The following information on the trajectory, accuracy and power of hunting cartridges comes from Rifles and Rifle Shooting by Charles Askins. Rifles & Rifle Shooting is also available to purchase in print.
Here is the Winchester definition of trajectory which I quote because it seems as good as any: “The trajectory of a bullet is the path it follows from the time it leaves the muzzle until it strikes the target. This path is a continuous curve. In its flight a bullet loses forward, or horizontal speed, and gains downward or vertical speed.”
When a bullet leaves the gun muzzle it begins to drop just the same as though it had been released from the hand. In one second of time during flight the projectile will drop the same distance that it would in the same length of time if allowed to fall from an elevation. Moreover the falling movement is progressive, as pointed out above. It follows then that if the bullet drops a certain distance in say a quarter of a second, it will fall twice that distance in the next quarter, being governed by the laws of gravity exactly as would a falling body without horizontal speed.
Keeping in mind the progressive rate of drop, it will be seen that it would not do to conclude that a rifle with a muzzle velocity of a thousand feet would have a trajectory but twice as high as one with two thousand feet velocity. While the trajectory would of course be governed by the time of the projectile over the course rather than by the initial velocity, yet I can illustrate this point with two well known cartridges.
The .22 long-rifle has a muzzle velocity of 1,103 feet, two hundred yard trajectory, 22 inches. The .30 U.S.A. Krag has a muzzle velocity of 2,000 feet, 200 yard trajectory, 5.41 inches; increase the Krag initial speed to 2,700 and we have a trajectory of 2.85 inches. Hence we can see the importance of gaining every additional hundred feet in muzzle velocity possible if the rifle is to do good work at long, unknown distances.
Trajectory, as measured in inches, is the rise of the bullet above a straight line between the muzzle and center of target, or point of aim, and is usually measured mid-way of the range. The term “rise of the bullet” is a technical expression, for in reality the bullet never rises above a straight line in extension of the bore of the barrel. The so called rise of the bullet has reference to the “sighting line,” the line of vision from the eye across or through the sights and to the target.
Sights are not so set on a rifle as to make the sighting line parallel the bore, but the rear sight is affixed at a higher elevation than the front which causes the path of the bullet’s flight to cut the line of sight, or as we say rise above it. If the line of sight really paralleled the line of bore, the bullet would be found to drop lower and lower the longer the range, and never rise above.
As it is, the bullet starts such distance below the line of sight as the front sight is above center of bore; then for some distance the ball travels beneath the line of sight until its path and the “line” converge when it “rises” above. From here on the ball continues to get farther and farther from the line of sight until it reaches a distance about six-tenths of the range, and then the two lines begin closing up until they meet at the center of the target.
The only true point-blank of a rifle is where the path of the bullet’s flight first cuts the line of sight, and this is only a very few yards from the muzzle, depending upon the elevation of the rear sight and the height of front sight above center of bore. The second point-blank, where the bullet again cuts the line of sight, is a variable distance, though we can fix an arbitrary point-blank by saying that a rifle shoots point-blank up to the distance the bullet rises but a slight amount above the line, call it two inches. In practical big game shooting a bullet whose path never leaves the line of sight more than the two inches can be said to be shooting point-blank for the distance.
Trajectory height must not be confused with the drop of the bullet from the straight line in extension of the axis of the bore. For example, a certain rifle with a 2,500 foot muzzle velocity has an eight and a half inch trajectory at three hundred yards, but if we shoot at that three hundred yard target with the rifle sighted for one hundred yards the ball will strike twenty-seven inches below the center. Hence we see the importance of sighting a rifle for the longest distance at which it will not exceed a certain trajectory height, since after we pass the spot at which the sights are aligned the drop of the projectile is very rapid compared with its rise above the sighting line.
The range at which we can fix our arbitrary point-blank, or sight the rifle for hunting, is a matter for the exercise of good judgment. The first thing to be taken into consideration is the initial velocity of the rifle. The .280 Ross and other three thousand foot velocity rifles have trajectories as flat at three hundred yards as the .30-30 has at two hundred; then of course the Ross can be sighted for three hundred yards with no more mid-range error than the .30-30 has at two hundred.
The game at which the weapon is to be used naturally has a bearing on the permissible trajectory height. For deer that are usually shot at distances under two hundred yards, and being small require close holding to reach a vital spot, it would not be wise to tolerate a mid-range error of five inches, the chances being that most of our shots would be taken at just the distance where the bullet was farthest from the line of sight, one hundred to one hundred fifty yards.
However, if the game were of a large variety, like elk, moose, or the larger African antelope, the three thousand foot velocity rifle with a trajectory of five inches at three hundred yards might well be sighted for that distance, and no especial difficulty should be had in holding a trifle low for the mid-ranges. For a deer rifle I should be inclined to place the highest practical trajectory height at four inches. This can be secured from a Ross or 7 mm. Mauser-Spitzer, at 250 yards, from the .30-30 at 165.
With the old-time black powder rifles the size of bull’seye in which the bullet must strike anywhere along its curve of flight was given at eight inches. It might strike the top of the eight-inch bull at one hundred yards and the bottom at two hundred, and the latter distance was supposed to be within the point-blank range of the rifle for big game shooting. However, with modern, high-power arms I should take the size of the bull at six inches, which circle the bullet must not leave up to the maximum distance.
If the rifle is to be sighted for the center of the bull at two hundred yards it is evident that the trajectory must be less than three inches high midway in order to keep within the bull. Such trajectory can be secured from a rifle having a muzzle velocity of 2,600 to 2,700 feet. A rifle with a lower velocity will still keep within the bull by sighting it to strike at six o’clock at two hundred yards in place of in the center. The difference between the two guns is that the higher velocity will keep within the bull for some distance beyond the stipulated range while the other will not. Thus we can see how flat trajectory very kindly makes amends for bad judgment of distances.
To come down to brass tacks, other things being equal, the trajectory of a big game rifle cannot be too flat. If it has but a one-inch trajectory at two hundred yards that is admirable. Furthermore a six-inch two hundred yard trajectory is the very highest permissible in a high-power rifle for any game. Increasing the muzzle velocity from 2,000 to 3,000 feet lengthens the distance at which the rifle will land in the circle nearly one hundred yards. All this is considered as other things being equal, remember.
In black powder days, sacrifices of accuracy, power, and range were made in order to secure flat trajectory. The old principle of sacrificing one essential to secure another still more important might still hold. Let us see. Suppose that in securing our three-inch trajectory at two hundred yards we had to sacrifice accuracy to such an extent that a circle of ten inches would be required to contain a pattern of shots. It is quite evident then that our flat flight would be useless since we could not keep within the given circle in any event. We may, therefore, take it as a simple statement of fact that trajectory and accuracy must be equal.
A three-inch trajectory with a ten-inch accuracy pattern is no better than a ten-inch trajectory with a three-inch pattern. But if we can combine a three or four-inch trajectory with a four-inch pattern, we have a great shooting gun—a great shooting gun that might still possibly lack power. I say might lack power because a flat trajectory implies power of itself if the bullet is of decent weight and right shape.
It is claimed for the military cartridges, like the ’06 Springfield, .280 Ross, 7 mm. Mauser, .25-50 Newton, that they combine in the greatest degree flat trajectory, accuracy, and power. If this is so, and there is not any question at all except as to the power with full mantled Spitzer bullet, they are a wonderful advance in cartridge making.
The power of a cartridge is a multiple of the weight of a bullet and its velocity. Rules for calculating the power of a bullet, given its weight and velocity will not avail much, for the information is generally found in ammunition catalogs, but here is a simple one that may be remembered: Square the given velocity and multiply by the weight of the bullet in one hundred grains and fractions thereof; for example, if the bullet weighs 100 grains multiply by one, if it weighs 250 grains multiply by 2.5. Divide the result by 4,508 and the quotient will be the energy.
Power and energy are almost synonymous terms. Penetration has little to do with the power of a cartridge, but the striking energy is usually taken at a fair measure of the killing qualities, provided the character of the missile is such that it will expend its full force upon the object struck. It follows that the shape and kind of bullet, whether full metal patched, soft-pointed, split-jacketed, or hollow pointed has much to do with the actual execution by a projectile of any given energy.
There is much room for the exercise of good judgment in the choice of a bullet for any particular species of game. First the velocity at which the bullet is to be sent must be taken into consideration. A bullet with a soft point, driven at two thousand feet, might penetrate just right and do good execution; sent at three thousand feet it would possibly expend its force upon the surface and fail to kill, even though its energy were much higher.
At a given velocity a certain kind of bullet may slip through an animal, merely stinging it, while at a higher velocity the ball might have an explosive effect on animal tissue, killing instantly. Diameter of ball is not to be entirely overlooked when considering killing qualities relative to energy. It is generally granted among big game hunters, that given like energy, the missile of largest caliber will have the greatest smashing power.
There is no subject of such perpetual interest to big game hunters as that of the correct shape of bullet to insure its expending its full energy in the right way. The object is, of course, to select a bullet that will penetrate sufficiently and yet expend its entire power on the animal. Naturally if we were shooting deer with a rifle powerful enough for elephants it would not be desirable to have the full energy spent upon the beast unless we wished to make mince meat of it.
Thus we have, in practical results, that the energy of a bullet, governing its killing power, is modified by its shape, character, weight, diameter, velocity, and the animal upon which it is to be used.
Accuracy and Power
Accuracy has been pretty well treated under the head of cartridges and elsewhere but it will do no harm to sum up here. The miniature cartridges should be capable of keeping ten shots in a one-inch circle at fifty yards. In such ammunition velocity and power are not of moment. Small game cartridges should have an accuracy capable of keeping ten shots in a three-inch at one hundred yards, velocity not less than 1,700 feet, and energy of five hundred pounds or better. Deer and antelope ammunition ought to be accurate enough to keep ten shots in a six-inch circle at two hundred yards, with a two hundred trajectory of not greater than six-inches, and striking force of 1,500 foot pounds or more.
Rifles for longer range game work, suitable for moose elk, caribou, mountain sheep, should have an accuracy equal to a six-inch pattern at two hundred yards, or preferably a trajectory of not greater than a four-inch circle at two hundred yards, velocity above 2,500 feet, energy from 3,000 to 3,000 foot pounds. Rifles of big bore for long range use should be capable of keeping a string of shots in an eight-inch circle at two hundred yards. Velocity should be from 2,400 to 2,600 feet, with trajectory to correspond. The power would range from three thousand to four thousand foot pounds.
Jungle rifles should be accurate enough to keep ten shots in a ten-inch circle at two hundred yards, velocity from 2,000 to 2,400 feet, energy from four to five thousand pounds. Elephant rifles should keep ten shots in a fifteen-inch circle, with velocity above two thousand feet, and energy of not less than five thousand foot pounds. In the case of match cartridges it is not worth while to give energy, trajectory, or velocity and they will be omitted from the table.
Most of the figures in the ballistic table which follows are taken from the catalogs of the Winchester and U.M.C. companies and may be accepted as correct. The ballistics of English cartridges are taken from the catalogs of Jeffery, Greener, and Westley-Richards. Usually their statements are rather indefinite, being about so and so—they fail to supply figures for free recoil, and that had to be calculated. Some of the figures for foreign cartridges I have secured from the American agents and I cannot vouch for their correctness. Probably they are approximately true.
It is human nature for a manufacturer to make the best possible showing for his arms and ammunition. For example, one agent who had a rifle giving a muzzle velocity of 2,900 feet gave the trajectory as considerably flatter than that of another rifle with similar weight and shape of bullet, having a speed of 3,100 feet; some builders with rifles having ballistics similar to the ’06 gave the free recoil as about half the ’06—in that case I had to do some guessing myself. Free recoil of automatic arms cannot be obtained in any instance.