Question

The turbine rotor of a ship has a mass of 8 tonnes and a radius of gyration 0.6 m. It rotates at 1800 r.p.m. clockwise, when looking from the stern. Determine the gyroscopic couple, if the ship travels at 100 km/hr and steer to the left in a curve of 75 m radius.

(a) 100.866 kN-m

(b) 200.866 kN-m

(c) 300.866 kN-m

(d) 400.866 kN-m

The question was posed to me during an internship interview.

This key question is from Effect of Gyroscopic Couple on an Aeroplane in portion Gyroscopic Couple and Precessional Motion of Machine Dynamics

Answer 1

The correct answer is (b) 200.866 kN-m

The explanation: Given: m = 8 t = 8000 kg ; k = 0.6 m ; N = 1800 r.p.m. or ω = 2π × 1800/60

= 188.5 rad/s ; v = 100 km/h = 27.8 m/s ; R = 75 m

We know that mass moment of inertia of the rotor,

I = mk^2 = 2880 kg-m^2

and angular velocity of precession,

ωP = v / R = 27.8 / 75 = 0.37 rad/s

We know that gyroscopic couple,

C = I.ω.ωP = 2880 × 188.5 × 0.37 = 200 866 N-m

  = 200.866 kN-m