I’ve previously written about some physical principles that act on projectiles from firearms, but there are a few more physics-based effects that act on bullets — some more so than others — which merit some discussion.
The Coriolis Effect
The Coriolis Effect doesn’t enter into handgun and rifle shooting to any practical degree, but it illustrates how much more of a challenge it is to fire projectiles over great distances with any accuracy. The Coriolis Effect is caused by the rotation of the Earth during the flight of the bullet. It’s always capitalized because it was first described mathematically by French physicist Gaspard de Coriolis in 1835.
In a nutshell, the Coriolis Effect is how one’s target will move underneath the path of a projectile while the projectile is in flight. When shooting in a northerly direction in the Northern hemisphere, the target will move clockwise (or to the right), and counterclockwise (or to the left) in the Southern hemisphere when shooting south. When shooting in an easterly or westerly direction, the range of the target will change slightly.
When dealing with the ranges typically experienced by the practical rifle shooter, the Coriolis Effect can be discounted, as it will have almost no measurable impact on the accuracy of the shot. It is, however, important for projectiles moving in a ballistic trajectory, such as artillery shells and ballistic missiles, which are in flight for several seconds or minutes and over much greater ranges. By the time such projectiles reach the points in space where they were intended to go, the target formerly occupying that point in space will have moved.
Shooting on a Slope
Common sense might tell you that a bullet fired along an uphill slope will lose velocity faster than one fired parallel with the ground or downhill, but in fact the effect of gravity on the bullet is about the same in either case. The vertical drop of the bullet in flight is far more controlled by the time the bullet is in flight than by the angle of flight.
However, the distance that the bullet will have to travel is going to be longer when the target is uphill or downhill from the firing line, as compared to a target at the same elevation, and thus the flight time of the bullet, and the amount of bullet drop, will increase.
This is a simple trigonometry problem. If we draw a right triangle where the legs are the horizontal distance from the gun barrel to the target and the vertical distance between the height of the gun barrel and the center of the target, the hypotenuse (the third side of the triangle) is the same length as the horizontal leg, so long as the gun barrel and the target are at the same elevation.
But raise or lower the target while the shooter remains in place, and the hypotenuse, which is the flight of the bullet, gets longer. This means that the bullet remains in flight longer, and drops more because of the effect of gravity. The adjustment that the shooter has to make to allow for this drop is more of a function of the length of the flight of the bullet than the angle at which it is fired.
Lead and Dispersion
When a target is moving relative to the shooter — which is the same thing in this discussion as when the shooter is moving and the target is stationary — the shooter will need to adjust the point of aim to allow for where the target will be when the bullet arrives, not where it was when the shot was fired. This calculation has to include adjustments for the reaction time of the shooter and for the time required for the rifle to eject the bullet after the trigger is pulled.
Taking these factors into account seems like splitting hairs for most practical situations, but they can be critical in precision shooting at moving targets, where the physics of the shot are constantly in flux. The errors stemming from lead can be reduced if the shooter uses a “sustained lead” and follow through, rather than trying to “snap shot” the target by aiming at a point ahead of the target and firing. If the horizontal velocity relative to the shooter is known, then some shooting calculators can adjust for this by including the speed of the target in the calculation.
Dispersion is the distribution of shots around the intended point of impact. The most common cause of wide dispersion is the failure of the shooter to use the same aiming point for each shot. It stands to reason that, all other things being equal, each bullet is going to behave like the one fired before it from the same rifle, and it is here that the shooter’s skill is most critical.
However, even when the shooter is able to use the same aiming point for each shot (such as when the rifle is in a bench rest or vise), there will be some dispersion due to the quality of the rifle and the consistency of the ammunition in use. These differences are most apparent at long ranges, and it is important to test each rifle and ammunition combination in a setting as close as possible as the anticipated tactical environment to establish what effect these factors will have on dispersion. This kind of testing and evaluation may reveal that the equipment in use is not of sufficient quality for the intended mission — regardless of how skilled the shooter might be.
Solving These Problems
Assuming that all of the factors described above are known, how does one use them to improve accuracy? Although it is possible to calculate the effect of each of these and make an adjustment in the aiming point with pencil and paper or a calculator, it is usually impractical. Manual calculation involves combining the results of multiple equations and inviting the opportunity for error.
If you’re going to go to this much trouble, you might as well acquire a ballistic calculator that will do the work for you, once the data has been supplied. The advantages of these calculators is that they take all of the factors into account simultaneously, and often provide a graphic solution of the sight picture or other visual aid that will assist the shooter in selecting the optimum aiming point for the situation.
There are smartphone apps and watches that assist with these calculations, although wearing one of the latter in roll call is likely to brand you as a pretender unless you happen to be a real sniper.
