When there is a firing elevation or depression angle, that is, when you’re firing with the barrel inclined upward (uphill) or downward (downhill), the bullet always hits higher than the aimed point. This happens when sights are zeroed on a level range, and then the shot is taken to a target positioned at the same distance but on a higher or lower ground, relative to the firing position, which forces the shooter to raise or lower the barrel to a degree.

Long range precision shooters, such as hunters or military personnel, operating in mountainous or hilly terrain, or those operating in urban terrain, constantly deal with this phenomenon. The error induced by firing at an angle is considerable, and must always be taken into account, especially when extreme accuracy is needed and/or when shooting over long distances.

To realize how much elevation influences a shot, I’ll give you an example: shooting with a .308 Win rifle zeroed at 100yds on a flat range, firing from an elevation angle of 15° (barely noticeable if not measured with a gauge) induces an error of 2.5in at 500yds, 7.5in at 800yds and 13.4in at 1000yds. If you need extreme accuracy, that’s just enough margin of error to keep you off target.

When the steepness of the elevation angle increases, the error dramatically increases, even at closer ranges. Shooting with the same rifle, zeroed at 100yds on a level range, with an elevation angle of 60°, you’ll shoot with an error of 5in just at 200yds (enough to keep you off the vital zone of a deer, for example) and 38in off at 500yds. Longer shots with such an angle are unlikely, but consider this: shooting with this angle at 1000yds would yield an error of 200 inches, literally enough to miss the “broad side of a barn!”

On the horizontal plane, the bullet does not follow a straight trajectory. From the moment it leaves the muzzle, it begins to be deflected by the effect of spin drift and, if present, wind.

Spin drift is the deflection caused by the gyroscopic motion of the bullet. This motion, aside from keeping the bullet stable and pointed forward, deflects it in the direction of the spin. If the barrel rifling has a right-handed (RH) twist, the bullet has a right-handed spin and is deflected toward right. Vice versa, if it has a left-handed (LH) twist, the bullet is deflected toward left. The amount of drift is in function of the spin rate relative to the bullet length. The higher the spin rate, the higher the drift. The spin rate depends on barrel twist rate and bullet speed. Shorter twist rates and higher bullet speeds produce higher spinning rates. On a future article we will examine the reason of the spin drift phenomenon.

Long Range Shooting: External Ballistics - Angle Shooting

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Wind: The air in which the bullet flies behaves as a fluid. When it moves, under the effect of wind, the bullet traveling through it tends to move with it. To better understand this concept, think of the bullet as a raft crossing a river. It moves forward toward the other bank, but at the same time, it is pushed downriver by the stream.  The result is that the raft does not reach the opposite bank at the point directly across from where it started, but instead lands further down-river. The bullet flying through a wind has the same behaviour.

Deflection, on the trajectory of a 175 HPBT SMK, for a wind at 10MPH coming perpendicular from the right.

 

The deflection caused by wind depends on several factors, including:

Wind speed: The higher the wind speed, the higher the deflection.

Time of flight: The shorter the time of flight, the shorter the time the bullet is pushed by the wind and, therefore, lower the deflection. Time of flight is dependent on bullet speed: the higher the bullet speed, the shorter the time of flight to a given distance.

Angle of incidence: A wind that blows perpendicular to the trajectory will have the most impact, while winds with different angles will have less influence. Winds that blow parallel to the trajectory, in other words head winds and tail winds, have no effect on the horizontal component of the trajectory.

Ballistic coefficient: Bullets with higher BC have better aerodynamics, so they are less affected by drag and their time of flight is shorter.

Bullet weight: Heavier bullets offer more resistance to the deflection. In addition, heavier bullets have often a higher BC.

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On the image above, you can see the effect of a 10mph wind, coming straight from the right, on a .308Win long range bullet. As you can see, the deflection is not linear, but parabolic. Indeed, with the distance increasing and bullet slowing down, wind deflection increases more and more.

Coriolis Effect must be taken into account when compensating on the horizontal plane. The error due to Coriolis force is always toward the right on the northern hemisphere, and always toward the left on the southern hemisphere. It is in function of latitude and bullet speed. It is negligible until about 1000y.

Light, as with the vertical plane, has an effect on the horizontal path of trajectory. Light angle changes can lead to subtle, but yet detectable, changes in point of aim and consequently in point of impact.