Question

1. ) The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.52 m and 1.06 m, respectively. The respective rotational speeds are 449 rev/min and 4,150 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

Answer 1

Solution:

Given :

d_mainrotor = 7.52 m

d_tailrotor = 1.06 m

_{main rotor} = 449 rev/min = 47 rad/s

_{tail rotor} = 4150 rev/min = 434.6 rad/s

Since : Speed of tip (v) = r = (d/2)

Thus : V_{main rotor} = (_{main rotor})(d_mainrotor / 2) = (47)(7.52/2) = 176.79 m/s

and, V_{tail rotor} = (_{tail rotor})(d_tailrotor / 2) = (434.6)(1.06/2) = 230.33 m/s

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

Vmain rotor	= 0.515	vsound
Vtail rotor	= 0.672	vsound