1. It is believed that the usual estimate attaches to accuracy of pointing at long range an importance which a closer study will show to be unwarranted.
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5. Before we can progress very far towards convincing anyone, a reasonable explanation must be offered to show how it can be possible for the opinion on the value of excellence in pointing at long ranges to be considerably in error. It would be absurd to claim to see truths which had completely escaped the notice of all others. It is not quite so unreasonable, however, to argue that at short ranges where modern gunnery developed, excellence in pointing had a predominating effect and one which was universally appreciated, but that in long-range firing one passes to a set of conditions where excellence in pointing has a materially reduced effect, and that the full meaning of these changes is not instantly appreciated.
6. At short ranges, under normal and usual conditions, the closer the pointer comes to firing when steady on the "bull" the better his percentage of hits. At short ranges in addition to being able to fire rapidly, the main requirement is good pointing.
7. While it sounds plausible until the matter is thoroughly gone into, it is only the most superficial view which regards long-range firing as being "practically like short-range firing, except that the target being further off, it requires giving more attention to good pointing." In reality, long-range firing is so unlike short-range firing that the statement quoted above is just about the last that should be made. Let us study these differences.
8. At battle ranges, with a danger space on the order of 50 to 100 yards, there is in general (and we do not hesitate to say normally), a fire-control error of several hundred yards in regulating the sight bar range. How often are hits possible? This one question and its complete answer comprise the whole theory of long-range naval gunnery, and unless we are clear in the matter, we work in the dark.
9. We hit because we have a certain amount of dispersion, not in spite of the fact that some dispersion exists. For, with the center of a salvo several hundred yards off the target, zero dispersion means zero hits just as surely as infinite dispersion does. Most hits come when the dispersion is 4/5 of the fire-control error. All this is relatively new, having been first published in 1911.
10. Acceptance of this idea has been slow. Some suspected that the expenditure of an equal amount of mathematical ingenuity would disclose a fallacy in it all, and rather looked for this to be done in case the matter were not too soon forgotten. Others considered it a paradox, the general knowledge of which would tend to furnish all concerned in gunnery with an excuse for being less painstaking. Hence to them it was something to be suppressed or ignored. "Fire when steady on the bull," and "make the pattern small," are admittedly good practical things to tell the pointer. But possibly we can, at the expense of a little easily spared accuracy of pointing, get a bit more speed out of him without exactly telling him everything we know. There are many arguments against taking everyone into our confidence. There is no reason for shutting our eyes to the real effect of having some dispersion in long-range firing.
11. Enough has been said to show some ways in which long-range firing differs essentially from that of short ranges. * * *
12. Understanding the effects of having dispersion, its causes have been studied and its nature investigated. Lately we have come more and more to thinking of the salvo as a whole. Often there are a dozen shots in a salvo and no way of telling which is which. So, borrowing the term from small arms, we speak of the "pattern" of a salvo, or the area within the limits of which all the shots strike. The idea in gunnery at long ranges is to superpose the salvo pattern over the target's danger space—then to fire as many shots as we can. Possibly the target happens to be in a gap in the pattern—and it is missed. But the next salvo may bring two hits. Percentages work out right in the end, and if we take care of the location of the limits of the pattern, the hits will take care of themselves.
13. What differences we can expect in individual cases between actual performances and what the law of probability indicates is a complicated subject, which has not yet been thoroughly developed mathematically. Experience shows, however, that though at times irregular, the patterns follow the theoretical distribution of shots so closely as to make it purposeless to attempt the individual analysis of the shots within their limits. Changing the mean dispersion changes the pattern size in the same ratio. Mean dispersion is the quantity easier dealt with mathematically, but we can at any time interconvert the two quantities by the following relation very recently published.
No. of Shots in Salvo | Ratio of Pattern Size to Mean Dispersion |
3 | 2.43 |
4 | 2.74 |
5 | 3.21 |
6 | 3.47 |
7 | 3.67 |
8 | 3.85 |
9 | 4.00 |
10 | 4.13 |
11 | 4.24 |
12 | 4.34 |
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14. Taking up in detail the most generally imagined causes of dispersion, it is helpful to consider how largely each may enter into the total effect.
(a) Velocity Differences Between Different Rounds.—At the P. G. where velocities are measured each round during ranging, it is easy to make range corrections which reduce the ranging to what it would be with a perfect powder. This makes a negligible improvement in dispersions. Powder used on shipboard is admittedly not perfect, but a definite knowledge of the amount of its average irregularity shows that the range differences introduced from this cause are not of an order of magnitude sufficient to begin to explain the dispersions noted in firing.
(b) Differences Between the Various Guns and Mounts in the Battery.—Perfection is unattainable and is not claimed in the way of having all guns droop exactly the same amount, and of having all gun platforms in firing, yield elastically in an identical fashion. But it is a matter of common knowledge that calibration results do not show up differences which would begin to explain the size of usual patterns on the basis of the guns systematically shooting differently.
(c) Guns Differently Laid.—Differences in laying the guns would make vertical errors proportional to the range. Actual vertical dispersions vary as a higher power than the first, thus arguing against dispersion being very closely related to this cause. (The same argument is also applicable in the paragraph (b) preceding.)
The mean dispersion in the whole salvo does not greatly exceed that of a single gun. It would if these guns were very differently laid. Checking the sights most carefully, or even firing by the director system to insure that the guns are laid alike does not, as is commonly expected, insure any appreciable reduction in the size of the pattern. At long ranges, to explain 500 yards in the pattern by aiming differences, one must imagine guns laid differently by over half a degree, or by a greater angle than the sun's disk subtends.
(d) Differences in Atmospheric Conditions in Flight.—An examination of the columns of the range table shows that it would take variations in atmospheric conditions beyond all reason to explain the range difference noted in the usual pattern. Fired together in a salvo, differences in atmospheric conditions between the different projectiles are too largely eliminated to be considered as a possible explanation of having the ordinary amount of dispersion.
15. Leaving speculation to others and studying simply to matters of the practical use of our present ordnance, all that remains to be said is that the major part of long-range dispersion must arise from misbehavior of the projectiles commencing at a time in their flight when there is no longer anything we can do for them. We are now ready to consider the minor part of long-range dispersion due to inaccuracies in pointing. If at a given range there is an aiming error of ±a feet on the vertical screen, while natural dispersion similarly measured amounts to ±b feet, then the dispersion which finally results is √(a2 + b2), or ±c feet. A good way to consider it is to think of a right triangle with the two sides of very unequal lengths. The very long side b is the natural dispersion, the very short side a is the mean error introduced by inaccuracies in aiming, hypotenuse c is then the total dispersion finally obtained as the result of the natural dispersion ±b, and the mean aiming error ±a. In such a very acute angled triangle the hypotenuse approaches the length of the longer side differing from it by less than a2/2b.
16. If, therefore, we introduce a mean aiming error equal to say 20% of the natural dispersion, it causes an increase in the dispersion not of 20% by any means, but of something less than ½ x 20% x 20%, or less than 2%. The percentage of hits is possibly even less affected and may even in many cases be increased.
17. As an illustrative example, consider a 12-gun ship firing 14-inch salvos at 18,000 yards at a ship of 20 feet free-board and 84 feet beam. With the two ships abeam of one another, this make a 49-yard danger space, or the equivalent of a vertical target 46.5 feet high. Let us say that the target is straddled by a salvo the normal pattern of which at this range is 1000 yards, the first shot being about 300 yards short and the last one about 700 yards over. The center of the impact is 175 yards from the center of the danger space, or is 167 feet too high on the vertical plane of the target.
18. Firing a little "on the fly" is the equivalent of being steady on a point somewhat further off in the direction that the cross-lines are moving, so the aiming errors we mention of plus or minus so many feet may be considered as including also inaccuracies due to not being quite steady. Let us assume quite arbitrarily, 3 classes of pointers and see how they would compare in final results. If pointers are assumed, who at 1800 yards made mean aiming errors of ±0, ±3, and ±6 feet on the vertical screen, they will at 18,000 yards make mean aiming errors of ±0, ±30, and ±60 feet. These classes of pointers may be designated for convenience as A, B, and C.
19. The 1000-yard pattern works out to a ± 230-yard mean dispersion, using the method of paragraph 13. This is equal to ±218 feet on the vertical screen, from which by the usual methods we have the following comparative showings:
? | Pattern size | Mean dispersion in range | Mean dispersion vertically | Per cent of hits |
Class A | 1000 yds. | ±230 yds. | ±218 ft. | 5.70% |
Class B | 1010 yds. | ±232 yds. | ±220 ft. | 5.65% |
Class C | 1062 yds. | ±239 yds. | ±226 ft. | 5.60% |
It will be seen how little the quality of the pointing enters into the percentage of hits. In such firing, all the work necessary to train this poorest class of pointers up to perfection would give only about one more hit in 57 hits, or only one more hit per 1000 rounds fired under these conditions.
20. We will carefully refrain from saying whether we consider the various arbitrarily assumed classes of pointers good, bad, or indifferent, or whether a 1000-yard pattern at this range is too large or too small. One should assume values to his own liking, work out several examples similarly, and then consider whether or not it is necessary to alter his previous estimate of the value of accuracy of pointing in long range naval gunnery.