A diagram to facilitate the study of external ballistics

The semi-graphical method about to do described enables solutions of many dynamical problems of a practical nature to do obtained with ease and rapidity. In particular, useful solutions can be found of problems relating to motion in a resisting medium in cases where the resistance is given as a function of the velocity which cannot be expressed by any simple algebraic form. In this paper the method is applied to the investigation of the motion of a projectile. Some of the curves obtained can be plotted directly from the ballistic table, but none of the curves are found in this way. They are derived by simple graphical processes from a primitive curve which represents the results of numerous experiments, reduced to give the resistance of a standard projectile, fired under standard conditions, as a function of the velocity. The curve, which is the basis of the diagrams given in the paper, is plotted from data given in the official 'Text-book of Small Arms,' 1909. From the educational point of view the method about to be described has the advantage that the essential scientific principles relating to the motion of a projectile can be taught rapidly, and without reference to the laborious methods of analysis by means of which the ballistic tables are derived from the experimental data. As will be seen, other functions, besides those given in the ballistic tables, can be plotted with ease, because elimination is done by mere projection with set-square and T-square. By the drawing of a ballistic diagram a student of gunnery becomes familiar with the general relations existing between the different functions involved; in fact the set of curves constituting the ballistic diagram will probably, when drawn by himself, persist as a permanent mental picture of reference which cannot but be useful to a gunnery officer.