gyroscope effect in ship due to pitching

1. Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423603
( An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Subject :- Theory of Machines II
T.E. Mechanical (302043)
Unit 5 GYROSCOPE
5.4.2 Gyroscopic Effect in Ship-Pitching
By
Prof. K. N. Wakchaure(Asst Professor)
Department of Mechanical Engineering
Sanjivani College of Engineering
(An Autonomous Institute)
Kopargaon, Maharashtra
Email: wakchaurekiranmech@Sanjivani.org.in Mobile:- +91-7588025393

2. Plane of Precession
Plane of
Spinning
Plane of Gyroscopic
couple
Axis of Spinning
AxisofPrecession
Plane of Precession
Plane of
Spinning
Plane of
Gyroscopic couple
INTRODUCTION

3. INTRODUCTION
Bow
Stern
Port
Starboard
Bow
Right
Left
• Bow is the fore-end of the ship.
• Stern is the rear-end of the ship.
• Starboard is the right hand side of the ship while looking
in the direction of motion.
• Port is the left hand side of the ship while looking in the
direction of motion.
• Steering is the turning of the ship in a curve while
moving forward.
• Pitching is the moving of the ship up and down the
horizontal position in a vertical plane about
• transverse axis.
• Rolling is the sideway motion of the ship about
longitudinal axis.
Stern
Bow
Stern
Port
Starboard
Bow
Right
Left

4. INTRODUCTION
Bow
Stern
Port
Starboard
Bow
Right
Left
Stern
Bow
Stern
Port
Starboard
Bow
Right
Left
Axis of Spinning
AxisofPrecession
Axis of Rolling
AxisofSteering

5. INTRODUCTION
Bow
Starboard
Stern
Port
Bow
Stern
Left
Right
Axis of Spinning
AxisofPrecession

6. Bow
𝜃
𝜃
INTRODUCTION
Pitching is the movement of a complete ship up and down in a vertical
plane about transverse axis.
In this case, the transverse axis is the axis of precession. The pitching of
the ship is assumed to take place with simple harmonic motion i.e. the
motion of the axis of spin about transverse axis is simple harmonic.
Angular displacement of the axis of spin from mean position
after time t seconds,
𝜃 = 𝜙. sin(𝜔1 𝑡)
𝜔1 = Angular velocity of S.H.M.
ϕ = maximum angle turned by ship during
piching from mean position
𝜔1 =
2π
(time period in SHM, tp)
=
2𝜋
𝑡 𝑝
The angular velocity of precession is
𝜔 𝑝 =
𝑑𝜃
𝑑𝑡
=
𝑑 𝜙. sin(𝜔1 𝑡
dt
= 𝜙𝜔1 𝑐𝑜𝑠𝜔1 𝑡
The angular velocity of precession will be maximum, if
cos 𝜔1.t = 1.
Hence Maximum angular precession will be
𝜔 𝑃𝑚𝑎𝑥 = 𝜙. 𝜔1 = 𝜙.
2𝜋
𝑡 𝑝
Let I = Moment of inertia of the rotor in kg-m2 , and
𝜔 = Angular velocity of the rotor in rad/s.
𝐶 𝑚𝑎𝑥= Mamimum gyroscopic couple,
𝐶 𝑚𝑎𝑥 = I. 𝜔. 𝜔 𝑃𝑚𝑎𝑥
𝜃
𝜃

7. Axis of Spinning
AxisofGyroscopicCouple
Plane of Gyroscopic Couple
Plane of
Spinning
Plane of Precession
INTRODUCTION
Axis of Spinning

8. Bow
Starboard
Port
Stern
Left
Right
Bow
Port
Axis of Spinning
AxisofGyroscopicCouple
Rotor Rotates in clockwise direction.
Ship is Pitching Upward
Gyroscopic EffectCondition
Observer: Bow End
Rotor: CW
Pitching: Upward
𝜃
Clockwise
AxisofReactiveGyroscopicCouple
SHIP WILL STEER TOWARDS PORT SIDE

9. Stern
Port
Starboard
Bow
Right
Left
Axis of Spinning
AxisofGyroscopicCouple
Rotor Rotates in clockwise direction.
Ship is Pitching Upward
Gyroscopic EffectCondition
Observer: Tail End
Rotor: CW
Pitching: Upward
𝜃
Clockwise
AxisofReactive
GyroscopicCouple
SHIP WILL STEER TOWARDS STARBOARD SIDE

10. Bow
Starboard
Port
Stern
Left
Right
Bow
Port
Axis of Spinning
AxisofGyroscopicCouple
Rotor Rotates in clockwise direction.
Ship is Pitching Upward
Gyroscopic EffectCondition
Observer: Bow End
Rotor: CCW
Pitching: Upward
𝜃
Anticlockwise
AxisofReactive
GyroscopicCouple
SHIP WILL STEER TOWARDS STARBOARD SIDE

11. Stern
Port
Bow
Right
Left
Starboard
Axis of Spinning
AxisofGyroscopic
Couple
Rotor Rotates in clockwise direction.
Ship is Pitching Upward
Gyroscopic EffectCondition
Observer: STERN End
Rotor: CCW
Pitching: Upward
𝜃
Anticlockwise
AxisofReactive
GyroscopicCouple
SHIP WILL STEER TOWARDS PORT SIDE

12. Stern
Port
Bow
Right
Left
Starboard
Axis of Spinning
AxisofGyroscopic
Couple
Rotor Rotates in Anticlockwise direction.
Ship is Pitching Upward
Gyroscopic EffectCondition
Observer: STERN End
Rotor: CCW
Pitching: DOWNWARD
𝜃
Anticlockwise
AxisofReactive
GyroscopicCouple
SHIP WILL STEER TOWARDS STARBOARD SIDE

13. Thank You….
13Subject :- Theory of Machines II