# Angular and linear velocity propeller

1. Feb 13, 2015

### henry3369

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
vtip2 = vplane2 + vtan2

3. 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?

2. Feb 13, 2015

### BvU

Tip trajectory is a spiral in the air. The 75 m/s does contribute (a little) in the square root of the squared sum.