The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.62 m and 1.01 m, respectively. The respective rotational speeds are 458 rev/min and 4137 rev/min. Calculate the speeds of the tips of both rotors.
main rotor | m/s |
tail rotor | m/s |
Compare these speeds with the speed of sound, 343 m/s.
v_{main rotor} / v_{sound} | |
v_{tail rotor} / v_{sound} |
here,
dia of main rotor, dr = 7.62 m
dia of tail rotor, dt = 1.01 m
Velocity of main rotor, vr = 458 rev/min
wr = 458 * (2*pi/60) = 47.961 rad/s
Velocity of tail rotor, vt = 4137 rev/min
wr = 4137 * (2*pi/60) = 433.225 rad/s
as, Velocity = angular velocity * radius
for main rotor:
vr = wr * dr/2
vr = 47.961 * 7.62/2
vr = 182.731 m/s
for Tail rotor:
vt = wt * dt/2
vt = 433.225 * 1.01/2
vt = 218.778 m/s or 219 m/s(rounded off)
as Velocity of sound = 343 m/s
Case 1 :
vmain rotor / vsound = 182.731 / 343 = 0.532 , about 53 %
Case 2:
vtail rotor / vsound = 219 / 343 = 0.638 , 63.8 % or 64 %(rounded
off)
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