KW to HP Formula Conversion

[DickDV]

I can't seem to make the numbers come out converting the HP formula (ft-lb x rpm/5252) to KW (N-m x rpm/9549).

If I substitute .746kw for hp and N-m/.74 for ft-lb I get

.746kw = N-m/.74 x rpm/5252

Solving for kw I get N-m x rpm/2899

What am I doing wrong?

 

[desertfox]

Hi DickDV

try this convertor:-

http://www.mr2ownersclub.com/converter.htm

desertfox

 

[electricpete]

Here is how I do it. When you have a formula with something like "P in horsepower", it represents a unitless quantity P/hp. Susbstitue P/hp and similar for other quantities and carry out standard unit analysis.

(P/hp) = (T/ft*lbf) * (N/rpm) / 5252

Multiply by conversions equal to 1 in square brackets:
(P/hp) * [hp/0.746kw] = (T/ft*lbf) *[0.74*ft-lbf/N-m] * (N/rpm) / 5252

(P/kw) = 0.746 * 0.74 * (T/N-m) * (N/rpm) / 5252

(P/kw) = * (T/N-m) * (N/rpm) / [5252/0.746 * 0.74]

Multiply out the quantity in brackets

(P/kw) = (T/N-m) * (N/rpm) / 9565
Pretty close to 9549... more decimal places on the conversion would probably recreate the number more exactly



=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

Correction: need extra brackets <> to clarify the meaning:
(P/kw) = * (T/N-m) * (N/rpm) / [5252/<0.746 * 0.74>]

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[waross]

Did I get this right?
I ft. lb. = 1.3558179483 Newton meters
5252/1.356 = 3874

(N-m x rpm/9549)
Should this be (N-m x rpm/3874)


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[electricpete]

Should this be (N-m x rpm/3874)

No. The two relationships stated by DickDv are correct. I provided above the conversion between the two relationships. Also we can start from first principlesand derive each of them:

P = T * 2 * Pi * N
Divide each side by hp
P / hp = T * 2 * Pi * N / hp
Multiply rhs by two items both equal to 1:
P / hp = T * (ft-lbf/ft-lbf) * 2 * Pi * N * (min/min) / hp
regroup terms:
P / hp = T/ft-lbf * 2 * Pi * N /min^-1 * (ft-lbf / minute) *1/ hp
add conversion:
P / hp = T/ft-lbf * 2 * Pi * N /min^-1 * (ft-lbf / minute) *(1/ hp) * <hp/<33000 ft-lbf/minute>
collect constants:
P / hp = T/ft-lbf * N /min^-1 / <33000/[2*Pi]>
compute constant:
P / hp = T/ft-lbf * N /min^-1 / 5250
Write in words:
Power in horsepower = Torque in ft-lbf * speed in rpm / 5250

P = T * 2 * Pi * N
divide each side by kw
P / kw = T * 2 * Pi * N / kw
Multiply rhs by two items both equal to 1:
P / kw = T * (N-m/N-m) * 2 * Pi * N * (min/min) / kw
regroup terms:
P / kw = T/N-m * 2 * Pi * N /min^-1 * (N-m / minute) *(1/ kw)
collect constants:
P / kw = T/N-m * 2 * Pi * N /min^-1 * (N-m / minute) *(1/ kw ) * <kw/[1000*N*m/sec]> (min/<60sec>)
P / kw = T/N-m * N /min^-1 / [1000*60/<2*pi>]
compute constant:
P / kw = T/N-m * N /min^-1 / 9549
Write in words:
Power in kw = Torque in N-m * Speed in rpm / 9549


=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[burnt2x]

Nope.
5252 evolves from the amount of foot-lbs/min of 1 HP which is 33,000.
When used on the HP-Torque formula:

P = w X Torque
 where:
   w = 2 X pi X N(rpm)

So, we divide 33,000 ft-lb/min by 2pi, the constants in the formula to simplify the equation, hence approx. equal to 5252.
WE have the formula:

    (Torque-ft-lbs) X Rev/min)
P =  -------------------------
             5252

P is in HP; Torque in foot-lbs

The same thing when doing it the metric way:
9550 is the result of converting the "minute" portion of RPM into "seconds" and the 2pi constant. 9550 comes from dividing 60 seconds/ 2pi. The result is 9.54929, say 9.55. If you will express the power in kW, then you need to multiply 9.55 by 1000, hence you will have 9550 as a constant of conversion.
P = Torque(N-m) X RPM/9550

 

[Skogsgurra]

A European perspective:

The European Horsepower is defined as 75 lifting 75 kg 1 m vertically in 1 second.

75 kg in Earth's gravity field is 9.81.., so 75 kg of mass equals 736 N. From which can be derived that 1 European Horsepower equals 736, sometimes 735 watts (gauge marks on slide rules have 735). It depends on how many decimals you use in g0.

If that is because European horses are weaker than the American horses or because a "convenient" number like 75 was chosen for the conversion, I don't know.

But I do know that this little discrepancy has caused some discussions over the years. We never use Horsepower for power - always watts. So, we don't bother to use the 736 factor either.

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[burnt2x]

Sorry, Epete beat me to the button.

 

[DickDV]

First, thanks to those who replied.

I'm having a bit of trouble seeing why the hp and Ft-lbf terms are "unitless". That has the effect of inverting the .746 and .74 multipliers and, as a result, 5252 gets divided by .746 and .74 instead of multiplied.

Hmmmm! I'm going to let my subconscious work on that awhile.

Thanks again to each who responded.

 

[cswilson]

Dick

A "forensic" technique I use when I get results that don't match is to compare my error to the numbers in the equations. I instantly applied it to your problem. You got a factor of 2899 when you should have gotten one of 9549. So:

2899/9549 = 0.304

Your two factors are 0.746 and 0.74. Their product is 0.552.

Now, note that 0.552^2 = 0.304. Coincidence? I think not!

This is a strong indication that you multiplied when you should have divided or vice versa (this accounts for the squaring).

The next question is why you made this mistake. I looked at your "formulas" for HP (ft-lb*rpm/5252) and kW (N-M*rpm/9549). I have grown to despise these types of "formulas" with constants in them because they are so prone to confusion. Let's look at them more carefully.

When you say that the formula for HP is (ft-lb*rpm/5252), what you really are saying is that

1 HP = 5252 ft-lb * rpm

(burnt2x provided the confirming derivation for this.) Note that 5252 is in the numerator, not the denominator.

Now we start our conversions very carefully.

1 HP * (0.746 kW / HP) = 5252 ft-lb * rpm

0.746 kW = 5252 ft-lb * rpm

1 kW = 7040 ft-lb * rpm

1 kW = 7040 ft-lb * rpm * (N-m / 0.74 ft-lb)

1 kW ~= 9549 N-m * rpm

Your problem came from the fact that this type of expression of units is fundamentally misleading. I have made the same type of mistake with formulas like this, which is why I could spot yours quickly.

Curt Wilson
Delta Tau Data Systems

 

[electricpete]

I did not say P is unitless, I said P/hp is unitless.
P is a physical varaiable representing power.
I can choose to express a given power level in many different units, but that does not change the physical variable.

For example I can write:
P = 10 KW = 7.5HP
The equals sign indicate that all three are the same even if I express them differently.

Now divide the equation by 1HP.

P/hp = 10 KW/hp = 7.5HP/hp = 7.5

I hope you agree 7.5 is unitless. The equals signs indicates everything is the same. So P/hp is a unitless quantity also. (Like I said. )

Consider now there are two different ways to write an equation.
1 - The standard way. P = 2*Pi*f * T. We can use any consistent system of units we want and the equation is still true (we dont' have to argue about the best units... just pick the ones you like). If we plug the units in for each quantity as we go, it provides a "double-check" that the units on each side match. (or else we know that we need to add more conversions). Most people that went to engineering school are very familiar and comfortable with this approach.

2 - The way that is common among textbooks geared for non-engineers: P = T * N / 5250 where P in hp, T in ft-lbf, N in rpm. The where and the fact that you are told what units to use are clues that this is a non-standard form. Someone tried to make the formula easier to doing the unit conversions etc for you. As you have discovered it can make lift a lot harder.

The bridge between the two forms is putting the 2nd form in a rational consistent unit basis. It states the numerical value of P in hp is equal to the numerical value of T in ft-lbf times the numerical value of speed in rpm divided by 5250. Each of these numerical quantities can also be viewed as a dimensionless quantity (a number). How do I calculate the number corresponding to "P in hp"? Take the physical variable P and divide by 1 hp (P/hp). That is the bridge between the two types of equations and I have provided several examples above how to apply it.


=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[Skogsgurra]

Hey, Pete!

What kind of horsepower is that?

I know that an American HP is a little bit more than a European HP. But never heard of one that is 1.333 kW

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[electricpete]

Yes, there was an obvious typo. Should be:

P = 7.5 KW = 10HP
The equals sign indicate that all three are the same even if I express them differently.

Now divide the equation by 1HP.

P/hp = 7.5 KW/hp = 10HP/hp = 10.0

I hope you agree 10.0 is unitless. The equals signs indicates everything is the same. So P/hp is a unitless quantity also. (Like I said. )

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[Skogsgurra]

You were close to overunity there, Pete. Big time.

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[rbulsara]

DickV:

I believe ft-lb=0.74*Nm and NOT Nm/.74.

This relationship is derived from the very fact that .746kW=HP

or 0.746(ft-lb* rpm/5252)=Nm*rpm/9549

This leads to Nm=1.35 ft-lb or ft-lb=0.74 Nm.

There are other factors involved that makes the division of rpm by different numbers in the two systems to come up with the same amount of power. I think your direct substitution is not appropriate.

 

[rbulsara]

My point is you need two independent equations to solve two variables. You have only one.

 

[DickDV]

rbulsara, I've checked with a couple of conversion tables and 1Nm does equal .74Ftlbf.

 

[DickDV]

I'm still having difficulty making the numbers work out correctly. For example, we know that a 1hp 1750rpm motor develops 3ft-lbf torque. Converting the 1hp to kw makes a .746kw motor develop 3ft-lbf torque.

Converting the torque to metric units gives us a .746kw motor developing 3/.74N-m of torque which is 4.05Nm.

Now, using the metric formula 1kw=Nm x rpm/9549 substituting the rpm we have 1kw=Nm x 1750/9549. Solving for the torque is 1 x 9549/1750 =5.46Nm. Reducing the motor power to .746kw reduces the torque in the same proportion so a .746kw motor develops 5.46 x .746 = 4.07Nm

Well, look at that! I think I just persuaded myself! Thanks guys, I think I've got it. Kind of a twisted way of coming into it but it works for me.

 

[Skogsgurra]

Another reason to go metric.

1 pound = .4536 kg = 4.448 N
1 foot = .3048 m
1 foot*1 pound = .3048*4.448 = 1.356 Nm or, inverted, 1 Nm = 0.7375 foot-pound

Data from the CRC Handbook section F.

Vive la Revolution Francaise! Without it, we would still be using feet and pounds ;-)

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...