Bullet Flight and Hunting Optics
by Chuck (Onehorse) Tarinelli
To understand how shooting game at long range is accomplished, it is helpful to have a basic knowledge as to how bullet flight and rifle optics work together. We’ll start by discussing the terms line-of-sight, line-of-departure (bore-axis-line), and bullet trajectory (flight path of the bullet).
For all intents and purposes, line-of-sight is an absolutely straight line for infinity. Think “laser”. Where it’s pointed is where it goes along its entire path, period. The optics in a rifle scope work like that. The center point where the vertical and horizontal cross hairs meet goes “straight out there” as far as we can see. Even though we normally think of this place where the reticles intersect as an aiming “point”; it may be helpful to also think of it as a continuous perfectly straight line that we are looking at on-end.
Likewise, the line-of-departure is a perfectly straight line which runs from the center of the bore of the rifle as far out as we can imagine. Think “forever”. When a bullet is in the rifle’s chamber, the line-of-departure would run from the tip of the firing pin through the center of the primer, center of the shell, bullet, barrel and beyond. It is the actual line on which the bullet is “aimed”. When we bore-sight a rifle by removing the bolt and looking down it’s barrel at where it is aimed, we are looking down the line-of-departure. Obviously, we can’t aim a rifle by looking down its barrel when the action is closed and we are ready to shoot. Hence, sights mounted above the barrel.
The trajectory is the actual flight path of the bullet. When a bullet is fired from a rifle, it starts responding to the laws of gravity and physics. Because the forward speed of a bullet decreases while the speed of its vertical drop increases, a bullet’s trajectory is not straight, but curved – actually a parabolic arc. This curve increases in relation to the amount of time the force of gravity has to work on the bullet. The farther away from the muzzle the bullet gets, the greater the curve of the arc. As shown in illustration A, (below), if the bore of the rifle barrel were parallel to the line-of-sight and horizontal (level) when fired, the bullet would start dropping below the line-of-departure almost immediately upon exiting the barrel. Because open sights or scopes are mounted on top of the rifle barrel, the line-of-sight is higher than the line-of-departure. In the case of a scope, the line-of- sight is usually about one and a half inches above the actual center of the bore. In this case, the bullet would leave the muzzle an inch and a half below the line-of-sight, start dropping away from both the line-of-departure and the line-of-sight and would fall at an increasingly faster rate until it hit the ground. Regardless of the velocity, after leaving the muzzle, the bullet would NEVER be as high as the center of the cross hairs in the scope.
To anyone who has done a little shooting, the last paragraph may sound somewhat strange. After all, when we shoot a rifle, the bullet DOES hit where it is aimed (where it’s sighted-in) and not several inches lower. We have also learned that the bullet “rises” through and above the line of sight, then falls back through and below it. Even though that’s what seems to happen, the flying bullet is always being acted upon by the force of gravity, it is ALWAYS FALLING from the line-of-departure. We’ll get to the reason for the illusion of a “rising” in a minute. First, we need to look at a few more facts about bullet trajectory.
The line-of-sight and line-of-departure remain perfectly straight because they are not effected by gravity in any way. This is so because they have no mass as they are only imaginary lines. On the other hand, the poor bullet is not so fortunate. If it were able to fly straight and unaffected by gravity or any other outside force, there would be no difference in where the shooter would have to aim whether the target were five feet or five hundred yards away. Enter Galileo Galilei.
As many of us learned in high school physics, Galileo formulated the laws falling bodies in the 17th century. In essence, he stated that the speed of falling bodies increases at a rate of thirty-two feet per second squared. A flying bullet, even the very fastest bullet, is a falling body and the longer it is in flight, the faster it falls.
Illustration B, (below) shows another interesting fact about bullet flight. According to Galileo, two bullets of different weights, flying at different speeds (even greatly different weights and speeds) will hit the ground at the same time when fired at the same instant from the same height and aimed at the same angle (1 shows the angle). Speed doesn’t keep a bullet in the air, and in this case, faster speed doesn’t keep one bullet in flight longer than the other bullet of less velocity. The only difference is that the faster bullet will have gone a whole lot farther down range when they hit. To get the slower bullet to impact at the same place as the faster bullet, requires that it is aimed at a different angle ( 2 ). Notice that the faster bullet has a “flatter” trajectory when both bullets are aimed to hit the same spot, and obviously it gets there sooner. That’s something to consider when choosing a caliber and/or load for long range shooting.
Although it is important for us to know about the effect of gravity on bullets, unlike Galileo, as hunters, we are less interested in the science of FALLING bodies and more interested in the science of BODIES falling. So, we’ll now get back to the illusion of the “rising” bullet and how it relates to hunting optics and shooting game at long range.
Who would have guessed?
We can’t change the laws of science, but by placing a sight on top of a rifle, we compensate for the differences between straight-line optics and curved trajectory by combining the two. In illustration A, we saw what the trajectory of a bullet would look like if the line-of-sight and the line-of-departure were parallel to each other, but in reality they are set at a very slight angle to each other. Illustration C, (below), shows how this actually works. This angle (exaggerated in the illustration) is what accounts for the idea of the rising bullet. Although the bullet does pass through the line-of sight from below, it never rises above the line-of departure. In a sense, a bullet is both rising and falling at the same time! It may be rising in relation to the ground, but it is still falling from the line-of-departure, even when the rifle is aimed and the bullet is fired in an upward angle.
Because the bullet trajectory is curved and the line-of-sight is straight, the bullet intersects the straight line-of-sight at two points along its path. With a typical hunting caliber, the bullet passes through the line-of-sight at about twenty-five yards (1), then falls back through the line-of-sight at a point about one hundred yards out (2). Notice, however, that the bullet path starts falling away from the line-of-departure as soon as it leaves the muzzle in both A and B and continues to do so during its entire flight. When sighting-in a rifle for hunting purposes, we need to adjust our sights so that the places where the bullet and line-of-sight intersect, the (1) and (2), give us the optimum results when shooting game at long (and short) range.
If we knew that all our shots at game would always be taken at the exact same range, we would only need to sight-in so that the bullet would impact the point of aim at that specific distance. It wouldn’t really matter how much the path of the bullet curved, or how far above the line-of-sight it might get during its flight, or how much it dropped below the line-of-sight after that given range. Since that is not the case, we need to determine the capabilities of the calibers which we are using at different practical hunting ranges and our personal shooting range limits. To start this learning process, we need to have a rifle that is sighted-in properly.
Next, we’ll look at how to sight-in a hunting rifle.