Gyroscopic Theory

Wg Cdr Rajagopal

Gyroscopes

Index

Gyroscope & Instruments

  • Gyroscopes are used in a variety of flight instruments
  • Directional gyro indicator and Gyro magnetic compass
  • Artificial horizon and Turn & slip indicator
  • Inertial navigation systems and Inertial reference systems
  • Yaw dampers and Auto pilot
  • Stabilization of radar scanners

Gyroscopic Theory

  • Gyroscope has a spinning disc called rotor which spins around its spin axis
  • Gyroscopes have two basic properties of rigidity and precession
  • A highly rigid gyroscope will have low rate of precession and vice versa
  • A gyroscope with its spin axis horizontal to earth surface is a horizontal gyro
  • A vertical gyro has its spin axis vertical to earth’s surface

Rigidity of Gyroscope

  • Rigidity is also called gyroscopic inertia of a high speed spinning rotor
  • The spin axis of a rotor maintains its direction to a point in space
  • The rule is valid only in the absence of any external force
  • The point in space could be a distant star

Factors affecting Rigidity

  • Rigidity is affected by rotor mass, effective radius and speed of rotation
  • Rigidity can be increased by increasing mass or diameter of rotor
  • Concentrating rotor mass in its perimeter helps increase rigidity
  • Increasing speed of rotation also increases rigidity

Precession of Gyroscope

  • Precession shifts the effect of an external force applied on the gyro
  • The effect of external force is felt at right angles to the point of application
  • When an external force is applied to move spin axis upwards
  • The spin axis will move to the right for a clockwise spinning rotor

Effect of force on Precession of Gyroscope

  • When an external force is applied to change the spin axis of a gyro
  • Gyro resists the change due to the external force
  • Moves the spin axis 90 deg displaced from the direction of force
  • In the direction of rotation of the rotor

Rate of Precession

  • Rate of precession is directly proportional to the torque applied
  • Precession rate is inversely proportional to the mass and speed of rotation
  • These help in maintaining the property of rigidity
  • Rate of precession = Torque applied / (Rotor Rpm x Moment of inertia)
  • A light weight gyro, rotating at lesser speeds would have higher precession
  • A heavy gyro, rotating at high speeds would be more rigid and precess lesser

Single Gimbal System

  • Gyro is mounted in a ring type of suspension system called gimbals
  • Gimbals provide the freedom of movement to the gyro
  • Single gimbal system provides the gyro with one degree of freedom
  • If the one degree of freedom is in line with longitudinal axis
  • Spin axis will not be disturbed by pitch up or down of aircraft
  • Spin axis will not be disturbed by banking left or right of aircraft
  • Yawing movement of aircraft will disturb the spin axis
  • Single gimbal system does not provide freedom to correct yaw

Two Gimbal System

  • In a two-gimbal system the inner gimbal is mounted on the outer gimbal
  • The outer gimbal then is mounted on to the frame of aircraft
  • Two gimbal system provides the gyro full freedom to move in any direction
  • The gyro can maintain its spin axis at a fixed point in space in all three axis
  • Spin axis would be un disturbed during pitch, roll as well as yawing movement

Function of Gyroscopes

  • Gyroscopes can be classified based on their functions
  • Displacement gyros measure bank, heading or pitch angles
  • Space gyros are unrestrained and are free to wander
  • Tied gyros are brought back to its original orientation by an external force
  • Earth gyros maintain their orientation with earth surface by gravity
  • Rate gyros help in measurement of rate of change like rate of turn

Displacement Gyros

  • Displacement gyros have two degrees of freedom by two gimbal system
  • Allows aircraft to pitch, roll & yaw without disturbing the spin axis
  • Space gyros are unrestrained and maintains position to a point in space
  • Require low real wander and are used in Inertial navigation system
  • Tied gyro have two degree of freedom and have their spin axis tied to a datum
  • Datum could be horizontal or vertical plane of earth
  • Earth Gyros are tied to the surface of earth by gravity
  • Directional Gyro Indicators use earth gyros

Rate Gyros

  • Rate gyros have a single gimbal system with one degree of freedom
  • Turn indicators use rate gyros

Air Driven Gyros

  • Air driven gyros use pneumatic power or air pressure to rotate the gyro
  • Pressurised air could be obtained from either of the three sources
  • A engine driven vacuum pump
  • Low pressure air from engine inlet manifold
  • Venturi mechanism outside the aircraft
  • High pressure air is accurately directed at the rotor to spin at a constant rate
  • Air driven gyro is independent of electrical power
  • It will work even in the event of a total electrical failure

Electric Powered Gyros

  • Electric powered gyros use alternating current driven electric motor
  • Electric powered gyros have some advantages over air driven gyros
  • Faster spin speed increases property of rigidity
  • Constant rotor speed reduces real drift
  • Sealed gyro unit is safe from interference
  • Rapidly achieve required rotor speeds
  • Initialisation is quite fast

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