The problem of target measurements has been the subject of much discussion in friendly debates since the early days of competitive ammunition tests. Apparently, everyone has his own, or someone’s else idea as to what should be the governing factors for determining the winner of ammunition tests, and, if he has sufficient perseverance, he eventually gets his ideas incorporated in the specifications governing these tests, even though the new thought may live but for one year.
From a historical standpoint this is indeed unfortunate, as it makes it almost impossible to draw an accurate comparison of the ammunition test records made from year to year and it does not allow a clear picture to be shown of the progress that is being made by the large cartridge manufacturers and Frankford Arsenal in the matter of perfecting the accuracy of ammunitions.
For instance—In the ammunition tests held at Sea Girt in 1913 for the selection of ammunition for the International Matches, the Winchester Repeating Arms Company was victorious in the three hundred meter contest by virtue of an average mean radius of 1.761 inches for ten ten-shot targets. In 1920 the Remington Arms Company won the Olympic six hundred yard ammunition contest with an average mean radius of 3.41 inches for thirty ten-shot targets. In 1923 Remington Arms Company ammunition won the International three hundred meter contest with a figure of merit of 2.80593 and in 1924 this company repeated with a figure of merit of 2.179. However, in this last case, the firing range was reduced to three hundred yards. What is the comparison between a mean radius at three hundred meters, a mean radius at six hundred yards, a figure of merit at three hundred meters and a figure of merit at three hundred yards? Now to make a hard problem, mix in a few mean errors, vertical errors and mean deviations for good measure.
As no one else seems willing to bother with the small details necessary to unravel this mystery, it falls upon the Ordnance Department to compile the records of ammunition tests and show, if possible, the progress that has been made.
For the one thousand yard Palma contest, this is comparatively an easy job as fortunately in all but one year the winner of this test was selected from the ammunition having the smallest average mean radius. The exception to this was in 1921, in which year the Board specified in the program that “targets will be judged by the ‘mean error’ instead of the mean radius as formerly. The mean error is the mean of the extreme vertical deviation and the mean vertical deviation. The mean radius may be taken for information but in view of the slow rate of fire will not be considered in the test, etc. Thanks to some lover of history, the mean radius was recorded by the Board, thereby enabling the 1921 test to be compared with tests conducted in other years.
In 1921 the battle of mean radius versus mean error reached its peak and the advocates of each system hurled round upon round of carefully prepared dissertations at each other. These arguments were not careless expressions of opinions, but rather conclusions reached after careful and lengthy studies which even reached into trigometric functions and idiosyncrasies of the elements. All of which disproves the axiom that “great minds run in the same channel.”
The most note worthy of these theses received by the Board came from Mr. Jarvis Williams, Vice-President of the Remington Arms Company, and exponent of the “mean radius,” and Major K. K. V. Casey, Director of Sales of the du Pont de Nemours Company, who, I believe, is the author of “mean error” system of target measurements.
In defending the mean radius system, Mr. Williams advanced the following arguments:
“With regard to the method of measurement, we have given a good deal of study to this matter during the past year and believe that the so-called ‘mean error’ determined upon by your Board is fundamentally wrong as a measurement of accuracy. The elimination of consideration of the horizontal dispersion of the shots prevents any weight being given to one of the most important, if not the most important characteristic of the ammunition, and one in which the rifleman is most vitally interested, namely, the wind-jamming qualities of the bullet. The principle natural causes of the dispersion of ammunition fired under uniform conditions are:
- Variations in velocity.
- Variations in whip or jump of barrel caused by variations in barrel time.
- Effect of wind.
- Mechanical inaccuracy in the construction of the bullet itself.
”Causes (a) and (b) usually result in vertical dispersion. Cause (c), the effect of the wind, usually results in horizontal dispersion, but if the wind is blowing more or less up or down the range, it also has considerable effect upon the vertical dispersion. Cause (d) is the most important one of all, in that it is most likely to produce the greatest dispersion, and dispersion from this cause may be either vertical or horizontal or a combination of both. This can be easily demonstrated mathematically, and because of the chance that an unbalanced bullet may have an absolute horizontal dispersion with no vertical dispersion, or an absolute vertical dispersion with no horizontal dispersion, or a combination of both, it seems to us that some form of target measurement should be used which takes into account this most important factor. ‘Mean radius’ does this; in fact, it takes into account dispersion in any direction from the center of impact, and we believe it to be the true figure of merit for the accuracy of any ammunition. Its one objection, that it takes into account horizontal dispersion by the wind, is most certainly offset by the fact that it is vitally important that the effect of the wind on a bullet be as small as possible, and, if thought advisable, the effect of variations in the wind blowing at the time the test is made can be reduced to a minimum, as in the past, by increasing the rate of fire.”
“Giving the same weight to the extreme vertical dispersion as to the mean vertical deviation, we feel is also fundamentally wrong as a measurement of accuracy in that the two extreme shots are given double the weight of the balance of the shots on the target. The figure that the rifleman is most vitally interested in, and which probably most accurately represents the real measurement of accuracy, is what is known as the ‘probable error;’ in other words, the probable dispersion of any individual shot from the point of aim. It can be mathematically demonstrated that the ‘probable error’ of any individual shot is directly proportional to the average error of a large number of shots. The average error is, of course, identical with the term ‘mean radius,’ which we ordinarily use, and if the ‘mean radius’ is directly proportional to the probably error, it follows that in itself it constitutes a system of measurement which fairly represents the comparative accuracy of various lots of ammunition tested under similar conditions.”
Mr. Williams recalled a most interesting experiment performed by the Remington Arms Company in 1921 which bears out bis contentions that mechanical inaccuracy in the construction of the bullet is of vital importance and mostly likely productive of the greatest dispersion. In this experiment bullets were purposely unbalanced by drilling a small hole in the base near one edge. By properly marking the cartridge to indicate the position of this hole and qualifying to the same position when the cartridges were inserted in the chamber of the rifle, they were able to produce a ten shot group approximately two inches in diameter at 100 yards. When, however, the cartridges were not qualified, but were put in the chamber in a “hit or miss” fashion, the shots were dispersed around the periphery of the circle approximately sixteen inches in diameter. In other words they made a practical demonstration of the fact that it is entirely a matter of chance as to whether the dispersion from an unbalanced bullet is vertical or horizontal, or a combination of both.
A practical and technical discussion of the so-called “x and y errors” can be found in Dr. F. W. Mann’s book, “The Bullet’s Flight from Powder to Target” (Part 3, pages 350-358 inc.).
Now getting back to the other side of the fence, we discover Major Casey focusing his “scope on Mr. Williams” one thousand yard group. After adjusting his machine rest, firing a few warming up shots, he comes back with the following:
“On the subject of measurement, it has been my own observation that in long range firing. eliminating wind, the greatest expected error is the vertical, in other words that there is nothing that vertical error will not show that the horizontal error shows. As to the question of giving too much value to the extreme, I might bring out the point that it is the extreme shot that leads the rifleman astray, it usually being the case that after one shot going wild in a vertical direction, it takes the rifleman from three to five shots before he will find himself and be able to make satisfactory progress with the score. It is well enough for the manufacturer or experimentor to talk about the ‘probable error’ but ‘probable error’ does not enter in the category of the rifleman. What interests him is actual error and that actual error occurs in the sequence of shots not from any established mean but from the center of the bull’s-eye. If the individual rifleman were able to place his center of impact coincident with the center of the bull’s-eye, he might then consider ‘probable error’ but unfortunately there is no way for him to do so. It is because of the great danger to the rifleman of the uncertain elements caused by a high or low shot that has resulted in so much agitation on the desirability of using unstraightened barrels.
“On the effect of wind, I might bring out that the vertical group is influenced by variations in the wind but to a very much less extent than the horizontal, but to this extent it will show in the case of a head or rear wind the relative ‘wind bucking’ qualities of different types of ammunition.
“From a practical rifleman’s standpoint, he gives very little consideration to the effect of head or rear winds from 600 yards down unless they are combined with other atmospheric conditions to influence elevation. But at 800, 900 and 1000 yards the rifleman will use a ‘rule of thumb’ method about as follows: That a wind of a certain velocity will have one-eighth the effect on elevation for a direct head or rear wind, that a direct cross wind of the same velocity would have in a horizontal direction at 900 yards one-sixth, at 1000 yards one-fourth. The figures given in the ‘blue book’ as to the effect in inches of a ten mile head and rear wind, as also the effect in inches of a ten mile cross wind will bear this out.”
Of course the practical rifleman does not use these exact figures. The ‘rule of thumb’ for cross winds is practically the number of hundreds of yards multiplied by the number of miles of wind per hour, divided by ten, which then gives him the amount of correction he will use on his wind gauge in one-quarter points. Any variation in either a 3 or 9 o’clock wind will be compensated for by using Captain Zalinski’s table of deviating components which are really the nearest fraction to the cosine of the angle. If a rifleman is shooting at one thousand yards and the wind is blowing ten miles an hour from 1.30 o’clock, he will, therefore, use a correction which works out miles per hour (10) multiplied by number of hundred of yards (10), equals 100, divided by 10 equals ten quarter points which applying the table of deviating components is then cut to three quarters resulting in a wind allowance of seven quarter points or one and three-quarter points. The effect of that same wind from the same direction on elevation would be two minutes of angle cut to three quarters or a correction of one and one-half minutes of angle. That is as far as the rifleman can apply the principles. Now to show the effect of a switch of this wind. If the wind were to switch from 1.30 to 3 o’clock, the rifleman would promptly have to increase his wind allowance by an additional three-quarters points or thirty inches, his total allowance then being 100 inches whereas were the wind to shift from 1.30 to 12 o’clock, the rifleman would make a change in his elevation of one-half minute of angle or 5 inches, his total allowance then being twenty inches.
”When the wind switches from 1.30 to 3 o’clock compelling the rifleman to increase his wind allowance it also causes him to decrease his elevation by fifteen inches.
“When the wind switches from 1.30 to 12 o’clock the rifleman increases his elevation by five inches but has to decrease his ‘wind allowance’ by seventy inches.
“This proves that elevation is influenced more by changes in the direction of wind between 10.30 and 7.30 or 1.30 and 4.30 than it is between 10.30 and 1.30, or 4.30 and 7.30. ”Inversely the same applies to the horizontal effect but to a much greater extent.
“Of course the figures used by the practical rifleman are only approximate as exact figures would vary with different makes of ammunition. especially in regard to their ‘wind bucking’ qualities. For instance: the rifleman might be able to ignore entirely the effect of a slight change of wind as far as his elevation is concerned but he could not ignore the effect of the same wind on the horizontal deviation, even assuming that the ammunition he was using had greatly superior ‘wind bucking’ qualities of any bullet of any ammunition developed to date. The ‘wind bucking’ qualities of any bullet of any ammunition are in reality a direct result of the time of flight or in other words the time in which that bullet is travelling through a moving body, (in this case the air) slightly compensated by inertia. This naturally throws the advantage to the heavier bullet. Other things being equal ( that is if the time of flight of two bullets is identical at any certain distance) the heavier bullet will have the slight advantage over a lighter one by reason of inertia, but this advantages shown equally well in a head or rear wind in its effects on elevations as it would be in a cross wind in its, effect on wind allowance although in a lesser degree. We want to realize in selecting ammunition for the use of the rifleman that theories are all right up to a certain point but not beyond the point where the rifleman can apply those theories.”
Well, there you have it. Take your pick. After careful consideration of the above and being prejudiced by expressions I have overheard while eavesdropping on the experts, I have reached the conclusion th1t the following compromise should satisfy all except those who will not see. Take the extreme spread, add one-half of the mean error, subtract the time of day and divide by Pi. Put it in the furnace, wait three minutes and then measure the “mean radius.”
While speaking of mean radius, it might be of interest to mention the Pan-American method of determination. A vertical line is drawn, dividing equally the number of shots on the right and left of this line. A similar, horizontal line is then drawn. The intersection of these lines is taken as the center of impact from which the mean of the distance to each shothole is computed. This method, of course, does not penalize the off shots as much as the true center of impact method.
“The Kentucky Rifle” describes the very unique method of measuring targets in the early part of the 18th century: “Group shooting was mostly from muzzle rest. In firing contests three to five shots were, as a rule, fired. At the conclusion of a string a wooden peg was inserted in each bullet hole and a piece of cord stretched around each peg. Later the cord was measured and the marksman with the shortest cord won. This was called ‘string measure.'”
One of the methods for determining accuracy of caliber .22 ammunition is by use of a disc of given diameter for a given range. If this disc will cover all shots on the target, the target is given a score of 100. For 10 shot targets, each shot falling outside of the disc penalizes the score ten points. Thus one shot falling outside of the disc would give the ten-shot group a score of 90.
If you care to go into scientific measurement of accuracy, consider the method used by the Coast Artillery. This, however, is not so much a test of ammunition as it is the function of the gun and accuracy of the fire as regards fire control and gunnery. A pyramidal target is towed by a tugboat and the shots observed from the tug and also from a land station. The tug observes the “over” and “shorts” while the station observes the “rights” and “lefts.” The shots are then plotted on a representation of a battleship with regard to angle of fall and horizontal and vertical profile of the battleship. The figure of merit is then computed from a formula which is a function of the number of hits and the time. The writer has never been an eye witness at a coast artillery test, but the above was offered by an ex-Coast artilleryman.
Table 1 shows the comparative accuracy of ammunition selected for the Palma and Olympic Matches from 1909 to 1925 inclusive.
In comparing these records, however, it should be remembered that the tests held up to 1921 were conducted with the rifles held in machine rests. In 1921 one half of the program was conducted in this manner and the other half with the use of the heavy Mann barrels held in “V” rests. Since 1921 all tests have been conducted with Mann barrels.
The Mann barrel has advantages over the machine rest as it is more “fool-proof” and demands less care. However, if great care is taken with the rifle as to the way it is embedded in the stock, particularly at the muzzle, and the way in which the rifle is placed in the machine rest, there is probably little, if any, difference in its accuracy as compared to the Mann barrels. It may be said that this was not borne out in the ammunition tests in 1921 when such a big variation was shown in the two types at the 1000 yard range.
In analyzing this test, however, it should be remembered that the winning National Match ammunition gave an average mean radius at 1000 yards with the machine rest of 8.62 inches as compared to 8.42 inches in the Mann barrel. Variation was very great in the Palma test of that year but this was due principally to unfavorable weather conditions. As soon as the Mann barrel test was completed and the machine rests installed, a “fish-tail” wind set in. Everyone knows what effect a wind of this type will have on a group fired at 1000 yards. A strictly accurate comparison, therefore, cannot be drawn between the Palma records made prior to 1921 and since 1921 due to the different conditions surrounding these tests. However, it is safe to say that a steady improvement has been made each year and the 1000 yard targets are gradually beginning to look like the old 300 meter targets.
The 300 meter records present a difficult problem to make a comparison that will be acceptable to ammunition experts, there being only one year in which the mean radius was recorded for this range. It was the consensus of opinion of the ammunition experts, that shot holes on targets made by super-accurate ammunition fired at 300 meters are so closely grouped that in many cases, it is nearly imp0ssible to locate the center of impact of each of the ten shots. For this reason, the accuracy has been determined by a so-called “figure of merit” which in this case represents the mean of the average of the extreme vertical deviation and the average of the extreme horizontal deviation of all targets.
While it is granted that it is difficult in some cases to speedily locate all of the ten shots on a three hundred meter target, in the recent ammunition test held at Aberdeen Proving Grounds, the writer saw some of the spectators attempt to “stump” the famous Mr. Harry Pope on an extremely difficult target. Two minutes observation with his pocket glass was required for the veteran gun expert to unravel the mystery. Again for the sake of history, it is believed to be a pity that the Board doesn’t specify that the mean radius may be recorded for the three hundred meter range.
In order to present a picture of the comparative accuracies made at the 300 meter ranges, a study has been made of the records compiled from the ammunition tests conducted by the Ordnance Department from 1920 to 1925, the records previous to 1920 being too incomplete to be of material value. The curves shown on Plate I were made from these records.
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