Gyro Compass

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Marine Gyrocompas s

GYROCOMPASS: It essentially consists of a gyroscope. It works on the principle of law of conservation of angular momentum. It utilizes two natural phenomena to provide directional reference: reference: earth’s incessant rotation and force of gravity. gravity. GYROSCOPE: A gyroscope consists of a mass in the form of a wheel or rotor which is suspended in such a way that it is free to spin about an axis passing through its centre of mass and perpendicular to the plane of the rotor. It is mounted on a circular ring in the same plane as the spin axis. This ring is connected to a vertical ring at points perpendicular to the spin axis in such a manner so as to permit the spin axis to tilt about its horizontal axis (in vertical plane) within the vertical ring. The vertical ring is connected to an outer member at right angles to the horizontal axis so that the spin axis can turn about its vertical axis (in horizontal plane).Ideal conditions warrant that the spin axis bearings should be frictionless so that any rotation imparted to the rotor is maintained. With this arrangement gyroscope is not constrained in any way so as to alter the direction of spin axis. It is then said to have three degrees of freedom. THREE DEGREES OF FREEDOM: 1. Freedom to spin, rotate about the spin axis. 2. Freedom to turn in horizontal plane or freedom to turn about vertical axis. Also described as freedom to drift in azimuth. Termed Termed as drifting (Dg). 3. Freedom to turn in vertical plane or freedom to turn about horizontal axis. Also described as freedom to tilt in altitude. Termed Termed as tilting (Tg) For gyroscope to be effective and efficient it should have large angular momentum, which means that it should rotate at high speed and should have large moment of inertia.

Gyroscope having three degrees of freedom is called “FREE GYROSCOPE” EARTH is the best example of free gyroscope in nature, because: It is freely suspended in space having no friction and thus having three  degrees of freedom. It is heavy and well balanced with the equatorial mass corresponding to the  plane of a rotor. (equivalent (equivalent to large moment of inertia)  Earth rotates at considerably high speed about its speed (equivalent to spin axis of rotor) GYROSCOPIC INERTIA: 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.

For more details please visit: www.captyashpal.blogspot.com

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Marine Gyrocompas s

The gyroscopic inertia of a rotor can be quantified by its angular momentum (H). This in turn indicates how much force is required to change the direction in which the spin axis points. H depends on S (angular velocity) & Ι (moment of inertia) and is given by: H= SI I (moment of inertia) is used in same sense in rotational motion as mass is used in linear motion. As mass is a measure of inertia in linear motion, moment of inertia is measure of inertia in rotational motion. Though mass is a constant quantity and represents the amount of matter Ι depends on mass, shape, size, distribution of mass about the axis and the position and orientation of the axis itself. In this case of rotor, greater the proportion of mass which lies towards the circumference of the rotor, greater will be the Ι and greater will be gyroscopic inertia for any given S. For this reason, rotors are designed with a heavier edge and a relatively lighter internal construction sufficient to maintain the strength of the rotor. This reduces the overall mass while enhancing the I H = ΙS , H = Angular momentum, I = Moment of Inertia of the cross 2 section about, the spin axis (Kmr ), Where, K = constant (depends (depends on the rotor’s mass distribution), distribution), m = mass of the rotor, r = radius of of the rotor, S = Angular velocity of the rotor

Therefore higher the angular momentum more the gyroscopic inertia and better the directional properties of the gyrocompass. gyrocompass. The two motions drifting (Dg) and tilting (Tg) are the result of gyroscopic inertia. inertia.

PRECESSION: This phenomenon is found only in spinning bodies. It is the movement of the spin axis when a force is applied to the spin axis of gyroscope. When a couple is applied about its horizontal axis, the spin axis will turn at right angles to the 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. This property is called PRECESSION. P is the resultant of rotational motion of the body and the T applied to its spin axis. The direction of P or the resultant of rotational motion and T is such that the tangent to the circle of rotation (representing rotational motion at any instant) tends to follow the vector of T and tries to fall in line with it. Precession, Precessio n, P= T/SI OR P = applied torque/ angular momentum 2 T= torque in Nm; S = speed in radians/sec; I = moment of inertia in kgm In brief, T applied in horizontal plane (or about vertical axis), causes P in vertical plane (or about horizontal axis) and vice versa

Both GI and P can be explained with the help of Newton’s first law of motion.


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Marine Gyrocompas s

Control Precession, Pc = B Sin tilt/H (B is constant = W x h; W= weight, h= turning arm) Damping Precession, Pd= S Sin tilt/H(S is constant = W x l; W = weight, l = offset of wt from vertical axis) The earth rotates about an axis through poles in 23h 56m 40.9s of solar time. This period called sidereal day and may be divided into 24 siderial hours. If latitude of observer is greater than polar distance of a body, the body will not set and will remain above rational horizon. 24 sidereal hours = 23h 56m 04s solar hours = 23.934444 solar hours. Solar time = sidereal time x 24 / 23.934444 Sidereal time = solar time x 23.934444 / 24 BEVIOUR OF GYROSCOPE AT DIFFERENT PLACES: PLA CES: AT POLES: Initially 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 0 in ACW direction. At a pole latitude is 90 ; therefore, maximum rate of Dg occurs at poles. Thus rate of Dg = 15 deg Sin lat (because Sin 90 = 1) AT POLES: 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. 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 tilt will be maximum; changing at the rate O of 15 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 Tg is maximum at equator i.e. zero latitude and minimum at poles (90 deg lat) Also when pointing East azimuth is maximum = 90 AT EQUATOR: Spin axis is initially pointing N. It will remain pointing there in N, with drift and tilt both zero. Here azimuth is zero and Tg is also nil. Thus rate of Tg = 15 deg Cos lat x Sin Az Consider now an observer in intermediate northerly latitude. The zenith will lie between celestial pole and celestial equator, and not over pole or over equator. For example consider 40 deg N. The plane of the celestial equator is inclined to to observer’s prime vertical vertical by 40 deg and will cut the horizon at an angle of 50 deg.


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Marine Gyrocompas s

The celestial pole lies 40 deg above the northern part of the horizon. As all circles of declination are parallel to the C.E. they also will cut the horizon at an angle = the complement of observer’s latitude. This means that as a star crosses the horizon it will be changing its azimuth s well as altitude. The radius of the circle traced out with celestial pole as centre will depend upon where the spin axis is initially pointing. If a free gyroscope is situated on the equator and lies with its axis east-west and horizontal, it can be thought of as pointing pointin g to a star which has zero declinatio n and is about to rise. The east end of the gyroscope axis will follow the movement of this star and will tilt upward as the star rises. After one sidereal day (23h 56m 04s) the gyroscope will have tilted through 360° in 24 sidereal hours. Maximum rate of tilting = 15° per hour If the free gyroscope had been situated on the equator with its axis lying north south, the north end would be lying towards the pole star and would then have no apparent movement relative to the earth. The rate of tilting thus varies from 0° to 90°. Rate of tilting also varies as the Sine of the azimuth A free gyroscope situated at a pole with its axis horizontal would have an apparent turntable motion due to the earth’s rotation, i.e. it would follow a fixed star round the horizon but it would not rise or set. The rate of tilting thus varies from a maximum when the latitude is 0° to minimum when latitude is 90°. Rate of tilting varies as the cosine of latitude Therefore we have the final conclusion: Rate of tilting = 15° Sin (Azimuth) Cos (Latitude)

Drifting: It is the apparent movement of a gyroscope in Azimuth. A free gyroscope situated at the North Pole with its axis horizontal will have an apparent movement, which is entirely in the horizontal plane. Its axis will appear to move in a clockwise direction when viewed from above due to the real counter clockwise rotation of the earth beneath. Thus the gyro drifts at 15° per hour. A free gyroscope situated at the equator with its axis horizontal will not drift at all, irrespective of whether its axis is set in the north-south or east-west direction. The rate of drift for a gyroscope with its axis horizontal thus varies from a maximum at the poles to zero at the equator. Thus rate of drift varies as the sine of the latitude. Rate of drift = 15° Sin (Latitude) (Latitude) per hour GYRO ADVANTAGES: High reliability; compact size; minimal siting constraints; small errors; ability to run repeaters and provide a heading reference for other navigational equipment.


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Marine Gyrocompas s

Combined Drift & Tilt: At intermediate latitude between the equator and a pole, the apparent motion of a free gyroscope consists partly of tilt and partly of drift. The projection of the spin axis’ path on to the celestial sphere is same as the circular path traced out by a star during a sidereal day. Tg is zero when spin axis is aligned with the meridian and Dg is zero when tilt of spin axis is same as altitude of the pole i.e. when spin axis is pointing at the pole. Following conventions to be kept in mind: E of meridian- Tg upwards or positive and vice versa Below pole – Dg eastwards or positive and vice versa Ellipse of undamped Gravity Controlled Gyro has 2 components: Dg: oscillation in azimuth and, Tg: oscillation in tilt. Both are interdependent. If one is made to disappear, di sappear, the othe r will also go away. E of meridian- Tg upwards or positive and vice versa. Tg is zero when spin axis is aligned with meridian and maximum tilt occurs at this moment. Dg is easterly when spin axis below the pole and vice versa. Dg is zero when tilt of spin axis = altitude of pole = lat of observer. Formulas for Dg and Tg have their limitations: These values are valid only at a particular instant. NEED TO CONTROL FREE GYRO: Thus the axis of a FG traces a circular path around the pole and keeps changing its position under the influence of Tg and Dg. FG of this sort is of no use 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 ubiquitous force of gravity is utilized for this purpose. 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 south end. Sperry compasses use top heavy effect with the help of liquid (Hg) ballistics. As the spin axis tilts from the horizontal, Hg travels to the lower end making it heavier and pulls it down. COG of the ballistic system falls out of the vertical. Weight of the transferred Hg acts downwards under gravity, causing the lowered end to be further pulled down and thus producing the desired control precession, Pc. Conventional Brown compasses using bottom heavy effect with the help of liquid ballistic (using oil as liquid, in which liquid is transferred from lower to higher side against gravity by air pressure generated within the rotor case) and directing this pressure on to the oil surface in the working bottles to force the oil up through connecting pipes to the higher bottles. This model however is now obsolete.. And


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Marine Gyrocompas s

modern Arma Brown compasses use bottom heavy effect with the help of torsion wires attached to the sensitive element. Twist in the torsion wires generates the required force to produce the desired precession, similar to one caused by bottom heavy as the spin axis tilts from the horizontal.

TOP-HEAVY CONTROL: When the spin axis is horizontal the COG of the weight passes through the center of the rotor producing no torque. The earth’s rotation will tilt the spin axis. When the gyro axis tilts the COG of the weight does not act through the center of the rotor and this weight produces a torque about the horizontal axis (or in the v ertical plane).This torque will result in P about the vertical axis (or 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 an easterly precession of that end when it is tilted downwards. And this direction turns out to be ACW in top heavy type gyros and CW in botto m heavy type gyros. PATH OF UNDAMPED GRAVITY CONTROLLED GYROSCOPE: In UGCG the control weight (whether BH or TH) merely causes the N end of spin axis to precess to westwards when above horizon and vice versa.

At equator: Path traced out by the N end of the spin axis is an ellipse, whose center is the N point of the horizon. Or the major axis coincides with the horizon and the ellipse is symmetrical about the horizon. This is because the lat being zero, the drift is also zero. The only vectors causing the movement of the spin axis are Tg and Pc The size of the ellipse will depend on the azimuth on which the spin axis is set initially. If a heavier weight was used the tilt of the spin axis when on the meridian would have been less (i.e. lesser the minor axis) but the a mplitude of the E-W extremities of the ellipse would not be affected. Other than Equator: Path is again elliptical but is not symmetrical about the horizon. Thus in gravity control gyroscope there are three vectors interacting with each other, instead of just two vectors (Dg and Tg). While the two vectors resulted in a circular path traced by the spin axis, centered about pole; the introduction of the third vector results in an elliptical path. The third vector is control precession (Pc), which acts westwards, when tilted upwards and eastwards when the axis is tilted downwards. This is true in both N and S latitudes. And Tg acts upwards when east of meridian and downwards when west of meridian. Dg acts eastwards, throughout, in N latitudes and westwards, throughout, on S latitudes. For this reason, in N latitudes the major axis of the ellipse is above the horizon and in S latitudes, it is below the horizon. And at equator, the major axis coincides with the horizon, since at equator, the Dg is zero. And the only vectors at work are Tg and Pc.


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Marine Gyrocompas s

In this elliptical path it is to be seen that, while the Dg vector remains same in size (15 Sin lat), but the Tg vector changes because Tg also varies with Sin Az and azimuth is continuously changing. Pc vector also changes in magnitude because Pc is proportional to Sin tilt. In general greater the lat greater the Dg and the greater must be the tilt to give a Pc to counteract the Dg. The controlled ellipse is, therefore, lifted relative to the horizon in N lat and depressed in S lat. At the meridian Tg is nil, but angle of tilt is maximum, Therefore, Pc is also maximum. Time taken to complete the ellipse depends on the degree of control (re lation between Pc, which is proportional to Sin tilt and Dg which is equal to 15deg Sin lat) provided, but is always less than sidereal day. Time period, T is given by = 2π√ (H / BE BE Cos lat), H is angular momentum of the rotor, B is the ballistic constant, E is linear speed of the earth. In commercial gyros this period is usually about 85 minutes. The size (amplitude of oscillation) and shape (proportion of major and minor axes) depends on degree of control, latitude and the initial starting position. In practice, the major axis is very large compared to minor axis. At equator centre of the ellipse coincides with horizon, in N latitudes it is above the horizon and in S latitudes it is below the horizon. If spin axis is initially set pointing at N and horizontal, the ellipse would be wholly above the horizon. Its centre would be at the same level as the settling level. At this level the displacement of Hg is same at all the points (which actually are only three points: left and right extremes of SL or the major axis and point of intersection of meridian and SL) At the extremes Pc balances the Dg. Thus if spin axis is initially pointed to point of intersection of SL and meridian at any lat, the displacement of Hg would be same as that for SL. Further at meridian there is no tendency for Tg. Thus Pc will exactly balance the Dg and in the absence of Tg spin axis will keep pointing to that point of intersection, called settling point. The elevation of SP depends upon P which in turn depends on T, MOI of wheel, spinning speed and the latitude. This SP is on horizon at equator, above horizon in NH and below horizon in SH. In Sperry compass this SP is not more than few minutes of arc from horizon Thus at a given lat, ellipse size will vary depending on the initial position of the spin axis, but they all will be symmetrical about the same SL. For a controlled gyro there will be one position where the controlled gyro will keep pointing there if set initially there i.e. pointing N, with a tit so that Pc exactly counteracts Dg. This will require a positive tilt in NH and negative negative tilt in SH. This however will be valid only for that position and as position changes the axis will begin to trace an elliptical path.

CONTROLLING THE GYRO BY LIQUID BALLISTIC: For more details please visit: www.captyashpal.blogspot.com

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Marine Gyrocompas s

Practically the gyro is controlled using a liquid ballistic, mercury. Mercury flows between pots in the north south axis under the influence of gravity when the gyro axis tilts out of the horizontal. COG of the ballistic system must coincide with that of the rotor. The above constitutes a top-heavy arrangement. The spin of the gyro axis is anticlockwise viewed from the south. DAMPING THE ELLIPSE: .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 spiral inwards, towards the equilibrium position, where the axis will settle and if disturbed from that position will return to it.

This is achieved by one of the following: 1. Damping in Azimuth - Damping precession (Pd) is towards the meridian – employed in Bottom Heavy Effect type gyros. 2. Damping in Tilt - Damping precession (Pd) is towards the horizon employed in Top Heavy Effect type gyros. The gravity controlled gyro never settles on the meridian. It keeps oscillating about the meridian. The gyro finally settles in a position, where fourth force (Pd) is introduced and all the four forces balance out each other. DAMPING IN TILT: This method is used in Sperry type compasses. Rotor casing is supported in a vertical ring which surrounds the casing in E-W plane. This vertical ring itself tilts about the horizontal axis in EW bearings, when the rotor tilts, because the rotor is supported within the vertical ring by bearings in the vertical axis. So when the rotor tilts, vertical ring tilts as well. The offset method of damping (damping in tilt) requires this ‘nominal’ vertical axis to tilt out of vertical. When horizontal, this damping weight has no effect. However when it tilts the damping weight exerts T about vertical axis causing Pd. Torque is applied about vertical vertical axis so as to cause downward downward precession when the north axis is tilted upwards and upward upward precession when the north axis is tilted downward. The idea is to produce the damping precession, Pd, which tries to bring the spin axis always towards the horizon. In other words Pd opposes the tilting (Tg) when spin axis is moving away from the horizon (i.e. when spin axis is E of meridian and above the horizon and when west of meridian and below the horizon); and supports the tilting, when spin axis is moving towards the horizon (i.e. when spin axis is W of meridian and above the horizon and when spin axis is E of meridian and below the horizon). At a point before the meridian, Pd and Tg will cancel each other out; so that the path of the spin axis will be horizontal before reaching the meridian. Between this point


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Marine Gyrocompas s

and meridian, Pd will be more than Tg so that meridian is crossed at downward angle. As soon as spin axis is W of meridian, Tg becomes downward. As a result each time spin axis comes back to the level of settling, (the level at which Dg = Pc), the azimuth must reduce. After some oscillations, it will reduce to zero. For this purpose, MB (mercury ballistic) is attached slightly E of the centre instead of placing exactly below the bottom. This offset functions as damping weight and provides torque about vertical axis and the desired precession (Pd). This gives spiral path. The spiral path is repeated and then the axle comes to rest. Shape of the spiral depends on ratio between T about horizontal axis and the corresponding T produced about vertical axis due to eccentric attachment of the MB. In all Sperry compasses this ratio is arranged to give damping %age of 66.67% each time. Thus amplitude of swing is reduced by 66.67% on each cycle. Gyroscope settles in about 3 cycles, if initial displacement is not more than 20 deg. DAMPING IN AZIMUTH: In this method, the amplitude of successive oscillations is damped or reduced by precession in azimuth, i.e. by P towards meridian. Such Pd is similar to Pc. But it acts with Pc when Pc is working towards meridian and opposite to when Pc when Pc is working away from meridian. Pd in azimuth is generated in similar way to Pc i.e. by T about horizontal axis. However precession created solely by gravity will not serve the purpose as its direction will depend only on weather tilt is up or down. Such Pd will only modify the rate of Pc but would not achieve damping. Arrangement needs to be made so that Pd is always directed towards meridian. This is achieved by creating T about horizontal axis and P in azimuth by flow of liquid under the flow of gravity when the spin axis tilts, but causing a lag between cause and effect by introducing a ‘restriction’ to the flow. The action of ballistic is then out of phase with the tilt which causes the flow. Thus while Pc is produced by bottom heavy effect, Pd is produced by top heavy effect. The resulting precessions are therefore, in opposite directions. SPIRAL PATH OF DAMPED GYROSCOPE: Spiral path is traced as a result of interaction of Dg, Tg, Pc and Pd causing the spin axis to settle in equilibrium position. Initially when spin axis is horizontal, there is neither Pc nor Pd. The end immediately acquires a positive tilt due to earth’s rotation. It will also drift to E. Immediately Pc and small quantity of Pd will be introduced. Pc reduces Dg and Pd counteracts Tg. At a certain stage tilt increases to value where Pc = Dg. The easterly Dg ceases here. The movement is vertical at this point under the influence of Tg which is maximum at this point. The rate of tilting will however be reduced by Pd. As tilt increases so does the Pc and Pd. Pc is now greater than Dg and spin axis moves towards meridian. This means the rate of Tg is reducing while the Pd is increasing. Thus a point comes before the meridian, where Tg = Pd and the maximum tilt is reached at this point and will be reducing westwards, causing the meridian to be crossed at a lower tilt (than the tilt


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Marine Gyrocompass

at meridian in case of ellipse). As the north axis moves west of meridian Tg is now downwards (while tilt is still up) and Pd also acts down pulling spin axis rapidly towards horizon. Due to this action of Pd, amplitude of oscillation is considerably reduced. Maximum western azimuth is reached at a certain stage, where again Pc = Dg and spin axis will move back to E towards meridian under the influence of all four vectors. Pc and Pd become zero and the spin axis becomes horizontal again. Below horizon Tg is downwards and Pd becomes upwards. Here again a point is reached where Tg = Pd, before the meridian itself. Then spin axis moves eastwards rapidly under the influence of Dg and Pc and cuts the meridian at lo wer downward tilt. Consequently with each half cycle the oscillation is damped or amplitude of the oscillation is reduced. Thus each time spin axis comes to settling level (where Dg=Pc), the azimuth must reduce. After a number of oscillations it is reduced to zero. The degree of damping is expressed by damping factor. This is defined as ratio of total swing in azimuth on two successive half cycles. GENERIC GYROCOMPASS: SENSITIVE ELEMENT: consists of rotor and casing supported in the vertical ring and the the compenspin axistor weights weights that give the the SE equal moments OI about 2 principle Has Phorizontal axisNTOM RING: supports the SE and is kept continually aligned with it so that the wire suspension of SE does not become twisted. It also carries the stem, slip rings, azimuth gear and compass card. It is through the azimuth gear that the phantom ring is aligned with the SE and by means of which the magslips are rotated to transmit the compass heading. MERCURY BOXES: are suspended from PR. Any thrust caused by N-S, out of balance of the MB’s is applied to the bottom of the casing by means of rods and pivot cups. THE SPIDER: is an iron casing which supports the PR and SE by means of stem bearings. The S is held in fixed relation to the FnA line of the ship and can rotate freely about the PR as the ship changes course. Attached to the S are follow up motor, which aligns the PR with SE, together with the fine and coarse magslip housings and gearings. GIMBAL RING: is an octaganol steel ring which supports te S and gimbals the compass in direction of pitch axis. BINNACLE RING: is the outermost ring inside which the GR is pivoted in roll axis. Dampers are also fitted.


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Marine Gyrocompass

ANTI SHOCKING MOUNTING: is not exactly part of compass, is fitted to minimize shock and vibrations.

WHY GYRO LESS EFFECTIVE AT HIGHER LATS: I should be noted that efficacy of top hvy control in causing Pc depends on rate of Tg which decreases away from equator until it is zero at poles.Hence sensitivity and accuracy of GC is greatly reduced in latitudes 70 and above.


Gyro Compass

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