# Speed Torque Power Calculation | Speed Torque Calculation | Speed Torque Formula

To understand the relationships between speed, torque, and power in a mechanical system, we can use the following key formulas:

### 1. **Power, Torque, and Speed Relationship (Rotational Systems)**

The most fundamental formula that relates power (P), torque (T), and rotational speed (N) is:

$$$$

Where:

- $P$ is power in watts (W),
- $T$ is torque in newton-meters (Nm),
- $\mathrm{\xcf\u2030}$ is angular velocity in radians per second (rad/s).

Since angular velocity $\omega$ is related to the rotational speed $N$ in revolutions per minute (RPM) as follows:

$$\mathrm{\xcf\u2030}=\frac{2\mathrm{\xcf\u20ac}\mathrm{N\; /}}{60}$$

We can substitute $\omega$ into the equation, and the power formula becomes:

$$P=(\frac{T\times 2\mathrm{\xcf\u20ac}\mathrm{N)/}}{60}$$

Where:

- $P$ is power in watts (W),
- $T$ is torque in newton-meters (Nm),
- $\mathrm{N\; is\; speed\; in\; revolutions\; per\; minute\; (RPM).}$

### 2. **Power in Horsepower**

If you want to express the power in horsepower (HP) instead of watts, you can use the conversion factor:

$$1\text{\hspace{0.17em}}\text{HP}=745.7\text{\hspace{0.17em}}\text{W}$$

Thus, the power formula in terms of horsepower is:

$${P}_{HP}=(\frac{T\times \mathrm{N)\; /}}{5252}$$

Where:

- ${P}_{HP}$ is power in horsepower (HP),
- $T$ is torque in pound-feet (lb-ft),
- $N$ is speed in revolutions per minute (RPM),
- 5252 is a constant derived from unit conversions.

### 3. **Torque Calculation from Power and Speed**

To find torque if you know power and speed, rearrange the equation:

$$T=(\frac{P\times \mathrm{60)\; /}}{2\mathrm{\xcf\u20ac}N}$$

Or in horsepower:

$$T=(\frac{{P}_{HP}\times \mathrm{5252)\; /}}{N}$$

Where:

- ${P}_{HP}$ is power in horsepower,
- $T$ is torque in pound-feet (lb-ft),
- $N$ is speed in RPM.

### 4. **Speed Calculation from Power and Torque**

To find speed $N$ from power and torque:

$$N=(\frac{P\times \mathrm{60)\; /}}{2\mathrm{\xcf\u20ac}T}$$

Or in horsepower:

$$N=(\frac{{P}_{HP}\times \mathrm{5252)\; /}}{T}$$

These formulas allow you to compute the interdependencies between speed, torque, and power in rotational mechanical systems.

### Example:

If you have:

- Torque $T=50\text{\hspace{0.17em}}\text{Nm}$
- Speed $N=3000\text{\hspace{0.17em}}\text{RPM}$

The power $P$ in watts is:

$$P=(\frac{50\times 2\mathrm{\xcf\u20ac}\times \mathrm{3000)\; /}}{60}=15,707.96\text{\hspace{0.17em}}\text{W}$$

**The speed and torque of a rotating machine are related through its power and rotational speed. The relationship is described by the following formula:**

Torque (T) = Power (P) / Angular velocity (Ï‰)

Where, T = torque in Newton meters (Nm) P = power in watts (W) Ï‰ = angular velocity in radians per second (rad/s)

To calculate speed and torque, you will need to measure or know the power input to the machine and its rotational speed. Once you have these values, you can use the above formula to calculate the torque and speed.

Here's an example calculation:

Suppose a motor is rated for 1000 watts and runs at 1500 revolutions per minute (rpm). To calculate its torque and speed, follow these steps:

Step 1: Convert the power to watts to the standard unit of measure, which is in watts. 1000 watts is already in the standard unit of measure.

Step 2: Convert the rotational speed from rpm to radians per second (rad/s) using the following formula:

Ï‰ = (2Ï€ x RPM) / 60

Where, Ï‰ = angular velocity in radians per second RPM = rotational speed in revolutions per minute Ï€ = 3.14 (approximate value of pi)

Substituting the values, we get:

Ï‰ = (2Ï€ x 1500) / 60 = 157.08 rad/s

Step 3: Substitute the values for power and angular velocity into the torque formula to get the torque:

T = P / Ï‰ = 1000 / 157.08 = 6.36 Nm (rounded to two decimal places)

So, the motor produces a torque of 6.36 Nm and rotates at a speed of 157.08 rad/s.

**The relationship between motor KW (kilowatts) and torque (T) can be expressed using the following formula:**

KW = (T x Ï‰) / 9549

Where: T is the torque in Nm (Newton-meters) Ï‰ is the angular velocity in radians per second

The constant 9549 is a conversion factor to convert the units of the formula into kW.

To use this formula, you will need to measure or know the torque and angular velocity of the motor. Once you have these values, you can calculate the motor KW using the above formula.

Alternatively, you can rearrange the formula to calculate the torque:

T = (KW x 9549) / Ï‰

Here's an example calculation:

Suppose a motor is rated for 5 kW and runs at 1500 revolutions per minute (rpm). To calculate its torque, follow these steps:

Step 1: Convert the rotational speed from rpm to radians per second (rad/s) using the following formula:

Ï‰ = (2Ï€ x RPM) / 60

Where, Ï‰ = angular velocity in radians per second RPM = rotational speed in revolutions per minute Ï€ = 3.14 (approximate value of pi)

Substituting the values, we get:

Ï‰ = (2Ï€ x 1500) / 60 = 157.08 rad/s

Step 2: Substitute the values for KW and angular velocity into the torque formula to get the torque:

T = (KW x 9549) / Ï‰ = (5 x 9549) / 157.08 = 303 Nm (rounded to two decimal places)

So, the motor produces a torque of 303 Nm when running at 1500 rpm and 5 kW power.

## Post a Comment