BALLISTICS. The name °ballistics'° ap plies to that division of mechanics which treats of the motion of projectiles.
This subject has engaged the attention of mathematicians and scientists for centuries, and approximate determinations of physical rela tions have been assumed as fundamental laws, and elaborate tables calculated on various hypotheses. A resume of these contributions to the science will be found under the caption GuNNEav, to which the reader is referred.
As a basis for the simple general discussion of both exterior and interior ballistics, certain general hypotheses, justified by present knowl edge derived from careful expenments in each case, will be made. These are: I. The motion of a projectile in the bore of a gun is such that the velocity, v, when the projectile has traveled a distance u along the bore is given by the relation au u This relation is derived from the records of measurements of time of recoil of a free car riage, measured by a tuning fork scoring on a blackened ribbon. In all cases the velocity is duplicated by a relation of this form with a fidelity as remarkable as will be found in the case of any accepted experimental law con nected with explosives.
2. The motion of a projectile in air is, at any point x,y, of its path or trajectory affected by two forces; namely, the force of gravity acting vertically downward with an accelera tion 9 feet per second, and the resistance of the air, acting in direct opposition to the mo tion of the projectile in its path. Experiment shows that the retardation due to air resistance is given by an expression of the form F (v) r= C in which F (v) is dependent on the velocity, v, alone, and increases with it; and C is given by the formula • w C=7,-- • in which di is the density of an atmosphere assumed as standard, d is the mean density of the air in the par ticular case under consideration, w the weight of the projectile in pounds, d the calibre of the projectile in inches; that is, the diameter of the projectile, i the "coefficient of form of the projectile, C the Monistic coefficient" of the projectile. The value of i is given by the formula 2 4n—I i=—.
7 n being the radius of the arc with which the ogive or head surface is generated, the radius being measured in calibres. i is unity for
n=2, which is the standard for ballistic table& Recent developments point to a value it =7 for projectiles of the future; this gives i thus practically halving the retardation, or doubling the ballistic efficiency of a projectile otherwise the same.
With these hypotheses, exterior and interior ballistics may be satisfactorily discussed and practical problems may be readily solved.
Interior Ballistics.—If v be the velocity, in feet per second, corresponding to a travel, u inches, along the bore, of a projectile of mass m and weight, w pounds; propelled by a charge, 4) pounds of povvder, fired in a powder chamber of volume, c' cubic inches; the cross section of the bore being a square inches; the total length of the rifled bore being U, and the total volume of the bore and chamber combined being C, the following relations obtain o c' dv P =r= 12 m du a' Ns =12 g ° (b + u)' P being the pressure in pounds per square inch for travel u The maximum pressure occurs when b — u T =" for which 16 ma' r 9 b For infinite travel V = and hence E ma' —2 represents the total energy of the powder charge pertaining to the translation of the projectile; and, as the powder charge is increased, the waste energy (that is, that used in doing work other than conferring velocity on the projectile) remaining approximately the same, while the total energy increases, it is seen that the efficiency per pound of powder should increase with the charge, other conditions remaining the same. Accordingly it would appear that a2 — m — = E 2 should increase with the powder charge; or, more strictly, with the powder charge per unit of chamber-volume. In metric units this ratio of powder charge to chamber is expressed by dividing the weight of the powder charge by the volume of the chamber; but, as our units are not so related, this ratio, called the "density of loading" is defined as the ratio of the weight of the powder charge to a volume of water which will exactly fill the powder chamber; and, as one pound of water occupies 27.68 cubic inches, the density of loading is 27.68 c' Accordingly.