Question

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 75.0 m/s 75.0 m/s, and the speed of the propeller tips through the air must not exceed 270 m/s 270 m/s. (This is about 80% of the speed of sound in air. If the propeller tips moved faster, they would produce a lot of noise.) What is the maximum possible propeller radius?

Answer 1

Answer:

r = 1.07 m

Explanation:

The maximum radius of the propeller that can be allowed is given by the following formula:

$v = r\omega\\\\r = \frac{v}{\omega}$

where,

r = maximum possible radius of the propeller = ?

v = maximum possible linear speed of the propeller = 270 m/s

ω = angular speed of the propeller = (2400 rpm)(2π rad/1 rev)(1 min/60 s)

ω = 251.33 rad/s

Therefore,

$r = \frac{270\ m/s}{251.33\ rad/s}$

r = 1.07 m