# RIFLED BARREL: FACTORS OF TRAJECTORY

Once the bullet has left the barrel, its trajectory is not straight; it starts a descending parable that leads it inexorably to the ground. There are many factors that determine its fall down; the most relevant ones are the gauge, the force of gravity. the weight of the projectile, the initial speed, the air resistance.  It’s easy to understand the effects of the two external factors to the phenomenon ballistic, gravity and air resistance: as for any body suspended in the air, the force of gravity tends to draw it down, while in the case of air resistance it realizes the only effect of reducing the velocity of motion of the projectile. There is also another factor typical of the atmosphere: the “wave resistance”. It consists in the compression of air in front of the projectile when it travels nearby the speed of sound and opposes further resistance.

The first thing to point out in the shot with a rifle, for sport or hunting, is that the sights are not on the same level with the barrel; the value is variable from 30 to 50 mm for the metallic sights until 60-80 mm of scope. It ‘important to know this distance in order to determine the zero point (ie projectile on the center of the target) of the various ammunition. Here are helpful the ballistic tables, but these indicate the average for each cartridge, suitable for all situations, but for the absolute accuracy, starting from these, it is necessary for the hunter or shooter to calcolate them everytime. In this case we have to remember that even for a single gauge there are many variants on the zero point because of the weight of the projectile and the type of charge.

The second element known for all is that while the line of sight is a straight line, the trajectory of the projectile is not, being as a parable which, for a large part of its stroke, is above the line of sight and then descends below. For accuracy, in its travel the projectile meets twice the line of sight: a first time when intersects it to pass above and a second time when crosses it to go toward the ground (zero point). Therefore, calibrating a weapon for example at 200 meters, the bullet, exiting the barrel, will be below the line of sight, then, in its central part, it will have risen above and then it will meet it in the 200 and then it will continue to descend. So if with a weapon perfectly calibrated to 200 meters I need to shoot at a target a hundred yards, I will have seek to under the center of the target by a distance of a few centimeters indicated by the ballistic tables.

Linked to descending part of the parable there is concept of coverage. This is the total space between the exit of the projectile from the barrel and the point where it touches the ground (reasoning on an hypothetical area completely horizontal). The maximum range (also 1.9-2.3 mi) is achieved with a weapon inclined by 45 ° (in the figure is given from the sum of the distances D1 + D2 + D3). Remaining within the hunting another element is more interesting: the useful coverage. This is the maximum distance within is possible to kill cleanly the game. Here the limit is reached between 320 to 430 yards fast gauge, but we have to advise to reduce it as much since at those distances perfectly is problematic to locate the point where to aim or other factors, not easily valuable, may come into as the crosswind.

In its advancement in the trajectory the projectile meets the resistance of the air that has variable effect depending on its form. In this case we have to evaluate the sectional density of the projectile and its ballistic coefficient.

The sectional density is obtainable by a complex formula: division of shot weight by its diameter. At the same weight, a shot with a smaller diameter will have more ability to penetrate the air resistance. The greater the number of sectional density, the greater will be the penetration capacity of the air by the projectile.

The ballistic coefficient is obtained with another mathematical formula where the value previously obtained (sectional density) is divided by a coefficient of the form which varies for each type of shot. Also in this case the greater will be the result of the division more effective will be the air penetration of the shot. This is because the projectile, in its trajectory, will have a longer trajectory and a more tense, yielding less energy in the parable and then keeping it for the impact on the target on which comes with greater accuracy.

Alessio Ceccarelli