Lately, we’ve been talking about long range shooting, but what better place to start then with some ballistics theory. In the last post in this series, bullet trajectory part 1, I talked about the variables that determine the vertical component of bullet trajectory. In this article we will examine what happens on the horizontal plane.
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.
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.
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.
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.
I will talk more thoroughly about light in a future post, but in the next article, I’ll talk more in detail about the Coriolis Effect. Stay tuned!