(From Rivista Marittima of September, 1913)
In the book entitled "Fondamenti di tattica navale" (Foundations of Naval Tactics), published in 1910, treating of the question of radius of action of the torpedo, we came to the conclusion that, with the ships of that day, at a range of over about 3500 meters, the use of the torpedo could not be ignored, but this use became advantageous only under such conditions that maneuvering had to remain entirely subordinated to the use of the gun. This conclusion was based upon ships armed with few torpedo tubes; at that time I laid stress upon concentrating more torpedoes against the same ship and upon firing torpedoes against a fleet of ships upon the hypothesis that each ship would make a single launch or, in other words, would be able to launch but one torpedo at a time.
The idea of arming the battleships with numerous long-range torpedo tubes now seems to be making way; for this reason we believe it opportune to discuss the importance of the torpedo on the hypothesis that each ship be able to make a multiple launch; we will proceed in the following order:
1st. Study of the probability of hitting with the single launch and with the multiple launch for the various angles of impact.
2d. Search for the most convenient method of making the multiple launch.
3d. Conclusions, upon the influence upon naval tactics, that can be predicted.
We propose to show that, even giving to the torpedo all the advantages that are nowadays admissible, these can easily be neutralized and that the gun still is the predominating arm of naval battles.
PROBABILITY OF HITTING
We will take a torpedo of 9000 m. run at 25 knots, and we will suppose that it combines the qualities that the French have sought in two distinct types of torpedo ("torpille-distance" and "torpille-vitesse"); we will then admit that by decreasing the run we can get greater speed, according to the ratio that we established in the book cited.
In the issue of this Revista of last May, Sub-Lieutenant Iachino made an interesting study of the probability of hitting with a single launch, and in its application to the above-mentioned torpedo, assuming the launch to be made against a ship 200 m. long at 18 knots speed, he has made a table of probability that is very favorable to this arm. It must be observed, however, that (though he may have made allowances) he took it for granted that he can limit the errors in the course and in the speed of the target to 5° and 1 knot respectively, supposing that these are determined from two sets of simultaneous bearings and ranges. We hold that when in offensive contact it will not be possible to obtain such accurate results; in fact, two adversaries will maneuver at long range and, though the course may change slowly, it is necessary to take the elapsed time of the torpedo's run into account, as in the following table:
Run in meters. 3000 4000 5000 6000 7000 8000 9000
Time of run in sec. 130 211 290 387 483 592 708
Se we think it optimistic, for the torpedo, to assume a mean error of ± 10° and ± 2 knots in the course and speed of the enemy, respectively; with this value, supposing that the weapon is perfect in itself, we have drawn the curves of 50 per cent probability of hitting, on the hypothesis of a ship at 18 knots.
These values are used in the following table, which we consider valuable because it serves as a basis for the calculation to which we shall refer later on; in this table c is the run and i is the angle of impact,1 taken from the bow of the target.
1Let t be the time of the run, ? and ?VN, the respective errors in the enemy's course and speed; then the resulting errors S? and Sv are given by the formulæ:
TABLE I
CURVES OF 50 PER CENT (METERS)
From this table, assuming a ship 200 m. long, we get another,
as follows:
TABLE II
PERCENTAGE OF SUCCESSFUL HITS IN THE SINGLE LAUNCH
The probabilities of hitting appear remarkably less than those deduced in the article referred to, but, admitting, as is logical, that the practical probabilities will always be considerably less than the theoretical probabilities, this table goes to show that, in the multiple launch, the probabilities of hitting will be much greater.
* * *
As is noted, in the multiple launch of torpedoes from one ship at the same target, the acknowledged offensive ability of the weapon helps to show that the torpedoes have slightly different errors with respect to the center of the target; the torpedoes ought to be launched so that they will form an unbreakable chain across which the enemy's ships may not pass without being struck. Not stopping to consider the method by which such an objective can be attained with the installations on the battleships, we will make some deductions for easily determining the probability of hitting. Firing a torpedo at a target whose length is L, in order to hit the ship the error must be less than or equal to ½L. If a multiple launch of two torpedoes is made, the maximum error from the center of the target, so that the ship will still be hit, is L, with three torpedoes this error can be 3/2L; and, in general, for n torpedoes the error can be –n/2L. This makes it evident that the multiple launch of n torpedoes, with a dispersion L between each two successive ones, has a probability of hitting equal to the probability of one torpedo fired at a ship of the length nL.
The probability, such that the multiple launch of n torpedoes may give a useful result, is then picked out of the table of the factors of probability, taking for the argument the factor nL/E (where E is the curve of 50 per cent given by Table 1) in the same way in which we took, for the argument in the single launch, the factor L/E. The percentage P that we thus obtain shows that in N salvos there will be, theoretically, NP/100 salvos in each of which a torpedo will hit the target.
We get, in this way, the following tables for the case of salvos or three or six torpedoes.
TABLE III
PERCENTAGE OF USEFUL SALVOS IN THE MULTIPLE LAUNCH (3 TORPEDOES)
TABLE IV
PERCENTAGE OF USEFUL SALVOS IN THE MULTIPLE LAUNCH (6 TORPEDOES)
* * *
In order to have the ideas well fixed in regard to the way the probabilities of hitting vary under different conditions, we refer to the elements that guide us in tactical maneuvers, in other words, to the range between the adversaries and to their relative bearings. From the arguments c and i (run of the torpedo and angle of impact) we pass to the arguments r and y, r being the distance between the adversaries at the moment of the launch and y being the angle that the line joining the centers of the formations of the two adversaries makes with the course of the target ship. This change of co-ordinates can be made by means of the following table where the values of c and i (in parenthesis) corresponding to value of r and y are given:
TABLE V
VALUES OF C AND i
In this table y varies between 30° and 150° on the hypothesis that the enemy may bring the launching ship to bear in the sectors of her maximum offensive gun power; no limitations for the angle of impact are established because we assume that the torpedoes launched are furnished with a firing pin that will work at any angle. We have underlined the values of the run which are not much greater than 9000 m. in order to preserve the form, but we have naturally thrown out the values that are very much greater than 9000 m.
In the first place, the above table gives an idea of the possibility of the launch, either single or multiple, independently of the greater or smaller probability of hitting indicated by Tables II, III and IV. The gist of this table can be memorized as follows:
TABLE VI
LIMITS OF POSSIBILITY OF THE LAUNCH
WITHIN 10,000 M. RANGE
In addition, Table V makes it possible to deduce, from Tables II, III and IV, the probabilities of hitting corresponding to r and y, or to obtain the two following tables:
TABLE VII
PERCENTAGE OF USEFUL LAUNCHES IN THE SINGLE LAUNCH
TABLE VIII
PERCENTAGE OF USEFUL SALVOS IN THE MULTIPLE LAUNCH (6 TORPEDOES)
* * *
We have been considering the probability of hitting a particular ship; now we ask ourselves if the target of two or more successive ships can be considered alone, that is, without successive solutions.
The target of two or more, ships is equivalent to a continuous fictitious target with respect to the course of the torpedo if it is not possible for the torpedo to cross the line drawn through the two ships without hitting one of them, that is, if a miss happens only when all the ships of the formation are on the same side of the course of the torpedo.
In the case of stopped ships this continuity would be true with respect to torpedoes coming from the sectors of the formation's minimum offensive power, that is, from those that are obtained by joining the opposite ends of the contiguous ships. In the case of moving ships the continuity of the target corresponds to the sectors which comprise the trajectories for which the above-mentioned lines joining the opposite ends of the contiguous ships represent the relative torpedo-target motion. In the single launch these sectors are restricted, and so the launch made, considering a formation as a single target, has a small probability of hitting.
For the multiple launch of n torpedoes it would be possible to make, in this way, an examination of the limits within which more ships can be considered as a single target, substituting, for the ships of length L, some fictitious targets of the length nL; we will confine ourselves to observing, although it has been said before, that two or more ships, 200 m. long, in column, and if they are 500 m. apart, form a continuous target for a multiple launch of six torpedoes. In fact, in such a case the fictitious targets overlap so as to form one continuous target.
Since, in this study, we assumed that the torpedo had all possible advantages, we will admit that with respect to the multiple launch the target is always continuous, for all formations nearer to column than to line.
* * *
From what we have said above we can arrive at the following conclusions:
1st. A ship can be considered in condition to launch, with a single launch or a multiple launch, when the target keeps her in the sectors of maximum offensive power of the guns (y = from 30° to 150°), only if the range is within the limit of about 3000 m. At ranges greater than about 5000 m. a ship will be able to launch only in case the enemy keeps her forward of the beam (see Table VI).
2d. The probability of hitting with the single launch (taking into account that the practical probability will be less than the theoretical probability) can be considered up to ranges of about 5000 m. if the target keeps the launching ship forward of the beam and not too far away (y = between 60° and 90°). This deduction, which we obtain from Table VII, together with what precedes, forces us to the conclusion that the single launch at ranges greater than 3000 m. will be exceptional. Above ranges of about 4000 m. it is safe to maneuver, against ships that cannot make a multiple launch, without considering the torpedo.
3d. The multiple launch gives great probabilities of hitting. This fact gives rise to the question: What difficulties does the execution of the multiple launch present?
EXECUTION OF THE MULTIPLE LAUNCH
A satisfactory solution of the problem of the multiple launch in salvo cannot be actually worked out in practice with submerged torpedo tubes.
We will consider the single triangle of launching ANS (see figure), N being the mobile point struck by the trajectory AS of the torpedo, and AZ and NX the courses. a indicates the relative bearing ZAN and ? is the angle of the launching tube from the bow, and ?is the angle of sight SAN.
In the case in the figure, where the adversaries head in the same general direction, we have
?=a—?,
and when they head in opposite directions,
?=a+?,
For the multiple launch on the basis of the ratio
the angles of sight ?1, ?2, ?3, . . . . would have to be calculated in functions of the relative bearings y1, y2, y3, . . . . corresponding to the dispersion that we wish to obtain in the salvo. So, for example, to obtain the error s=NN1 with respect to the mobile point N, indicating by y1 the angle AN1X and by ? the angle N1AN, we have
Y1=Y+?,
where ? can be found from the triangle N1AN in functions of s, of y and of the range r=AN, also taking into account the distance between the launching tubes. Having deduced the angles of sight the problem would be solved if the torpedo tubes could be trained as easily as guns; but if this is true of above-water tubes, it must naturally be thrown out in the case of submerged tubes.
We cannot count upon continuous aim, so the solution that we seek is for clamped tubes, giving to the tubes the angles of train ?1, ?2, ?3, . . . ., to be found from the above-mentioned ratios. But with submerged tubes the angle of train is fixed; therefore, in order to put into practice a solution of the kind indicated above, two methods present themselves: 1st, to have the tubes installed in conveniently divergent directions; 2d, to have the tubes parallel but equivalent to tubes that can be trained, the torpedoes being equipped with (guidasiluri) outside gyrosetting devices.
The first of these methods cannot be adopted because, since the tubes will not train, their divergence cannot satisfactorily correspond to the variation of the range of the enemy and of his relative bearing; in other words, we cannot adopt an average solution.
As for setting the gyroscope, even admitting that it works perfectly, it is clear that this cannot be as good as continuous train; in fact, the torpedo once placed in the tube, with the gyroscope set in a certain way, it is difficult to change the setting of the gyroscope without withdrawing the torpedo.
For this reason the gyroscope can give a prepared setting (the angle of train arranged beforehand); so we would, perhaps, assume too much should we ask the gyroscope to lay the torpedo's course within one degree of the desired course, as we would have to do in order to get the proper divergence between the trajectories of the torpedoes launched in salvo. For this reason we admit that the gyroscope permits us to consider the torpedo tubes as trainable in parallel in relation to the angles of departure that the gyroscope gives. But if, with parallel training, we launch the torpedoes simultaneously, the zone of the enemy's course that is struck will generally be too small; without the necessity of substantiating this argument with the formulas, it is sufficient to remember that, in the case of parallel courses, the zone struck by a salvo is hardly equal to the distance between the two end torpedo tubes. Evidently the zone struck varies according to the angle between the course of the launching ship and the course of the target, and also according to the angle that the trajectories of the torpedoes make with the course of the launching ship; taking into account that, owing to the inclination of their courses, the torpedoes will intersect the enemy's course at different moments, it is easy to see that the dispersion of a salvo may be, in certain cases, even less than the distance between the end torpedo tubes, and that, in this case, the probability of hitting will be but little greater than that of a single launch.
The problem of the multiple launch cannot therefore be solved by the salvo method; so we must look into the successive launch, assuming that, as we said above, the torpedo tubes can be trained in parallel.
* * *
We indicate as usual by a and y the relative bearings of the two opposed ships, A (launching ship) and N (target ship), by VA and VN the speeds; let di be the distance between two torpedo tubes. The interval of time ? that there must be between the launches in order to have two torpedoes make an uncrossable barrier of a breadth L, is given by the formula
which is easily deduced and in which the term of the denominator takes + or — according as the ships are heading in approximately the opposite or the same general direction, respectively.
For launching more torpedoes, it will therefore suffice to have a directing station of launching, with an instrument which will give the data for firing the first torpedo, and to launch the other n—I torpedoes at equal intervals of time ?, a and y being given what are considered the mean values for the time n?. This method is practically identical with that which we recommended for the multiple launch from torpedo-boats2; in fact, that method differs from this only because, on a torpedo-boat, it is not possible to take account of the interval of time between the launchings.
2For this method refer to "Sul problema del lancio" in Rivista Marittima of December, 1912, at Office of Naval Intelligence. It consists of applying corrections to the angles of sight with all tubes laid parallel.
In order for the method to be applicable it is necessary that ? be small enough; so the method gives the best results when the adversaries are steaming in approximately opposite directions. If, on the other hand, they are steaming in approximately the same direction, the resultant of the speed of the two ships along the normal to the line joining their centers, i. e.,
VA sin a—VN sin y,
is nearly zero and so ? is very large, and is infinite if, for example, the two ships steer the same course; therefore the method is not applicable in such a case.
* * *
In view of what precedes we can state:
1st. The method to adopt for the multiple launch is the method of successive launches.
2d. That if the adversaries are steaming approximately in the same direction the successive launch is not possible and therefore the launch can be made only in salvo, taking into consideration, however, that in this case the dispersion of the different torpedoes is limited to that due to accidental errors, in other words, that the probability of hitting becomes greatly reduced because the errors of the torpedoes differ very little with respect to the center of the target; thus we may have more than one torpedo hit, but it is more probable that the whole salvo will miss the target. Small dispersion of a salvo is a highly desirable factor in gun fire, but is here a serious defect because we are under conditions similar to those of a fire that cannot be improved, owing to the impossibility of seeing the point of fall, and yet is able by a single blow to put the target out of action.
TACTICAL CONCLUSIONS
The deductions obtained furnish an answer to the question: What will be the influence of the torpedo upon tactical maneuvers?
In the use of the gun, for weapons of equal power, we are obliged to enter within the range of the enemy's guns in order to have him under the fire of our own guns; on the contrary, with the torpedo it is possible (and therefore logical) to maneuver, with respect to the enemy, so that it will be impossible for the enemy to make a launch in conformity with Table VI.
Therefore the torpedo, at great range, would have the effect of causing the adversaries to keep each other abaft their beams; the mental vision of such a battle would for this reason become that of an indecisive action in which the adversaries would draw away from each other as soon as they came within range.
In such a case, in order to provoke a resolute battle, it would be necessary for one of the adversaries to give up the development of his maximum offensive power during the period of approach, that is, to approach in a frontal formation, taking into account that a ship head-on, or very nearly so, has the minimum probability of getting hit by the torpedo, as we see from Table VII and from all that is said about the launch against a formation. A consideration of this sort leads us to think that the importance of head-on gun fire may increase with the progress of the torpedo.
It does not, however, seem necessary that the use of the gun should be sacrificed to the great extent that the head-on approach requires. In fact, speaking of the torpedo, we naturally allude to the multiple launch with a good dispersion; but we can fight steaming in the same general direction as the enemy's course and, in this case, when the launch is not impossible, the probability of hitting is very limited; if one of the adversaries does not want the torpedo to enter into the contest, he can gain his point with great ease; all he has to do is to steam in the same general direction as the enemy, and he can fight, taking only the gun into consideration, that is without running any chances, as long as the range does not get below the limit within which even the single launch has a good probability of hitting.