Question

A ship propelled by a turbine rotor which has a mass of 5 tonnes and a speed of 2100 r.p.m. The rotor has a radius of gyration of 0.5 m and rotates in a clockwise direction when viewed from the stern. Find the gyroscopic effect when the ship sails at a speed of 30 km/h and steers to the left in a curve having 60 m radius.

(a) 38.5 kN-m

(b) 48.5 kN-m

(c) 58.5 kN-m

(d) 68.5 kN-m

I had been asked this question by my college director while I was bunking the class.

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

Answer 1

The correct option is (a) 38.5 kN-m

To explain I would say: Given : m = 5 t = 5000 kg ; N = 2100 r.p.m. or ω = 2π × 2100/60 = 220 rad/s ; k = 0.5 m

v = 30 km / h = 8.33 m / s ; R = 60 m

We know that angular velocity of precession,

ωp = v/R = 8.33/60 = 0.14 rad/s

and mass moment of inertia of the rotor,

I = m.k^2 = 5000(0.5)2 = 1250 kg-m^2

Gyroscopic couple,

C = I.ω.ωp = 1250 × 220 × 0.14 = 38 500 N-m = 38.5 kN-m