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Gyroscopic Couple Basic | Principle | Examples

Introduction to Gyroscopic 

‘Gyre’ is a Greek word, meaning ‘circular motion’ and Gyration means the whirling  motion. A gyroscope is a spatial mechanism which is generally employed for the study of precessional motion of a rotary body. Gyroscope finds applications in gyrocompass, used in aircraft, naval ship, control system of missiles and space shuttle.

gyroscopic action
fig 1 .Gyroscope Mechanism 
A gyroscope consists of a rotor mounted in the inner gimbal. The inner gimbal is mounted in the outer gimbal which itself is mounted on a fixed frame as shown in Fig. When the rotor spins about X-axis with angular velocity ω rad/s and the inner gimbal precesses (rotates) about Y-axis, the spatial mechanism is forced to turn about Z-axis other than its own axis of rotation, and the gyroscopic effect is thus setup. The resistance to this motion is called gyroscopic effect.

GYROSCOPIC COUPLE 


                         The turning moment which opposes any change of the inclination of the axis of rotation of a gyroscope.


Direction of Spin vector, Precession vector and Couple/Torque vector 
with forced precession 

To determine the direction of spin, precession and torque/couple vector, right hand screw rule or right hand rule is used. The fingers represent the rotation of the disc and the thumb shows the direction of the spin, precession and torque vector




Direction of Spin vector, Precession vector and Couple/Torque vector


Direction of Spin vector, Precession vector and Couple/Torque vector



Case : 


Consider a rotor rotating in anticlockwise direction when seen from the right, and to precess the spin axis about precession axis in clockwise and anticlockwise direction when seen from top. Then, to determine the active/reactive gyroscopic couple vector, the following procedure is used.

 Turn the spin vector through 90 degree in the direction of  precession on the XOZ plane 

 The turned spin vector will then correspond to the direction of active  gyroscopic couple/torque vector

 The reactive gyroscopic couple/torque vector is taken  opposite  to active gyro vector direction 



Direction of active and reactive gyroscopic couple/torque vector
Direction of active and reactive gyroscopic couple/torque vector 


Examples Of Gyroscopic Couples : 


GYROSCOPIC EFFECT ON SHIP 

Gyroscope is used for stabilization and directional control of a ship sailing in the  rough sea. A ship, while navigating in the rough sea, may experience the following three different types of motion:
(i) Steering—The turning of ship in a curve while moving forward

(ii) Pitching—The movement of the ship up and down  from horizontal position in a vertical plane about transverse axis 

(iii)Rolling—Sideway motion of the ship about longitudinal axis. 

For stabilization of a ship against any of the above motion, the major requirement is that the gyroscope shall be made to precess in such a way that reaction couple exerted by the rotor opposes the disturbing couple which may act on the frame.

Ship Terminology  
 (i) Bow – It is the fore end of  ship
(ii) Stern – It is the rear end of ship
(iii) Starboard – It is the right hand side of the ship looking in the direction of motion
(iv) Port – It is the left hand side of the ship looking in the direction of motion

ship terminology

 Consider a gyro-rotor mounted on the ship along longitudinal axis (X-axis) as shown in above image and rotate in clockwise direction when viewed from rear end of the ship. The  angular speed of the rotor is rad/s. The direction of angular momentum vector, based on direction of rotation of rotor, is decided using right hand thumb rule.

Gyroscopic Effect on Aeroplane 

     Aeroplanes are subjected to gyroscopic effect when it taking off, landing and negotiating left or right turn in the air.

Let us analyze the effect of gyroscopic couple acting on the body of the aero plane for various conditions. 

aeroplane front and rear

Case (i): PROPELLER rotates in CLOCKWISE direction when seen from rear end and Aeroplane turns towards LEFT 

                           aeroplane taking turn to left



Case (ii): PROPELLER rotates in CLOCKWISE direction when seen from rear end and Aeroplane turns towards RIGHT 

  Case (iii): PROPELLER rotates in ANTICLOCKWISE direction when seen from rear end and Aeroplane turns towards LEFT 
Case (iv):  PROPELLER rotates in ANTICLOCKWISE direction when seen from rear end and Aeroplane turns towards RIGHT 

Stability of Automotive

                                  two wheeler taking turn

                      A vehicle running on the road is said to be stable when no wheel is supposed to leave the road surface. In other words, the resultant reactions by the road surface on wheels should  act in upward direction. For a moving vehicle, one of the reaction is due to gyroscopic couple  produced by the rotating wheels and rotating parts of the engine. Let us discuss stability of two and four wheeled vehicles when negotiating a curve/turn.

stability equation


Stability of Four Wheeled Vehicle negotiating a turn

                     When a vehicle moves on a curved path, a centrifugal force acts on the vehicle in  outward direction through  the centre of gravity of the vehicle. Total Gyroscopic Couple is Found out by making plus of Effect of Gyroscopic Couple due to Engine and Effect of Gyroscopic couple due to Wheel.

gyroscopic couple acting on four wheeler car body




                                                                                                               




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