8 replies to this topic

[Patrice L'Rodent]

Hi Everyone,
I need a little help with a math problem.

The factor 5252 is the 'magic number' when calculating bhp from rpm and torque in ft/lbs, ie
torque/5252 X RPM = BHP.

Can anyone tell me the factor to use when calculating kilowatts from rpm and torque expressed in newton meters ?

Thanks in anticipation.
PDR

[david_martin]

fundementally power = torque * speed

where the speed is the angular velocity in radians per second and the torque and power are in self consistant units.

So power = torque * (2 *pi * speed / 60 / 1000) should give you power in kilowatts if the torque is in Newton metres and the speed in RPM

[Patrice L'Rodent]

Thank you David
I should have known that (Do know that !!) But it is almost midnight here and I should be in bed.
Goodnight
PDR

[Greg Locock]

smallest of niggles - that will give you power in watts, not kW.

By the way 5252 is 33000/(2*pi) - it isn't a magic number at all!

[Wuzak]

power = torque * (2 *pi * speed / 60 / 1000)

Gives power in kilowatts, as the factor of 1000 is in there..

[david_martin]

Originally posted by Greg Locock
smallest of niggles - that will give you power in watts, not kW.

If I had written it as power = (torque / 1000) * (2 * pi * speed / 60), would that convince you it is correct?;)

[Patrice L'Rodent]

Thanks all,
I knew 5252 isn't 'magic', just a term of endearment when you are too tired to do the math...just needed 'jump starting'
The new 'Magic' number I was looking for...according to my calculator... is 9550
Thanks again
PDR

[Greg Locock]

Oops, sorry, how did I miss that 1000?

[Julius]

Power = Torque (T) * Angular Velocity (V) = T * V (equation 1)

The trick is to convert this relationship to units with which we are familiar.

For the fps case:

Converting RPM to Angular Velocity
1 RPM = (2 * Pi)/(60 s) = [2 * (Pi/60)] (rad/s) [comment: the term radians (rad) is dimensionless ]

Relating ft-lb to Horse Power
1 HP = 550 ft-lb/s [comment: this constant that will be used in the equation below .]

Now, using eq 1 & dimensional analysis, HP expressed in Torque (ft-lb) and Angular Velocity (RPM)

HorsePower = [T ft-lb] * [(HP * s)/550 ft-lb)] * [RPM (2* pi rad)/(60 s)] = (T * RPM)/5252.11

Or, more or less HP= (T * RPM)/5252 [comment: where Torque expressed in ft-lbs ]

For the mks case:

Converting RPM to Angular Velocity
1 RPM = (2 * Pi)/(60 s) = [2 * (Pi/60)] (rad/s) [same as done above for fps case ]

Relating N * m to KWatts
1 KW = 100 Watts = 1000 * N*m /s [comment: constant that will be used in the equation below .]

Now, using eq 1 & dimensional analysis, KW expressed in Torque (N*m) and Angular Velocity (RPM)

KiloWatts (KW) = [T ft-lb] * [(KW * s)/1000 N-m)] * [RPM (2* pi rad)/(60 s)] = (T * RPM)/9549.29

Or, more or less HP= (T * RPM)/9549 [comment: where Torque expressed in N*m ]