Question

The heavy turbine rotor of a sea vessel rotates at 1500 r.p.m. clockwise looking from the stern, its mass being 750 kg. The vessel pitches with an angular velocity of 1 rad/s. Determine the gyroscopic couple transmitted to the hull when bow is rising, if the radius of gyration for the rotor is 250 mm.

(a) 4.364 kN-m

(b) 5.364 kN-m

(c) 6.364 kN-m

(d) 7.364 kN-m

I got this question by my school teacher while I was bunking the class.

My question comes from Effect of Gyroscopic Couple on an Aeroplane in portion Gyroscopic Couple and Precessional Motion of Machine Dynamics

Answer 1

The correct answer is (d) 7.364 kN-m

The best explanation: Given: N = 1500 r.p.m. or ω = 2π × 1500/60 = 157.1 rad/s; m = 750 kg;

ωP = 1 rad/s; k = 250 mm = 0.25 m

We know that mass moment of inertia of the rotor,

I = mk^2 = 46.875 kg-m^2

Gyroscopic couple transmitted to the hull (i.e. body of the sea vessel),

C = I.ω.ωP = 46.875 × 157.1 × 1= 7364 N-m = 7.364 kN-m