Angular and linear velocity propeller

In summary, the maximum radius of the airplane propeller must be determined in order to ensure that the speed of the tips of the blades does not exceed 270m/s, which would create excessive noise. This can be calculated using the equation vtip2 = vplane2 + vtan2, where vplane represents the forward airspeed of the plane and vtan is the tangential velocity of the propeller. The direction of vtip is also tangential to the direction of motion of the propeller.
  • #1
henry3369
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Homework Statement


You are designing an airplane propeller that is to turn at 2400 rpm (Fig. 9.13a). The forward airspeed of the plane is to be 75m/s, and the speed of the tips of the propeller blades through the air must not exceed 270m/s. (This is about 80% of the speed of sound in air. If the speed of the propeller tips were greater than this, they would produce a lot of noise.) What is the maximum possible propeller radius?

Homework Equations


vtip2 = vplane2 + vtan2

The Attempt at a Solution


I know how to solve this equation to find the maximum radius, but I'm having trouble understanding the derivation of the equation. I know that vplane points in the direction of the plane's motion; thus, the propeller also has this same velocity in the same direction. Then angular velocity can be related to tangential velocity by v = rw. How does the vector sum of these two result in the velocity of the tip of the propeller and isn't the direction of vtip also be tangential to the direction of motion of the propeller so vtip = vtan?
 
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  • #2
Tip trajectory is a spiral in the air. The 75 m/s does contribute (a little) in the square root of the squared sum.
 

FAQ: Angular and linear velocity propeller

What is the difference between angular velocity and linear velocity of a propeller?

Angular velocity is the rate of change of the angular position of a propeller, measured in radians per second. Linear velocity, on the other hand, is the rate of change of the linear position of a propeller, measured in meters per second. In other words, angular velocity refers to how fast the propeller is rotating, while linear velocity refers to how fast the propeller is moving through space.

How are angular velocity and linear velocity of a propeller related?

Angular velocity and linear velocity of a propeller are related through the radius of the propeller. The linear velocity is equal to the angular velocity multiplied by the radius of the propeller. This means that as the radius of the propeller increases, the linear velocity also increases, while the angular velocity remains the same.

Why is it important to understand angular and linear velocity of a propeller?

Understanding angular and linear velocity of a propeller is crucial for designing and optimizing propellers for different applications. It allows scientists and engineers to determine the optimal size and shape of a propeller for a specific use, such as in aircraft or marine vehicles. It also helps in predicting the performance and efficiency of a propeller.

How can angular and linear velocity of a propeller be measured?

Angular and linear velocity of a propeller can be measured using various instruments such as tachometers, accelerometers, and speedometers. These instruments use different methods, such as optical sensors or magnetic sensors, to measure the rotation and movement of the propeller and calculate the angular and linear velocity.

What factors can affect the angular and linear velocity of a propeller?

The angular and linear velocity of a propeller can be influenced by multiple factors, including the shape and size of the propeller, the power and torque of the engine, the density and viscosity of the fluid it is moving through, and external forces such as wind or water currents. These factors can impact the efficiency and performance of a propeller and must be considered in its design and operation.

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