External ballistics is the part of the science of ballistics that deals with the behavior of a non-powered projectile in flight. External ballistics is frequently associated with firearms, and deals with the behavior of the bullet after it exits the barrel and before it hits the target.
When in flight, the main forces acting on the projectile are gravity, drag and if present wind. Gravity imparts a downward acceleration on the projectile, causing it to drop from the line of sight. Drag or the air resistance decelerates the projectile with a force proportional to the square of the velocity. Wind makes the projectile deviate from its trajectory. During flight, gravity, drag and wind have a major impact on the path of the projectile, and must be accounted for when predicting how the projectile will travel.
The effect of gravity on a projectile in flight is often referred to as bullet drop. It is important to understand the effect of gravity when zeroing the sighting components of a gun. To plan for bullet drop and compensate properly, one must understand parabolic shaped trajectories.
Use of ballistics tables or ballistics software based on the Siacci/Mayevski G1 drag model, introduced in 1881, are the most common method used to work with external ballistics. Bullets are described by a ballistic coefficient, or BC, which combines the air resistance of the bullet shape (the drag coefficient) and its sectional density (a function of mass and bullet diameter). Sectional density is a very important aspect of a bullet, and is the ratio of frontal surface area (half the bullet diameter squared, times pi) to bullet mass. Since, for a given bullet shape, frontal surface increases as the square of the caliber, and mass increases as the cube of the diameter, then sectional density grows linearly with bore diameter. Since BC combines shape and sectional density, a half scale model of the G1 projectile will have a BC of 0.5, and a quarter scale model will have a BC of 0.25.
In general, a pointed bullet will have a better drag coefficient (Cd) or ballistic coefficient (BC) than a round nosed bullet, and a round nosed bullet will have a better Cd or BC than a flat point bullet. Large radius curves, resulting in a shallower point angle, will produce lower drags, particularly at supersonic velocities. Hollow point bullets behave much like a flat point of the same point diameter. Bullets designed for supersonic use often have a slight taper at the rear, called a boat tail, which further reduces drag. Cannelures, which are recessed rings around the bullet used to crimp the bullet securely into the case, will cause an increase in drag.
Wind has a range of effects, the first being the effect of making the bullet deviate to the side. From a scientific perspective, the "wind pushing on the side of the bullet" is not what causes wind drift. What causes wind drift is drag. Drag makes the bullet turn into the wind, keeping the center of air pressure on its nose. This causes the nose to be cocked (from your perspective) into the wind, the base is cocked (from your perspective) "downwind." So, (again from your perspective), the drag is pushing the bullet downwind making bullets follow the wind.
A somewhat less obvious effect is caused by head or tailwinds. A headwind will slightly increase the relative velocity of the projectile, and increase drag and the corresponding drop. A tailwind will reduce the drag and the bullet drop. In the real world pure head or tailwinds are rare, since wind seldom is constant in force and direction and normally interacts with the terrain it is blowing over. This often makes ultra long range shooting in head or tailwind conditions difficult.
The vertical angle (or elevation) of a shot will also affect the trajectory of the shot. Ballistic tables for small caliber projectiles (fired from pistols or rifles) assume that gravity is acting nearly perpendicular to the bullet path. If the angle is up or down, then the perpendicular acceleration will actually be less. The effect of the path wise acceleration component will be negligible, so shooting up or downhill will both result in a similar decrease in bullet drop.
Often mathematical ballistic prediction models are limited to "flat fire" scenario's based on the rifleman's rule, meaning they can not produce adequately accurate predictions when combined with steep elevation angles over -15 to 15 degrees and longer ranges. There are however several mathematical prediction models for inclined fire scenarios available which yield rather varying accuracy expectation levels.
Air temperature, pressure, and humidity variations make up the ambient air density. Humidity has a counter intuitive impact. Since water vapor has a density of 0.8 grams per litre, while dry air averages about 1.225 grams per litre, higher humidity actually decreases the air density, and therefore decreases the drag.