ABSTRACT
When the projectile has left the environment of the gun, including the effects of the exiting propellant gases that momentarily surround it, it enters the realm of the exterior ballistician. Here, it is subject to the force of the pressure of the atmosphere that it is flying through, the force induced by its spin, and the force due to the acceleration of gravity. The projectile in flight is no longer constrained in lateral motions by the walls of the gun and, as a free body, can develop motions that are complex and occasionally inimical to the intent of its user and embarrassingly, to its designer. The study of these motions and the progress of the projectile to its target are the subject of this part of the book. We will begin with the simplest case, consideration of the projectile as a point mass
flying in a vacuum with only the force due to gravity acting on it. Then we will proceed to introduce the force due to the pressure of the air, but still considering the projectile as a mass concentrated at a point. Finally, we will consider the projectile as a three-dimensional body acted upon by the air, its spin, and gravity. In the final sections of this part of the text, we shall examine the complex motions arising from the coupling of projectile dynamics and aero-mechanical forces. Our object will be to examine the conditions necessary for a precise, predictable, satisfactory trajectory enabling the projectile to fulfill its terminal ballistic utility. Since this text is intended to have a broad scope, some of the material is not derived in
detail. The reader is encouraged to seek the more detailed treatments in the references noted throughout each section. Many of the principles and terms concerned with fluid mechanics required for the
understanding of interior ballistics were introduced in Section 2.7. These principles will be extended in this section with a view toward an exterior ballistician-commonly called an aero-ballistician. We shall first examine the elements of a trajectory as depicted in Figure 6.1. These terms
are commonly used in the military by gunners and researchers alike. Although most of the symbols and terms in this figure are self-explanatory, some require comment. First is the so-called map range. This is the range to the target that the gunner would see if he or she were to plan firing using a map. The base of the trajectory is quite important and is defined as being level in a plane with the firing point. Gunners of large caliber weapons and mortars take great care in assuring that the sights on the weapon are leveled in the direction depicted as well as the plane out of the paper. Since larger ordnance fires over extensive ranges, it is common to assume that the origin
of the trajectory is coincident with the ground beneath the artillery piece. The line of site and angle of site (yes, they are spelled that way in much of the literature) are what the gunner uses to aim at the target. As you can see, they only assist in determination of the pointing of the weapon and the relative height of the target. An important feature of this diagram is the line of departure. You have probably noticed
that it is not collinear with the elevation of the weapon (i.e., where the bore is pointed).
The reality is that a projectile almost never leaves the bore of a gun aligned with the bore-we shall discuss this in detail later. For now, we will simply state that this is due to the dynamics of the projectile and gun aswell as aerodynamic effects. It should be noted that Figure 6.1 is drawn as two dimensional. The out-of-plane angular position of the projectile at muzzle exit is known as lateral or azimuthal jump. This will combine vectorially with the vertical jump that is depicted to give a resultant jump vector. The angle of lift and line of fall are defined for the level point; however, it is common to
see these used at the target even though, officially these quantities at the target are called angle of impact and line of impact (sometimes shot line). The aerodynamics and ballistics literature are quite diverse and terminology is far from
consistent. This has particular significance in the coordinate systems used to define the equations of motion. In this text, we shall use the coordinate system of Ref. [1] as depicted in Figure 6.2. The primary difference between this scheme and those of, say, Refs. [2-5] is that the y-axis is deemed to be positive pointing up, with the z-axis as positive to the right as opposed to the z-axis down and y-axis to the right. This makes sense to the authors with up being a more intuitive positive direction. The only issues (and some people consider them significant) with this scheme are that first, the nice right handed naming convention of the aerodynamic coefficients is disturbed (as we shall see later x-y-z corresponds to l-n-m
