Question

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.70 m and 1.03 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

(a) The speeds of the tips of both rotors; main rotor 181.02 m/s and  tail rotor 223.8 m/s.

(b) The speed of the main rotor is 52.8 % speed of sound, and the speed of the tail rotor is 65.2 % speed of sound.

Linear speed of main motor and tail rotor

v = ωr

where;

• ω is the angular speed (rad/s)
• r is radius (m)

v(main rotor) = (449 rev/min x 2π rad x 1 min/60s) x (0.5 x 7.7 m)

v(main rotor) = 181.02 m/s

v(tail rotor) = (4,150 rev/min x 2π rad x 1 min/60s) x (0.5 x 1.03 m)

v(tail rotor) = 223.8 m/s

Speed of the rotors with respect to speed of sound

% speed (main motor) = 181.02/343 = 0.528 = 52.8 %

% speed (tail motor) = 223.8/343 = 0.652 = 65.2 %

Thus, the speed of the main rotor is 52.8 % speed of sound, and the speed of the tail rotor is 65.2 % speed of sound.

Learn more about linear speed here: https://brainly.com/question/15154527

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