Question

The turbine rotor of a ship has a mass of 3500 kg. It has a radius of gyration of 0.45 m and a speed of 3000 r.p.m. clockwise when looking from stern. Determine the gyroscopic couple upon the ship when the ship is steering to the left on a curve of 100 m radius at a speed of 36 km/h.

(a) 11.27 kN-m

(b) 22.27 kN-m

(c) 33.27 kN-m

(d) 44.27 kN-m

The question was posed to me in exam.

Question is from Effect of Gyroscopic Couple on an Aeroplane in section Gyroscopic Couple and Precessional Motion of Machine Dynamics

Answer 1

Right answer is (b) 22.27 kN-m

Easy explanation: Given : m = 3500 kg ; k = 0.45 m; N = 3000 r.p.m. or ω = 2π × 3000/60 = 314.2 rad/s

When the ship is steering to the left

Given: R =100 m ; v = km/h = 10 m/s

We know that mass moment of inertia of the rotor,

I = mk^2 = 708.75 kg-m^2

and angular velocity of precession,

ωp = v/R = 10/100 = 0.1 rad/s

Gyroscopic couple,

C = I.ω.ωp = 708.75 × 314.2 × 0.1 = 22 270 N-m

  = 22.27 kN-m