Since the catastrophe at Tsushima, technical literature has been devoted to questions of naval tactics in a specially thorough way; and the great interest shown in the subject is made evident by the fact that every new idea is immediately taken up by technical journals for lively discussion both at home and abroad. The question of speed takes the lead in these discussions on naval tactics; and, in the course of its discussion, seems to have assumed a more tangible form, but also seems to have been gradually exhausted.
No matter what may be the effective worth of purely deductive mathematical derivations as they appear again and again in technical writings, they have, at all events, a certain value even if all those absolute hypotheses necessary to geometry are greatly modified in war on account of all kinds of unforeseen events, and if many ingeniously constructed mathematical proofs have to be abandoned. To such hypotheses belongs, for instance, the initial position which two fleets occupy before the beginning of a battle.
As a mathematician, the line officer draws two fleets at certain distances from each other, and parallel to each other; assigns them speeds differing more or less, and puts them into motion in accordance with the purpose of his geometrical investigation; but, as a practical tactician, he knows that two fleets cannot be set up like chessmen, in order to attack each other at a given signal, but that the gunnery fight is preceded by a fight for position, a contest of tactical talents and efficiencies for the most favorable initial position. No one will deny that this initial position, which, under some circumstances might give an important tactical advantage to one of the two opponents, is playing a great role in modern naval tactics which is governed by the working of the battery; there are experts who even say that the outcome of the battle depends on it alone. "Good scouting, tactical training, and superiority in speed are the means which help the commander-in-chief to obtain a favorable initial position"; true, but how is this to be carried out practically? On the battlefield of the open sea, where both opponents have the equal advantage of tactically unbounded mobility, it is wrong to act on such ideas. It is easy to say: "Try to gain a leading position," but what does "leading" mean in naval tactics, if this conception can be paralyzed by a simple evolution on the part of the opponent? Under normal conditions, we must not assume that the first shot will immediately follow the mutual sighting of two fleets and all the less, a decisive gun-fire. The distance at which a hostile fleet can be made out in its approximate formation and course is about twice as great as the range at which it is possible to take up an effective gun-fire. At Tsushima, where the conditions for seeing were not entirely favorable, about half an hour elapsed between the sighting of the main bodies by each other and opening fire; and it must also be borne in mind that the Russian fleet did not attempt a single one of the tactical maneuvers befitting the conditions, but even shortened the interval mentioned above by maintaining its course.
It has been maintained that Togo's favorable initial position across and ahead of the deep route of advance of the Russians was the chief cause of his victory. This view, however, cannot be sustained if we may accept the testimony of the Russian Captain Semenoff. On the contrary, Togo's tactics will be regarded in a remarkable and not at all favorable light if the movements of the opposing fleets took place approximately as this witness reports. According to him, Togo not only needlessly sacrificed his ideal initial position, but, by turning toward his opponent, put himself in a tactical position which would have been fatal to him if he had been opposed by a fleet better trained in gunnery and tactics.
The battle of Tsushima hardly contains the material for studying the importance of the initial position; first of all, because a real fight for such a position did not take place at all; secondly, because the disparity in tactical training of the two fleets could not justify general conclusions. Failing examples from war history, the mathematical method is the only one left; and, if it be admitted that geometrical considerations have a certain justification in the field of naval tactics, it may be further affirmed that they are not so much justified during the fight as when the guns have not yet spoken, and have not yet shattered purely tactical geometrical investigations to fragments; namely, in the fight for initial position. We accomplish nothing if we content ourselves with determining that one initial position is favorable and another unfavorable; we get nowhere if we say: "This and that material and abstract method aid in reaching a favorable initial position." We must rather investigate whether, how, and under what circumstances it is possible to win an advantage over our opponent in battle by means of the initial position.
THE MEANING OF INITIAL POSITION.
Initial position is the relative position of two opposing forces with reference to power of concentration, wind, weather, and sun at the moment when it becomes possible to commence an effective gun-fire.
Therefore, it is not a question of relative position at sighting each other, but of that position which represents the result of the tactical considerations and movements up to the beginning of the actual fight, and from which the first blow should be given. The weather and lee-gauge no longer play the important role they did during the era of sailing fleets; and opinion is divided as to which of these is the more favorable in modern naval tactics. With reference to the position of the sun, there is no doubt. But by far the most important factor is power of concentration, to which all other factors must be subordinated, and eventually sacrificed if necessary. The contest for initial position is therefore synonymous with the contest for power of concentration.
POWER OF CONCENTRATION.
Although the idea is clear enough in itself, it nevertheless does not convey exactly enough what the tactician desires to express. The ability to concentrate his strength on one point does not exhaust the problem which the tactician has to solve, as the following investigation will show:
In Diagram 1, let the fleet A, located at the center, be one on which the fleets B-H, occupying various initial positions, want to concentrate their fire. It must be strongly emphasized that the diagram is purely theoretical, and therefore represents situations which will probably never arise in practice. Its purpose is merely to show what kind of positions, in naval tactics, are to be considered favorable or unfavorable, and in what degree. There is purposely no attempt made at the precise meaning of "front" and "rear."
- B fleet is equal to A fleet in power of concentration, also B' fleet, for no one of these three fleets is able to concentrate more fire on one point of the enemy than the enemy can return.
- C fleet is somewhat superior to A fleet, because the individual ships of her column considered by themselves are in full possession of their power of concentration (in contrast with the wing ships of A fleet).
- D fleet cannot make use of her full power of concentration (the hostile head of column does not bear abeam of the middle of D fleet), but is superior to A fleet in this respect.
- E fleet has an important superiority over A fleet (the last two-thirds of A fleet have too great a range, and besides, are limited by the arc of train of their guns; while E fleet, on the other hand, has full power of concentration against the nearest wing of A fleet).
- F fleet is somewhat more superior in power of concentration to A fleet than E fleet is.
- G fleet is raking A fleet with her entire fire, to which A fleet can only reply with a very limited fire.
- H fleet represents the ideal position: she can bring not only the maximum of her power of concentration to bear on her raked enemy, but also robs him of target surface by drawing in her wing.
Therefore, it is not only one's own power of concentration (B and C fleets) which represents the ideal initial position, but the problem is only solved if, first of all, the enemy's power of concentration has been reduced to a minimum at the same time (H fleet). The intermediate positions approach the ideal position more or less. The ruling principle runs as follows:
Not to lose, under any circumstances, more power of concentration than the enemy is deprived of. The best way is to gain in power of concentration as the enemy loses.
THE APPROACH OF TWO FLEETS.
The manner of approach of two fleets depends principally on their strategical aims; here we have to distinguish between three different cases:
- One fleet tries to avoid a conflict and reach a place of refuge, while the other fleet tries to prevent this and force a fight.
- One fleet tries, before accepting battle, to combine with another, while the opposing fleet tries to prevent the union of the two forces, and to fight them in detail.
- Each of two hostile fleets seeks a decisive battle.
In cases (a) and (b), the approach is merely strategical; the strategical aim is the principal one; there can be no question of a fight for initial position in these cases until after the attainment of the strategical aim. But tactics comes strongly into play when a fleet is forced to recognize that its strategical aim cannot be attained, and that a fight can no longer be avoided; the strategical aim must then be abandoned; and the fight for initial position begins. Example of case (a): Tsushima, where Rojestvensky had to abandon his strategical aim on sighting the Japanese main body, at the very latest; and should have immediately commenced the fight for initial position; this, however, he failed to do. Example of case (b): Port Arthur on August 10, 1904, when the Russian commander recognized the impossibility of attaining his strategical aim (junction with the Vladivostock cruisers) without a battle with Togo. At this moment, the fight for initial position should have begun. Here, again, it was not done. The case of (c) demands our special attention. Where both opponents have no other aim than to find each other and fight a decisive battle, where the whole spirit and thought of each is concentrated on obtaining the most favorable initial position by every available means, we have the necessary conditions for a simple and clear investigation of the question, By what laws is the fight for the initial position governed?
Since wireless telegraphy attained such a predominating influence in carrying out strategical scouting, it is not as easy as it was to distinguish clearly between strategical and tactical scouting. Strategical scouting must furnish information about the position, course, and strength of the main body of the enemy; this information can be given if the distance between the two main bodies is fifty miles, or even more. Is it possible to begin the fight for initial position at this stage of operations? Certainly, if a fight for the weather or lee-gauge with reference to wind and sun is to be considered, it is thinkable and probable that it will commence during the strategical scouting. This operation might be called the fight for the "bearing at sighting," for the bearing on which the enemy is finally sighted will generally approximately coincide with the principal line of fire.
In the above example (diagram 2), both fleets, A and B, will try to establish a reciprocal line of sighting each other running approximately NE.-SW.; and both A and B will try to get to the SW. side of this line. An approach of both fleets in the indicated direction will result from this effort. Speed and the accuracy of the information reported by the scouts concerning the position and course of both main bodies will naturally fix the course to be steered; and a mathematical investigation of the outcome would be futile. The fight for the "bearing at sighting" will soon enter a stage where regard to wind and sun must yield to the real fight for initial position, for power of concentration. During this period of transition, the moment will have to be sought at which strategical scouting ends and tactical scouting begins.
THE FORMATION OF THE FIGHTING LINE.
Whether column be the most favorable battle formation, or whether some other formation should be adopted, does not belong to this discussion. For our investigations, we must, at all events, accept the column, as it represents the simplest geometrical form, and can best be dealt with mathematically. A formation in several columns is best for the approach of a large fleet (about twelve ships or more) during the period of strategical scouting, because, in this way, the commander-in-chief keeps control of his ships for a longer time, and because the fighting line can readily be formed from such a formation. It is hard to lay down any fixed rule as to when the time for this has come. Handiness, supervision, and quick understanding of signals require the cruising formation to be maintained as long as possible; in addition to which, much time would be lost if a change of front became necessary after the fighting line had been established, and circumstances might make this maneuver complicated and difficult. On the other hand, anxiety about a possibly untimely establishment of the fighting line is relieved by performing this evolution somewhat too soon rather than too late. Generally, it can be accepted that the battle formation will be adopted before the two main bodies sight each other, or, at the very latest, when they sight each other. If we accept this as the basis of our observations, the normal position of two fleets during the tactical approach will be represented by two keel lines, with more or less converging courses.
TACTICAL SCOUTING AT SEA.
Naval tactics, simple as they are in themselves on account of the uniformity of the battlefield, would be no art if their problems could be solved by dividers and rulers. It is one of the most difficult problems of practical naval tactics to do accurate scouting concerning the formation and course of an entirely visible but still far-distant column of ships. The stereoscopic power of vision of the human eye is very wide, for near objects, but, at distances of 6000, 7000, and 8000 meters and more, it cannot take in ships bodily. At such great distances, separate ships appear as silhouettes; a column of ships, a column of silhouettes. The difficulty cannot be overcome even when the eye is aided by glasses, because the field of vision decreases as the distinctness of separate objects increases; and a wide field of vision is necessary to tactical scouting. It is a matter of every-day occurrence that it is impossible to make out whether a distant column is making a course converging with, parallel to, or diverging from ours. It is also a well-known fact that column can hardly be distinguished from echelon at great distances ; one has nothing to go by except the form in which the silhouettes of the ships appear. A ship appears to us in its whole length only when it presents its full broadside to us; this length, however, decreases with the cosine of the angle of obliquity; and, as the cosine of small angles changes very slowly, and only becomes 24 at about three points, the result is that it is difficult to distinguish a formation in echelon (less than three points) from column. A long practical experience, no less than a trained eye, is necessary to insure accurate observation, and efficiency in tactical scouting.
THE FIGHT FOR POWER OF CONCENTRATION.
(a) Establishing a Position Forward or Abaft the Beam.
Two equally long columns, steering the same, or converging, courses, are in the same tactical position with reference to each other, if their heads of column are at the same distance from the theoretical point of collision. The initial position, in this case, is reached as soon as the leading ships of both columns arrive at a range (say about 7000 meters) corresponding to good probability of hitting and effect. The thing to do is to have an advantage, a leading position, over the enemy on arriving at this initial position. If both fleets have the same speed, the distance of both heads of column from the theoretical point of collision will always remain the same. The result of the fight for initial position would be nil on both sides in such a case. This case is the simplest, and will seldom arise in practice, because, first of all, there will always be a certain difference in speed; and, secondly, which is more important neither of the two opponents will know who is the nearer to the theoretical point of collision at the beginning of the fight for the initial position. It is evident, from diagram 3, that the distance of one's own (A) head of column and the hostile head (B) from the point of collision K can only be obtained by the trigonometrical solution of the triangle AKB, in which, however, only two parts (e and the angle a) are known. It is true that, theoretically, it is possible to solve the triangle AKB by means of the triangle ABC, but the sides AB and AC (distances of the hostile wing from one's own head of column) can only be known when range-finders give accurate results.
The bearing of the hostile head of column gives, in itself, no means of establishing which of the two columns possesses the leading position; but we can establish the relations which exist between the bearing and the angle included between both columns (diagram 4). The angle must be found by which the hostile head of column (A) ought to bear forward of the beam without one's own fleet (B) losing its leading position.
It is evident from the diagram that B fleet retains a leading position under all circumstances as long as its head of column lies between the two points D and K, that is, as long as the angle KDA =90, or is greater than 90. But the head of B fleet can only drop back the distance BD without losing a leading position, that is, the bearing of the head of column from A may be, at the most, the angle ? forward of the beam. Now, the angle ? = the angle ?, and the arc AB = the arc BC. The angles a and k subtend equal arcs of the same circle, a at the circumference, and k at the center. Therefore, ? = ½k. In other words, if a fleet wants to make sure of a leading position, the angle by which its head has the enemy's head bearing forward of the beam must not exceed one-half of the angle included between the prolonged courses of the two fleets. The following rule serves to apply this mathematical conclusion practically: If you have not a superiority in speed, estimate the angle between your own and the enemy's course too small rather than too large, divide it by two, and as a factor of safety, subtract a certain per cent more. The angle so obtained represents the maximum by which the enemy's head may bear forward of the beam.
(b) Maintenance of an Obtained Leading Position.
If a fleet thinks it has gained a leading position according to the preceding rules, at the beginning of the fight for initial position, the problem becomes: How maintain it? Let us suppose that the enemy does not undertake a tactical parry. A fleet in the conscious possession of a leading position would develop an involuntary tendency to pass ahead of the enemy, in order to obtain, on opening fire, one of the positions E, F, G, or H (see diagram under "Power of Concentration"). This drawing ahead of one's own column will be accomplished by making and maintaining the bearing of the enemy's head at 90. If in the beginning, this angle be greater than 90 it must be reduced to 90 by gradually turning toward the enemy, and then kept constant (diagrams).
If the angle be less than 90 at the beginning, it must be increased to 90 by maintaining the previous course, and then kept constant (diagram 6).
(c) Speed.
It is evident that speed plays an important part in the fight for initial position.
A leading position, obtained at the beginning, need not be lost on account of inferiority in speed.
First of all, it is very hard to establish, in the course of a fight for initial position, which of the two fleets is the faster. It is obviously an error for any one to suppose that he can make sure of the existence of a difference in speed because one of the two opponents changes its bearing one way or the other; or that he can draw the conclusion that the speed of both fleets is the same because the bearing remains constant. The last example (diagram 6) shows that, in spite of equal speeds, a continuous change of bearing takes place; and the following diagram, No. 7, shows that, for the assumed speeds of 12 knots (A fleet) and 10 knots (B fleet), the bearing remains the same for both opponents, and that B, in spite of inferiority in speed, wins the leading position on arriving at the initial position, and has greater power of concentration.
(d) The Tactical Parry.
The preceding deductions assume that the opposing fleet maintains its course. This gives rise to the necessary and proper objection that A fleet is not compelled to maintain its course.
We have already proved that a fleet is never in danger of being outmaneuvered in the fight for initial position as long as it keeps the enemy's head bearing abeam. It is incontestable that this is always possible, given enough sea room. Therefore, let us take A fleet abeam of the head of B fleet. What will be the result? (diagram 7). Both fleets will steer parallel courses abreast of each other; this does not, however, destroy our assumption that both fleets want to fight. Therefore, they must converge.
A tactical parry will be necessary that is, against the leading position of the hostile fleet, and against the danger of inferiority in power of concentration on arrival at the initial position as soon as it is determined with certainty that the enemy has a more leading position, and that he cannot be deprived of this advantage by holding on to the previous course. Naturally, the parry consists in turning away to leeward, whereupon a fight on the inner circle commences, while the other fleet loses its leading position, and turns on the outer circle. The later tactical developments were recently discussed in articles in this publication; and are not within the scope of this article. The moment the inner column turns away may be viewed as the end of the fight for initial position, the fleet which turns away giving up the contest, as it were. To seize upon this moment correctly, and not let it slip, is the problem of the fleet in the more unfavorable position. The struggle for the more favorable position would not be so interesting and instructive as it is tactically if one could arrive at a recognition of his unfavorable position, and the necessity of a counter maneuver, by means of mathematical calculations; the fight for the initial position would then be reduced to the low level of mechanical, soulless work, while it is just the intellectual qualities that betoken tactical genius. The difficulty in the tactical ability to get information at sea is that it renders it impossible for the tactician to always determine whether he or his enemy is in the more unfavorable position; whether the chances are that he will win the more favorable initial position by holding on to his course, or whether he must turn. For an illustration of this, let us turn back to the last diagram, No. 7. The chief of B fleet has the enemy's head bearing abeam, and, in spite of the approach of both columns, this bearing does not change with reference to the course of B fleet. He can, therefore, be sure that he cannot be outmaneuvered if he holds on to this course. On the other hand, the chief of A fleet has the head of B bearing somewhat forward of the beam, but is unable to conclude from this that B fleet has a more favorable position than A fleet, because he has no means of knowing how his own head will bear from B. Therefore, B has no cause to attempt a tactical counter maneuver, especially as, during the fight for the initial position, the bearing from B's head does not become more unfavorable, but remains constant. If, during the approach, the feeling be not aroused in A that he holds a tactically unfavorable position, but, on the contrary, A fleet holds its course to Ay, he loses the fight for initial position, and cannot correct his error; in the effort to outmaneuver B, and acting on the wrong belief that he can do this by holding on to his course, he is himself defeated and outmaneuvered.
THE NUMERICAL VALUE OF TACTICAL POSITIONS.
It is very easy to see, from a tactical diagram, which of two fleets possesses the more favorable position; but it is very difficult to compare several tactical positions with each other, and determine which is the more favorable, and how much. It seems essential to find a method to get at the numerical value of a tactical position (with reference to the enemy), to fix upon a weight number as it were, especially as this article will conclude with a short synopsis which will show to what different results the fight for initial position can lead under manifold assumptions.
The value of a position evidently depends only on the size of the angle of convergence of both courses, and on the angle by which the enemy's head bears forward or abaft the beam; and, generally, the value must increase directly as the former (?) increases and the latter (?) decreases (diagram 8). This gives us, first of all, the product sin ? cos ?.
This formula needs a further addition, since:
- The result will be nil if neither side has an advantage.
- The result will be infinitely large or infinitely small, if one of the extreme cases arises.
- The result will be negative if a favorable position becomes an unfavorable one.
The function tangent (? - 2?) satisfies these conditions. The formula, therefore, becomes sin ? cos ? tan (? - 2?).
In the following, the correctness of the formula will be tested :
How does the advantage of A fleet change with a change of assumption?
1. Angle ?.
- ? increases: therefore, sin ? also increases, and A's advantage increases. 90° has the maximum sine, therefore A's advantage is greatest when the angle of convergence of the two courses is 90°.
- ? decreases: sin ? decreases, and A's advantage decreases. If ft be zero, sin ? is zero, and the product of the formula becomes zero; also A's advantage is entirely lost, as soon as the angle ? becomes zero; and the courses will be parallel.
2. Angle ?.
- Angle ? increases: cos ? decreases, A's advantage decreases directly as the angle a increases; and becomes zero as soon as a becomes 90°
- Angle ? decreases: cos ? increases, A's advantage increases directly as a decreases, and reaches a maximum when a equals zero, that is when the hostile heads bear abeam from each other.
3. tan (? - 2?).
- The product sin ? cos ?, by changes in the angle ? and ?, evidently will be equally influenced by the factor tan (? - 2?), since tan (? - 2?) increases or decreases to the same extent with the increase or decrease of sin ? and cos ?.
- If ? = 90°, and ? = 0, tan (? - 2?)= tan 90° = ∞, and the whole product of the formula becomes infinitely great. In this case, the ideal position (crossing the T) is reached.
- If ? = 2?, tan (? - 2?) = tan 0° = 0. The whole product of the formula becomes zero; therefore, A's advantage is also zero (the case has been reached which was discussed under "Establishing a position forward or abaft the beam "; both heads of column are equally distant from the ideal point of collision).
- If 2? > ?, the angle becomes negative, the tangent is therefore negative, and the whole product of the formula negative; that is, the favorable position has become an unfavorable one.
If we admit, under normal conditions, that two fleets sight each other at from 13,000 to 15,000 meters, and that, during the approach to about 10,000 meters, the fight for the initial position has so far developed that the course and also the angle of convergence of both columns has been approximately determined, it is not difficult to ascertain, with the aid of assumed values of the angles a and ft, in which initial positions both fleets will arrive on their previous courses, as soon as both heads have approached to about 7000 meters.
Example: Two fleets, A and B, in the course of a fight for the initial position, have arrived at such a position with relation to each other, distance 10,000 meters, that the prolonged courses include an angle of 30, and in which A has the head of column of B bearing about one point forward of the beam. Both fleets have the same speed. At a distance of 7000 meters, how will the initial position of A compare with that of B?
1. A fleet: If the heads of column are 7000 meters from each other, the angle ? = 10° (easily proved graphically or trigonometrically).
cos ? sin ? tan (? - 2?) = + 0.087
2. B fleet: For B fleet in the same position, a = 20 (easily
proved, as in the case of A).
cos ? sin ? tan (? - 2?) = - 0.083
The result is negative on account of tan (? - 2?); for ? = 30°, and 2? 2 X 20 =40°. The difference is therefore negative (-10°).
A fleet is therefore 0.087 + 0.083 = 0.17 points more favorably
situated as to initial position than B. The formula, therefore, permits all possible tactical situations to be evaluated numerically, and to be compared with each other. The practical worth of the formula need not be considered; it can be used, at all events, as, for instance, in tactical war games, the aim of which is the fight for the initial position, and in which it is a question as to which fleet, and to what extent, has conquered its enemy in this tactical fight for position, in bringing both fleets to a decision on the basis of tactical maneuvers.
EXPLANATION OF THE TABLE.
- In order to avoid decimals, resulting from the formula, all determined values are multiplied by 1000.
- The figures not in parentheses give the values for the fleet to which the angles ? and ? apply; those not in parentheses, values for the opposing fleet.
- With converging courses, a fleet will never reach such a position that its center will have the enemy's head bearing abaft the beam. This is necessarily so, for a fleet in such an advanced position would, at the proper time, have turned toward the enemy in order to maintain the enemy's head abeam at all events, not to have it abaft the beam. Therefore, the table only gives angles a by which the enemy's head will bear forward of the beam. Where numbers are omitted from the parentheses, it means that impossible cases have arisen; therefore, values have not been calculated.
Example: During the fight for the initial position, a fleet gains a position in which the enemy's head of column bears 15 forward of the beam. Let the angle of convergence of the two columns be 55. In power of concentration, it will have a tactical advantage of about +376 points; the enemy's fleet will be more unfavorably situated by about 296 points; that is, the difference amounts to 376 + 296 = 672 points.
CONCLUSION.
The preceding essay represents an effort to clear up the idea of initial position, to investigate and test it, and to find out by what general points of view the fight for the favorable initial position will be carried out in large modern battleships. The motive of the essay lies in the fact that, though the idea of initial position has recently been much made use of in both native and foreign technical literature, it has never been analyzed in its details. The value of a favorable initial position in a modern naval battle is evident. In most tactical discussions, more and more importance is given to the necessity of a skilful tactician being sure of holding a leading position; but it has not yet been determined where the key lies to the correct tactical evolution. This key has not been found in the preceding essay; and cannot be found. Perhaps the moment of its arrival has been found, and the law formulated which may serve the practical naval tactician as a support for his thought and action in the fight for the favorable initial position.
Just as an equation with two unknown quantities cannot be solved if we only have a single equation as a hypothesis, in the fight for the initial position there are too few hypotheses available to permit the solution of the various unknown quantities. The science of mathematics here fails us; but it would be improper and ungrateful to therefore exclude mathematics from considerations of naval tactics. On the contrary, we cannot do without it at all, if we want to fix upon the fundamental elements of naval tactics, and guard against elementary errors.
The worth of mathematical investigations must not be estimated too high; for in the last resort, practical ability is the ruling factor. Without knowledge, however, ability is not conceivable; and this knowledge cannot be better obtained than by a theoretical investigation of the concrete case, and by logical conclusions about the real.