DISCUSSION
Dispersion and Accuracy of Fire.
REAR-ADMIRAL B. A. FISKE, U. S. Navy.—While it is clear that Lieutenant Long's able article brings out sharply an important but neglected truth, it is equally clear that its effect will be beneficial only in so far as the inference drawn from it is correct.
If the inference drawn be incorrect, the lesson it conveys may be ignored: it may even be perverted to a wrong use.
That an incorrect inference may be drawn by some officers seems probable: in fact it is believed that some officers have actually drawn the incorrect inference that the article teaches that our salvos are bunched too closely.
Of course, the correct inference is that the article teaches that our fire control errors are too great, and should be reduced.
If this inference be drawn, the article will be most beneficial, because everybody will then see the necessity for training men to use the range finder.
CAPTAIN J. H. GLENNON, U. S. Navy.—I think the discussion of this question could be improved by strict adherence to technical terms, the present tendency being to use such terms too loosely. This loose use of words is at first a convenience, but in the last analysis leads to confusion. There is a mathematical theory of errors quite as exact as other mathematics based primarily on the equal probability of committing any given error and its equal in the opposite direction. This premise is only approximately true with gun fire and especially with errors in the range direction, as will become apparent if we consider that many of the errors are made in small angles at the gun itself; and the effect of a downward angle is not the same in diminishing range as that of an equal upward angle in increasing it; nor have decreases in muzzle velocity the same value in decreasing range as have equal increases in velocity in the opposite direction. The application of the theory of errors then to gun fire can only be approximate. It is or should be presumed that a spotter of any capacity will in the long run have his mean point of impact on the target point of aim.* From this target, then, as projected on the sea along the line of fall of projectiles, equally probable range errors will be practically equal, long or short. The extreme range error, long or short, will be about three times the mean range error (or average of all range errors), and for practical purposes may be taken three
*It may eventually be demonstrated that due to the method of spotting a certain spotter averages a certain amount short or long. This should be applied as a permanent correction to his ranges.
times exactly. The proportion is equally true for any kind of errors—vertical, lateral, radial, or absolute, made by projectiles fired under the existing or any chosen conditions. It is of course not true for wild, tumbling, accidental, or random shots, or for shots fired under conditions of a different kind.
There are a multitude of causes of error in gun fire, but whatever the separate mean errors due to the various causes may be, the most probable value of the combined mean error will be the square root of the sum of the squares of these separate mean errors (following the theory of errors) and the chance of hitting will be diminished according to the same theory as the final mean error is increased. This, it should be understood, is in the long run. One great dispersion may at times accomplish a hit where a short dispersion could not with the same mean point of impact (not the target) for the salvo, but it can work a miss equally well where a short dispersion would get two shots in the target.
A shot-gun is a weapon that fires a great number of projectiles in a short time. Anyone of these minor projectiles will suffice for the bird or object ordinarily fired at, and the endeavor is to cover the space in which the bird or object may be. There is no method of correction for successive shots, as it is not possible to determine by sight where most of the shots have gone. Two bodies moving in the same portion of space are the more apt to collide as their sizes or that of either is increased, and in the shot-gun the working size of the projectile, taking all with spaces as one projectile, is increased to a limit where it is considerably greater than that of the target. But if the desire were to hit the bird or object as often as possible with individual projectiles, and if hits could be noted on a larger target around such object, it is sufficiency apparent that a much greater number of hits could be gotten by successive shots with an accurate weapon than by the same number of projectiles fired from a shot-gun; as, for example, by the use of a gallery rifle at a mark on a target at shot-gun ranges. And do the best we can with gun and instruments, due to the outside influences such as fluctuations in atmospheric refraction, in strength of wind, in barometric pressure, with holes in the air, variations in temperature of charge and gun, varying vibratory droops or rises of gun-muzzle, varying spring or jump for different mounts or for the same mount with different training, varying uncompensated vertical angles of axis of elevation of gun, etc., there will always be relatively to a ship-target more than sufficient similarity to a shotgun dispersion with even our best salvos. If we are considering only one salvo or are not going to, or cannot, spot at all, and the range finder is not adjusted to the gun by a known mean correction for the range used and under the prevailing conditions, it would, without doubt, be better to waste a certain amount of ammunition by throwing in an intentional controllable dispersion by simply firing the guns with varying range settings covering the probable range error. This would simulate a good shot-gun, but if continued would make for very primitive target practice. It is a method adapted to an unlimited supply of ammunition and corresponding capacity of weapon to use it, and is especially available for small arms and with the battle conditions of land forces.
The line of advance for larger guns seems always to point in the direction of precision with men, instruments, implements and methods. Controllable dispersion has a value under certain circumstances, not inconsistent with precision in method. But great dispersions, if not worked according to a progressive system with sights set as regularly increasing increments and with guns fired in succession, put the spotter entirely in the air. In short, large gun errors make large spotter errors, and ships that are trying to make records choose every favorable condition, calm, clearness, uniform temperature of magazines, etc., with a view to reducing every mean error due to any of the numerous causes as much as possible, well knowing that their various poor scores have been due to a failure to overcome some one or more of these embarrassing conditions in the past. Errors, reduce them as we may, are altogether too large, and everything possible should be done to eliminate them. It is no more necessary to separate the spotter error from the gun error proper than it is to separate the refraction or other types of error, and with the accurate methods of recording now beginning, it may soon be practicable to differentiate the one as well as the others, down to a point where the spotter and the pointer and other persons involved with various causes of error could be intelligently marked as to qualification for the posts they thus occupy, as well, we might add, as could the accuracy of the gun unit itself, in the state at which it has at length arrived through increasing age and use.
LIEUT.-COMMANDER RIDLEY MCLEAN, U. S. Navy.—I find this a most difficult paper to discuss, on account of the fact that it arrives at no final conclusion, which has a practical bearing on gunnery training.
The paper, if read casually, especially by the many young officers in the service who have given the question little thought, might readily be construed into a mathematical demonstration that dispersion in gunnery was a good thing and that in practical gunnery training it was not necessary to reduce dispersion to the minimum limits possible.
If this academic discussion of the relation between fire control errors and dispersion errors is to have this effect, the paper is pernicious and inimical to practical gunnery training in the navy.
A popular novel a few years ago demonstrated that for certain reasons a certain number of fleas were good for a dog, but still the average dog, despite all possible care, has a sufficient number for the purpose; so also in practical gunnery, I feel that, strive as hard and as intelligently as we may, we shall always find that we have more dispersion than we want, and any treatise or paper, however correct may be its mathematics, which leads the service to regard dispersion with equanimity—in fact which leads us to regard dispersion in any other light than as the very greatest enemy to efficient gunnery—cannot but have a bad effect.
Lieutenant Long concludes that fire control errors must be reduced to the minimum possible, and states that then "it will be apparent at once whether dispersion is too small or too great to insure the greatest number of hits.”
Academically this statement is true; practically it is not true, because we can never arrive at a point where we can say that fire control errors have been reduced to the mathematical minimum. Fire control errors vary so much with the spotters, with the range finders, with the condition of spotting glasses, with atmospheric conditions, and with dispersion itself, that it seems utopian to state that we can ever arrive at such a state of training throughout the service as to justify us in stopping to consider whether or not our dispersion is too small.
This paper states that an examination of the Atlantic fleet records for 1911 and 1912 shows that, maintaining the same fire control errors, the hitting would have been increased by increasing the dispersion.
It is presumed that this statement is correct, yet it in no wise follows that dispersion ought to have been greater—it simply proves that fire control errors should have been less.
In deciding whether or not dispersion should ever be increased, let us not be led too far by purely mathematical deductions. Let us rather consider what we are striving to attain. The mathematics of the paper has merely demonstrated that for a given error in fire control, E, there must be a certain dispersion, D, to give the maximum number of hits, but as the paper itself states that all of our energies should be expended to reduce E to zero and when E becomes zero D must also become zero, it would follow that similar efforts should be made to reduce the dispersion error to a minimum.
So much for the mathematics involved. But let us consider an actual target, range 10,000 yards, salvos of seven 12-inch, 2850 f. s. shots being fired at it, and let us disregard all lateral errors and assume that in each salvo the dispersion between different shots is uniform. Certainly the maximum results can only be obtained when the shots are well bunched and when the center of impact coincides with the center of the target. A mean vertical dispersion of about 8 feet under such conditions, which would make the salvo cover a zone about 105 yards wide, would land all shots on a target 30 feet high. A mean vertical dispersion of 13feet, corresponding to a width of zone of about 16o yards would render four, the greatest possible number of hits. A mean dispersion of 26 feet vertically would result in only one hit if center of impact coincided with center of target, two hits if slightly displace done way or the other.
Two hits would thus be a maximum possible score with a mean dispersion of 26 feet, which corresponds to a zone about 312 yards wide; one hit is the maximum possible for any mean vertical dispersion in excess of 50 feet, which corresponds to a zone 625 yards wide.
Under these conditions it doesn't matter within the width of this zone where the target is, it will get one hit and no more, assuming the salvo is correctly aligned. With more than 50 feet mean vertical dispersion the target may be straddled, but you may or may not make a hit.
Now, it is perfectly true that when a material fire control error exists, dispersion is necessary to obtain a hit, which is-to say, that a perfectly bunched salvo which for any reason falls short or over, will make no hits at all, whereas if these shots were dispersed sufficiently one or possibly even two hits might be made; also it is perfectly true that with a considerable dispersion, fire control errors within the limits of that dispersion will not affect the score; but it is fallacious to use either of these facts as an argument in favor of dispersion, for the simple reason that gunnery training must be based on a system which leads to a high score, and a high score with any material dispersion is mathematically impossible.
If we remember that two hits on a 30 foot target is the maximum possible score when the shots are uniformly dispersed through a zone 300 yards wide (which at 10,000 yards range is not in any sense a wide dispersion), and one hit the maximum possible when the shots cover a zone 600 yards wide, and that neither one hit nor even two hits out of a salvo of seven shots can be considered sufficiently high a score to be considered a goal, it follows that every effort should be made to reduce dispersion to the smallest possible limit, and consequently we must reduce our fire control errors so that we can utilize the greatest accuracy of fire that it is possible for us to attain. Any other method is false training.
It may readily be shown that under certain conditions a greater number of hits would have been obtained by increasing the dispersion, but it can never be shown that a really high score could ever be obtained in that manner. Dispersion absolutely precludes a high average score, and though it may render a low average almost certain, it must be remembered that low averages won't win battles.
LIEUT.-COMMANDER T. T. CRAVEN, U. S. Navy.—In considering the question under discussion, which involves practical long range firing from a ship, one is impressed with the lack of accurate data on which to base conclusions.
The methods which have been in vogue for ascertaining the amounts by which the targets have been missed at target practice, together with the reliability of these data as a basis for precise argument, are probably well understood.
In his discussion of the "Accuracy and Probability of Gun Fire," page 134, Article 140, Exterior Ballistics, the late Professor Alger makes the following statements:
"Evidently the less the mean errors of a gun the more important it is to accurately regulate its fire; if the distance of the mean point of impact from the target is more than three times the mean error of the gun, there will be practically no hits at all.
"…Thus we see that a gun may be severely handicapped by its own accuracy if the range is not known with in 10 percent."
The truth of the opening statement contained in the first paragraph requires no elucidation. That in the second paragraph is shown to be correct in the deductions that precede it.
Lieutenant Schuyler aptly closes his well-written notes on this same subject in Volume 37, NO. 3, Whole No. 139, of the UNITED STATES NAVAL INSTITUTE PROCEEDINGS, with the statement that" … their importance seems to justify the systematic collection of data and further study."
We have seen the range constantly and rapidly increase within the last few years and this is primarily because the so-called fire control errors have been steadily reduced. The 10 per cent error considered by Professor Alger in 1904, when 5000 yards was thought to be a long range, would be regarded as excessive to-day at double that distance.
There has been a corresponding improvement in all of the methods of long range control and a decrease of the dispersions incident to materiel has also been accomplished.
The advances that have resulted in heavy guns becoming weapons of precision have permitted the successful control of fire at long range. Any improvement in the accuracy of the guns, which results in a further decrease in dispersion, will bring about a corresponding improvement in the facility of control afloat and an increase in hitting power.
The fact that the performance of the gun has directly to do with fire control, and perhaps the establishment of the range, must not be overlooked. While it is manifest that the errors of gun fire are due to a variety of causes, it is also evident that the fire control officer afloat has to deal with the summation of all the parts of which it is composed, i.e., the whole error.
A reduction in any one of the composing parts reduces the whole error and constant, systematic, and continued effort must be directed toward searching out and eliminating such of these parts as may be reduced or eliminated.
With accurate guns, dispersion can be regulated at will. Without accurate weapons as well as accurate instruments and methods of fire control accurate gunnery is impossible.
The author has, after a considerable discussion, arrived at the crux of his argument in the self-evident, well-understood conclusions that—
“In order to assist the spotter there must be the least possible dispersion," and "when everything possible has been done to reduce fire control errors, and dispersion has been kept as small as possible, target practice firing will show what range and deflection errors are obtained. These firings will also give the dispersion of salvos, and it will be apparent at once whether the dispersion is too small or too great to insure the greatest number of hits."
LIEUTENANT W. R. VAN AUKEN, U. S. Navy.—The article by Lieutenant Long on "Dispersion and Accuracy of Fire" is a most timely one. At present, ships are not getting the percentage of hits at long ranges which are, and must be expected. An Arkansas or Wyoming not hitting at long ranges is not to be feared by a Michigan whose guns are hitting. It is most important now to consider how to increase the hitting efficiency of new ships, for no type of battleship of the largest displacement and guns is superior to older ships in gun fire unless the weight of metal hitting is a fair percentage of that thrown from the firing ship on each broadside.
From results of firing where spotters have controlled the fire, it seems impossible to get the mean point of impact of salvos nearer than 150 yards to the center of danger space. In such salvos, the average mean dispersion was about 50 yards. Now, from a consideration of this article and that by Ensign Schuyler on "Dispersion in Salvos," published in September, 1911, it is granted to be true that the mean vertical dispersion to attain a maximum percentage of hits at any range or target should be equal to 4/5 or 80 per cent of the distance of the mean point of impact from the center of the danger space. If many salvos are fired, where there are vertical dispersion and fire control errors it is admitted this relation will hold true. In battle where an enemy's ship is 500 to 600 feet in length, lateral dispersion will cause few, if any, misses. In theory and practice, this mean lateral dispersion is about equal to the mean vertical dispersion at long ranges. Sounder battle conditions, only mean vertical dispersion need be considered. Hence with the existing fire control error of 150 yards, there should theoretically be about 120 yards mean dispersion to secure the maximum hits. As this is admitted to be at least twice the dispersion that exists now, it is seen that a large percentage of hits are lost.
Though at present, spotters have not materially reduced their errors in controlling salvos of reduced dispersion, the fact remains that we cannot afford to even consider an increase of dispersion beyond that which is brought about by natural and expected gun errors. As dispersion has been reduced somewhat, the fire control efficiency has not kept apace. The materiel seems to be ahead of the fire control training. This reduced dispersion has not as expected reduced the fire control errors.
After reading this article of Lieutenant Long's, one ought not to seriously consider making an increase in dispersion. We cannot afford to be satisfied with the present fire control errors and assume that no improvement can be made at long ranges—through training or by study of the science of gunnery. In bringing about a greater dispersion by any means and working for a scattered salvo in the hope of getting one or two hits by luck, we would convert our modern battery into a large "shot-gun" and sacrifice every- thing to pure luck. By all means we should seek for small dispersions and work for reduced errors in control of the fire at long ranges.
As regards the fire control error it is believed that its principal component is that due to spotting. This statement is based upon the average records of spotters at spotting practice compared with the fire control errors in actual battle practice. This spotting error can be decreased by systematic training and a study of the science of gunnery. It is believed that range finders combined with the spotting will halve the present fire control errors, and with this, a natural mean dispersion of 20 to 30 yards will about agree with the dispersion of theory.
Gun fire at long ranges is based on science, and now, more than ever, all ordnance officers should be conversant with the action of powder, ballistics, Probability of hitting and all elements bearing upon the trajectories of Projectiles fired at long range. These problems involved in long range control will require deep study and careful investigation. It would seem that a special gunnery ship could be assigned for this duty, and in addition to study carried on aboard, practical experiments could be made at various ranges in spotting, range finding and the limits of long range firing.
It is reasonable to expect that improvement can and will be made in the control of long range salvos. No hap hazard work will bring this about. What is needed is a calibration range, "Gunnery Experts" ship, target Practice conducted at long ranges by officers trained on the gunnery ship, a range finder experimental station, and a study of the science of gunnery.
LIEUTENANT G. L. SCHUYLER, U. S. Navy.—It is only comparatively recently that we have begun to awaken to the fact that in view of the impossibility of getting the center of impact on the center of the target, what hits we make are not in spite of dispersion, but by virtue of it. Lieutenant Long's excellent article about winds up the presentation of this side of the argument and it is hoped that familiarity with it and with Ordnance Pamphlet No. 410 will dispel some mistaken ideas on this matter which are only too prevalent in the service at large.
The dispersions now being less than the desired 8o per cent of the fire control errors, those who would further decrease dispersion before fire control errors are further decreased do so with a mathematical certainty that they will, on the average, fare worse than now.
There are in the service many officers who will ignore the entire argument because, on the face of it, it does not seem proper that the pointers who aim most carefully should be poorest rewarded in hitting. In a way, it almost offends our sense of right and wrong to see carelessness apparently rewarded. It should not be, we say. But sentimental reasons will not stand against mathematical ones.
For the benefit of those who would believe it if it all did not sound like such rank heresy and opposed to what they have grown to believe almost religiously, it should be stated that the idea is not at all novel in small arm fire at long ranges. Perhaps when they find it a perfectly established and well-recognized fact in small arm fire, they can begin, perhaps grudgingly, to admit there may be something in it after all.
"The Rifle in War," by Captain Eames, U.S.A., is interesting reading in this connection and it is instructive to read of what is called the "combined sight." This means, usually, that the front rank and rear rank set sights at different ranges to increase dispersion, to make it bear a more favorable relation to the probable error in estimating the range of the object. When the dispersion is properly increased more hits are expected. When we get to know of this principle in small arm fire, maybe we can with less distrust listen to those who claim it is just the same with naval guns.