In: Physics
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)
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