Speed Calculation of a Helicopter Rotor

What is the linear speed of the tip of the helicopter rotor blade?

A model of a helicopter rotor has four blades, each 3.4 m in length from the central shaft to the tip of the blade. The model is rotated in a wind tunnel at 550 rev/min.

Answer:

The linear speed of the tip of the blade is approximately 196 m/s.

To calculate the linear speed of the tip of the blade, we can use the formula: linear speed = radius x angular speed. In this case, the radius of each blade is 3.4 m and the rotor is rotating at 550 rev/min.

First, we need to convert the angular speed from revolutions per minute to radians per second. Since 1 revolution is equal to 2π radians, we multiply the angular speed by 2π to convert it. Therefore, 550 rev/min is equivalent to 550 x 2π / 60 = 57.9 rad/s.

Next, we can calculate the linear speed by multiplying the radius by the angular speed. So, linear speed = 3.4 m x 57.9 rad/s = 196 m/s.

The linear speed of the tip of the blade can be calculated using the formula for speed. In this case, the length of the blade's path (or circumference) for each rotation is multiplied by the number of rotations per minute, and then converted from minutes to seconds, giving a result of approximately 196 m/s.

The calculation involves the understanding of rotational motion and speed. The distance a point on the blade tip covers when the rotor makes one complete revolution is its circumference, which is the length of the blade multiplied by 2π. If you multiply this by the number of revolutions per minute and then convert that speed to meters per second, you get the answer.

The formula used for this calculation is: linear speed = 2πr x number of rotations/60. By substituting the values into the formula, we get linear speed = 2π x (3.4 m) x (550 rev/min) / 60 sec, resulting in a linear speed of approximately 196 m/s.