Question

In: Physics

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.59 m...

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.59 m and 1.01 m, respectively. The respective rotational speeds are 453 rev/min and 4129 rev/min. Calculate the speeds of the tips of both rotors.


m/s (main rotor)


m/s (tail rotor)


Compare these speeds with the speed of sound, 343 m/s.


(vmain rotor / vsound)


(vtail rotor / vsound)

Solutions

Expert Solution

Speed of sound = V = 343 m/s

Diameter of the main rotor = D1 = 7.59 m

Radius of the main rotor = R1 = D1/2 = 7.59/2 = 3.795 m

Angular speed of the main rotor = 1 = 453 rev/min = 453 x (2/60) rad/s = 47.44 rad/s

Speed of the tip of the main rotor = V1

V1 = 180 m/s

Ratio of the speed of the tip of the main rotor with the speed of sound = f1

f1 = 0.525

Diameter of the tail rotor = D2 = 1.01 m

Radius of the tail rotor = R2 = D2/2 = 1.01/2 = 0.505 m

Angular speed of the tail rotor = 2 = 4129 rev/min = 4129 x (2/60) rad/s = 432.4 rad/s

Speed of the tip of the tail rotor = V2

V2 = 218.4 m/s

Ratio of the speed of the tail rotor with the speed of sound = f2

f2 = 0.637

a) Speed of the tip of the main rotor = 180 m/s

b) Speed of the tip of the tail rotor = 218.4 m/s

c) Ratio of the speed of the tip of the main rotor to the speed of sound = 0.525

d) Ratio of the speed of the tip of the tail rotor to the speed of sound = 0.637


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