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5.4.2 gyroscope effect in ship pitching
This document discusses gyroscopic effect in ship pitching. It defines key ship terminology like bow, stern, port, and starboard. It explains that pitching is the up and down motion of a ship about its transverse axis. The direction a ship steers due to gyroscopic effect depends on the direction of spin of the gyroscope, the observer's location on the ship, and whether the ship is pitching up or down. For example, if observed from the bow and the gyroscope is spinning clockwise as the ship pitches up, the ship will steer towards the port side.
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5.4.2 gyroscope effect in ship pitching
- 1. Sanjivani Rural EducationSociety’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 Planeof 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 isthe 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
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- 6. Bow 𝜃 𝜃 INTRODUCTION Pitching is themovement 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 Planeof 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 RotorRotates 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 RotorRotates 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 RotorRotates 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 RotorRotates 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 RotorRotates 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