Shaft Torque, Power, and Speed

The power of a rotating shaft can be found by:

$$H=T\omega$$

where:

• $H$ is power, in watts $\text{W}$
• $T$ is torque, in $\text{N}\cdot \text{m}$
• $\omega$ is angular velocity, in $\text{rad}/\text{s}$

When dealing with RPM, we can use the conversion:

$$T=9.55\frac{H}{n}$$

where $H$ is power in watts and $n$ is the angular velocity in terms of RPM.

In U.S. customary units, we have:

$$H=\frac{FV}{33000}=\frac{2\pi Tn}{33000(12)}=\frac{Tn}{63025}$$

where:

• $H$ is power in horsepower $\text{hp}$
• $T$ is torque in $\text{lbf}\cdot \text{in}$
• $n$ is shaft speed in $\text{rev}/\text{min}$
• $F$ is force in $\text{lbf}$
• $V$ is velocity in $\text{ft}/\text{min}$