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

ID: 1430461 • Letter: T

Question

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.55 m and 1.02 m, respectively. The respective rotational speeds are 458 rev/min and 4,129 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.
vmain rotor / vsound =   vtail rotor / vsound =   The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.55 m and 1.02 m, respectively. The respective rotational speeds are 458 rev/min and 4,129 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.
vmain rotor / vsound =   vtail rotor / vsound =   main rotor     m/s tail rotor     m/s

Explanation / Answer

Given
   main rotor and tail rotor diameters are d1 = 7.55 m, d2 = 1.02 m
   their radii r1 = 3.775 m, r2 = 0.51 m


rotational speeds W1 = 458 rev/min = 458/60 = 7.63 rev/s = 47.75 rad/s


and for tail rotor W2 = 4129 rev/min = 68.82 rev/s = 432.40 rad/s

and for speed V = r*w ==> V1 = r1*W1 = 3.775*47.75= 180.26 m/s, vmain rotor / v sound = 180.26/330 = 0.55


for tail rotor speed V2 = r2*W2 = 0.51*432.40 = 220.524 m/s , Vtail rotor / v sound = 220.524/330 = 0.67