ANGLE OF DESCENT OF BULLET

297

to be in a straight line, or practically so, for a considerable distance, and then, when the speed failed, to curve quite suddenly until the projectile fell perpendicularly, it has been recognised fully since the experiments of Robins in 1740, that this is not the case, but that the effect, firstly, of gravity, and then of the resistance of the air, is to make the path of any projectile into a curve. This curve, while it is very gradual in the beginning of the flight, becomes steeper and steeper during its whole length, for the double reason that the projectile is retarded by the resistance of the air, while its downward motion, due to gravitation, is constantly increasing.

The angle of descent of a bullet at different distances can very easily be found if a complete table of angles of elevation for the particular rifle is available. The method was devised by Sir Henry Halford, and is thus stated in the official Text Book for Small Arms, 1894 :

First find the increase of angle required to cover the last yard of the distance at which it is desired to find the angle of descent.

To do this, add the increase of angle for the last 100 yards of this distance (a) to the increase of angle required for the 100 yards beyond it, (B) and divide the sum by 200. This will give the mean increase of angle for each yard of these 200 yards.

'This mean increase, though accurate enough for practical purposes, may be corrected for the precise yard in question by

subtracting

a + B
100

The formula will then be N

= angle of descent in minutes.

Example.-Find the angle of descent of the Lee-Metford bullet at 1,000 yards range.

Referring to the Table of angles of elevation, second 1000 × (13.804 +15.094)

column,

==

200

13.804+15.094
100

= 144.49'

-289-144-201' 2° 24.201', which is the mean angle of descent for the last yard.'

Plates XL and XLI show the comparative heights reached

by the bullets of military rifles in a flight of 500 and 1,000 yards.

Similar diagrams have often appeared, but a comparison of the kind is vital to an appreciation of what modern rifles are when compared with the more ancient ones, the object being to represent the form of the curves made by the different bullets. The height has been enormously exaggerated in proportion to the length of the curve. In the 500 yards diagram (Plate XL, fig. 1), whereas on the vertical scale a quarter of an inch represents a height of one foot, on the horizontal scale a quarter of an inch represents 60 feet, and the whole 500 yards is compressed into a little more than 6 inches. The curve made by the Enfield or Snider bullet is, as will be seen at once, the highest, reaching in the 500 yards flight a height of 11 feet 4 inches, well above the height of a horseman's head, while for the middle 300 yards of its flight it is too high to catch a six-foot man standing upright. The trajectory of the Martini-Henry, 450 bore, with a bullet of 480 grains, and an initial velocity of 1,300 feet per second, culminates at a little beyond 250 yards at a height of just under 8 feet 6 inches, so that its whole flight is within the height of a mounted man, and for only about 150 yards would it fail to endanger an infantryman. The trajectory of the 402 [experimental] rifle is similar on the whole to that of the Martini-Henry, but decidedly flatter. The two lower curves offer a striking contrast to the upper ones. The bullet of the Lee-Metford, 303 bore, weighing 215 grains, and projected with a velocity of 2,000 feet per second, rises only just over 4 feet from the line of aim in the same distance, and would therefore strike the kneeling figure of a man at any point in the whole trajectory. The 256 Mannlicher, with a bullet of 156 grains, and 2,350 feet velocity, rises not much more than 3 feet in the same distance. We have to guard against the error of supposing that because the curve is a constantly increasing one it is, with the high velocities of modern times, one of which the angles really are extremely steep. The necessity of exaggerating in diagrams the height of curves in relation to their length, as well as the habit the eye has of judging the trajectory of a bullet, which it cannot

OYDS.

100

200

300

FIG. 2

400

500

TRAJECTORY OF 303 RIFLE AT 1000 YARDS IN ACTUAL PROPORTIONS.

easily follow, by analogy from that of a cricket ball or a golf ball, which it can follow, tends to mislead the perception of the true proportions of the curves of bullets. The whole trajectory of the 256 rifle for the first 300 yards of its flight, although in every point it is a curve, would be contained in a straight 12-inch pipe, and the small diagram given (Plate XL, fig. 2) will give some idea of the real shape of the curve made by the 303 bullet in a flight of 1,000 yards. Plate XLI shows similarly the trajectories at 1,000 yards. In it ⚫05 inch is equal to one foot vertically, but to 21.7 feet horizontally.

Flat as the curves are, yet the vertical height reached by the bullet in the course of its flight at the long ranges becomes considerable. The bullet of the Enfield muzzle-loading rifle rose more than 75 feet in a flight of 1,000 yards; the Martini-Henry bullet rises about 44 feet; the Lee-Metford bullet about 25 feet; and that of the 256 rifle 21 feet only above the line of aim. In firing at 2,000 yards the LeeMetford bullet reaches a height of about 195 feet, between 1,100 and 1,200 yards, the muzzle of the rifle being pointed no less than 170 yards above the mark aimed at. It is hardly necessary to say that the whole journey of the bullet along the curve of the trajectory is somewhat longer than the straight line joining the two extremities of its flight. The difference thus introduced is, in reality, very small. At 1,000 yards, with the Lee-Metford, the path of the bullet is less than one foot longer than the straight line, and at 2,000 yards it is about 2,005 yards.

A knowledge of the trajectory is sometimes useful, and may at times enable one to take a shot when some object apparently intervenes without really interfering with the flight of the bullet. The writer has more than once stalked and killed rabbits, firing under the belly of an intervening cow, because it was evident that the bullet would not rise so high as to touch it. He has several times seen the bull's-eye struck at 900 or 1,000 yards when the target was partly obscured by intervening cattle within two or three hundred yards of the firer or the target. In deerstalking, when it has been a question whether some slight intervening rise of ground or tussock would or would not be cleared by the