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Derive the equation for the gyroscopic couple on a naval ship during pitching.

Mumbai University > MECH > Sem 5 > Theory Of Machines 2

Marks: 5 M

Year: Dec 2014

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Pitching of the ship is usually considered to take place with simple harmonic motion.

The angular displacement θ of the axis of spin from its mean position is given by,

θ=φsinw0t

where φ=the maximum angle turned from the mean position.w0=Angular velocity of SHM=2π/TT=Time period

Angular velocity of precession,

Wp=dθ/dt=φw0cosw0t

This is maximum when cos w0 t = 1.

Therefore, maximum angular velocity of precession wp = φ w0

Gyroscopic couple

C = Iwwp = Iw (φ x 2π/T)

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