or whatever is at the center of rotation). If you replace that wrench with a 4 ft wrench and apply the same 10 lb of force, you are applying 40 ft-lb of torque. But if the wrench doesn't move, then you are delivering zero horsepower in either case because power requires that force be applied through a distance.

If the torque is being applied and there is rotational motion, then power IS being developed and the amount of power is proportional to the product of the torque and the rotational speed. The same torque at twice the speed results in twice the power, but twice the torque at the same speed also results in twice the power.