GYRO compass and its principle

 GYRO COMPASS

The Free Gyroscope

This consists of a rotor, supported in such a way that it is free to have its spin axis pointing in any direction. (the free gyroscope is also referred to as the ‘sensitive element’.)

The method of support for the gyroscope must therefore provide three degrees of freedom:

1. freedom to spin about its own axis;
2. freedom to tilt about a horizontal axis;
3. freedom to turn in azimuth about a vertical axis.

A free gyroscope has 2 properties which are used in the construction of the gyrocompass:

1. Gyroscopic Inertia,
2. Precession.

Gyroscopic Inertia (sometimes referred to as ‘rigidity in space’:

• A freely spinning gyroscope will maintain its axis of spin in the same direction with respect to space irrespective of how its supporting base is turned.

• It resists any attempt to change its direction of spin.
• Thus a free gyroscope has high directional stability.
• This property is called GYROSCOPIC INERTIA or RIGIDITY IN SPACE or DIRECTIONAL STABILITY.
• This is based on Newton's First Law of Motion which states: Everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by external forces to change that state.

Precession:

• This phenomenon is found only in spinning bodies.
• It is the movement of the spin axis when the force is applied to Gyroscope.
• Precession always acts at 90° to the direction of applied force.
• To determine the direction of precession, rotate the applied force 90° in the direction of the rotor spin.

• When a couple is applied about its horizontal axis, the spin axis will turn at right angles tothe applied force in the direction of the spin of the wheel.
• Similarly, couple applied about the vertical axis will make the spin axis turn about the horizontal axis in the direction of the spin axis of the wheel.

The Effects Of The Earth’s Motion On A Free Gyroscope

• Due to the gyroscopic inertia of a free gyroscope, the spin axis will remain to point in a fixed direction in space, i.e. towards an imaginary gyro star on the celestial sphere. 
• As the earth rotates on its axis fixed stars in space appear to move. 
• This movement is noticed as a change in altitude and azimuth, resulting in the star appearing to trace out a circular path. 
• Depending on the observer’s latitude and the declination of the star, the circular path traced out by the star may either wholly be above the horizon or maybe carried below the horizon at some stage.
• If a star appears to show this movement then the spin axis of a free gyroscope will also trace out a circular path as it remains pointing at the star.
• The movement of a star can be described in terms of ‘altitude’ and ‘azimuth’. The terms used to describe the same movement of the spin axis of a free gyroscope are ‘tilt’ and ‘drift’.

Tilt

• It is the angle of elevation or depression (upward or downward motion) of the spin axis above or below the Horizontal.
• Equivalent to a true altitude of the Gyro star.

Tilting

• This is the rate of change of Tilt of the spin axis. It is given by the formula
• Tilting = 15° Sin (Azimuth) Cos (Latitude) / Hour
• Az will always be in quadrantal form.
• It is +ve or upwards when spin axis points east of the meridian &
• -ve or downwards when spin axis points west of the meridian

Drift(Azimuth)

• The direction in which the spin axis points w.r.t. the true North.
• In respect to the Gyro, this is also known as Drift.

Drifting

• Drifting is the rate of change of Azimuth of the spin axis.
• It is given by the formula
• Drifting = 15° Sin (Latitude) per hour
• The formula is only applicable if the spin axis is almost horizontal or the Tilt is close to zero.
• Drifting is +ve or easterly when spinning axis points below the pole &  -ve or westerly when spinning axis points above the pole.

Motion of Gyro at Poles

• Initially if the spin axis is kept horizontal. The axis maintains constant tilt and drifts around the horizon @ 15 deg/hour.
• This rate is same as the earth’s rate of rotation (360 deg /24 hours).
• At N pole the drift is in clockwise direction and at S pole it is in ACW direction.
• At a pole latitude is 90; therefore, maximum rate of Dg occurs at poles. (Dg = 15 deg Sin lat/Hour )
• If initially spin axis pointing at zenith i.e. at a tilt of 90.
• It will continue pointing in the same direction with no tilt and drift.

Motion of Gyro at Equator

• Spin axis is initially pointing E. (like a body at E on rational horizon and zero declination).
• There will be no drift and tilting will be maximum; changing at the rate of 15deg per hour.
• The azimuth will remain 090 and after meridian passage it will be 270, with tilting now changing @ -15/hour (negative sign to show downward tilt)
• Thus Tilting is maximum at equator i.e. zero latitude and minimum at poles (90 deg lat) Also when pointing East azimuth is maximum = 90.
• Hence the tilting formula Tilting = 15° Sin (Azimuth) Cos (Latitude) / Hour
• If the Spin axis is initially pointing N.
• It will remain pointing in North direction, with drift and tilt both zero.
• Here azimuth is zero and Tilting is nil.

Motion of Gyro at intermediate latitude

• As discussed above the Spin Axis will point towards the Imaginary gyro star
• As the gyro star crosses the horizon it will be changing its azimuth as well as altitude and tracing a path in the sky centred at the pole.
• Hence the spin axis will also keep on Drifting & Tilting.

Controlling The Gyro

The spin axis of a freely suspended gyro traces out a circular path as it remains pointing in a fixed direction in space, i.e. the apparent motion due to the earth’s rotation. The requirements of a gyrocompass are that the spin axis should point in a fixed direction, True North, 000°T.

In order for the gyroscope to do this it must be made to:

• seek North,
• settle and remain pointing North.

North Seeking

• Only with free gyro cannot be used for direction determination.
• Thus a system is required, which can not only sense this movement but also apply a force to
• control the movement due to Dg and Tg.
• The force of gravity is used for making free gyro North Seeking.
• This method of making the gyroscope North seeking is termed ‘Gravity Control’.
• The principle may be shown by suspending a weight on the spin axis.
• This is done in two ways, known as top-heavy effect and bottom-heavy effect.
• Top-heavy effect requires the rotor to rotate in ACW direction and bottom-heavy effect requires CW spin, when viewed from the south end.
• It has the effect of converting the circular path traced out by the spin axis into an elliptical path.

The result is that the spin axis oscillates backwards and forwards across the meridian but does not settle and point in a fixed direction.

Top Heavy Control:

• The gyroscope is made North Seeking by attaching a weight to the rotor casing above the COG of the rotor.
• When the spin axis is horizontal the COG of the weight passes through the centre of the rotor producing no torque.
• The earth’s rotation will, however, tilt the spin axis.
• When the gyro axis tilts the COG of the weight does not act through the centre of the rotor and this weight produces a torque about the horizontal axis (or in the vertical plane).
• This torque will result in Precession in the horizontal plane that tends to take the spin axis towards the meridian.
• This precession is called control precession (Pc).
• The direction of spin of the rotor must be in such as to produce a westerly precession of the North end of the spin axis when that end is tilted upwards.
• And this direction turns out to be ACW in top-heavy type gyros 

Bottom heavy Control:

• This direction turns out to be clockwise in bottom-heavy type gyros
• The path traced by the N end of the Spin Axis is now elliptical.
• Because in gravity control gyroscope there are three vectors interacting with each other (Dg, Tg & Pc), instead of just two (Dg and Tg).
• While the two vectors resulted in a circular path traced by the spin axis, centred about pole;
• The introduction of the third vector results in an elliptical path.

Understanding the Ellipse:

• Control precession (Pc), acts westwards, when Spin Axis is tilted upwards and eastwards
• when the axis is tilted downwards.
• Tilting acts upwards when east of meridian and downwards when west of the meridian.
• Drifting is always Eastward as this ellipse is formed below the pole.
• In this elliptical path, it is to be seen that, while the Dg vector remains same in size  (15xSin lat),
• but the Tg vector changes because Tg also varies with Sin Az and azimuth is continuously
• changing. (Tilting = 15° Sin (Azimuth) Cos (Latitude) / Hour)
• Pc vector also changes in magnitude because Pc is proportional to tilt.
• In commercial gyros, the time period to complete one revolution of the ellipse is usually about 84-85 minutes.

North Settling:

• Controlling Gyro by Liquid Ballistic
• Practically the gyro is controlled using a liquid ballistic, mercury.
• Mercury flows between pots in the N-S axis under the influence of gravity when the
• gyro axis tilts out of the horizontal.
• COG of the ballistic system coincides with that of the rotor.
• This is similar to a top-heavy arrangement. The spin of the gyro axis is anticlockwise viewed from the south.
• In order to make the gyro settle and point in a fixed direction, i.e. 000°T, it is necessary to impose a further precession which will damp out the gravity controlled elliptical path traced out by the spin axis.
• This method of making the gyroscope North settling is termed ‘Damping’.

Damping the Ellipse:

• We know that gravity controlled gyroscope also cannot be used as a compass because the axis does not point along the meridian, but oscillates along the ellipse repeatedly.
• Thus some form of damping is needed to damp these oscillations and make the axis settle in equilibrium along the meridian.
• In damping, the controlled ellipse becomes a spirally inward, towards the equilibrium position, where the axis will settle and if disturbed from that position will return to it.

There are 2 ways of achieving damping:

• Damping in tilt (in case of top heavy type gyro) - when the spin axis moves out of the horizontal the damping precession opposes this movement, bringing the spin axis back to the horizontal.
• Damping in azimuth (in case of bottom heavy type gyro) - when the spin axis moves out of the meridian the damping precession opposes this movement, bringing the spin axis back to the meridian.

Damping in Tilt: (in case of top-heavy effect)

• In this method of damping, the damping precession Pd opposes the movement of the spin axis
• when the spin axis is moving away from the horizon and assists it when moving towards the horizon. The torque about the vertical axis causes damping precession in tilt, i.e. up or down.
• Damping precession depends on the angle of tilt, the greater the tilt, the greater the damping precession.

Effect of damping in tilt on the ellipse

• As the controlled gyro follows the first part of the ellipse, the damping precession will oppose the tilting. This means the gyro’s angle of tilt when reaching the meridian, is not as great as for the undamped gyro. 
• Thus the control precession is less and the eastward drift is greater, therefore, the gyro spin axis will not travel as far west. 
• As the gyro spin axis returns to the horizon the damping precession will assist its return. 
• As the axis tilts below the horizon the damping precession will oppose it, reducing the maximum angle of tilt downward and thus reducing the eastward drift and control precession. 
• The gyro therefore does not travel as far East. Next time around the ellipse, the damping precession will again oppose movement away from the horizon, so again the maximum angle of tilt will be reduced making the ellipse smaller. 
• Eventually, the gyro will settle where the control precession cancels the drift and the damping precession cancels the movement of tilt.

Applying damping in tilt:

• Damping in tilt is achieved in the Sperry MK 20 gyrocompass by adding a small weight (17 gr) on the top of the rotor case. 
• The weight is offset to the west of the vertical axis.

• With the spin axle horizontal, weight is directly above the tilt bearings and hence causes no precession. 
• When the axle tilts, the weight has a tipping effect on the gyro. Since the weight is offset, the tipping will have a vertical and horizontal component.
  
• The vertical component generates a torque around a horizontal axis which causes a precession around the vertical axis at the same direction of Pc. 
• This component is seen/calculated within the control force. The horizontal component generates a torque about a vertical axis which causes a precession (Pd) around a horizontal axis. 
• This opposes the tilt and brings the spin axis towards the horizon.

How to compensate for the damping error?

• The damping error in gyro compasses which utilize damping in tilt is to be removed. (Like Sperry gyro compasses)
• The First method is by a mechanical means in which the latitude is set. The whole phantom
• ring turns according to the set latitude therefore the compass card turns to eliminate
• the damping error.
• By using a torque motor which produces a precession to cancel the drift at settling point
• and hence causing the spin axis to point north. This is the same motor used for
• correcting the speed error.
• In digital gyro compasses, this error is simply corrected by feeding (inputting) the
• latitude to the microcomputer unit. 

Damping in azimuth:

• In this method of damping, the damping precession opposes the movement of the gyro spin axis when it is moving away from the meridian and assists the movement when moving towards the meridian.
• The torque about the horizontal axis will cause a damping precession in azimuth. It depends on the rate of tilting, the greater the rate of tilt, the greater the damping precession.