Hunting Rifle Ballistics

By Mike Nelson

The following are general truths applicable to hunting rifles. Though the target shooter might refine some of the following, and the engineer or physicist might take exception to some of the explanations and descriptions, for the sake of those without advanced study in physics, explanations are kept simple, and the author will gladly supply technical argument as to their general accuracy. In truth, most are offered without compromise.

Hunting Rifle Ballistics - Overview
With your rifle sighted in at some selected range, and confirmed by at least three shots with your hunting ammo, you are ready for the hunt. In the field, with your quarry in your sights and apparently within range, you take your shot. The firing pin hits the primer, the primer ignites the powder; the powder burns quickly, creating hot gases, increasing pressure in the chamber, and propelling the bullet through the barrel. As the bullet travels down the bore, the rifling causes it to spin. When the bullet exits the muzzle, it is on its own, spinning and moving down range via inertia. Collision with air molecules gradually slows the bullet, and, unsupported by the barrel, the bullet begins to fall from the force of gravity. The sighting in procedure has aimed the barrel slightly upward, so the force of gravity is somewhat compensated by the upward angle of the initial trajectory. As the bullet proceeds down range, it rises above the line of sight, proceeds upward a bit, then begins to fall, crossing the line of sight again at the selected sight-in range, and continues to proceed down range with a reducing horizontal velocity and increasing downward velocity. If the quarry is within the sight-in range, or no more than perhaps 25 yards beyond the sight-in range, the bullet will strike within a few inches of the aim point. If the quarry is nearer, the point of impact will be a bit above the aim point; if more than 50 yards beyond the sight-in range, the point of impact will be several inches below the aim point, perhaps missing the quarry altogether.

Myth, Magic and Fundamental Physics
Bullets, like all other physical objects in the universe, are subject to the laws of nature, especially laws of motion. The basic laws of motion tell us that physical objects, whether at rest or in motion, remain so unless acted on by external forces. The primary physical forces on a bullet are expanding gasses, rifling, air resistance, and gravity. Most perceptions, misconceptions, and arguments about bullet travel can be resolved by considering the consequence of these forces. Minor forces include cross wind, which can move the impact point to the side. Other, minor forces have no significant effect in any reasonable shooting situation. If one cannot identify the forces that account for any claimed bullet behavior, then the claims fall into the myth/magic category and would best be disregarded.

An object set in motion by an exterior force and continuing under its own inertia.

The curve a projectile describes in space.

Trajectory - Theoretical vs. Actual
Theoretically, a bullet trajectory would be parabolic; because of the deceleration cause by air resistance, it isn't. Fortunately, for the most effective portion of the trajectory, it is close enough to parabolic to be treated as such by most aspects of rifle ballistics.

The study of the path of projectiles, particularly those shot from artillery or firearms.

A firearm with spiral groves in the barrel to impart spin to the bullet. The gyroscopic forces of spin help stabilize the bullet, similar to the way they help stabilize a toy top. The spinning helps keep the bullet pointed in the general direction of travel, minimizing wind resistance, thus keeping the trajectory uniform, reliable, and predictable.

The distance a bullet travels in the barrel while making one revolution.

Bullet Energy
Bullet energy is determined by weight and velocity. For any given bullet, weight is constant, and velocity decreases gradually from air resistance as soon as the bullet leaves the barrel, slowly draining off energy. Upon impact, some or all of the remaining energy is imparted to the object struck.

Air Resistance
Without air resistance, a projectile would not change velocity until it hit something.

Without gravity, a projectile would travel in a straight line until it hit something.

The process of adjusting the line of sight (whether open sights or optical sights) such that, at a given distance, the bullet trajectory and the line of sight intersect.

Sighting-In Considerations
The sight line is straight; because of gravity, the trajectory is an arc. Vertically, the bullet crosses the sight line twice, once near the barrel on the way up, and once down range on the way down. The bullet will not rise above the bore line after it leaves the muzzle; rather, it begins to fall. The bullet arcs upward because the barrel is angled slightly upward.

Sight Adjustment
The rear sight is moved in the direction that you want the projectile to go; the front sight is moved in the opposite direction that you want the projectile to go.

Sight-In Range
The downrange distance at which the sight line and the bullet trajectory intersect.

Trajectory for the Typical Hunting Rifle with a Scope
Most hunting scopes will be mounted 1.5 inches above the bore. If the scope is set so that the line of sight coincides with the bullet impact at 25 yards, the bullet will be below the line of sight between the muzzle and the 25 yard point of impact, above the line of sight between that point of impact and the second point of impact that coincides with the line of sight. That second point will generally be between 150 and 200 yards, depending on the particular bullet velocity. The maximum height of the trajectory above the line of sight, a point often referred to as the "mid-range trajectory," will usually be between two and four inches, again depending on the velocity of the bullet.

Velocity Compromise
The major factor affecting trajectory is the muzzle velocity. All bullets, as well as anything else on earth, fall at the same rate, 32 ft/sec.2 (i.e. 32 feet per second per second). Thus the faster the velocity, the further down range it gets before it falls too much to be useful. The slower the velocity, the higher the arc necessary to hit a downrange aim point, and the less energy available when it gets there.

Energy Compromise
Energy is determined by bullet weight and velocity. The hunter needs enough of each to effect a kill without destroying too much of the quarry; therefore, the caliber and bullet should fit the hunt.

Bullet Selection
For quick, clean kills, a bullet must penetrate sufficiently to reach vital organs, and it must, by expansion or fragmentation, damage tissue enough to cause significant bleeding. Thin-jacketed varmint bullets are made to expand and fragment quickly. Deadly for varmints, such bullets might only aggravate a large animal and inflict no major damage. Heavily jacketed bullets might completely penetrate, leaving only a small wound and little or no bleeding. The best bullet for the quarry penetrates deeply and expands to increase tissue damage. Bullets are likely the least expensive items for the hunt; get the best available for your quarry, and make every shot count. Be sure to fine tune your sights or scope with the bullet you will be using in the field. If you sight in with one bullet, then hunt with another, your point of impact might be several inches away from your point of aim.

Bullet Energy Calculations
For a bullet weight, W, in grains, and a velocity, V, in feet per second, the kinetic energy, E, in foot pounds is: E = W x V x V / 450450. Energy is independent of caliber; a 100 grain bullet of any caliber at 2800 feet per second (fps) at the muzzle has 1740 foot pounds of energy and at 200 yards still retains about 1500 foot pounds of energy. Since energy is proportional to mass, a 200 grain bullet would have twice the energy. Since energy is proportional to the square of the velocity, changes in velocity make major changes in the energy. For example, a 100 grain bullet at 2200 fps, would have only 1074 foot pounds of energy, about 60% of its energy at 2800 fps. (This illustrates the major difference between the 30-30 and the 30-06, our most popular hunting calibers.)

The Energy Formula. Energy is equal to mass times velocity squared divided by two. Bullet specifications typically report weight in grains, which must be converted to slugs the English unit for mass. First, the weight in grains must be converted to pounds. This is done by dividing the weight in grains by 7000. (1 lb. = 7000 gr.) The conversion from pounds to slugs requires dividing the weight in pounds by the acceleration of gravity, which, on our planet, is approximately 32.175 ft/s/s.

Why do we have so many calibers?
Simply because we can. Tinkerers, amateur and professional, have the freedom and the technology to modify brass and chambers, so they do. Successful "wildcat" cartridges become commercially viable, and another option is added for the rest of us.

What are the best calibers?
The answer is mostly subjective, and, like colors of paint, we have many more choices than we need. Fortunately, rifle calibers, like much of our clothing, can be divided into three categories, small, medium, and large.

Small calibers - .22 and under.
Small calibers are for small game. Though the more powerful 22's, such as the .223, can take small deer, even if legal, it would be best to use a larger caliber for anything larger than a coyote.

Medium calibers - the 25's.
The 6 mm Remington, 243 Winchester, and others in this category are small enough for varmints and large enough for deer. They are generally not appropriate for anything larger than deer.

Large caliber - .270 and up.
Small, fast . 270 and .30 caliber bullets can be used for varmints, and heavier ones, at sufficient velocity, are adequate for any North American game animal except, perhaps, large bear and moose. Some consider the .30 caliber ideal for North America. For most of us, a good, .30 caliber rifle would be all we need for serious hunting. Add a good .22 for plinking, and anything else is hard to justify.

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Copyright 2004 by Mike Nelson. All rights reserved.