Question

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.

(v_{main rotor} / v_sound)

(v_{tail rotor} / v_sound)

Answer 1

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