Question

An aeroplane makes a complete half circle of 50 metres radius, towards left, when flying at 200 km per hr. The rotary engine and the propeller of the plane has a mass of 400 kg and a radius of gyration of 0.3 m. The engine rotates at 2400 r.p.m. clockwise when viewed from the rear. Find the gyroscopic couple on the aircraft.

(a) 10.046 kN-m

(b) 11.046 kN-m

(c) 12.046 kN-m

(d) 13.046 kN-m

I got this question in a national level competition.

My enquiry is from Effect of Gyroscopic Couple on an Aeroplane in chapter Gyroscopic Couple and Precessional Motion of Machine Dynamics

Answer 1

The correct answer is (a) 10.046 kN-m

For explanation: Given : R = 50 m ; v = 200 km/hr = 55.6 m/s ; m = 400 kg ; k = 0.3 m ;

N = 2400 r.p.m. or ω = 2π × 2400/60 = 251 rad/s

We know that mass moment of inertia of the engine and the propeller,

I = mk^2 = 36 kg-m^2

and angular velocity of precession,

ωP = v/R = 55.6/50 = 1.11 rad/s

We know that gyroscopic couple acting on the aircraft,

C = I. ω. ωP = 36 × 251.4 × 1.11 = 100 46 N-m

  = 10.046 kN-m