The Mean Point of Impact.
By Rear-Admiral Bradley A. Fiske, U.S. Navy
If a salvo were fired from a battleship in a modern navy at a target 10,000 yards distant, the mean vertical deviation of a 12-inch long-pointed projectile of say 2400 f. s. would be between 20 and 30 feet, and the mean deviation in range between forty-seven (47) and seventy (70) yards, depending on the degree of excellence of her gun pointers.
Assuming the three cases of a mean vertical deviation of 20 feet, 25 feet and 30 feet, respectively, and a target 30 feet high, the probability of hitting is shown in the following table. Four cases are considered: one case assumes the mean point of impact to be on the center of the target, another case assumes the mean point of impact to be 50 yards short or over; another case assumes it to be 100 yards short or over, and the other assumes it to be 150 yards short or over.
Mean vertical deviation Mean point on center of target Mean point 50 yard short or over Mean point 100 yards short or over Mean point 150 yards short or over
20 feet Prob. 45% Prob. 33% Prob. 12 ½% Prob. 2 1/3%
25 feet Prob. 36.8% Prob. 29.8% Prob. 16% Prob. 5.7%
30 feet Prob. 31% Prob. 27% Prob. 17% Prob. 8.2%
To get a cleat idea of the meaning of this table let us imagine two hostile fleets meeting in battle, fleets otherwise equal and having gun pointers of equal skill, but one fleet, A, having a means of getting the sight bar range at 10,000 yards with an average error of only 50 yards (no matter what the means might be), while the other fleet, B, had a means whereby the error was 100 yards. In this case, if the gun pointers were well trained and the weather good, the mean vertical deviation would be only about 20 feet, and A would hit B two and a half times as often as B would hit A. Or if A had a means by which its sight bar range was 100 yards wrong, while B's was 150 yards wrong, A would hit B five times as often as B would hit A. Or if A had a system whereby he got the sight bar range with an error of 50 yards, while B's error was 150 yards, A would hit B 12 ½ times as often as B would hit A.
Inasmuch as to find the range at 10,000 yards with an error of only 150 yards is a distinct problem, and inasmuch as the conditions of the atmosphere and the temperature of the magazines cause the range of projectiles to vary considerably at any given elevation, and inasmuch as, if the mean point of impact be near the center of the target, it is obviously desirable to have the dispersion as small as possible, it would seem that the problem of hitting a distant target at sea is divided into three very well defined parts: first, to find the sight bar range, in order to ascertain how to put the mean point of impact as close as possible to the center of the target; second, to direct and control the fire, and third, to make the dispersion as small as possible.
The first part naturally divides itself into two parts also: first, to find the correct range; second, to ascertain the corrections due to atmospheric and temperature conditions, so that if this correct range be given to the gun pointers the mean point of impact will be near the center of the target. The second and third parts of the problem are, of course, matters of fire control and training of gun pointers.
In June, 1909, the writer published in the NAVAL INSTITUTE PROCEEDINGS an article called "The Sight Bar Range," which contained the following sentences. The range-finders mentioned were Barr and Stroud range-finders of 54-inches base.
There are two ways of finding the sight bar range; one is by correcting a previous sight bar range by spotting from aloft, and the other is by measuring the range directly with range-finders.
If either method be used, it is first necessary to calibrate all the guns. If the spotting method be used, all guns of each caliber must be calibrated with a standard gun of that caliber; if the range-finder method be used, each gun must be calibrated with the range-finder that is to get its sight bar range.
On October 9, 1908, the Tennessee and the Washington, being then 2040 yards apart, steered courses diverging three points, by order of the commander of the second division, for half an hour, and then converged three points, taking simultaneous reciprocal range measurements every five minutes, each having first held up her "corrector" for the range-finder of the other ship. Then each telegraphed her measurements to the other ship.
The wind that day was marked in the log as 3 to 4, and the sea as "moderate." The speed was 11 knots and the wind was on the starboard bow. The conditions for range-finder work at sea seemed average, except the rate of change of range, which was much greater than would probably occur in battle, being 162 yards per minute.
There were 13 observations varying between 2040 yards and 7300 yards. The average disagreement between the range-finders was 33 yards, and the square root of the average of the squares of the ranges was 4874 yards. That is, the disagreement between the two range-finders was 33 yards at 4874 yards.
It is mathematically probable that the true ranges were somewhere between the measurements given by the two range-finders; that is, that the average error of the two range-finders was probably 16 ½ yards at 4874 yards; which is 25 yards at 6000 yards.
It may be objected that the true range may not have been between the readings of the two range-finders, because both range-finders may have read either over or short. This, of course, is true; but if so, the reason was simply that the marks on the "correctors," which were made on board the Tennessee, may not have been placed at exactly the right distance apart; but this would be an error wholly remediable, because the Washington Navy Yard could easily make correct correctors.
However, I had the accuracy of our corrector tested at a known range, when the ship anchored at Panama, by sending our corrector on board the Weft Virginia, correcting both our range-finders by it, and immediately thereafter taking twenty measurements of the distance of the cathedral with each range-finder.
Mr. Russell took these observations, and the mean of twenty observations with the Barr and Stroud range-finder No. 883 was 6949 yards; and with range-finder No. 882 was 6956 yards. The average disagreement of the readings of range-finder No. 883, with its own mean, was n.8 yards; of range-finder No. 882, was 14.9 yards. The range of the cathedral, as measured from the chart, our position being plotted with the utmost care, was 6925 yards. Mr. Russell took every precaution against self-deception, being honestly anxious to ascertain the truth.
The difference between 6925 yards and 6956 yards is 31 yards; and the error corresponding to 31 yards at 6925 yards is 231/2 yards at 6000 yards.
The writer feels justified in concluding therefore that, with an amount of training no greater than that given a gun-pointer, the error of the range-finder method, used at sea under average conditions, may be assumed to be about 25 yards at 6000 yards.
This takes no account of the fact that the range-finder is an instrument that can be improved, and that one can practice with it a great deal at sea.
Thus far, no mention has been made of any factor except accuracy.
Therefore, it may be objected that, even if it be granted that the range-finder method is the more accurate when no guns are firing, yet the range-finder itself is liable to be jarred out of adjustment by the shock of gun-fire.
To this may be replied that—
(a) The turret range-finder mounted on top of the turret of the Arkansas now the Ozark was not jarred out of adjustment when five 12-inch shots were fired, on April 15, 1007.
(b) The range-finder of the Tennessee was not jarred out of adjustment at her battle practice in November, 1908. Of course, the shrouds and stays of the lower mast and topmast were up taut and the pedestal of the range-finder was carefully stayed.
(c) It is easy to make a range-finder so strong, mechanically, that it could not possibly be jarred out of adjustment.
It may also be objected that the vibration of ship during gun-fire is so great that no observer could possibly get range-finder readings.
To this it may be replied that there must be occasional "cease firings." in order to ascertain the range, no matter what method be employed. When using the spotting method it is necessary to wait after each turret shot or salvo until the splash is seen before any correction can be made to the last sight bar range, say 10 seconds; similarly when using the rangefinder method a new measurement can be begun in less than five seconds after the discharge, and completed in five seconds more—under average conditions. This ten seconds is not time lost, in either case, because during this time the guns are being loaded.
Postscript.
Since this article was mailed to the Naval Institute it has been pointed out that the article may be construed as advocating the abolition of spotting. The article does not advocate the abolition of spotting.
The writer believes in spotting; that is, in having observers above the smoke, who tell, from the fall of the projectiles, whether the range used was too small or too great.
He believes, however, that spotting should be auxiliary to range finding; not that range finding should be auxiliary to spotting.
It seems to him that the principal role of spotting is simply that of raising or lowering the mean point of impact, by correcting for some actual change of I. V. of the index of powder being used, if it occurs; or some change in the "coincidence adjustment" of the range-finder, if it occurs; or for both.
So why not use spotting simply to regulate the coincidence adjustment of the range-finder (or range-finders) and raise or lower the mean point of impact in this way? This can be done by a simple mechanical device.
The danger of depending upon spotting alone may be seen when we recognize the fact that, if the enemy has good range-finders, and if the enemy's admiral, after the fleets are drawn up in parallel columns, will carry out the well-known "follow my leader" tactics, changing the course of the leader back and forth, say one point each side of the middle course, he will change the range irregularly and frequently, back and forth, about 93 yards a minute; the fleet speed being here supposed to be 15 knots.
The gradual changes of course and distance will not bother the enemy's range-finders, so they can keep our range all the time; but on our lofty and exposed fire-control platforms, our armies of spotters, change-of-range projector-men, and telephonists will not be able to find and transmit correctly the sight bar range.
Since this article appeared the writer has heard many arguments among officers on the subject of getting the mean point of impact on the target; the minority contending that the range-finder offers such a promising means that we should do our utmost to get good range-finders, to mount them on pedestals as short as possible, on as firm foundations as possible, with covers to protect them from the wind, and that we should train a body of range-finder observers at least as carefully as we train gun captains; the majority standing firm on the platform that it is useless to work along this line, because "practical tests in the fleet" have conclusively proved that the range-finder is inaccurate and unreliable.
Other navies, especially the British and the German, have a greater respect for the range-finder than we have. This was to be expected of the British, because the Barr and Stroud range-finder is a British product, and the British Navy made exhaustive tests of that instrument many years ago. But the Germans seem to have stolen a march on everybody and to have solved scientifically and practically the whole problem of placing the mean point of impact on the target. If our information is correct they have already devised and adopted a method of applying the necessary temperature and weather conditions to the range tables, and have already actually built range-finders of long base into their turrets, where they are protected not only from gun fire, but from the wind, and where they can be given a mounting very firm vertically, but leaving the instrument free from bending forces horizontally, thus almost eliminating the effects of the vibration of the ship and the shock of gun fire.
If our information is correct (and it probably is) the Germans have employed their marvelous ability in applying the principles of science to practical affairs (which is the most potent single cause of their pre-eminence in all departments of endeavor, which ability is developed in their leaders to the point of genius)—they have employed this ability to increase the fighting power of their fleet by a means as efficacious as the increase in the number of the ships.
Our attitude towards the range-finder is freely disclosed in the Navy Register, which is not a confidential publication, but is sent everywhere. The Navy Register shows by the ratings given to men, and the extra pay allowed for various services, the values which we attach to various positions and duties. There is not one word said about range-finder observers, and yet practically every other specialty in a ship is recognized. Besides the various ratings themselves we have over a dozen positions in which special remuneration is awarded; which practically states to every navy the fact that we attach no importance whatever to range finding.
Yet there is no work in a ship which requires greater skill than that of range finding; in fact, it may be truthfully asserted that more special and personal skill is required to do range finding under difficult conditions than to do any other work on board ship. Not only is this work difficult, but it is exceedingly important. It is to be exercised in the most critical time that a naval officer can imagine—the opening of a battle—in those few pregnant moments that decide which fleet is to secure the initial advantage—almost the same thing as victory.
Yet our Navy Register shows that we attach less importance to the man who is to get us the opening range in battle than to a coxswain of a steam launch, captain of the hold, jack-o'-the-dust or tailor's helper.
One result of our attitude is the well-known fact that we have not a single trained range-finder observer in the navy. Another result is that we thoughtlessly mount our range-finders on flimsy supports, where they vibrate tremendously, and are literally "shaken with the wind."
Another result is that we have allowed another navy to get ahead of us in a matter which involves victory or defeat in battle, and in which we took the lead five years ago.
A peculiar phase of the situation is the small amount of training needed in order to get fairly good results. During the past year the writer has caused the Barr and Stroud range-finders of the Fifth and Third Divisions to be used whenever occasion offered; and in all cases the instrument has seemed to respond gratefully to good care and skilful handling.
On June 30, 1912, while at anchor at Key West, I directed Lieutenant (j. g.) Frank Russell and Ensign Leslie L. Jordan, who had had a fair amount of experience with the range-finder, to take a series of ten readings each of the distance of the Sand Key Light House. The range-finder (i5-foot base) had not been corrected for two or three weeks, and we did not know the exact distance of the light house, but these readings would show how closely the range-finder would repeat. The mean of Mr. Jordan's readings was 10,746 yards, and the mean of the variations of his readings from 10,746 yards was 39.7 yards. The mean of Mr. Russell's readings was 10,743 yards, and the mean of his variations was 29.1 yards. In all cases Mr. Russell and Mr. Jordan made the optical contact without knowing the reading of the scale, and then read the scale.
Mr. Russell then took ten readings of an uncharted smoke-stack. The mean of his readings was 12,020 yards, and the mean variation of his readings from 12,020 yards was 30 yards.
As this was extremely good, I determined to ascertain the degree of accuracy of the range-finder at the first opportunity.
On July 3 I had the position of the Georgia very carefully plotted. The distance of the lighthouse from the position of the range-finder was measured on the chart as carefully as possible and found to be 11,050 yards.
I then directed the New Jersey to hold up her corrector board to the Georgia, and directed the Georgia to adjust the 15-foot range-finder on the forward turret by the New Jersey's board. This was done, but as soon as it was done the ship swung so that the range-finder would not bear on the lighthouse.
The next forenoon, however, the ship swung back to her former position, and Mr. Russell took the following ten readings:
No. Readings Variation from Mean Variation from Range by Chart
1 11,025 5 25
2 10,975 45 75
3 11,000 30 50
4 11,050 20 0
5 11,050 20 0
6 11,025 5 25
7 11,050 20 0
8 11,025 5 25
9 11,075 45 25
10 11,025 5 25
110,300 200 250
Mean 11,030 20 25
Half an hour later Mr. Jordan took the following ten readings:
No. Readings Variation from Mean Variation from Range by Chart
1 11,075 17 25
2 11,100 42 50
3 11,025 33 25
4 11,050 8 0
5 11,105 47 55
6 11,050 8 0
7 10,995 63 55
8 11,100 42 50
9 11,005 53 45
10 11,075 17 25
110,580 330 330
Mean 11,058 33 33
The conditions under which these observations were made were better than the average; the atmosphere was fairly clear, there was not enough wind to shake the instrument, and the ship was steady. Yet, it must be distinctly comprehended, these conditions did not increase the accuracy of the range-finder; they merely permitted accuracy to be obtained without requiring a very high degree of skill from the observer.
The tests made in the Georgia supply a curious and gratifying verification of the results obtained in the Tennessee. To say that the results obtained in the Tennessee as published in the INSTITUTE PROCEEDINGS were received with incredulity would be to put the matter mildly; but nevertheless they were correct. In the article published in the INSTITUTE PROCEEDINGS the conclusion was, "With an amount of training no greater than that given to a gun pointer the error of the range-finder method used at sea under average conditions may be assumed to be about 25 yards at 6000." Now this was with a 54-inch range-finder. With that range-finder the error at 11,000 yards would have been 25 multiplied by 112 divided by 62, or 84 yards, supposing the atmosphere to be perfectly clear in both cases. With a similar range-finder having a 15-foot or 180-inch base the error at 11,000 yards would have been 84 multiplied by 54 divided by 180, or 25.2 yards.
If it be granted that these tests prove that the range-finder itself is accurate, and that, if properly handled under favorable conditions, excellent results will be obtained, it remains simply to recognize the fact that unfavorable conditions, such as vibration, wind and relative movement between target and range-finder, do not, and cannot, alter the accuracy of the range-finder as an instrument. They merely make it necessary for the observer to be skilful. This seems to mean that we ought to mount range-finders properly, and to train observers, so that under difficult circumstances we shall be able to take advantage of all the accuracy of which the instrument is capable, shorten the time of getting the mean point of impact on the target, and keep it as close to the center of the target as possible.