In a constant-horsepower motor, what happens to the torque when the speed is cut in half?

In a constant-horsepower motor, the relationship between horsepower (HP), torque (T), and speed (N) is described by the equation:

[ HP = \frac{T \times N}{5252} ]

This indicates that, for a given horsepower level, torque and speed are inversely related. Therefore, if the speed is reduced, torque must increase in order for horsepower to remain constant.

Specifically, if the speed is cut in half, the equation can be rearranged to solve for torque as follows:

If the original speed is ( N ) and the torque is ( T ), with horsepower held constant, we can set up the relationship:

When the speed is halved (( \frac{N}{2} )):

[ HP = \frac{T' \times \frac{N}{2}}{5252} ]

To maintain the same horsepower, we need:

[ \frac{T' \times \frac{N}{2}}{5252} = \frac{T \times N}{5252} ]

This simplifies to:

[ T' \times \frac{N}{2} = T \times N ]

Solving for ( T' ) gives