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FLEET COMMUNICATION MEMORANDUM 4RM-37  (3 June 1937)

Subject: Analysis of Radio Direction Finder Tracking Methods.
Inclosure: (A) Copy of "Radio Direction Finder Tracking Methods by a Single Ship" by Lieutenant M. S. Adams, U. S. Navy.

      1.      Efficient radio direction finding and tracking for wartime purposes is a subject of such importance that no effort should be spared to develop Fleet equipment and to extend thorough training in these arts to officers and enlisted men at every available opportunity.

      2.      The Commander-in-Chief has noted with keen interest the results of previous tests on this subject, and particularly the excellent results obtained by ships where the navigator, acting as the tracking officer, has coordinated the data obtained by the direction finder and tracking crews with accurate navigation. As an aid in the study of methods to be employed, the Commander-in-Chief is pleased to publish to the Fleet Inclosure (A).

      3.      Careful study, evaluation, and publication of results of radio direction finder tests and tracking exercises by Type Commanders to their commands, are welcomed, as such a course of action will stimulate interest and result in a much desired better understanding of present Fleet capabilities in this regard.

FOREWORD

      The inclosed analysis of RDF tracking methods was undertaken in December, 1936, after two heavy cruisers had made a zero score. In addition to independent study, the reports of weekly tracking exercises submitted by ships of Cruiser Division Four were scanned for methods and ideas. These reports yielded much information of value, both negative and positive.

      This study concludes that the method described in paragraph 6 is the most likely to produce results under most circumstances. This procedure has been used consistently with good results on the weekly tracking exercises by the PENSACOLA, and was first suggested to me by the Navigating Officer of that ship, Lieutenant Commander P. W. Warren, U. S. Navy.

      The purpose in writing this analysis was to furnish officers unfamiliar with this type tracking a general view of the factors involved. It is hoped that this study will form the nucleus around which may accumulate future information of this subject. The work in preparation has been done in my capacity as Division Radio Officer and no personal claim whatsoever is made to the included material. Freedom to quote and to use any part of this analysis is fully granted to officers interested in extending this study.

M. S. ADAMS.

A STUDY OF RADIO DIRECTION FINDER TRACKING METHODS BY A SINGLE SHIP

By Lieutenant M. S. Adams,

Radio Officer, Staff Commander Cruiser Division Four

A.   THE TIME-BEARING METHOD

      1.      The time-bearing method of radio direction finder tracking is based on the assumption that the characteristic contour of a time-bearing curve will remain constant for a lengthy period thus allowing the curve to be projected accurately. This assumption is correct only under certain conditions. Actually, most time-bearing curves cannot be projected accurately. A study of a number of time-bearing curves drawn under various conditions indicates that all curves fall into one of two types.

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       (a)  The near-straight-line curve
     A time-bearing curve approximating a straight line, which can be projected with fair to exceptional accuracy, will be obtained under the following conditions:
(1) When the relative courses and speeds of the target and tracking ships are such as to give a constant bearing. The two ships may be converging or diverging. The time-bearing curve will be absolutely straight and can be projected perfectly.
(2) When the target and tracking ships are moving in approximately the same direction at about equal speeds. The curve obtained may not be absolutely straight but the extremely slow change of bearing obtained will be uniform enough to allow projection with fair accuracy.
(b) The S-type curve
     When the ships' movements do not conform with those mentioned above, extremely erratic time-bearing curves will be obtained. These curves will resemble somewhat the letter S and cannot be projected with any certainty of accuracy. The S-type curve includes all curves which cannot be placed definitely in the near-straight-line type.

      2.      There is one situation in which the time-bearing curve may be a near-straight-line curve or an S-type curve depending upon the direction in which bearings are allowed to move. This situation is encountered when the two ships are closing on a nearly constant bearing. It is discussed fully in paragraph 7. In differentiating between the near-straight-line curve and the S-type curve, it must be borne in mind that S-type curves do not show wide changes of bearing and large variations in the rate of change of bearing throughout the curve. These characteristics are present in part of every S-type curve but they may not be present in the part being plotted. The curve as plotted may have all the appearances of a near-straight-line curve but it cannot be projected because of variations present in the phantom part of the curve. For example, place the tracking ship on a course and consider that it is to continue on this course for four hours. Then place the target ship on the bow in a position, and with a course and speed, that will cause it to cross ahead of the tracking ship during the fourth hour. The time-bearing curve for the first two hours will appear to be a projectable near-straight-line curve. During the fourth hour it will curve sharply. It is apparent that any attempt to project such a time bearing curve will give a very poor solution regardless of the course taken during the second two hours.

      3.      Before attempting to describe the way in which the different types of time-bearing curves can be obtained, it is desirable to analyze their use. If the angle between any two bearings is extremely small, the slight errors incident to plotting make it extremely difficult to cross these bearings at the proper point on the chart. In addition to this normal inaccuracy in plotting bearings any slight error in either bearing will cause a very large error in the position obtained. Therefore, the bearings obtained from the real and phantom curves near the point of intersection of two time-bearing curves cannot be used with accuracy. In order to obtain trustworthy results, bearings must be taken from the time-bearing curves only in the vicinity of their extremities. This limitation imposes the necessity of using the projected curve where it is least likely to be accurate. Therefore, the largest possible difference between the bearings, actual and projected, must be sought in order to compensate for the errors normally to be expected. The next question: How can the greatest difference between actual and projected bearings be obtained?

      4.      First, let us consider the possibility of obtaining two near-straight-line time-bearing curves from which widely separated bearings may be obtained. Since the tracking officer has no idea of the distance between the two ships or of the course and speed of the target ship, he cannot parallel the target on the first leg except by pure luck. This fact necessitates his seeking a converging or diverging course that will give a constant bearing. Determination of the proper course to obtain a constant bearing will consume some time. Still more time probably will be consumed before the tracking officer has enough information to determine the approximate course and speed of the target. He then will have solved only part of the problem. He must attempt to select a course and speed that will give a projectable line and will also give bearings which differ by fairly large angles from those of the first curve. The tracking officer has given himself a problem that almost defies solution. He must choose his course on the basis of his estimate of the target course which may be twenty-five or thirty degrees in error. Yet, the slightest error in the selection of his course will give either a non-projectable curve or one having bearing differing from those of the first curve by too small an angle. The worst feature of this situation

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is that a non-projectable curve obtained in this manner may also have bearings that differ from the projected first leg by too small an angle to allow any solution of the problem. From this analysis, it appears that certainty of a solution by the time-bearing method is obtained only when one curve is purposely a near-straight-line curve and the other is purposely an S-type curve with the widest possible change of bearing. Naturally, with this type solution, bearings from the phantom of the straight line curve can be crossed with bearings from the "S" curve but there is no phantom of the "S" curve from which bearings may be taken to cross with bearings from the straight line curve. This type of solution permits of two procedures. Bearings may be crossed to obtain either the initial position of the target or the final position.

      5.      To obtain the initial position, course, and speed, the first curve is the "S" curve while the second is the near-straight-line curve. The tracking officer must endeavor to choose a first course that will give the widest possible change of bearing. While running the first leg, he determines the approximate course of the target by means of the navigation plot. At the end of two hours he changes to a course that approximately parallels the target course. Exact parallel is not necessary because the direction of movement of the target has been determined closely enough to avoid an "S" during the second leg. With the two curves thus obtained the tracking officer can determine the course, speed, and initial position of the target. However, it should be noted that the curve obtained on the second leg may not be absolutely straight, in which case accurate projection is difficult. From a theoretical standpoint, there is nothing to prevent his seeking a constant bearing on the second leg. That is, the near-straight-line curve may be obtained in the manner described in paragraph 1(a) (1) instead of l(a) (2). From a practical standpoint the value of this practice is doubtful. In seeking a constant bearing, the course must be changed several times. This changing of course prevents the use of bearings for any purpose other than the correct determination of the proper course to obtain a constant bearing. This is true because RDF bearings that have not been taken from a faired time-bearing curve are more confusing than helpful. Therefore, from the time the tracking officer starts seeking a constant bearing until he settles on a course, no progress is made toward solution of the problem. At the start of an exercise, this lack of progress can be accepted as a preliminary evil to an accurate solution. There is always the certainty that a slight change of bearing may be accepted without serious consequences if the correct course for constant bearing is not found quickly enough (see paragraphs 6 and paragraph 7). However, during the second half of a tracking exercise this lack of progress cannot be accepted with the same mental ease. The tracking officer has already obtained enough information to feel that he can set limits on possible target movements. He is most anxious to check his limits and narrow them to a final answer. He knows that if he continues trying to obtain a constant bearing and succeeds, he has the solution. If he fails, he has absolutely nothing but his original limits. Last but not least, he knows that if he cannot obtain a constant bearing he must accept a curve of the type described in paragraph 1 (a) (2). Yet, the longer he waits before he accepts this change of bearing, the further the curve must be projected and the less accurate his final answer is likely to be. Apparently the use of a constant bearing on the second leg is an "All or Nothing" proposition. From the above analysis, it appears that the procedure which determines the initial position direct has definite disadvantages. The principal disadvantage of this procedure is obvious when the method of RD (T) scoring is considered. Inasmuch as the final position of the target is the one desired, the accuracy of that position depends not only upon the accuracy of determining the initial position but also upon the accuracy of the solution of course and speed. With respect to the final position all errors are cumulative for the entire four hours. The other procedure for this type solution gives the final position direct and is therefore preferable.

      6.      To obtain the final position, course, and speed of the target, the first curve must be a near-straight-line curve and the second an S-type curve. As mentioned in paragraph 4, the tracking officer must take a converging or diverging course that will give him a constant bearing. Since there seldom will be any reason for using the diverging course, this discussion will be based on use of the collision course. A collision course can be found only by trial, therefore, a number of trial courses will be necessary. Under certain circumstances, a collision course cannot be obtained and the RD (T) exercise cannot be worked by this procedure. These circumstances will be explained in paragraph 8. Seemingly a great amount of time might be wasted before the collision course could be definitely ascertained. It is true that most of the first two hours probably will be used for this purpose but this time is not wasted if the collision course is actually found. As soon as the tracking officer is sure of the collision course, he can project the resulting straight-line time-bearing curve backward and forward indefinitely. Likewise, he can project his navigation plot backward for the position he would have had at the start of the problem had he been on the collision course all of the time. At the end of the time required to determine and check the

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collision course, the tracking ship should change to a course that will give the greatest possible change of bearing. A cross between bearings taken from these two time-bearing curves will give the course, speed, and final position of the target. This procedure has two drawbacks. First, determination of the proper course to obtain a constant bearing is difficult. Second, under certain circumstances, attainment of a constant bearing is impossible.

      7.      There is one situation in which the method of paragraph 6 may be used only with care. Upon numerous occasions tracking officers have given up hope of locating the exact collision course and have accepted a small change in bearing on the first leg. This small change in bearing was found to give fairly accurate results in most cases, but under certain conditions it gave extremely poor solutions. An analysis of several problems in which poor results were obtained showed that in every case the first curve which should have been straight was actually an S-type curve which had not been recognized as such. Most of these cases were of the type mentioned in paragraph 2. That is, the target ship was allowed to move slowly ahead without realization of the fact that it would cross ahead within four hours if the tracking ship remained on the same course. This situation should be avoided because it destroys the mooring board check and is likely to result in no solution by the time-bearing method if not carefully handled. If it must be used, a target bearing on the bow should be made to move away from the ahead position instead of toward it. The change in bearing must be extremely small to keep the target from changing its rate of change of bearing appreciably.

      8.      It is now desirable to discuss the manner in which these different curves can be obtained. In paragraph 6, emphasis has been placed on the collision course. Articles 6207 to 6210 of FTP 146 explain how to determine the collision course by trial. This explanation should be studied before any effort is made to use the time-bearing method as in paragraph 6. Before the method of paragraph 6 can be used effectively, the tracking officer must be certain that he can obtain a collision course. In time of war, it is very unlikely that a heavy cruiser would have any occasion to track an enemy ship under circumstances in which a collision course could not be taken. However, an RD(T) exercise may be constructed in a manner that will prevent attainment of a constant bearing. For example, if the course of the target is approximately 90 degrees from its bearing from the tracking ship and the target is allowed more speed than the tracking ship, a collision course cannot be obtained. In order to ascertain whether a constant bearing can be obtained, it is recommended that the tracking ship head for the target to determine its direction of movement. Then change course 90 degrees in the direction of movement. If the target continues to draw ahead after this change, a collision course cannot be taken. If the orders for the tracking exercise do not limit the speed of the target to the extent that a collision course can be taken regardless of the target's course, this check should be made. The question of obtaining a diverging course that will give a constant bearing is rather intricate. If a collision course can be taken, a diverging course that will give a constant bearing can be taken by changing course in a direction opposite to that given in FTP 146. If a collision course cannot be taken, a constant bearing can be obtained in a diverging course by continuing the changes of course recommended by FTP 146. Unfortunately, a constant bearing obtained in this manner will be obtained too late to be used in the manner described in paragraph 6. The type of near-straight-line time-bearing curve mentioned in paragraph 1(a) (2) is found by paralleling the target at approximately the same speed. The use of this type of curve seems to be limited to the method described in paragraph 5. Determination of the proper course for the best S-type curve depends on circumstances and the method used. When using the method prescribed in paragraph 6, a good course for the second leg is one approximately 60 degrees from the bearing obtained while on a collision course and in the direction that will give the greatest change of bearing. That course is obviously one that tends to make the tracking ship run under the stern in the opposite direction from the course of the target. In using the method described in paragraph 5, a good first course is determined as follows:  Place the target "Dead Ahead" and determine to which side it is moving, then change course approximately 60 degrees away from the direction of movement.

B. THE MOORING BOARD METHOD

      9.      Comments indicate that a good many officers believe the mooring board method will not work in all cases. This method has been severely criticized as being critical and subject to large errors. From study, the conclusion has been reached that much of the difficulty experienced in working the mooring board method has been caused by the violation of one or more of the principles upon which the method is based. These violations are generally caused by the selection of wrong courses and failure to realize wherein errors multiply themselves. Critical solutions

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likely to give indeterminate answers or large errors can be avoided with certainty only if the principles of the method are thoroughly understood. However, given fairly accurate bearings, good results should always be obtained from the correct use of the mooring board method.

     10.      There are two satisfactory methods of using the mooring board. First, using a constant bearing on the first leg and a wide change of bearing on the second. Second, using a wide change of bearing on both legs. The first of these methods works perfectly with the time-bearing method in which a collision course is used on the first leg (paragraph 6). The second method will not work with the time-bearing method. Some of the principles involved in the mooring board solution are discussed in the following paragraphs.

     11.      The slope of a relative movement line may be determined mathematically or graphically. Without doubt, the mathematical method is more accurate than the graphic method when bearing lines are absolutely correct. However, bearings are seldom accurate enough to warrant the use of mathematics. The width of a pencil point is likely to cause an angle to be read incorrectly. Under the circumstances, the extreme accuracy of the mathematical method is generally more of a hindrance than a help. The graphic method usually gives better results.

     12.      Large angles between the bearings minimize the errors in slope of the relative movement line as well as fairly large errors in the RDF bearings. This fact is proved in the following manner. Draw three bearing lines five degrees apart. Draw a slope line which cuts the two outside bearings on circle 10. Introduce an error in the slope line by drawing the line from 10 on the first bearing to 9.7 in the third bearing. Repeat the same procedure with bearings twenty degrees apart instead of five degrees. It will be seen that in the second case the slope lines are much closer together. In the same manner, bearing lines may be drawn with angles smaller than five degrees and larger than twenty degrees. It will be seen that the larger the angles, the smaller the error in the slope line; and conversely, the smaller the angles, the larger the error in the slope line. This principle makes desirable the largest possible angles between bearings.

     13.      The slope of the relative movement line cannot be determined when there are very small angles between bearings. In attempting to use successively smaller angles, a limit is reached after which the most accurate bearings obtainable and the most accurate plotting possible will not give the correct slope of the relative movement line. This limit is reached when bearings are still several degrees apart. Naturally, the larger the scale of the mooring board being used, the lower will be this limit.

     14.      If there is no change in bearing, the slope of the relative movement line is parallel to the bearing. This principle is obvious but it is often misused. Many officers believe that when small changes in bearing are obtained they may employ this principle by averaging these bearings. It is not true that this procedure will give accurate results. The following sketches (fig. 1) show that bearings cannot be averaged to obtain the correct slope of a relative movement line. The lesson to be drawn from these three paragraphs is clear. Unless the tracking officer is certain that he can get on a course that will give a constant bearing, he must take a course that will give the largest possible change of bearing (Important Point there). The mooring board method will not work satisfactorily when small changes of bearing are obtained.

     15.      The first course to be steered cannot be picked until an indication of the target's movement has been gained. Since the bearing must be absolutely steady or there must be a large change of bearing, it is apparent that any course picked arbitrarily may defeat the solution. Before starting the problem, the tracking officer must have made up his mind whether he will use the constant bearing or the large change of bearing method. If he decides to use the constant bearing method, he must immediately set about determining the collision course. Should he decide on the other procedure, he must pick a course as in paragraph 5. That is, he should head for the target until an indication of the direction of its movement is obtained. Then his course should be changed approximately 60 degrees in a direction opposite to the movement of the target in order to obtain the largest possible change of bearing. In attempting to make an early determination of the direction of movement of the target, it is better to place the target "dead ahead" rather than on either bow. If placed on the wrong bow, it will have to cross ahead. This means a slower change of bearing and a later indication of direction of movement. Since the direction of movement right or left is all that is necessary at first, it is desirable that the target be "dead ahead" where the change is most likely to be large.

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     16.     (a) The course and speed for the second leg should never be decided upon and cannot be picked properly until the first relative movement line has been determined. A second course must be chosen that will give the widest possible change of bearing. No great difficulty is experienced in picking the second course if the first was run for a constant bearing. A turn to a course approximately 60 degrees from the bearing obtained on the collision course and in the direction causing the greatest change of bearing will give the desired results. It should be noted that this is exactly the same course recommended for the time-bearing method when the first course is a collision course (paragraph 6). If a large change of bearing is obtained on the first leg, the second course is more difficult to determine.

             (b) Before entering into the discussion of the manner of determining the second course under these conditions it is desirable to emphasize the following facts. A set of bearings obtained while the tracking ship is on one course determines nothing more than the slope of a relative movement line. After the slope of a relative movement line is determined its relative speed locus can be drawn from the head of the tracking ship's speed vector. The intersection of the two relative speed loci determines the target vector. It is only after the lengths of these relative speed vectors have been found that the relative movement lines can be determined.

             (c) With these facts in mind let us return to the determination of a second course which produces a large change of bearing. Such a course must fulfill the following three conditions in so far as possible without violating the principle of paragraph 12.

                 (1) A second course and speed must not be used that will allow the second speed vector of the tracking ship to lie along or near the first relative speed locus. This condition is specifically mentioned in the Mooring Board manual as one that will destroy the solution due to acute angles.

                 (2) The second relative speed locus should be as nearly perpendicular as possible to the first relative speed locus. This gives the best possible angle between the relative speed loci and greatly decreases course and speed errors arising from errors in slope of the relative speed loci.

                 (3) The second course should be as nearly perpendicular as possible to the mean bearing which may be expected on the second leg. Owing to the fact that the target bearings generally can be made to continue movement in the same direction as on the first leg or be made to reverse direction, there will usually be two perpendiculars that may be drawn. One of these probably will violate the principle of paragraph 12 and must be discarded.

     17.     The above three desirable conditions are usually met in what appears to be an ideal manner when the courses of the two ships are in the same general direction. This situation gives the best angle between crossed lines but violates the principle of paragraph 12 by failing to get a sufficiently large change of bearing. The three desirable conditions are generally incompatible when any other course is chosen. All three can seldom be satisfied at once if the principle of paragraph 12 is met. Since a wide change of bearing is necessary for accuracy, the incompatible conditions must be accepted and compromised. The manner of arriving at a good compromise will be illustrated by diagrams. Three extreme problems will be illustrated. In each case, the two ships are placed fifty or sixty miles apart with the target bearing 090 from the tracking ship. A speed of ten knots is used for both ships. In the first problem the target ship is placed on a course 285. In the second it is placed on a course 000 and in the third on a course 075. In each case, the tracking officer heads direct for the target until he determines its movement to be toward the north and then chooses his first course 60 southward of the target bearing. The three examples apply equally well for a target heading toward the south since the first course taken by the tracking ship in this case would be 60 to the northward of the target bearing. In each case it is assumed that bearings have been taken at approximately ten minute intervals and a time-bearing curve constructed to fair the direction finder bearings. Bearings have been picked from the faired curve for 0 hour, 1 hour, and 2 hours. These bearings have been plotted on the mooring board and the slope of the first relative movement line determined. This slope line has been transferred to the tracking ship speed vector to form the first relative speed locus.

             (a) In the sketches shown in Fig. 2, the tracking officer has shown the first relative speed locus and is ready to make his choice of a second course. Let us examine the mooring board for known factors. First, the original bearings taken when the target was "dead ahead" indicated that it was moving northward. This eliminates any target course south of the 090 270 line. From an inspection of the first relative speed locus, it can be seen that the target must be moving on a course between 270 and approximately 300. A knowledge of the limiting

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speed of the target will limit the possible courses greatly. Second, the fact that the possible courses are limited to approximately 30 degrees of arc permits drawing a perpendicular to the first relative speed locus at the mean point of possible target speeds. This gives a good idea of how to meet condition (2). Third, any course from approximately 130 to 320 taken by the tracking ship will violate condition (1). A number of these courses will also violate the principle of paragraph 12. Fourth, the limiting courses show that the target cannot be making good much distance to northward. Under the circumstances, if the tracking ship heads to the left of the last bearing of the target and on a northerly course, the bearings of the target will reverse direction and move toward the south. If the tracking ship moves on a course to the right of the last bearing and east of 130, the bearings of the target will continue to move toward the north. We may now establish the perpendiculars to the mean bearings that may be expected by heading either northward or eastward. With the perpediculars for conditions (2) and (3) drawn, it is apparent at once that a course of approximately 340 fully meets conditions (1), (2) and (3). Its one weakness is that it violates the principles of paragraph 12. Although the course chosen satisfies condition (3), both ships are known to be moving toward the northwest and therefore the change of bearing will be much less than it would be if a course were chosen that lay along the other perpendicular to the probable mean bearing. To completely satisfy condition (3) using this line would require a course of approximately 105. From an inspection of the diagram, it may be seen that this course would give an acute angle between the two relative speed loci. However, if a course of approximately 80 were used, a compromise would be effected which would partially satisfy conditions (2) and (3) while completely satisfying condition (1). Also, it does not violate the principle of paragraph 12. A course of approximately 80 is considered preferable to one of approximately 340.

             (b) In the sketches shown in Fig. 3, the tracking officer has drawn the first relative speed locus and is ready to make his choice of the second course. Let us examine the mooring board for known factors. First, the original bearings taken when the target was "dead ahead" indicated that it was moving northward. This eliminates any course south of the 090270 line. From an inspection of the first relative speed locus, it can be seen that the target must be moving on a course between approximately 350 and 090. An examination of the bearings of the navigation plot with the mooring board shows that a target course between approximately 045 and 090 is impossible because the speed the target would have to make on these courses could not give the bearing changes encountered. Second the fact that the possible courses are limited permits drawing a perpendicular to the first relative speed locus at the mean point of possible target speeds. This gives a good idea of how to meet condition (2). Third, owing to the fact that the target is heading very close to north (between 350 and 045) any northerly or northwesterly course by the tracking ship will cause the bearings to change slowly. The principle of paragraph 12 would be violated. In order to continue a large change of bearing, bearings must continue to move to the north. Fourth since the bearings must move to the north, we may assume a probable mean bearing for the second leg and draw the perpendicular to it as a reference line. From inspection of the two sides of the perpedicular, we again see that the course (about 300) which most nearly meets the ideal of conditions (1) and (2) and (3) violates the principle of paragraph 12 because the two ships are both on northerly courses which slows the rate of change of bearing. To meet best the requirements of condition (3) and not violate the principle of paragraph 12, would require a course of 120. Such a course meets poorly conditions (1) and (2) so a compromise is necessary. A course of approximately 080 should give the best results.

             (c) In the sketches shown in Fig. 4, the tracking officer has drawn the first relative speed locus and is ready to make his choice of the second course. Let us examine the mooring board for known factors. First, the original bearings taken when the target was "dead ahead" indicated that it was moving northward. This eliminates any course south of the 090 270 line. From an inspection of the first relative speed locus, it can be seen that the target must be moving on a course between approximately 050 and 090. A comparison between the mooring board and the navigation plot may restrict further the course and speed limits. Second, the fact that the possible courses are limited permits drawing a perpendicular to the first relative speed locus at the mean point of possible target speeds. Third, any course between approximately 045 and 180 will not meet the requirements of condition (1) because of acute angles. Fourth, the small change of bearing encountered plus the fact that the course is known to be away from the tracking ship insures that any change of course to the southward will continue the bearings changing in the same direction as before. A change of course to the northward will cause the bearings to reverse direction and move southward. As a result of these two possible movements of bearings, we may draw two perpendiculars to probable mean bearings. Suppose we consider the one that meets the requirements of condition (3) when the ship is on a southerly course. The required course cannot be taken because the requirements of condition (1) cannot be met properly. The

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course fulfilling both conditions (1) and (2) does not meet condition (3). The southerly course cannot be taken. This leaves the northerly course to be investigated. A course of 345 will make the speed vector lay along the desired perpendicular. This course will meet all the requirements of the other two conditions without violating any principle of the mooring board.

     18.     Upon completion of the determination of the course and speed of the target by the mooring board method, the relative position of the target must be determined. In locating the relative position of the target, the tracking officer should not be satisfied with the determination of the relative movement line for the last leg only. Both relative movement lines should be determined. If the two lines meet on the bearing common to both the first and second courses, the solution may be assumed to be accurate. At least, the errors introduced prevent further check on the answer. If the relative movement lines are found to cross on a bearing not common to both courses steered, at least one relative movement line is incorrect. Therefore, it may be assumed that the course and speed determined are incorrect. If this situation is encountered, the correct procedure must be determined from the conditions of the particular problem. Possibly one course steered gave a smaller change of bearing than the other. If one direction finder operator took bearings for four hours, he probably became tired and uncertain of his bearings during the last part of the problem. If the direction finder operator shifted at the end of two hours, possibly one was not as good as the other. It is possible that none of these conditions appear to effect the problem and one relative movement line is believed to be just as good as the other. The tracking officer must decide on the merits of the case and attempt to adjust the relative movement lines so they will meet on the proper bearing. Naturally, any adjustment of the slopes of the relative movement lines requires a readjustment of the slopes of the relative speed vectors. This changes the course and speed of the target. The tracking officer can always check his estimates by the navigation plot. The important consideration is that the tracking officer has a check on his solution. As long as adjustments are made utilizing the best information at hand, errors are likely to be decreased.

     19.     It is a well known fact that the best direction finder operators using perfectly calibrated direction finders do not always get absolutely correct bearings. In order to eliminate faulty bearings and average normal errors a faired time-bearing curve is essential. Bearings applied to the mooring board must come from this faired curve, preferably chosen at equal time intervals. This applies equally to the navigation plot.

C.  TWO COURSES VERSUS THREE OR MORE COURSES FOR THE TRACKING SHIP.

     20.     In speaking of the number of courses of the tracking ship, only the courses that are actually used in the plotting are included. Preliminary exploratory courses used to determine the first plotting course or the collision course are eliminated. In making this analysis of tracking methods, only two plotting courses were used. This procedure allows solution by the navigation method in addition to other means. It was found that the use of more than two courses usually allows too short a time on a single course to give definite results. If a constant bearing is desired, the use of more than two courses cuts down the time allowed to check the collision course properly thereby reducing its reliability. If a wide change of bearing is desired, the time allowed on one course will not give a wide enough change of bearing to avoid a violation of the principle of paragraph 12. If indefinite results are obtained by the time-bearing or mooring board methods, the navigation method must be relied on alone. In order to be sure of having at least two methods of obtaining the answer, it is believed that no more than two courses should be used.

D.  SUMMARY.

     21.     From this discussion may be drawn the following conclusions:

             (a) When a constant bearing is obtained on the first leg, it may be projected accurately both backward and forward for as long a period as may be desired. This allows a good solution by both the time-bearing and mooring board methods. This is true regardless of what course and speed are used by the target. As long as the tracking officer has speed available that is equal to or greater than the target speed and knows how to get a constant bearing, a good solution can be obtained. However, failure to obtain an absolute constant bearing defeats the mooring board method and may defeat the time-bearing method unless carefully handled.

             (b) When the mooring board is used, with the largest possible change of bearing on both legs, the solution is always good. The reconciliation of the two relative movement lines gives


a fair check on the accuracy of the solution. The time-bearing method cannot be used coincidently with this method.

             (c) When an "S" type curve is obtained on the first leg and a straight line curve on the second leg, the time-bearing method is generally indefinite and subject to large errors. The mooring board method is generally unsuitable and gives indefinite or critical solutions.

     22.     As a result of this analysis, it appears that the tracking officer may expect good results by the methods of paragraph 21 (a) or (b) but cannot depend on any other method to give good results under all conditions.


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- 9 -


 

FIGURE 1.

 

- 10 -


 

MOORING BOARD

FIGURE 2.

 

- 11 -

 


 

FIGURE 3.

 

- 12 -

 


 

FIGURE 4.

 

- 13 -

 


SOURCE:
National Archives & Records Administration, Seattle Branch
Record Group 181, 13th Naval District Commandant's Office Central Subject Files, 1925-42

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