Gyroscopic Principle

2 Laws Of Gyrodynamics

  1. Rotating body is mounted in a way that
  • has freedom of movement about any axis,
  • passing through its center of mass

Thus;

  • Apply force to Rim of spinning rotor perpendicularly
  • Force transfers 90˚ around rim in direction of spin
  • Rotor will tilt/veer in that direction instead of direction of applied force
    -This direction is called Precession
  1. Rotating body mounted in a way that
  • has complete freedom of movement about any axis
  • passing through its center of mass is permitted

Result:

  • Spin axis fixed in inertia space
  • However much the frame moves.
  • I.e Free gyro > spin axis point at a precise position in space

Result: Any force applied perpendicular to plane of rotation

  • will transfer 90˚ around the body in direction of rotation and
  • cause body to move in the direction of that force

Gyroscopic properties

Important properties

Rigidity

Precession

Angular change in direction of plane of rotation under influence of applied force

Resistance from any attempt to make it change direction of plane of rotation

Depends on 3 factors

Mass

angular speed

radius of gyration (k) of rotor

  • greater mass
  • greater resistance offeres to change direction of plane of rotation
  • Usually made of heavy metal e.g brass
  • Greater speed
  • Greater resistance offered
  • Controlled speeds of 20,000 rpm to ensure rigidity
  • Greater the radius
  • Greater resistance
  • Disc shaped so that bulk of its mass is out near the rim

Sperry's rule

Predicts direction of precession if

  • Direction of rotation
  • Direction of disturbing force
    are known
  1. Follow plane of force onto rim of rotor

2.Move application of force on the rotor rim 90 around the rim in the direction of rotation of rotor

  1. Precession occurs on direction of force at new point of application

Factors

Value and direction of applied force

Angular velocity

  • Increasing the magnitude
  • Increases rate of precession
  • Slower the rotor spins
  • Greater the rate of precession

Moment of inertia

  • Greater the moment of inertia
  • Slower rate of precession

What they are

Heavy metal rotor and shaft

Rotates around spin axis

Rotor assembly

The Rotor

  • Mounted in a ring
  • that pivots in another ring
  • that pivots in a heavy frame

Arrangement allows for

  • Rotor freedom of movement about three
  • Which passses through center of gravity of rotor
  • and are perpendicular ot each other
  • Spin axis AA
  • Horizontal axis BB
    Vertical axis CC
    -The two rings are called gimbals

Gyroscopic models

Displacement Gyro

  • 2 axes of freedom
  • maintain spin axis during aircraft manoeuvres
  • gimbals allow the casing to move while spin axis remains fixed
  • relative movement between casing and rotor detected as aircraft movement

Attitude Situation Indicator (ASI)

Horizontal Situation Indicator (HSI)

  • Indicates Pitch and Roll
  • Spin Axis vertical in relation to aircraft when its straight and level
  • Frame securely fixed to aircraft
  • Gimbal rings permit relative movement between rotor and frame
  • Thus if pitch and roll, does so relative to gyro rotor
  • This remains vertical to earth's surface
  • Indicates Yaw
  • Spin Axis mounted aligned with Lateral Axis
  • Frame fixed to aircraft
  • Gimbal ring permits frame rotate horizontally relative to Gyro Rotor
  • Thus if frame rotate to starboard or port, it does so relative to Gyro Rotor
  • This will remain in its original position