# Torque Speed

on . Posted in Classical Mechanics

Torque speed, abbreviated as $$T_s$$, also known as torque speed characteristic, refers to the relationship between the torque and rotational speed of a mechanical system, typically an electric motor.  It describes how the torque output of the motor changes as the rotational speed varies.

In an electric motor, torque is the rotational force that causes the motor to produce mechanical work.  Speed, on the other hand, represents the rotational velocity of the motor.  The torque speed provides information about how the motor's torque output varies at different speeds.  The torque speed of a motor is typically graphically represented as a curve.  At low speeds, the motor can often generate a high amount of torque, allowing it to overcome inertia and start heavy loads.  As the speed increases, the available torque may decrease due to various factors such as motor design, electrical characteristics, and mechanical limitations.

The torque speed is influenced by several factors, including the motor's design, winding configuration, magnetic field strength, and supply voltage.  It is essential to consider the torque speed when selecting a motor for a specific application, as it determines the motor's ability to deliver the required torque at different speeds.  Understanding the torque speed is crucial for engineers and designers in various industries.  It helps them select the appropriate motor for a particular application, assess the motor's performance, and determine its operating limits.  It also aids in optimizing system efficiency, ensuring smooth and reliable motor operation, and preventing excessive mechanical stresses or motor overheating.

## Torque Speed formula

$$\large{ T_s = \frac {5252\;HP }{\tau} }$$

### Torque Speed - Solve for Ts

$$\large{ T_s = \frac {5252\;HP }{\tau} }$$

 horsepower, HP torque, τ

### Torque Speed - Solve for HP

$$\large{ HP = \frac {Ts\;\tau }{5252} }$$

 torque speed, Ts torque, τ

### Torque Speed - Solve for τ

$$\large{ \tau = \frac {5252\;HP }{Ts} }$$

 horsepower, HP torque speed, Ts

Symbol English Metric
$$\large{ T_s }$$ = torque speed $$\large{\frac{lbf-ft}{sec}}$$ $$\large{\frac{Btu}{s}}$$
$$\large{ HP }$$ = horsepower   $$\large{\frac{lbf-ft}{sec}}$$ $$\large{\frac{Btu}{s}}$$
$$\large{ \tau }$$  (Greek symbol tau) = torque $$\large{lbf-ft}$$ $$\large{N-m}$$ 