Question

*photo attached* The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.67 m and 1.01 m, respectively. The respective rotational speeds are 444 rev/min and 4,130 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 178.3 m/s and  tail rotor 218.4 m/s.

(b) The speed of the main rotor is 0.52 speed of sound, and the speed of the tail rotor is 0.64 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) = (444 rev/min x 2π rad x 1 min/60s) x (0.5 x 7.67 m)

v(main rotor) = 178.3 m/s

v(tail rotor) = (4,130 rev/min x 2π rad x 1 min/60s) x (0.5 x 1.01 m)

v(tail rotor) = 218.4 m/s

Speed of the rotors with respect to speed of sound

% speed (main motor) = 178.3/343 = 0.52 = 52 %

% speed (tail motor) = 218.4/343 = 0.64 = 64 %

Thus, the speed of the main rotor is 0.52 speed of sound, and the speed of the tail rotor is 0.64 speed of sound.

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

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