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CHAPTER 5

GENERAL REQUIREMENTS OF SONAR SYSTEMS

Operational Planning
 

This chapter discusses attempts that are being made (1) to cope with some of the special operational difficulties encountered in trying to obtain information by echo ranging and (2) to apply such information to tactical problems. From this information the military specifications of new equipments are obtained.

SEARCH OPERATIONS

Echo ranging is used by the Navy for several purposes, not all of which are directly connected with naval warfare. Echo ranging as an aid in antisubmarine warfare is only one of its applications, though perhaps it is the most important and dramatic. Regardless of its use, the success of echo ranging is conditioned by the systematic execution of a carefully considered operational plan. Such a plan is based on the consideration of the following functions that underwater echo ranging can successfully perform:

1. To establish contact with the target by using sound.
2. To maintain contact with the target and identify it.
3. To obtain accurate determinations of the range and bearing of the target.
4. To determine the rate at which the range and the bearing are changing-that is, the range rate and bearing rate.

Each of the last three of these functions successively depends on the preceding ones.

The present discussion is restricted to the application of echo ranging to search operations in anti-submarine warfare as prosecuted by a surface vessel.

  In a search operation three different missions can be assigned to the surface vessel or squadron. These missions are:

Hunt: To find as many enemy submarines as possible with little or no information as to their position at any earlier time.

Location: To find a specific enemy submarine whose position at an earlier time is known with reasonable accuracy.

Screen: To establish a zone (the screen) around a friendly area (a shipping lane or a moving convoy) so that all enemy submarines must pass through the screen in order to attack, and then to detect all enemy submarines while they are in the screen.

There are several differences among these three assignments. Hunt and location missions are offensive, and the submarine may be expected to use evasive maneuvers. The screen mission is defensive, and its objective-the prevention of a successful attack by a submarine-is partly achieved if the submarine is forced to use evasive tactics.

The success of these missions obviously depends on the probability of establishing sonar contact-that is, on the probability that when a ping is transmitted, a recognizable echo will be returned. Intelligent operational plans can be worked out only if all the factors affecting this probability are known and their effects evaluated. The effects of some of these factors are easily evaluated. For example, in the hunt operation, success may be equally probable if the echo-ranging vessel searches a wide area superficially or a smaller area intensively. In the location mission, success is assured if the vessel has sufficient speed to make an exhaustive search of a sufficiently large but limited area,

 
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provided that self-noise at high speed does not make the sonar inoperative.

The effects of other factors are not easy to evaluate. The most important factors to be evaluated are:

1. Range of the target.
2. Bearing deviation-that is, the difference between the actual bearing of the target and the transducer heading.
3. Relative bearing of the target.
4. Depth of the target.
5. Echo strength of the target.
6. Prevailing sound conditions.
7. Speed of the echo-ranging vessel.

To solve the problem of maneuvering a ship so as to bring the sonar into a position that will ensure a high probability of obtaining echoes, the cumulative effect of all the factors must be analyzed. Many operational rules, based on experience and a small amount of theoretical analysis, have been formulated. However, no complete solution of this operational problem has been made.

For this discussion, if it is assumed that adequate data are available on the last four factors listed, only the probability of establishing sonar contact based on the range and bearing of the target need be examined.

Probability of Detection

Single ping. -Assume that a target is in the vicinity of a sonar and that a single ping is transmitted. The detection probability can be exhibited on a contour map, like the one shown in figure 5-1. This figure is entirely schematic and is presented merely to illustrate the discussion of general principles. It does not represent the facts of any actual situation.

The position of the echo-ranging sonar is indicated at the bottom of figure 5-1. If the target is situated on a given contour, the number shown on the contour designates the probability of detection. Such a number is called the detection probability. For example, if a target is on the 60-percent contour, a single ping will return a recognizable echo 60 percent of the time. If the target is inside the 60-percent contour, this probability will be greater.

For all search operations, it is important that the area of each contour be as large as possible.

  The maximum value of a typical detection probability also should be large. In order to obtain a single number that describes the contour diagram, the areas between any two adjacent contours are multiplied by the average value of the detection probability, and the various products thus obtained are added. The result is called the effective search area of a single ping. For example, the area between the 30-percent contour and the 40-percent contour is measured, and this quantity is multiplied by 35 percent, the average probability in the area. Then the process is repeated for all the zones, and the sum of the individual products is computed.

In order to obtain a larger area, the beamwidth could be increased. An increased beamwidth, however, would make the bearing determination less accurate, and thus the gain of one advantage would cause the loss of another. In the design of an all-purpose pinging sonar the various requirements must be balanced carefully against one another.

Detection probability of a stationary target and a
stationary sonar.
Figure 5-1. -Detection probability of a stationary target and a stationary sonar.

 
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Successive pings.-In practice, surface vessels do not rely on a single ping for detection, although the tactical situation may force a submarine to do so. The analysis of the advantage of repeated pings in operational practice is complex; only a few major principles can be discussed here.

The simplest case is that in which both sonar and target are at rest and in which two pings are sent out. Then it is possible for an echo to be recognized (1) on both the pings, (2) on either of the pings, or (3) on neither of the pings.

Let W1 be the probability that a single ping will return a recognizable echo for the given position of the target. Then the probability that the echo will not be detected is evidently

1-W1.  (5-1)

Let us assume that the detection probability for the second ping is the same as if the first ping had not been transmitted. This condition is not likely, for the operator may have been doubtful of the echo from the first ping and may have ignored it, but a doubtful echo from the second ping is, under these conditions, very likely to be considered certain-especially if a range recorder is used. This effect becomes increasingly important as the number of pings increases. For simplicity, however, memory and comparison effects are ignored.

Wn v W1
Figure 5-2.-Detection probability Wn for n pings in terms of the detection probability W of a single ping.

  The probability that the second echo will not be detected is also

1-W1.

The probability that neither of the two echoes will be detected is the product of the two probabilities-

(1- W1)2.  (5-2)

Hence the probability that at least one of the two echoes will be detected is

W2=1-(1-W1)2.  (5-3)

If n pings are transmitted, the detection probability is

Wn= 1-(1- W1)n.  (5-4)

Graphs of this equation for several values of n are shown in figure 5-2. Figure 5-2 shows an increase of detection probability with each successive ping. This increase is most rapid for intermediate values of W1. If W1>0.5, five pings will make detection practically certain.

Effects of motion. -If the echo-ranging vessel is in motion, the calculation of the probability of making sonar contact with a target by using successive pings becomes more complicated. If the target also is in motion, additional complications arise.

In the case of a stationary target and a moving echo-ranging vessel, suppose that the target was on contour W' of the first ping but that the motion of the sonar has resulted in placing it on contour W" of the second ping. Then, by reasoning similar to that in previous paragraphs and again i by ignoring memory and comparison effects, the probability of detection by either or both of the two pings is

W=1-(1-W')(1-W").  (5-5)

Values of this function are given in table 8.

TABLE 8.-Detection Probability for Two Pings-Moving Sonar and a Stationary Target

W"\W' 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.1 0.19 0.28 0.37 0.46 0.55 0.64 0.73 0.82 0.91
.2   .36 .44 .52 .60 .68 .76 .84 .92
.3     .51 .58 .65 .72 .79 .86 .93
.4       .64 .70 .76 .82 .88 .94
.5         .75 .80 .85 .90 .95
.6           .84 .88 .92 .96
.7             .91 .94 .97
.8               .96 .98
.9                 .99
 
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Detection probability of a stationary target and
a moving sonar.
Figure 5-3.-Detection probability of a stationary target and a moving sonar.

Arbitrary values of W' are arranged in the top row, those of W" are in the left-hand column, and the corresponding values of W are in the body of the table. For example, suppose that when the first ping is transmitted, the target is on the 60-percent contour and that the motion of the sonar has resulted in placing it on the 50-percent contour for the second ping. Then W' equals 0.6, W" equals 0.5, and from the table, W equals 0.8.

Table 1 can be used to construct a contour map similar to that in figure 5-1. Such a map is shown in figure 5-3. The two successive positions of the sonar are shown at the bottom. It is assumed that the detection probability of each ping is identical with that diagrammed in figure 5-1, and that the pings were transmitted with the same transducer heading. The motion of the transducer between pings has been greatly exaggerated for purposes of illustration.

Comparison with figure 5-1 shows that each contour-for example, the 50-percent contour-has greatly expanded and encloses more than twice the area of the same contour for a single ping.

  Moreover, the maximum value of the detection probability has increased from 75 percent for the single ping to nearly 90 percent for the two pings. Consequently, the effective search area of the two pings is more than doubled.

The amount by which the effective search area of the overlapping pair exceeds twice the area of a single ping has been exaggerated by the exaggerated motion of the sonar. In practice this amount is somewhat less than that shown, but the effect is nevertheless appreciable. Also, in practice, more than two overlapping pings are used, and the probability of echoes is increased further.

A moving target has a different effect than a moving sonar. Suppose that a moving target is detected at a certain point, P, at a time, to, and that at a later time, t, it is necessary to estimate

Detection probability of a moving target and a
stationary sonar.
Figure 5-4.-Detection probability of a moving target and a stationary sonar. A, Change brought about in figure 5-1 after an interval of time; B, change in figure 5-1 after twice the interval.

 
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Probability contours for three successive pings,
allowing for the motion of both target and echo-ranging
vessel.
Figure 5-5. -Probability contours for three successive pings, allowing for the motion of both target and echo-ranging vessel.

its position. In order to illustrate the principles involved, suppose that between to and t no further pings are sent out and that the direction and speed of the target are unknown. Then it is possible to draw probability contours, showing the probability of the locations of the target at given points at time t. These contours are circles with centers at point P. The radii of the contours depend on the probability that the target moves with the

  given speed. As the time interval, t minus to, increases, these radii also increase because the unknown motion of the target has more time in which to take effect.

These same considerations can be applied to the time interval between pings. If the ping is sent out at time to, figure 5-1 shows the probability that, if the target is at a given place, it will detected. At a later time, t, but before the next ping, the target may have moved. Consequently, figure 5-1 does not show the probability that, if the target is at a given place at this later time, it would have been detected at the earlier time to. But it is possible in principle to work out the contours for this "prior-detection" probability. The unknown motion of the target causes the contours of high probability to shrink as t increases. This effect is shown schematically in figure 5-4, A and B, for two successive values of t.

If several successive pings are sent out, shrunken prior-detection contours must be combined, as explained with figure 5-3. The result of such a succession of pings is shown schematically in figure 5-5. This figure represents the state of affairs at the time the echoes from the third ping are being received, and the contours show the probability that, if the target is then at a given point, it will be detected then or will have been detected earlier.

The motion of the sonar and target is exaggerated in figure 5-5 to emphasize important points. Note that, because of the unknown motion of the target, the 80-percent contour in figure 5-5 has a much smaller area than the 80-percent contour in figure 5-3. This condition exists even though the contour in figure 5-3 is based on three pings and that in figure 5-5 on only two.

 
Target Bearing
 
The foregoing considerations of the probability of establishing sonar contact have been restricted to simple conditions. In general, the possibility of taking action against a target in a given area depends on (1) how completely the area can be searched in a short time and (2) the ability of the operator to maintain sonar con tact with the target once he has contacted it. The first of these requirements makes it desirable to design the sonar so that the search area of the ping is large.   The second requirement conflicts with the first. Special devices have been designed to satisfy these conflicting requirements. These devices will be discussed after a preliminary examination of the operational problem in terms of the simplest sonar.

MAINTAINING CONTACT

After a signal has been transmitted, the sonar operator is on the alert for a sound contact with the target-either as he listens to the sound from

 
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the loudspeaker or as he watches the chemical range recorder. For example he might detect a break in the background reverberation or noise.

Having made a contact, he is concerned chiefly With maintaining it. Maintaining contact is difficult with ordinary sonar gear. The target may move out of the sound beam, either to the right or to the left. Because of the relatively long interval between echoes, the uncertainty as to the direction in which the beam should be rotated is a serious shortcoming in sonar design.

BEARING DEVIATION

The target bearing is the direction of the line joining the transducer to the center of the target and is not necessarily given by the transducer heading, which is the direction of the axis of the sound beam. Because of the width of the sound beam, an echo may be received even when the axis does not bear on the center of the target (for example, the conning tower in a submarine). Thus, the target bearing and transducer heading may not coincide. The difference between them is called the bearing deviation. When the bearing deviation becomes greater than a certain amount, the echoes become too weak to be heard.

As the sonar operator has control of the transducer, he knows its heading. The conning officer, however, wishes to know the target bearing. If the bearing deviation is small, it can be ignored. Unfortunately, every attempt to reduce it increases (1) the probability that the target may move out of the sound beam and (2) the seriousness of the uncertainty mentioned above. Thus, every solution must be a compromise between conflicting requirements.

It is not only the beam pattern of the transducer and the target width that affect the possible magnitude of the bearing deviation; the echo level and the level of the background noise and reverberation are also instrumental. If reverberation is limiting, the possible deviation also depends on the Doppler shift of the echo.

CROSSING THE TARGET

The first solution of maintaining contact and determining bearing was the operation known as crossing the target. In this operation, the transducer heading is systematically changed more rapidly than the target bearing changes. When

  the sound beam is trained off the target, the motion of the transducer is reversed and is continued until the sound beam leaves the target on the other side. This method tends to eliminate bearing uncertainty. Whenever no echo is obtained the operator knows on which side of the beam he will find the target. The two limiting transducer headings thus obtained are called cut-ons. The average of two successive cut-ons is taken as the best approximation to the target bearing.

Although the procedure is practicable, it has many disadvantages. It is time-consuming, for it requires at least four, and often more, pings to obtain one value of the target bearing; hence, before this value is known to the sonar operator, the target may have moved, rendering the information more or less obsolete.

SPLIT TRANSDUCERS

Present solutions of maintaining contact and determining bearing all involve the use of a transducer that has been split into two or more segments. The first application of the split transducer was with searchlight equipment. The two hydrophones were constructed in semicircular shape and of such dimensions that they could be mounted in the same space as the older circular transducers. Moreover, if electric connections are changed before transmission, the projected sound beam can be made identical with that of the older circular transducer.

The physical principles involved can most easily be explained by considering a pair of identical hydrophones, mounted a distance a apart, with

Three successive stages in the passage of a plane
wavefront from the target to a transducer having two hydrophones.
Figure 5-6. -Three successive stages in the passage of a plane wavefront from the target to a transducer having two hydrophones (marked "1" and "2") spaced a distance a apart.

 
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Diagram containing phase-lag circuit.
Figure 5-7. -Diagram containing phase-lag circuit, showing how a desired phase difference between the currents from the two hydrophones is obtained.

their acoustic axes parallel to each other and perpendicular to the line joining the two hydrophones. The general arrangement is shown schematically in figures 5-6 and 5-7. It is assumed that the pattern of the two hydrophones consists of a single broad lobe, as shown by the dotted line of figure 5-9.

Suppose an echo or other single-frequency sound is incident on the hydrophones from a direction that makes the angle α with the acoustic axes. Each wave then reaches the hydrophone closest to the target before it reaches the other hydrophone, and the alternating currents generated by them are not in phase. Under the circumstances shown in figure 5-6, the current from No. 2 is in advance of that from No. 1. This condition is shown in curves A and B of figure 5-8. The

  phase angle β can be calculated as follows: After reaching hydrophone No. 2, the wave must travel a distance, l, before reaching No. 1. This distance is

l=a sin α,  (5-6)

which is l/λ wavelengths. Because 1 wavelength is equivalent to a phase change of 360°, the angle β is

β=360° (a/λ) sin α.  (5-7)

If the current generated by No. 1 is

C1=C(α) cos ωt,  (5-8)

then that generated by No. 2 is

C2=C(α) cos(ωt+β).  (5-9)

The function C(α) is determined by the directivity pattern of the separate hydrophones-shown by the dotted curve in figure 5-9. The graphs of the two currents, C1 and C2, are shown in curves A and B of figure 5-8.

If the current from hydrophone No. 2 is passed through a phase-shifting network, the phase shift β can be altered by any desired amount-say θ.

Currents plotted against the phase angle.
Figure 5-8. -Currents C1, C2, and C2', of figure 5-7, plotted against the phase angle ωt, and showing the phase difference β and β-θ of figure 5-7.

 
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The result is the current

C2'=C(α) cos (ωt+β-θ), (5-10)

which is shown graphically in curve C of figure 5-8. The vector diagrams of the circuit shown in figure 5-7 indicate the relation of the three currents. If C1 and C2' are combined, the resulting current1 is

C=C1+C2'=C(α)[cos(ωt)+cos(ωt+β-θ)]  (5-11)

C1+C2'=2C(α) cos½(β-θ) cos[ωt+½(β-ω)]  (5-12)

Graph of equation (5-13).
Figure 5-9. -Graph of equation (5-13) for a/λ=4, and for θ=90°.

The level of the electrical output is thus

L=20 log [2C(α)] +20 log cos [½(β-θ)].  (5-13)

The first term of this expression is essentially the directivity pattern of the individual hydrophones. The second term also depends on the direction from which sound comes, because β depends on α.

The graph of the resultant level, L, for the case in which is a/λ is 4 and θ is 90°, is shown by the solid line of figure 5-9. As a result of connecting the two hydrophones together, the single broad lobe of each obviously has been changed into several narrower lobes.


1 In deriving the equation for C, the following trigonometric relation has been used: cos A+cos B=2 cos ½ (A+B) cos ½ (A-B).

239276°-53-8

 

Values of the lobe angles.
Figure 5-10. -Values of the lobe angles, shown in figure 5-9, as a function of λ/a and n, the order of the lobe.

As a result of the phase-shifting network, the axis of the new main lobe does not coincide with that of the original lobe, and the side lobes are not symmetrically located. Figure 5-10 can be used to determine the positions of the lobes for any value of the quantities θ, λ/a, and the order of the lobe, n.

In this graph (figure 5-10) the lobe angle is the point at which the new and original beam patterns are tangent (figure 5-9), and the integer n is zero for the main lobe, ±1 for the first lobes on each side, ±2 for the pair of second lobes, and so forth. The phase lag, θ, is measured in degrees.

Shift of main lobe of beam pattern in the BDI
system.
Figure 5-11. -Shift of main lobe of beam pattern in the BDI system.

 
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Bearing-Deviation Indication

All bearing-deviation indicating (BDI) devices use split transducers. The purpose of BDI devices is to translate into a polarized-magnitude difference the small echo-signal phase difference between the two halves of the transducer.

For transmission the two semicircular parts are connected so as to produce the normal beam of a

Diagram of the BDI system.
Figure 5-12. -Diagram of the BDI system.

circular diaphragm, which is illustrated by the center pattern of figure 5-11. The center pattern shows the normal beam of a circular diaphragm. The two side patterns show the beams for the two halves of the circuit. For reception, the two halves are connected as shown in figure 5-12.

Note that there are two symmetrical output channels. The connections of the right channel are the same as those for the pair of hydrophones

  Graph of currents from the two channels as a
function of bearing deviation.
Figure 5-13. -Graph of currents from the two channels as a function of bearing deviation.

in figure 5-7. The connections of the left channel differ only in that the phase lag also is introduced into the output of No. 1. The beam pattern for the right channel thus has its main lobe deflected to the right, as shown by the right-hand curve of figure 5-11; the main lobe of the left channel is deflected to the left. These deflections are shown more clearly in the rectangular-coordinate system used in figure 5-13. The ordinates are the currents out of the two channels. In practice these currents are rectified, as indicated in figure 5-13; the diode rectifiers are shown in figure 5-12.

The rectified output currents may be used for various purposes. They are commonly connected to an indicator, which may be a cathode-ray oscilloscope, in such a way that the deflection of the

Graph of the difference between the currents
from the two channels as a function of bearing deviation.
Figure 5-14. -Graph of the difference between the currents from the two channels as a function of bearing deviation.

 
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indicator is proportional to the difference between the currents in the two channels. This difference is plotted as a function of bearing deviation in figure 5-14. Note that if the bearing deviation is not too great, the difference current is proportional to it. Confusion can occur if the deviation is greater than the limits set by the double arrow of figure 5-14.

Standard Bearing-Deviation Indicator

The standard BDI provides a visual indication of the sound incident on the transducer. When the transducer is trained on the exact center of the source (figure 5-15, B), the incident sound strikes both halves of the diaphragm simultaneously. This condition is indicated by a brightening of the luminous trace on the screen of the cathode-ray tube.

When the transducer is trained slightly off the center of the target (figure 5-15, A and C), the incident sound waves strike one of the transducer

  halves before the other. This action causes the brightened spot on the screen to be deflected in the direction of the half on which the sound first impinges. A deflection to the left thus would show (1) that the source is to the left of the transducer bearing and (2) that the operator must train left to get a center bearing. Conversely, a deflection of the brightened spot to the right would indicate that the operator must train right. A strong signal can produce a right and a left deflection of equal magnitude, thus indicating a center bearing.

Because the BDI reacts to all sound energy incident on the transducer, it must be used in conjunction with a loudspeaker in order to distinguish between echoes and reverberations (figure 5-15, D), and between echoes themselves-particularly between the echo from a submarine and that from its wake. For this purpose the visual perception is supplemented by listening to a loudspeaker.

Four diagrams illustrating BDI.
Figure 5-15. -Diagrams illustrating BDI. A, Deflection of the trace to the left by a target on the left of the transducer heading; B, transducer heading on the center bearing, causing the trace to brighten; C, deflection of the trace to the right by a target on the right of the transducer heading; D, echo distinguished from reverberations.
 
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Scanning Sonar
 
The problem of rapidly searching a wide area led to the development of scanning sonars. The principle employed is to use the necessary interval between pings to search the widest possible area. In this way the area searched per ping and the amount of information received per unit of time are both increased. Two main types of scanning sonar have been designed-one transmits short pulses of sound, and the other transmits a continuous signal of varying frequency.

PULSE-TYPE SCANNING SONAR

Pulse-type scanning sonar equipment is, in effect, a combination of two types of ultrasonic echo-ranging and listening equipments operating simultaneously. One provides a continuous visual display of acoustic reception from all directions, and the other provides audio response from any desired single direction. The single-direction type is the exact equivalent of "searchlight" sonar. The function of detection by echo ranging is accomplished by transmitting a pulse of sound power in all directions and then scanning in azimuth for all echoes, which are made to appear as bright spots on a cathode-ray tube screen at the correct bearing and at a distance from the tube center proportional to the range. A more detailed investigation of a particular echo is obtained by training the audio system to the bearing indicated. The resulting audio output assists in identifying echoes, as well as in providing the signal for accurate range determinations. The reception of signals from noise sources, which is possible without transmission, produces a continuous radial pattern on the cathode-ray tube screen at the proper bearing, and the audio character of this noise may be ascertained by training the audio system along that line or bearing.

At any instant the outgoing train of waves occupies a ring-shaped region (figure 5-16) marked "wave train." The radius of this region increases with time. Echoes can be returned to the transducer at a given instant from only a small region-the "active volume" shown as cross hatching in figure 5-16-which is determined by the ping length, ro, and the angular width of the beam. This region is located at half the range of the

  wave train and has half the extent of the wave train; its width, or extent in bearing, is limited by the directivity of the transducer on reception. Because the receiving beam pattern of the transducer is rotating, the active volume describes a spiral path. The radius of the spiral increases with half the velocity of sound; the speed of the active volume in the spiral path is much greater than this velocity.

In order for the active volume to encounter every possible target at some time, the beam pattern must not be rotated too slowly. Otherwise, the condition illustrated in figure 5-17 results; there is a dead area between the rings of the spiral traced out by the active volume. This dead area is shown unshaded, and echoes from targets in it are not received. In this case, the distance, S, of the spiral is greater than the ping length, ro. If the beam pattern makes one revolution during the ping duration to of the signal, S equals ro, and there will be no dead areas. If to is expressed in milliseconds and ro in yards, ro equals

Figure 5-16. -Wave train and active region for a rotating receiving beam pattern.
Wave train and active region for a rotating receiving beam pattern.

 
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Spiral showing gap as a result of rotating a beam pattern too slowly.
Figure 5-17. -Result of rotating a beam pattern too slowly.

0.8to, because to equals 2ro/v seconds, where v is the velocity of sound.

Conversely, if the rotation of the beam pattern is fixed, the ping must have a duration of at least one revolution. Thus, if the beam pattern is rotated at 1,800 rpm, one revolution takes place in 33.3 milliseconds, and consequently the ping length must be greater than 0.8 times 33.3, or 26.7 yards. A value of 30 yards for ro is safe if the active area is truly rectangular.

A consequence of the rotation of the beam pattern is that the echo will not have the same duration as the transmitted pulse. The echo will be received only while the beam pattern is passing the target. If the effective width of the beam pattern is θ degrees, the echo from a point target-that is, a target smaller than the active area-will be received during θ/360 of a revolution. For example, if θ equals 11° and the speed of rotation is 1,800 rpm, the duration of the echo is approximately 1 millisecond. Expressed in yards, the echo length, r1, is 0.8 yard. The echo length, r1, must be distinguished from the ping length, ro. In every case, r1 is smaller than ro and is independent of the

  ping length, provided the ping length is of the required order of magnitude.

The shortness of the echo duration is a consequence of the increased velocity with which the active volume moves. This increased velocity of the active region is the primary characteristic of pulsed scanning sonar.

The short duration of the echo, in its turn, has the following consequences:

1. Doppler discrimination is much impaired.
2. Because the spectrum of the short echo extends over many critical bandwidths of the ear, the advantage of the ear over other methods of perception is lost.
3. The pass band of the receiver must be at least wide enough to pass the short echo. This width involves increased noise levels.
4. The level of the reverberation, being determined by the volume of the active region, Is comparable to that of a standard sonar that transmits a ping of length ro and is thus greater than for a ping of length r1.
5. The coherence of the reverberation is comparable to that of sonars transmitting pings of length r1.

These five effects tend to reduce the maximum range obtainable on a given target unless compensated either by a suitable device for detecting the echo or by the following effect.

6. The target strength of an extended object is determined by the size of the active volume and is therefore that which is characteristic of standard sonars transmitting pings of length ro.

PLAN-POSITION INDICATORS

The high rate of rotation of the beam pattern makes it impossible for an operator to follow the changes in its heading with his unaided senses. This factor and effects 1 and 2 of the preceding list, make it necessary to use special devices to portray the echo and render the bearing and range of the target perceptible. These devices are called plan-position indicators (PPI).

The only device of this kind that is feasible for the high rates of rotation involved is a persistent-screen cathode-ray tube. The spot of this scope is made to describe a spiral path in synchronism with the active area. The path of the spot on the

 
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screen is thus a map of the path of the active area. The brightness of the spot is controlled by the intensity of the received sound, so that an echo is seen as a brighter spot than the background of reverberation and noise. Because of the synchronization of the spot with the active area, the echo appears at the proper range and relative bearing on the screen.

If there are several targets in the field, they will be portrayed in their proper relative positions. Echoes obtained from reefs or sand banks appear on the screen as brightened areas. Thus a scanning sonar with a PPI presents the operator with a complete map of the underwater situation.

ROTATING-TYPE SCANNING SONAR

In theory, the transducer of a scanning sonar Could be directional and rotated about a vertical axis. However, the bulk of the transducer and the high rotational speeds required make this design impracticable.

Similar results can be accomplished by using a ring of stationary transducer units and connecting them in succession by means of a commutator (figure 5-18). In figure 5-18, however, only 12 transducer units are shown, whereas in practice 48 are used. Each of these is connected to one segment, B, of a stationary commutator. These

Diagram illustrating cathode-ray scanning sonar.
Figure 5-18. -Diagram illustrating cathode-ray scanning sonar.

 

Principle of scanning a sector rather than the
complete horizon.
Figure 5-19. -Principle of scanning a sector rather than the complete horizon.

segments are contacted by a rotating brush, A, which connects five or six transducer units to the receiver at any one time. As the brush rotates, these units are disconnected in succession and replaced by others farther along the ring. The result is that the receiving beam pattern of the array is markedly directional and rotates with the brush, A.

Because sliding contacts would generate too much electrical noise, a small gap is provided between the moving element, A, and the commutator segments, so that the brush is replaced by one plate of an electric capacitor. The received signal is thus connected to the receiver input by capacitive coupling rather than by conduction. This coupling, however, does not entirely eliminate commutator noise.

A second proposal for avoiding electric noise involves the elimination of all moving parts, and the use of electronic switches to perform the commutation.

In chapter 6 a typical scanning system is discussed in detail.

Sector-Scan Indicators

The echo length resulting from the necessarily rapid motion of the active volume can be increased somewhat by scanning only a sector rather than the complete horizon. In this case the path of the active volume must be somewhat as shown in the schematic diagram in figure 5-19, and its speed can be reduced.

 
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The oscillation of the receiving beam pattern can be accomplished by a modification of the principles already discussed in connection with the BDI.

F-M SCANNING SONAR

The long delay between the transmission of the signal and the reception of the echo, which is caused by the low velocity of sound, is a handicap in search operations. A pulsed scanning sonar utilizes this delay to scan all bearings, thus effectively increasing the speed of the active area.

The delay period also can be used to make other than single-frequency transmissions. Obviously, if the delay period is so used, a given echo must be associated with a given transmission. The idea can be illustrated very simply, as follows:

If the maximum practical range is about 3,000 yards, the maximum time delay is about 4 seconds. Suppose (1) that during these 4 seconds 8 pulses are transmitted at ½-second intervals, and (2) that the frequency of each pulse differs from that of its predecessor by a stated amount. The frequencies of the pulses may form the tones of the major diatonic scale; if so, a musically inclined listener, on hearing an echo, can recognize its pitch and thus identify the ping responsible for it-provided, of course, that both source and target are stationary. Otherwise, doppler effect will alter the pitch of the echo. Some means has to be provided for recording the time and the transducer heading for each ping so that the range and bearing of the target can be determined.

Although this illustration is greatly oversimplified, it serves to introduce the discussion of a sonar that uses the f-m principle.

In practice it is simpler to change the frequency gradually rather than by abrupt steps. The frequency is decreased at a constant rate for some seconds; then, when it approaches the lower limit of the pass band of the receiver, it suddenly is increased to its original value, and the constant rate of decrease begins again. The principle is explained by the time graph of the transmitted frequency shown in figure 5-20, A. The transmitted sound frequency is a sawtooth signal. The intensity of the transmitted sound is kept constant during the transmission.

A target located in the sound beam returns a continuous echo and, if both the sonar and the

  target are stationary, this echo reproduces the constant frequency change of the transmitted signal. In figure 5-20, A, the solid curve is the frequency-time graph of the sawtooth signal; the dotted curve, that of the echo. Because of the time delay between transmission and echo, the sawtooth graph of the echo lags behind that of the signal by 2r/v second. The time interval indicated by T in figure 5-20, A, is the sawtooth interval. During a portion of the sawtooth interval, the echo frequency is less than the transmission frequency by a difference f'. During the remainder of the sawtooth interval the echo frequency is greater than the transmission frequency by a difference, f. This difference is illustrated by figure 5-20, B, in which the difference in frequencies between signal and echo is plotted as a function of time. The frequency difference, f, remains constant for relatively long periods and then jumps suddenly to the value, f'.

The frequencies are subtracted electrically by applying the heterodyne principle-a voltage tapped from the transmitter is combined with the echo signal in a heterodyne stage of the receiver. The range is determined from either of the

Principle of f-m sonar.
Figure 5-20. -Principle of f-m sonar. A, Transmitted frequency and the echo frequency as a function of time; B, frequency difference as a function of time.

 
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frequency differences f or f'; the calculation of range from frequency difference is given later in this discussion.

Up to this point it has been assumed that there is only one target in the sound beam. If there is more than one returning echo, each echo will have its time graph of frequency, the displacement of which, relative to the graph of the signal, depends on the range of the target. The output of the receiver thus contains components of several frequencies-one pair of frequencies for each target in the sound field. This complex output must be analyzed into its components in order to determine the range of the several targets.

The active volume from which echoes are being received occupies the whole sound field. Furthermore, with omnidirectional projectors and hydrophones, no scanning of the field is possible. Thus, the basic principle of continuous transmission sonar in achieving effective detection is to employ a maximum size of the active volume, rather than to increase the speed of a small active volume as is done in pulsed-scanning sonar. The method just outlined for accomplishing this effective detection is called f-m sonar.

When used with a stationary projector and hydrophone, f-m sonar is not a bearing-scanning device. If it is used with an omnidirectional projector and a rotating receiving hydrophone, however, it becomes a scanning sonar with reduced active volume, but is different from the pulsed type.

Parameters of F-M Sonar

Relation between target range and echo frequency.-How the frequency difference between the echo and the transmitted signal determines the range is apparent from the following discussion and from figure 5-20.

The duration of one sawtooth waveform is T seconds. During this interval the frequency varies at a constant rate from F+s to F; where s is called the sweep of the frequency. In one model, the QLA, F is 36 kc and s is 12 kc. T is usually from 1 second to 12 seconds.

The following relations exist between the several parameters:

1. The constant rate of frequency decrease is s/T kilocycles per second.

  2. The delay time for an echo from range, r, is 2r/v seconds.

3. In by 2r/v seconds the frequency therefore decreases by (2r/v)(s/T) kc and the frequency difference, f, shown in figure 5-20, A, is

f= 2r/v s/T kc.  (5-14)

4. From equation (5-14), the range, r, is

r= vT f/2s.  (5-15)

5. The frequency difference, f, is maintained for T- 2r/v seconds. At the end of this interval the transmitted signal has reached the bottom of the frequency sweep and returns to the top of the sweep. During a succeeding time interval equal to 2r/v seconds, the echo frequency is less than the transmitted signal frequency by f' kc (figure 5-20), where

f'=s-f.  (5-16)

If the sawtooth interval, T, is several times greater than the delay time of echoes from the maximum range, frequency f is less than s/2 and frequency f' is greater than s/2.

6. The duration of frequency f' is considerably less than the duration of frequency f. Consequently, it is economical to ignore frequency f' and concentrate on the determination of frequency f.

Determination of frequency difference and range.-From equation (5-15) it is evident that f must be known to determine r. The range, r, is determined as follows:

Suppose the heterodyned output (the hydrophone output mixed with a sample of the signal) is passed through a band-pass filter that is centered at f kc, and that has a width w kc. This filter then passes an echo if its frequency lies within the band between f-w/2 and f+w/2. Thus the sound energy admitted by this filter comes from a certain active area (figure 5-21), which is a sector of a circular ring.

 
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A battery of such filters can be used to establish a series of channels, each of which is constantly alert to echoes from a certain active area. The dimensions of the area corresponding to a given filter can be calculated easily. The greatest range from which the particular filter under consideration will accept an echo is, from equation (5-15),

rmax=vT (fw)/2s,

and the smallest range is

rmin=vT (fw)/2s,

The radial extent, ro, of the area is the difference between the two ranges, and thus

ro=vTw/2s.  (5-17)

The other dimension of the active area can be determined by the range and the width of the receiving beam pattern; and from elementary geometry, its mean value is the product of the mean range and the angular width of the beam expressed in radians.

The dimensions of the active area are proportional to the sawtooth interval T and, in so far as they are determined by T, are under the operator's control. For example, if T equals 12

Active areas associated with the individual
channels in f-m sonar.
Figure 5-21. -Active areas associated with the individual channels in f-m sonar.

  seconds, s equals 12 kc, and w equals 35 cycles per second, then ro equals 27.6 yards. Reducing the value T to 1 second would make ro equal 2.3 yards, if v is taken equal to 4,742 feet per second.

As has been remarked, each of the channels is almost constantly alert to targets in the particular area associated with it. These areas are indicated in figure 5-21. As the active area of each channel is stationary, the whole sound field (figure 5-21) can be covered by making the areas of adjacent channels overlap slightly.

Because of the exclusion of frequency f', each channel normally is inert for a fraction of each sawtooth cycle. However, this fraction can be made as small as desired or even can be eliminated by means of a recent ingenious development.

The fact that the active areas are stationary may give the impression that the range cannot be determined as precisely as with pinging sonars. However, the precision is the same as for a ping length equal to ro. The quantity ro defined by equation (5-17) can be called the effective ping length of f-m sonar.

Range and bearing indication.-The range is read on an oscilloscope with a persistent screen. The filters corresponding to the various mean ranges of the several channels are arranged so that their output brightens the trace of the cathode-ray tube at a point where the scalar distance from the center of the tube is proportional to frequency f and thus to the range. The bearing of the echo spot on the oscilloscope corresponds to the hydrophone heading.

Echo duration.-The duration of the echo depends on whether the hydrophone is stationary or is being rotated. If the projector is nondirectional, the echo received by a stationary hydrophone has a duration nearly equal to the sawtooth period, T. If the hydrophone is rotated, the echo duration is reduced and may become equal to the time required for the hydrophone beam to sweep across the target. The rate of rotation can be made as small as required to obtain an echo of any desired duration less than T. In this respect f-m sonar differs from the pulsed scanning sonars described previously.

The rate of rotation, however, cannot be increased beyond a certain critical value. This limitation is imposed by the use of filters, which require a finite time interval to respond fully to the

 
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echo. The minimum time interval depends on the band-pass width, w, of the filter and must be greater than 1/N second, if w is in cycles per second. In other words, if the beam pattern of the hydrophone rests on a point target less than the time required for 1 cycle at the band-pass frequency, the echo will not be detected.

Suppose that the hydrophone is rotated at a rate of N rpm and that its beam width is θ°. A complete revolution requires 1/N minutes, which equals 60/N seconds. The beam occupies θ/260 of a revolution; thus the time required for it to sweep across a given point θ/360 times 60/N, or θ/6N seconds. Hence, it is necessary that

θ/6N > 1/w,

from which it follows that N must be less than

θw/6.

For example, let θ equal 11° and w equal 35 cycles per second; then N must be less than 65 rpm. The echo duration for 65 rpm is 29 milliseconds; the corresponding echo length is 23 yards. If the rotation is slower the echo length increases.

Doppler range error.-It is clear that, because f-m sonar uses the frequency of the echo to determine the range of the target, the Doppler shift resulting from a possible relative motion of sonar and target introduces an error into the indicated range. The magnitude of this error must be evaluated.

F-m sonar is calibrated to give the indicated range, ri, according to equation (5-15)-

ri= vTf/2s.

This equation gives the correct range if the target is not moving, but it is necessary to calculate the error in ri caused by the Doppler change of frequency when the range is opening or closing.

In all echo-ranging operations three instants of time must be considered. These instants are (1) t1, the time at which the primary sound was transmitted from the transducer; (2) tT, the time at which the echo was reflected from the target; and (3) tE, the time at which the echo was received.

If there is any relative motion of sonar and target, the range is different at these three times.

  Call the corresponding ranges r1, rT, and rE. In pulsed sonar the range indicated is always rT regardless of the possible motion of sonar and target. The differences between r1, rT, and rE are negligible. This fact can be verified quickly if it is remembered that a speed of 1 knot is equivalent to 0.56 yard per second, so that a speed of 25 knots involves an error of less than 50 yards in a range of about 3,000 yards.

None of the three ranges just defined is the range indicated by f-m sonar. Range ri is defined by equation (5-15). In order to calculate ri the following three ultrasonic frequencies must be distinguished:

1. F1, the frequency that was being transmitted at time t1.
2. FE, the frequency that was being transmitted at time tE.
3. F'E, the frequency of the echo that was being received at time tE.

The quantity, f, of equation (5-15) is obviously F'E-FE hence,

ri=vT/2s(F'E-FE).  (5-18)

The frequencies FE and F'E must be examined more closely. To simplify the calculations, the sonar is assumed to be stationary. No error is introduced by this assumption if dR of equation (5-20) is interpreted as the range rate. When the target reflects the sound its range is rT, and the transmitted frequency, by the time tE, has been reduced by (2rT/v)(s/T): The possible motion of the target will not affect this quantity. Thus, the frequency being transmitted at the instant when the echo is received is

FE=F1-(2s/vT)rT  (5-19)

The frequency of the echo, on the other hand, is affected by the motion of the target. From the theory of the Doppler effect, the value F'E is approximately

F'E=F1±(2dR/v)F1  (5-20)

where dr is the range rate of the target. If equation (5-19) is subtracted from equation (5-20),

F'E-FE=(2s/vT)rT±(2dR/v)F1,  (5-21)

 
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and if equation (5-21) is substituted into equation (5-18),

ri=rT±(dRT/s)F1.  (5-22)

The error in the indicated range, as shown by the last term in equation (5-22), is therefore proportional to the velocity of the target and is zero only for stationary targets.

For example, let T equal 12 seconds; s equal 12 kc, and F, equal 36 to 48 kc; then

TF1/s=36 to 48 seconds.

The range error is thus the distance moved by the target in 36 to 48 seconds. The larger error occurs when the sawtooth frequency, F1 is high and the

  smaller error occurs when it is low. The distance traversed in 48 seconds by a submarine at 10 knots is slightly more than 200 yards.

Note that the error is also proportional to the sawtooth period. Thus, if T had been 1 second in the example, the range error would be the distance moved by the target in 3 to 4 seconds, or about 20 yards, at a speed of 10 knots.

This range error is very similar to the range correction which must be made in determining the time to fire on a moving target. It has been proposed to utilize this similarity so that the indicated range of f-m sonar can be used without this correction in fire control problems. For this application, it is essential for the frequency to increase rather than to decrease during each sawtooth period.

 
Location of Small Objects
 
The echo-ranging equipment in use at the beginning of World War II was designed for the detection of relatively large submarines. As the war progressed it became imperative to design equipment for the detection of mines and other small objects. The standard test object in this development work was a sphere 3 feet in diameter. The target echo strength of such a sphere is some 20 db lower than that of a large submarine. Because of this small echo strength, the ranges in small-object detection generally are comparatively short and thus are limited by reverberation rather than by background noise.

In order for an echo to be detected against a background of reverberation, the total echo strength of all the scatterers in the active volume of a ping must be less than the echo strength of the sphere; otherwise, the reverberation intensity is greater than that of the echo and masking prevents detection.

The echo strength of the reverberation can be decreased by reducing the size of the active volume. There are two ways in which this decrease can be accomplished: (1) The ping length can be decreased; and (2) the beam can be made narrower. The second method is not suitable for shipboard installations because it involves a decrease in the effective search area and thus causes great difficulties in maintaining contact with the target. This situation leaves only the ping length as an

  available parameter for reducing the size of the active volume.

The use of short pings is thus a characteristic of many sonars designed for small-object detection. In this phase of echo ranging, the reasons for the success of scanning sonars-which do not use short pings-are not clearly understood; however, their success probably depends on the plan-position presentation of the echo, or upon the limitation of the active volume by the scanning process.

RATIO OF ECHO TO REVERBERATION AS A FUNCTION OF PING LENGTH

According to the theories that have been previously explained, the reverberation intensity is proportional to the ping length, ro. The echo level, on the contrary, is independent of ping length except when the ping length becomes less than the variation in range for different parts of the target. If the target is complicated its target strength is less for short pings. This condition exists because the echoes from some parts of the target no longer overlap those from other parts. However, if the target has a smooth surface, with no irregularities of dimensions comparable to 1 wavelength of the sound, this reduction in target strength will probably not occur. The theory of echo formation has not been worked out sufficiently to cover this point.

 
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The results show that the echo-reverberation ratio increases with decreasing ping length even when the ping length is as small as one-eighth the diameter of the sphere. They also show that this ratio generally decreases with increasing range out to 400 yards, thus supporting the idea that reverberation, rather than background noise, is the limiting factor in this work. Such results are rather surprising because a wide-band receiver is necessary for the use of these very short pings. The qualitative distinction between reverberation   and noise largely disappears at these ping lengths, for both reverberation and noise sound alike to the listener and have a similar appearance on an oscillogram. Consequently, these experiments are the best evidence that reverberation, and not noise. is the masking agent. This high level of reverberation is due to a combination of factors, principally the shallow water and the short range. Both are typical of the conditions under which the equipment must operate.
 
Variation of Gain
 
The optimum gain setting is the one which makes the masking background just audible. If the gain is less than the optimum, weak signals will not be heard even though they are stronger than the background. If the gain is much greater than the optimum, there is danger that a signal will overload the amplifier, resulting in (1) distortion and (2) a reduction of the signal-background ratio in the airborne output.

This situation is complicated when reverberation is the masking background, because the reverberation level varies greatly during the period following transmission.

The obvious solution for this problem is to devise a sonar receiver in which the gain continuously increases during the period following transmission of the ping. The receiving circuits for accomplishing this time variation of gain (TVG) are controlled by the discharge of a capacitor that is charged (During the transmission. The rate at which the gain increases can be controlled by altering the resistance of the discharge circuit. The total increase in gain can be adjusted by altering the voltage to which the capacitor is charged.

Although TVG improves the operation of the echo-ranging equipment, it fails to meet all the requirements. One disadvantage of TVG is that the gain is increased in a regular manner. This regular increase of gain would be satisfactory if reverberation decreased in an equally regular manner, but reverberation decrease is not always regular, especially in shallow water. Consequently, the possibility of using the background to control the instantaneous gain was explored.

Circuits that can control the gain automatically

  are common in radio receivers. Such circuits are called automatic volume controls (AVC). The use of AVC circuits in sonar receivers, however, has proved to be very disadvantageous. AVC circuits can be adjusted to respond rapidly or slowly to changes in the input. If they respond to the rapid fluctuation of reverberation, they also respond to the change in intensity due to the echo. This response is unavoidable, because the reverberation signals last about as long as those of an echo from a point source. With this adjustment the AVC reduces the gain during the time the echo is being received-an obviously undesirable situation. If, on the other hand, the AVC is adjusted so that it does not reduce the gain during the echo. it becomes so sluggish that it fails to respond to the slower changes in mean reverberation level-for example, to the peak of bottom reverberation.

A compromise solution, called the reverberation-control of gain (RCG), has been developed. RCG is similar to TVG in that the gain constantly increases during the period following transmission. It is similar to AVC in that the momentary level of the receiver input controls its operation. In RCG, however, it is the rate of increase of gain that is controlled and not the gain itself. It is obvious that an RCG circuit cannot reduce the gain at the instant the echo arrives; it merely reduces the rate at which the gain increases while the echo is being received. Thus, it does not have the disadvantage of an AVC circuit.. RCG responds somewhat, to the special characteristics of reverberation at a specific time and place and thus does not have the disadvantage of a TVG circuit that is improperly adjusted for the momentary conditions.

 
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Maintenance of Close Contact

The development of deep-diving, high-speed submarines presented a serious problem. The echo-ranging equipments in use at, the beginning of World War II were not capable of maintaining sonar contact on a deep submarine when the range was closed. The deeper the submarine was operating, the greater the "lost-contact" range. Sometimes the contact was lost at 600 yards because the submarine passed under the lower limit of the sound beam. A loss of contact made it impossible to attack successfully, because the high speed of the submarine enabled it to be a considerable distance from the point of lost contact.

This problem can be overcome by mounting the transducer like a searchlight, so that it can be (1) rotated about, a vertical axis and (2) tilted about a horizontal axis. If the axis of a tilting beam

  transducer is depressed toward the deep target, and hence away from the surface, the echo level can be increased and the surface reverberation decreased. A sonar equipped with the tilting-beam transducer can also determine the depth of a target, as will be explained later.

Another method, known as maintenance of close contact (MCC), changes the connections of the transducer elements so that the beam becomes very broad in the vertical plane. This change is accomplished by a switch so that at long ranges the beam pattern is undisturbed because the distortion of the beam reduces its efficiency. This inefficiency is inconsequential at the shorter ranges, where contact would be lost if the MCC feature were not used.

 
Depth Determination
 
Both the depth and the horizontal range of the target can be determined by mounting a transducer so that the beam can be tilted in the vertical plane. The geometry of the situation is shown in figure 5-22. The range indicator of the sonar

Geometry of depth determination.
Figure 5-22.-Geometry of depth determination.

equipment shows the slant range, R. The depth of the target below the projector is Y and its horizontal range is X. If the angle of tilt, θ, is known, the values of X and Y can be calculated from the equations

X=R cos θ
and
Y=R sin θ.  (5-23)

Various automatic or semiautomatic methods of performing this calculation have been devised.

REFRACTION ERROR

Equations (5-23) assume that the sound rays are straight lines, as shown in figure 5-22. If the rays are refracted (figure 5-23), the values

  computed from this equation are Xo and Yo instead of the actual values X and Y. The errors Y-Yo, and X-Xo can be quite large, especially when there is a marked downward refraction.

The errors arise from two causes: (1) The sound does not travel in a constant direction, and (2) it does not travel at a constant speed. The determination of the corrections to be applied is similar to a problem in exterior ballistics. The problem can be solved by the same methods, but when there is a marked thermocline the magnitude of the correction required is increased, as is also the accuracy required in making the approximate calculation. Semiautomatic methods have been developed to speed the application of the correction during combat.

Effect of downward refraction on depth determination.
Figure 5-23. -Effect of downward refraction on depth determination.

 
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Integrated Sonar System

The integrated sonar system is an attack system. It is composed of several sonar and fire control equipments operating in a reciprocal information and control network.

The antisubmarine system used at the outbreak of World War II consisted of a single echo-ranging equipment. From the equipment, the bearing and slant range of the target could be obtained. The procedure of "crossing the target," previously explained, established the bearing rate. If this information was plotted on a maneuvering board and if a stop watch was used to time the development of the attack, the range rate could be determined, as well as the approximate course and speed of the submarine. The conning officer guessed the depth of the submarine from the range at which sonar contact was lost because of the targets passing under the sound beam.

By the time the lost-contact range was reached, the ASW vessel was on its attack course and was proceeding to saturate the area with depth charges. This method was fairly effective against the old type of submarine with riveted construction, because the pressure hull could be ruptured by a nearby explosion. One disadvantage of delivering a depth-charge attack against a modern submarine is that the pressure hull with its all-welded heavy-metal construction can withstand anything but a direct hit or a very near miss.

Other disadvantages of delivering a depth-charge attack on a modern submarine are as follows:

1. Because the charges sink very slowly, a large lead must be taken to place them well ahead of the target. Thus, contact is lost before the charges are dropped. The time between lost contact and the point of dropping the charges, plus the time required for them

  to sink to the proper depth, gives the submarine time to evade.

2. After contact is lost on a high-speed target, it is difficult to regain. When a depth charge explodes, it sets up a turbulent area that returns strong echoes. The submarine may escape from the area because echoes from the turbulent area mask the echoes from the submarine.

To attack a modern submarine successfully the following requirements must be met:

1. After contact has been established it must be maintained until the submarine is put out of action.
2. Only ahead-thrown weapons that explode on contact should be used.
3. The depth and horizontal range of the target must be determined as well as its bearing, speed, and course.

An integrated system has been designed to meet and to coordinate these requirements. This system requires two echo-ranging equipments-one equipment for azimuth search, which furnishes the slant range and bearing, and the other for depth search, which furnishes the depression angle of the target. From the slant range and depression angle a sonar resolver computes the depth and horizontal range. To obtain the most accurate sonar information possible, the equipment must be stabilized so as to remove the components of own ship roll and pitch. Such a system requires a stable element and a stabilization computer. An underwater battery fire-control system is used to solve the fire control problems of the (1) target course and speed, (2) course that own ship should steer, and (3) time to fire. Included in the system are plotting devices for keeping track of the attack as it develops.

 
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