# Power/Torque relations

1. Jul 7, 2009

### stickers

Hi all..

I've been seeing the famous equation which 'converts' horsepower into torque: HP = Torque (lb/ft) * rpm / 5252. The 1/5252 comes from 2*PI/33,000.

Power (rotational) is simply torque * angular velocity, isn't it? When I try to plot the imperial version, I get the typical graph with HP and torque intersecting at 5252rpm. But when I try to plot the same torque values in metric using Power (kW) = Torque (Nm) * rpm * 2*PI/60, I get something wayy different with the power and torque curves not even intersecting.

Am I missing out on something? =/

2. Jul 7, 2009

### FredGarvin

$$P(kW) = \frac{T(Nm) * \omega (rpm)}{9549}$$

The 9549 comes from $$\frac{60*1000}{2 \pi}$$
You're forgetting the factor of 1000 by the looks of it.

Last edited: Jul 7, 2009
3. Jul 8, 2009

### stickers

Ah.. so that's how. I've seen this 9549 number before, but couldn't figure out how it was derived. Thanks!

But i've tried plotting typical values for torque for this equation, and I still don't get the typical curves. That equation means the curves will intersect at 9545rpm isn't it? How do we get the typical curve intersecting somewhere in the middle?

4. Jul 8, 2009

### KLoux

What do you mean by the "typical curves?" Do you mean for an automotive engine or for an electric motor? These motors have different characteristics that can make the torque-rpm and power-rpm curves very different.

For example, a typical DC motor torque-speed curve has a flat (constant-torque) region from 0 RPM up to some "base speed," at which point the torque starts to decrease as the speed increases (constant-power region). If you were to overlay a power-speed curve, it would start at zero and increase linearly up to the base speed, at which point it would level off. The curves would not necessarily intersect at the same speed, torque, or power for all DC electric motors. What is true, however, is that at any point on the curve, the torque-power-speed relationship that you and Fred posted holds.

-Kerry

5. Jul 8, 2009

### FredGarvin

It works for me just fine

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6. Jul 8, 2009

### mheslep

You use Excel for these quick plots?

7. Jul 8, 2009

Yup.