The How and Why of Long Shots and Straight Shots.
On a windy, unpleasant day in 1746, a great mathematician and philosopher was exhibiting to a select company in the gardens of the Charterhouse his skill in shooting round a corner with a bent gun-barrel. If he had requested the editor of the Cornhill Magazine of the day to publish his experiments, it is probable that he would have been refused. Now, when every morning paper informs us at breakfast, in its best type, of how far off we may be killed, and the evening papers analyze the same with the commencement of a hot debate on the French Treaty, to give us a pleasing subject for our dreams, we think that perhaps our unprofessional readers may like to know the how and the why of these far-reaching organs of peace on earth and good-will among faithful allies.
Supposing, then, reader—for it is to such that this article is addressed—that you are wholly ignorant of the science of gunnery, and of its principal establisher, Benjamin Robins, and have, therefore, been laughing at him, the poor silly philosopher,—if you will read the following extract from his work on Gunnery, you will see that if he did a foolish thing, he certainly sometimes wrote a wise one:—“I shall, therefore, close this paper with predicting that whatever State shall thoroughly comprehend the nature and advantages of rifled-barrel pieces, and, having facilitated and completed their construction, shall introduce into their armies their general use, with a dexterity in the management of them, they will by this means acquire a superiority which will almost equal anything that has been done at any time by the particular excellence of any one kind of arms; and will, perhaps, fall but little short of the wonderful effects which histories relate to have been formerly produced by the first inventors of fire-arms.”
Now to our distinguished countryman, Mr. Benjamin Robins, is due the credit of having first pointed out the reasons why smooth bores—and smooth bore is now almost as great a term of reproach with us rifle volunteers as dog is with a Turk—were constantly, in fact, universally, in the habit of shooting round corners, and the experiment mentioned was only a means of bringing the fact more strikingly before the obtuse faculties of the Royal Society, whom we may imagine to have been intense admirers of brown-bess—also now a term of reproach in constant use. Mr. Robins did more; he pointed out the advantage of elongated rifle bullets; showed us how to determine—and partially, as far as his limited means permitted, himself determined—the enormous resistance of the atmosphere to the motion of projectiles; in fact, smoothed the way for all our present discoveries; and, treason though it be to say so, left the science of gunnery much as we have it now. Though principally from increased mechanical powers of construction, better material and improved machinery, we have advanced considerably in the Art or practice of destruction.
Let us endeavour, first, to understand something of the movement of gun-shots in their simplest form. A gun-barrel, consisting of a bar of metal thicker at one end (where it has to withstand the first shock of the gunpowder) than at the other, is bored out throughout its length into a smooth hollow cylinder; this cylinder is closed at one end by the breech, which has a small opening in it, through which the charge is ignited. A charge of powder is placed in the closed end, and on the top of this the ball, say, a spherical one, such as our ancestors in their simplicity considered the best. The powder being ignited, rapidly, though not instantaneously, becomes converted into gas, and the permanent gases generated will, at the temperature estimated to be produced by the combustion (3,000° Fahr.), occupy a volume under the pressure of the atmosphere alone of over 2,000 times that of the bulk of the powder. This point, as well as the elasticity of the gases, both of the permanent ones and of the vapour of water or steam from the moisture in the powder, has never been accurately determined,[15] and various estimates have been formed; but if we take Dr. Hutton’s—a rather low one, viz.—that the first force of fired gunpowder was equal to 2,000 atmospheres (30,000 lbs. on the square inch), and that, as Mr. Robins computed, the velocity of expansion was about 7,000 feet per second, we shall have some idea of the enormous force which is exerted in the direction of the bullet to move it, of the breech of the gun to make it kick, and of the sides of the barrel to burst it. Notwithstanding Mr. Robins’ advice, we certainly never, till very lately, made the most of the power of committing homicide supplied by this powerful agent; but we used it in the most wasteful and vicious manner. All improvements—and many were suggested at different times to remedy defects, which he principally pointed out, like the inventions of printing and of gunpowder itself—lay fallow for long before they were taken up. They were premature. If our fathers had killed men clumsily, why should we not do the same? No one cared much, except the professionals, whether it required 100 or 1,000 bullets, on an average, to kill a man at 100 yards’ distance. Now we take more interest in such amusements; every one’s attention is turned to the best means of thinning his fellow-creatures; and we are not at all content with the glorious uncertainty which formerly prevailed when every bullet found its own billet: we like to kill our particular man, not his next neighbour, or one thirty yards off.
In order to see why we are so much more certain with our Whitworth, or Enfield, or Armstrong, of hitting the man we aim at, let us first examine how a bullet flies; and then by understanding how (badly) our fathers applied the force we have described to make it fly, we shall be able to appreciate how well we do it ourselves.
In consequence of the sudden generation of this enormous quantity of gas, then, in the confined space of the barrel, the bullet is projected into the air, and if it were not acted on by any other force, would proceed for ever in the line in which it started; gravity, however, at once asserts its sway, and keeps pulling it down towards the earth. These two forces together would make it describe a curve, known as the parabola. There is, however, another retarding influence, the air; and though Galileo, and Newton in particular, pointed out the great effect it would have, several philosophers, in fact the majority, still believed that a parabola was the curve described by the path of a shot. It remained for Mr. Robins to establish this point and to prove the great resistance the air offered: to this we shall have to recur again presently. Let us first see how a shot is projected. If the bullet fitted the bore of the gun perfectly, the whole force in that direction would be exerted on it; but in order that the gun might be more easily loaded—and this was more especially the case with cannon—the bullet was made somewhat smaller than the bore or interior cylinder; a space was therefore left between the two, termed windage, and through this windage a great deal of gas rushed out, and was wasted; but the bad effect did not stop there: rushing over the top of the bullet, as it rested on the bottom of the bore, it pressed it down hard—hard enough in guns of soft metal, as brass, after a few rounds to make a very perceptible dint—and forcing it along at the same time made it rebound first against one side and then the other of the bore, and hence the direction in which it left the bore was not the axis or central line of the cylinder, but varied according to the side it struck last. This was one cause of inaccuracy, and could, of course, be obviated to a great extent, though at the cost of difficulty in loading, by making the bullet fit tight; but another and more important cause of deflection was the various rotatory or spinning motions the bullet received from friction against the sides of the bore, and also from its often not being a homogeneous sphere; that is, the density of the metal not being the same throughout, the centre of gravity did not coincide with the centre of the sphere as it should have done.
No. 1.
Looking down upon the spinning bullet.
Let us try to understand the effect of this rotation. A bullet in moving rapidly through the air, separates it; and if its velocity is at all greater than the velocity with which the air can refill the space from which it has been cleared behind it, it must create a more or less complete vacuum. Now when the barometer stands at thirty inches, air will rush into a vacuum at the rate of 1,344 feet per second; and if the bullet is moving at a greater velocity than this, there will be a total vacuum behind it. But it can be easily understood that even when moving with a less velocity, there will be a greater density of air before than behind. If the bullet be rotating on a vertical axis—that is, spinning like a top, point downwards, as in the diagram No. 1, from left to right, in the direction indicated by the crooked arrow, at the same time that it is moving forward (sideways it would be in the top) as indicated by the straight arrow,—it is evident that the left half rotates with the general motion of translation of the bullet, and the right half backwards against this motion, and therefore that on the left side it is moving quicker relatively to the air through which it is passing than on the right side. And its rough surface preventing the air escaping round it on that side, while it, as it were, assists it on the other side, the air becomes denser where shown by the dark lines, and tends to deflect the bullet in the other direction, that is, in the direction in which the anterior or front surface is moving.[16]
No. 2.
Looking at the bullet sideways.
If the bullet rotate on a horizontal axis at right angles to the direction of its motion of translation (that is, like a top thrown spinning with its point sideways, when it would strike the object thrown at with its side), shown in the diagram No. 2; if the anterior portion be moving, as shown by the arrow, from above downwards, it is evident, for the same reasons, that the air will become denser, as shown, and assist the action of gravity in bringing the ball to the ground—that is, decrease the range. A spherical bullet resting on the bottom of the bore of a gun would always have a greater tendency to rotate in this manner than in a contrary direction; for the friction against the bore would be augmented by the weight of the ball in striking against the bottom, and diminished by it when striking against the top.
Shot were constructed in 1851 to try the effect of rotation in the above-mentioned and in the opposite directions. They were made excentric, that is, lop-sided, by taking out a portion of the metal on one side, and replacing it either with a heavier or lighter body. The manner in which they would rotate was, therefore, known; for, not to use too scientific language, the light side moved first, and according to the relative positions of the heavy and light side when placed against the charge so the rotation took place. Thus, when the light side was resting against the bore of the gun, the rotation was exactly contrary to the direction shown in diagram No. 2; and a range of 5,566 yards was obtained from a 10-inch gun, being 916 yards farther than with a concentric shot from the same gun. The deflections to the right and left were proportionately large, according as the light side was placed to the left or right.
We need not specify further; this will be sufficient to show the reason why the smooth bore with a spherical bullet never made a straight long shot, for it was not only that the bullet did not go in the direction in which it was aimed, but it did not even follow the direction in which it started. This was well shown by Mr. Robins in the experiment we commenced with. He bent the end of a gun barrel to the left, and aimed by the straight part. As would be naturally expected, the shot passed through the first tissue-paper screen 1½ inches to the left of the track of a bullet, which had been previously fired from a straight barrel in the same line with which the crooked barrel had been aimed, and 3 inches to the left on the second screen; but as he had predicted, and as the company could hardly have expected, on the wall which was behind, the bullet struck 14 inches to the right of the track, showing that though it had gone at first as directed by the bent portion of the barrel, yet as the bullet in being turned had rolled against the right-hand side of this portion of the barrel, it had a rotatory motion impressed upon it, by which the anterior portion moved from left to right, and the bullet, after moving away from, turned back and crossed the track of the other bullet again, or was incurvated to the right.
We now see why spherical bullets from a smooth bore, though they may fly almost perfectly accurately a short distance, cannot be depended on in the least for a long distance, as the bullet which might strike within 1 inch at 100 yards would not strike within 2 inches at 200 yards, and still less within 3 inches at 300 yards of the mark at which it was fired.
The cause of these deflections we have seen is almost wholly rotation or spin. The object of the rifle is to place this rotation under our control, and if the bullet must spin, to make it spin always in the same direction, and in the way which will suit our purpose best. With this object the interior of the cylindrical bore which we have been considering as smooth, is scored or indented with spiral grooves or furrows. As we are merely concerned with the principles, and not with the constructive details, we need only mention that the number of these grooves varies in different rifles from two to forty; that their shape and size, though dependent on certain conditions, is, we might almost say, a matter of fashion; and that Mr. Whitworth, in his almost perfect rifle, uses a hexagonal bore, and Mr. Lancaster makes a smooth oval-bored rifle; but that in all, the deviations from the circle of the interior cylinder do not pass straight from end to end of the barrel, but spirally, and constitute, in fact, a female screw. The bullet, fitting tight and entering the grooves, is constrained to rotate while being forced out of the barrel by the gunpowder, in the same manner that a screw is necessarily twisted while being drawn out of a hole or nut; and this rotation or spin being impressed upon it by the same force which projects it from the barrel, continues during the flight. This spin is different in direction from those we have been considering previously; it is like the spin of a top thrown point foremost, the axis of rotation coincident with the line of flight. While it remains in this position (coinciding with the line of flight) none of the deflecting effects of the air we have mentioned can come into operation, as the resistance is equal on all sides; and not only that, but if there are any irregularities on the surface of the ball, as they are brought rapidly first on one side and then on the other of the point or pole of rotation, they can have no effect in deflecting it to one side more than to the other. Hence the accuracy, or straight shooting, of our modern gun, the rifle.
We have before mentioned that Robins pointed out the enormous effect of the resistance of the atmosphere to the passage of a shot; and “because,” as he says, “I am fully satisfied that the resistance of the air is almost the only source of the numerous difficulties which have hitherto embarrassed that science,” viz. gunnery, he considered it above all things necessary to determine its amount; for which purpose he invented the Ballistic Pendulum and Whirling Machine. His experiments were made principally with small bullets; but a more extended series of experiments was made by Dr. Hutton with the same machines, and on the Continent and in America by Major Mordecai, with a ballistic pendulum of improved construction. It appears from these that when a ball of two inches diameter is moving with a great velocity, it meets with a resistance of which the following examples will give an idea: at a velocity of 1,800 feet per second the resistance is 85½ lbs., and at a velocity of 2,000 feet, 102 lbs. If we wish to increase the range, then, we must overcome this resistance in some way. As the resistance is nearly proportionate to the surface, that is, twice as great on a surface of two square inches as on a surface of one square inch, we must do so by increasing the weight of the shot. For it is evident that if two shot of different weights start with the same velocity, and meet with the same resistance, the heavier one, having the greater momentum, will maintain its velocity the longest. Throw a cork and a stone of the same size with the same force—the cork will only go a few yards, while the stone will go perhaps ten times as far. In the smooth-bored cannon this could only be effected partially by increasing the size of the shot, when the surface exposed to the resistance of the air increased only as the square of the diameter, while the weight increased in a greater ratio, as the cube of the diameter. Hence the longer range and greater penetration of heavy guns. As, however, with a rotating body the tendency is always for the axis of rotation to remain parallel to its original direction—thus a top while spinning may move about the floor, but remains upright on its point, and does not fall till the spin is exhausted—we have with rifles a means by which we can keep a bullet always in the same direction. In order to comply with the condition, then, of exposing a small surface to the resistance of the air while the bullet’s weight is increased, we reject the spherical form, and make it a long cylinder; and to make it the more easily cut through the air, we terminate it with a conical point.
Thus compare Mr. Whitworth’s 3-pounder with the ordinary or old 3-pounder; the shot weigh the same, but the diameter of Mr. Whitworth’s 3-pounder shot is 1·5 or 1½ inches, while the diameter of the old 3-pounder shot is 2·91 inches, or nearly three inches; and the surfaces they expose to the resistance of the air are 2·25, or 2¼ square inches, and 8·47 nearly, or nearly 8½ square inches; that is, Mr. Whitworth’s bullet, with the same weight to overcome it, meets with a resistance of a little more than a quarter that which the old bullet met with, and has the advantage of a sharp point to boot. Hence the enormous range attained,—9,688 yards.
The very same causes which make the fire of a rifle accurate, tend also to make it inaccurate, paradoxical as it may seem; but this inaccuracy being to a certain extent regular and known beforehand, is not of so much consequence, though it is a decided disadvantage. It may—not to be too mathematical—be explained thus:—The axis of rotation having, as we said, a tendency always to remain parallel to its original direction, when a rifle bullet or picket (the long projectile we have described) is fired at a high angle of elevation—that is, slanting upwards into the air, in order that before it fells it may reach a distant object,—it is evident from the diagram, that if the direction of the axis of rotation remains, as shown by the lines p p p, which represent the shot at different portions of the range parallel to the original direction in the gun, the bullet or picket will not always remain with its point only presented in the direction in which it is moving, but one side of the bullet will be partially opposed to the resistance of the air. The air on that side (in front) will be denser than behind, and the disturbing or deflecting influences before described will come into operation, the two opposite tendencies described in the text and the note to a certain extent counteracting one another. While at the same time the resistance of the air has a tendency to turn the bullet from the sideways position in which it is moving with respect to the line of flight (and the effect of this is the greater the less spin the bullet has to constrain it to keep its original direction), the result of which force, conspiring with the force described in the note, is to give it a slight angular rotation round another axis, and deflect the bullet by constantly changing its general direction (this second axis of rotation) to the side to which the rifling turns. This was exemplified in the late practice with Mr. Whitworth’s gun. When firing at the very long range of 9,000 yards the 3-pounder threw constantly to the right from 32 to 89 yards.
No. 3.
The rotation of the earth about its axis tends to throw the projectile always to the right of the object aimed at. Space will not permit of our entering on this subject; but the principle is the same as that which in M. Foucault's experiment with the vibrating pendulum caused its plane of vibration apparently to constantly deviate to the right.
The time of flight of the shot from Mr. Whitworth’s 3-pounder gun is unknown to us; we are unable, therefore, to calculate the deflection due on this account, but as an illustration we may give this deflection, calculated for the long range attained with the 10-inch gun (5,600 yards), from Captain Boxer’s, R.A., Treatise on Artillery. He finds it to be very nearly 11 yards.
Windage, one of the faults of the spherical bullet, permitting a great escape of the gas, and therefore wasting the force of the powder, has been overcome in various ways in the cylindro-conical picket. The Minié principle consists in hollowing out the base of the ball conically, placing in this hollow an iron cup or piece of wood, which being driven forward by the explosion of the charge further into the conical hollow, enlarges or expands the ball, and makes it fit tight and take the impression of the grooves, though the bullet, when put into the gun, is small enough to be easily rammed down. It is now found that the conical hollow alone, without the cup or plug, is almost equally effective in expanding the ball. We have termed this the Minié principle; Captain Norton, however, undoubtedly has a prior claim (which has been allowed by the British Government, we believe) to this invention. He was before his time. There was no cause for, and therefore the shooting mania was not strong upon us.
With breech-loaders, doing away with windage and making the bullet take the rifling, is an easy matter. The breech into which the bullet is put at once, without being passed through the muzzle, is made slightly larger than the rest of the bore; the bullet on being pushed forward by the force of the powder is squeezed into the narrower portion, and effectually prevents all escape of gas. It is thus with the Armstrong gun. Robins said of the breech-loaders of his day, “And, perhaps, somewhat of this kind, though not in the manner now practised, would be, of all others, the most perfect method for the construction of these barrels.” Mr. Whitworth, on the other hand, uses—well, we have avoided details thus far, and every newspaper has described them so fully, that our readers must be thoroughly acquainted with them. Let us conclude, as we began, with Robins, and hope that his prediction that “they,” the armies of the enlightened nations which perfect rifles, “will by this means acquire a superiority which will almost equal anything that has been done at any time.”