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CHAPTER 9

STABILIZATION

Introduction

In order to understand the theory of operation of a stabilized sonar system, it is necessary first to comprehend the general nature of the stabilization problem. A brief explanation of the stabilization problem is provided in the first part of this chapter. Following this explanation, the   stabilization problem as it affects the two basic types of stabilized sonar systems is described. Readers not familiar with fire control symbols should refer to the Appendix before studying this chapter. A brief summary of the stabilizing system is given at the end of this chapter.
 
The Stabilization Problem
 
The position or direction of a line in space-whether it is a line of sight, a line of sound, or any other line-is specified by angles measured about certain reference axes the positions of which are known. In many fire control systems, the position of the line of sound is established by angles measured about axes which are horizontal and vertical in space. These horizontal, true-zenith axes are used to measure such angles as relative bearing Brq and depression Eq for the dual single-axis and three-axis systems. These systems are used in the two types of stabilized sonar equipment.

Equipment mounted on the plane of the deck, or on a plane parallel to the deck, however, positions a line in space in response to information which is ultimately referred to one of the deck systems of coordinates in which the reference axes are perpendicular and parallel to the deck. This information is called a deck, deck-zenith system of coordinates. These coordinates apply to such angles as sonar train B'r'q and depression E'q's for the dual single-axis system. (See figure 9-7.)

Ordinarily, the horizontal, true-zenith axes and the deck, deck-zenith axes are in alignment only at the infrequent intervals when the deck plane is horizontal. Most of the time the two sets of axes are being continuously displaced with respect to each other by the tilting movement of the deck.

  In order to measure the degree of displacement of these axes from each other, a stable element is used. The stable element is normally trained to B'r, the bearing of the main battery director. Thus the stable element measures these angles using B'r as a reference. In order to stabilize the sonar equipment the reference line about which the angles are measured must be changed from B'r to the bearing of the sonar target. This conversion is the function of the stabilization computer.

The method by which a stabilization computer, in conjunction with a stable element, is used to relate information measured with respect to two different systems of coordinates for the purpose of stabilizing a sonar system is illustrated by the following problem. Suppose a ship is riding at anchor with the sonar equipment trained on a stationary target. As determined by the sonar operator, the line of sound is fixed in space and the angles of relative sonar bearing Brq and depression Eq, which establish the position of the line, have fixed values because they are measured with respect to a system of horizontal, true-zenith coordinates. But the position of the line of sound in the dual-single axis system is established by the sonar train B'rq and the depression E'q', which are measured with respect to a deck, deck-zenith system of coordinates. Because the deck,

 
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deck-zenith axes are continually moving in space as the ship rolls and pitches, these angles are continually changing in value. If the target moves, the changes in the values of these angles also become a function of the movement of the target.

To determine the varying values of B'rq and E'q' in this problem it is necessary to relate mathematically the fixed values of Brq and Eq with the continually varying angles that measure the roll and pitch of the ship. The fixed values of Brq and Eq are supplied to the stabilization computer from the sonar equipment, and the continually varying values of the angles measuring the roll and pitch of the ship are supplied to the stabilization computer from a stable element. The stabilization computer combines the trigonometric functions of these angles into the proper mathematical equations from which the

  continuously varying values of B'rq and E'q' can be computed. The computed values of these angles are then applied to the drive mechanisms of the system to keep it continuously positioned on the desired line of sound.

Thus the function of the computer is to receive angles measured with respect to one set of coordinate axes and the angles of roll and pitch (or angles convertible to roll and pitch) and to compute from this data angles measured with respect to another set of coordinate axes.

The stable element is the piece of equipment which provides a fixed system of axes (to which the variable angles caused by roll and pitch may be compared)-and the gyroscope is the heart of the stable element. It is important therefore to understand the characteristics of a gyroscope.

 
Fundamentals of the Stable Element
 
PROPERTIES OF A FREE GYRO

If a heavy wheel is mounted so that its shaft is free to turn in any direction, it is known as a free gyroscope or free gyro. Usually the mount is constructed with three mutually perpendicular axes about which the wheel may turn. Thus in figure 9-1 the wheel is free to spin about axis A,

Properties of a free gyro.
Figure 9-1 -Properties of a free gyro.

to turn about B, and to turn about C. The gyro wheel is located so that its center of mass coincides with the intersection of these three axes.

  For purposes of illustration, all bearings are considered to be without friction. It is evident that the gyro wheel, when not rotating, is in a state of indifferent or neutral equilibrium; that is, it remains in any position in which it is placed. In addition, it yields in the direction of any force which tends to rotate it about one of its axes, just as any free mass moves in the direction of an applied force.

If the wheel is set spinning rapidly, it exhibits entirely new phenomena. It resists rather than yields to an applied force. A force, F, applied at point D of figure 9-1, produces a torque about the axis B. This torque, instead of rotating the frame in the direction of the applied force as it would do if the wheel were not spinning, is opposed by the frame.

Additionally, the wheel starts to rotate slowly (precess) about axis C in the direction indicated. If the mount is without friction, as was assumed, this action continues as long as the force is applied at D.

Similarly, a force applied at D in a plane through axis B tends to rotate the wheel about the C axis but the gyro resists this motion and turns instead about the axis B.

A pressure applied to the gyro wheel frame always results in reaction forces at the bearings. If, as in the cases illustrated by this figure, the

 
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applied force and bearing reaction are not in the same straight line, these forces form a couple which tends to rotate the gyro wheel axis. The free gyro does not, however, turn about the couple axis but rotates about another axis perpendicular to the couple axis. Thus, in figure 9-1, a couple about axis B results in a rotation or precession of the wheel and frame about C.

Experiments show that, neglecting inertia, the gyro does not resist translation, that is, motion which keeps the spin axis A parallel to its original position.

RIGIDITY OF PLANE

Rigidity of plane is that property of a gyro by which the gyro tends to maintain the plane of its wheel parallel to its original position in space. This property results from the fact that a mass in motion can have its direction of movement changed only by applying a force to the mass.

PRECESSION

Precession is the name given to the slow movement of a gyro wheel resulting from the application of an external force or couple which tends to rotate the spin axis of the gyro.

Figure 9-2 shows a rapidly spinning gyro in which the axis of spin is A. A couple represented by forces F-F' tends to twist the gyro wheel about the couple axis B perpendicular to, and in the same horizontal plane as, A. Consider a small section of the wheel rim at D. Due to the rotation of the wheel, section D has a high linear velocity in the direction DE.

The couple F-F' exerts a force upon this small mass along DH and so accelerates it in this direction. During a short interval of time this acceleration gives the particle a component of velocity DH. The result of combining velocities DE and DH is a new velocity DG, equivalent to a rotation through an angle about axis C. Therefore the effect of a couple F-F' acting about the B axis is to cause a slow rotation of the gyro wheel about the C axis. This rotation is known as precession.

In order to obtain a high rigidity of plane and slow precession, gyro wheels are made heavy in weight and are operated at a high rate.

It has been shown that if the gyro wheel is freely supported as in figure 9-1 and a force or couple is applied about the axis B, the wheel does

  Precession.
Figure 9-2 -Precession.

not turn about an axis C at right angles to the axis of the applied couple.

To determine the direction of precession apply the following rule: The axis of a freely mounted gyro tends to turn or precess in such a direction that it becomes parallel to the axis of the applied torque, by the shortest path, and with the rotation of the wheel in the same direction as the applied torque.

APPARENT ROTATION

Assume now that the gyro wheel supported by its universal mounting as before is placed at the equator of the earth with its A axis vertical, as shown in position 1 of figure 9-3. To an observer standing on the earth the wheel appears to rotate at the rate of one complete turn in 24 hours. This rotation might seem puzzling were it not remembered that it is the earth that is turning-not the gyro.

EFFECT OF FRICTION

In the practical construction of the mounting described, some friction is inevitably present at the trunnion bearings. Assuming for the moment that the bearings of the horizontal axis B (figure 9-1) have slight friction, it is apparent that the

 
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Apparent rotation.
Figure 9-3 -Apparent rotation.

earth's rotation applies a slight turning moment or couple to the gyro wheel. A free gyro, however, does not turn in the direction of an applied couple but precesses around an axis 90° from the couple. Consequently the slight friction in bearings of axis B causes the gyro wheel to precess about the axis C. With proper construction of bearings B this precession may be made very slow.

In the case just described it was assumed that the bearings determine the ability of a gyro wheel to maintain its plane or rotation fixed in space against the friction of bearings B. If, to take an extreme case, the supporting frame were locked

Effect of latitude.
Figure 9-4. -Effect of latitude.

  about axis C (X, figure 9-1), the gyro wheel would immediately lose its resistance to the friction of bearings B and so would partake of the earth's rotation just as if the wheel were not spinning. The importance of extreme freedom about axis C is therefore apparent.

EFFECT OF LATITUDE

It has been noted that the earth's rotation causes an apparent rotation of a gyro which is set spinning with its A axis perpendicular to the earth's surface. At the equator this apparent rotation appears to be a straight backward gyration (with respect to the earth's rotation) at the rate of one revolution every 24 hours about a north-south axis. At either pole this phenomenon does not occur (again assuming frictionless bearings), because the gyro axis A is already parallel to (or an extension of) the earth's axis, as in figure 9-4. At any point or latitude between the pole and the equator, however, the wheel appears to gyrate once every 24 hours about an axis parallel to the axis of the earth's rotation, and in a direction opposite to that of the earth's rotation, as in figure 9-5.

Gyration between equator and pole.
Figure 9-5 -Gyration between equator and pole.

COMPENSATION

In any application of the gyro to precision instruments, corrections for the earth's rotation, friction, acceleration, turning, and other factors must be applied if the gyro is always to spin in a fixed plane with respect to the earth's surface at any latitude.

Compensations for these errors are not dealt with here, as their operation is not essential in understanding the principles of the stable element.

 
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Stable-Element Construction
 
The stable element is used (1) to measure movement of the deck in level and crosslevel angles or in roll and pitch angles, depending on the connections of the stable element, and (2) to transmit these angles as synchro signals. The principal part of the stable element is an electrically driven gyroscope that establishes a horizontal-reference plane from which the level and crosslevel angles are measured.

There are three follow-up systems in stable-element equipments-the train, the crosslevel, and the level follow-up systems. In some equipments the train is locked on zero, and the outputs are in terms of roll and pitch instead of level and cross-level. The follow-up system for train determines the error between the bearing of the equipment that is being stabilized and the bearing of the training frame in the stable element. When the

  stable element supplies roll and pitch, however, the train follow-up system is not used and the B'r input to the stable element is locked in the zero position. In stable elements having outputs of level and crosslevel, the train follow-up is used to rotate the stable element to the bearing of the equipment that is being stabilized.

The follow-up systems for level and crosslevel are identical and are actuated by electric error signals, which originate in the gyro unit. These signals are amplified and are used for actuating the level and crosslevel motors, which drive not only the synchros transmitting the level and crosslevel angles to the equipment to be stabilized but also the level and crosslevel follow-up circuits. If the stable element is modified and the train input locked, the output is then roll and pitch instead of level and crosslevel.

 
Level and Cross-Level Receiver System
 
A spherical diagram illustrating the relationship between the angles of level L, crosslevel Zd, director train B'r roll M, and pitch N is shown in figure 9-6.

Angular inputs which indicate the attitude of the deck with respect to the horizontal are supplied to the computer by a stable element. The space reference of the stable element is a gyroscope which rotates about a vertical axis to maintain continuously an a-c electromagnet in a fixed position. Above the electromagnet are two sets of follow-up coils, the fields of which are at right angles to each other, one for level L and the other for crosslevel Zd control. Both sets of coils are supported on the inner gimbal of two mutually perpendicular gimbals. When the motion of the ship displaces the coils with relation to the electromagnet, follow-up systems are actuated by the coils to move the gimbals in such a direction as to restore the original position of the coils with respect to the electromagnet. The angular movement of the level and crosslevel follow-up controls causes the signals across the level L and crosslevel Zd transmitters to change in correspondence with the attitude of the gimbals and thus measure the attitude of the deck with respect to the horizontal.

239276°-53-13

  One of the stable elements from which the computer may receive tilt angle inputs is the Stable Element Mk 6. This instrument is trainable and is used usually in conjunction with the Gun Director Mk 37. As the director trains to position a line of sight, it generates a signal corresponding to the angle of director train, B'r, which is transmitted by synchro to the stable element in order to drive the stable element through the same angle. Because the stable element normally is trainable, its cross-level and level axes are rotated about an axis perpendicular to the deck and in a plane parallel to the deck. Pitching and rolling which may occur at the angle of director train are measured about the level and crosslevel axes, respectively. Thus as the stable element trains through B'r, continuously changing values of L and Zd are generated for continuously varying values of B'r and are transmitted to the various stabilized equipments on the vessel. When the necessary electrical connections are made the same angular values are received by the computer.

If the tilt angles transmitted from a stable element, not locked on zero, were used directly in making the stabilization computations for the various fire control systems serviced by the computer,

 
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the train angle at which these tilt angles were measured would also be required in the computations, thus needlessly complicating the computer circuits. If tilt angles measured at the fore and aft axis of the ship were used, where the angle of train is zero, only the tilt angles would be required for the stabilization computations and the computer circuits would become less complicated. For this reason the functions of L, Zd, and B'r are converted by the required trigonometric equations

Spherical diagram illustrating various angles in sonar problems.
Figure 9-6. -Spherical diagram illustrating various angles in sonar problems.

  into the functions of N and M, which are the tilt angles at the fore-and-aft axis.

The level and crosslevel receiver system performs this conversion. This system consists of three input servos which are positioned through the angles of level L, crosslevel Zd, and director train B'r. The resolvers in these servos are connected in such a manner that the components of these angular functions are related according to the equations in the functional diagrams shown in figure 9-11. The rotation of the servomechanisms accomplishes a continuous simultaneous solution of these equations. The solution is in terms of the angles of roll M and pitch N. If a gyro which has been locked on zero is used, the angles supplied to the computer are measured directly in roll and pitch, eliminating the need for the level and cross-level receiver.

ROLL AND PITCH COMPUTER SYSTEM

The computer circuit, described in the section on the level and crosslevel receiver, is located partly in the level and crosslevel receiver and partly in the roll and pitch computer. The two resolvers in that part of the computer circuit which is located in the roll and pitch computer rack control two output servos, which, in turn, position various resolvers through the angles of roll M and pitch N.

 
Dual Single-Axis Stabilization System
 
In the problem of determining a line of sound to an underwater target with a dual single-axis below-decks system like that of the QHB and QDA, two sound heads rotatable about axes in the deck must be positioned properly as shown in figures 9-7 and 9-8.

Each sound head generates along a plane of sound. The sound heads are rotated so as to make their planes of sound intersect on the line of sound to the target. Sound plane A is rotated about an axis perpendicular to the deck through the train angle B'r'q and sound plane B is rotated about an athwartship axis parallel to the deck through the tilt angle E'q's. Both of these angles are measured with respect to deck, deck-zenith coordinate axes, but the required fire control information is computed as relative bearing Brq and

  the depression angle Eq, both measured with respect to horizontal true-zenith coordinate axes. In order to position these sound heads properly, the computed data Brq and Eq must be converted through the use of M and N into B'r'q and E'q's in the dual single-axis stabilization system and transmitted in that form to the drive mechanisms of the two sound heads.

Note that the spherical diagram indicates the depression angle at the line of sound as E'q'. If this were a two-axis system, E'q' would be the proper depression order, but because of the QDA sound head is not trainable, in the QHB-QDA dual single-axis system, E'q's must be used instead.

The dual single-axis stabilization unit in the computer consists of (1) two input servos which are used to position mechanically two resolvers

 
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Dual single-axis stabilization problem.
Figure 9-7 -Dual single-axis stabilization problem.

through the angles Eq and Brq, (2) two resolvers which are mechanically positioned through the angles M and N by the servos in the roll and pitch

  computer or the roll and pitch receiver, and (3) two servos which are positioned by their resolvers through the angles B'r'q and E'q's. The resolvers are connected in such a manner that they relate the functions of the four input angles in trigonometric equations which produce in simultaneous solution the functions of B'r'q and E'q's for synchro transmission to the drive mechanisms of the sound gear.

Dual single-axis system.
Figure 9-8 -Dual single-axis system.

 
Three-Axis Stabilization System
 
In a three-axis below-decks system a line of sound is positioned about three axes of rotation relative to the deck, as shown in figures 9-9 and 9-10.

Although movement about the three axes of rotation occurs simultaneously, for the sake of explanation, the operation of the system may be treated as though it occurred in sequence as follows. The system must train in the plane of the deck to position its crosslevel axis in a vertical plane through the line of sound, but the train angle input is computed in the horizontal-true zenith angle of relative bearing, Brq. Therefore, this angle must be converted by parts of the computer circuit in the three-axis stabilization system through the angles of roll M and pitch N into the deck, deck-zenith angle of B'rq. Once it has been positioned in the vertical plane through the line of sound, the crosslevel axis is rotated through the crosslevel angle Zdq until the level axis is horizontal. Then the level gimbal is rotated

  about the level axis through the level angle Lq to bring the sound head into the horizontal plane. From this point the level gimbal is tilted through the depression angle Eq to bring the sound head onto the desired line of sound. In actual practice, the latter two steps are accomplished by continuously subtracting Lq from Eq. The angles Zdq and Lq are derived by the simultaneous solution of trigonometric equations relating M, and N, and Brq.

The three-axis stabilization system utilizes two sections in the Mk 59 computer. In one section, resolvers are mechanically positioned by input servos through the angles M, N, and Brq. The resolvers are connected so that they solve for Zdq and Lq, which are then introduced by means of their respective output servos into the stabilizing drive mechanisms of a three-axis below-decks system like the SQG sonar. The synchro differential transmitters in the Lq output servo receive Lq as a mechanical displacement and subtract it

 
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from Eq, which is received as an electrical signal. In the other section, Brq, N, and M are introduced

Three-axis stabilization system problem.
Figure 9-9 -Three-axis stabilization system problem.

  into their resolvers in that order to produce the train angle B'rq. An output servo positions the drive mechanism of the sonar gear through B'rq.

Three-axis system.
Figure 9-10 -Three-axis system.

 
Computer Units
 
The functional diagram in figure 9-11 shows the complete computer with 5 stabilized outputs. The number of outputs can be altered to supply the needs of different installations. In determining the composition of a Computer Mk 59, the following factors are considered:

1. The type of stable element used to furnish deck tilt angle data. If the stable element is the Mk 6 or an equivalent, a level and crosslevel receiver rack and a roll and pitch computer rack are required. If the stable element is the Mk 7 with alteration for roll and pitch output, or an equivalent, only a roll and pitch receiver is required.

2. The types and quantities of stabilization racks required are directly dependent on the types and

  quantities of fire control gear on board ship which require stabilization.

3. The inclusion of a power supply with the computer depends upon the requirements of the particular fire control system with which the computer is to be associated. If the fire control system operates off a central supply, the power supply rack may be omitted from the computer. If the fire control system operates off a series of decentralized power supplies, a power supply for the computer may be necessary. The use of a power supply determines the number and size of terminal compartments required. If a power supply is used, a single large compartment is usually sufficient. If no power supply is used, it is more convenient for symmetrical arrangement to use two smaller terminal compartments.

 
Integrated Sonar System
 
The stabilization computer and stable element are ordnance equipments and therefore are not among the equipments maintained by the   electronics division. The information in this chapter is included so that the electronics officer can understand better the nature of the electrical orders of
 
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FOLDOUT - Figure 9-11 -Functional diagram, Mk 59 Mod 0.

FTypical QDA, normal azimuth, and MCC
azimuth sonar beams.
Figure 9-12 -Typical QDA, normal azimuth, and MCC azimuth sonar beams.

stabilization injected into the sonar equipments.

Figure 9-12 shows the sound beams used in a complete stabilized sonar system. In practice, the edges of the beams are not sharp lines as shown. The normal azimuth beam, shown in figure 9-12 as a half-round pencil, is employed during search and while closing the target. If the target is deep, the normal azimuth beam passes above it except at long ranges. Thus the operator can use the maintenance of close contact (MCC) feature for target s at close range. The MCC beam used in this system is approximately the same width in the horizontal direction as the normal azimuth beam, but the MCC beam extends over most of the quadrant from the surface downward. Although the MCC beam is inefficient for use at long ranges, at short ranges the echo strength increases sufficiently to permit the azimuth equipment to maintain contact and to determine range and bearing practically up to the point of passing over the target.

Figure 9-13 illustrates the interflow of functions between the units comprising a complete stabilized sonar system. The system illustrated comprises the QDA, QHB, and OKA, and is one of the systems in use today. The input to the system is in

  the form of level and crosslevel angles, and, therefore, the computer is equipped with a level and crosslevel receiver, which must first convert these angles to roll and pitch in order for them to be used in the computer. Note the by-pass switch which, when thrown to the search position, allows the azimuth sonar to receive stabilization signals, but the depth-determining equipment is unstabilized. In the attack position both of the equipments are stabilized.

The principal functions of the stabilization computer are:

1. To convert the angles of level, L, and cross-level, Zd, which exist when the stable element is trained away from 0 relative bearing, to angles of roll, M, and pitch, N. The information obtained from this conversion can be used to stabilize the sonar system, which is not usually on the same bearing as stable element train, B'r. In some systems the stable element has its B'r input locked on zero. In this case its output is in roll, M, and pitch, N, directly, thus eliminating the need for this function of the computer.

2. To combine roll and pitch with the relative sonar target bearing in the horizontal plane Brq, to produce B'r'q, the relative bearing in the deck plane, in order to maintain the azimuth transducer on the same true bearing and hence counteract the tendency for roll and pitch to carry the beam to one side or the other.

3. To combine roll, pitch, and relative sonar target bearing, Brq, with the depression of the beam relative to the horizon, in order to compute E'q', the beam depression relative to the deck.

The order, E'q', is the correct tilt angle for all phases of ship roll and pitch of a depth transducer which is trained on the target, as is the case in a three-axis system. E'q' is also the correct depression of that portion of the broad QDA beam which extends along the bearing of the target.

 
Tangent Solver
 
If the target lies dead ahead, the order, E'q', is the correct order to which to tilt the QDA transducer to contact the target for any phase of ship roll or pitch. If the target bears off the bow, however, the QDA transducer must be tilted to a somewhat greater angle than E'q' in order to   contact the target because for any position of the transducer, the beam depression is greatest dead ahead, and is less for bearings off the bow. If the beam were broad enough, the depression of the portions of the beam that extend athwartships would be zero; that is, the beam would lie along the
 
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Block diagram of a stabilized sonar system.
Figure 9-13. -Block diagram of a stabilized sonar system.
 
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surface at 090 and 270 relative. If the transducer were tilted to 10°, the beam in the forward direction would be depressed 10°, while the portion of the beam extending along a bearing of 045 relative would be depressed only about 7°.

The tilt order, E'q's, produced in the tangent solver is conveyed through the attack search switching cabinet and by-pass switch to the CT synchros which are mechanically geared to the

  shaft of the hoist-tilt mechanism in the QDA. If the transducer is not in the position represented by the order E'q's, the rotors of the CT synchros will not be oriented properly with respect to the fields produced by the order signal. As a result, a voltage is delivered by the CT synchro rotors to the tilt-control amplifier unit, which drive the system in the proper direction to align it with the order, E'q's.
 
Conclusion
 
In short, the heart of the stabilized sonar system is the computer, which receives stabilizing inputs from the stable element. The stable element uses either the main director train or the fore-and-aft axis of the ship as its reference. The computer converts these stabilizing inputs into the proper voltages to be used with the stabilized sonar system, which is usually on a different reference axis. The computer also supplies stabilizing information to different units of equipment, such as   searchlights, radar systems, torpedo tubes, and guns, as required by the ship.

As the ship rolls and pitches the stable element measures the angles of deviation from the true horizontal. The computer then converts these angles into level and crosslevel signals to be added to the angles of depression and train, which are generated in the sonar system. The result is that the lines or planes of sound remain stable and on the target regardless of the gyrations of the ship.

 
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