CHAPTER VI. The Comparative Efficiency of Projectiles from the Ballistic Standpoint. INCE the value of C varies directly as the weight and indirectly as c for any given diameter, formula 9, and inasmuch as C measures the ability of the projectile in overcoming the resistance of the air, it follows that the greater the value of C, the greater this ability of the projectile. It is evident that the value of C may be increased either by increasing the weight or decreasing the value of c (for any diameter), or by both. The weight may be increased either by increasing the length of the projectile or using material of the greatest specific gravity compatible with the cost of production and tensile quality, or by both methods. Inasmuch as the material now used has probably the greatest specific gravity, the length must be increased. It is also evident that there must be a maximum limit to the length. The maximum weight of a projectile is determined by the laws of interior ballistics, including twist, Vol. 11. From the definition of c, formula 11, the greater the value of n, the less the value of c. From this standpoint, the longer the pointed head of the projectile, the less the value of c. But from the standpoint of steadiness the center of gravity, moment of inertia and radius of gyration are important factors. There are three distinct forms of projectiles with many modifications therefrom. The Paraboloidal head is the solid of revolution generated by a semi-parabola, BOEC, Fig 5, rotating upon its axis, OB. The Ogival head is the solid of revolution generated by the segment, CFOB, Fig. 5, of the circle rotating upon its chord, OB. The chord becomes the axis of the head and produced becomes the axis of the projectile. AC is the diameter of the projectile. The Conical head is a solid of revolution generated by a right triangle, CNOB, rotating about its perpendicular OB. The energy required to move a given weight a given distance varies inversely as the time. If one wishes to toss a ball across the street, it requires less energy and greater time, than if he threw it with all his might, in which case it would require more energy and less time for the flight. Let the spaces, Fig. 5, between the parallels represent units of pressure upon the heads of the paraboloidal, the conical and ogival projectiles. What may be proven true of one molecule of air may be proven of all molecules. Suppose that a molecule strike the apex, O, by the paraboloidal head it will be moved to L, while the projectile moves forward to 1; the conical head will move the molecule to N, while the projectile moves forward to 3, and the ogival will move the molecule to M, while the projectile moves forward to 2. That is, in each case the molecule has been moved aside exactly the same distance, the same amount of work has been done by each projectile but in different times. The paraboloidal head did the work while moving from 0 to 1; the ogival while moving from 0 to 2; and the conical while moving from 0 to 3. For this particular space the paraboloidal expended the most energy, and the conical the least, to accomplish the same amount of work. Or to state the law differently and generally, that part element of each of the three heads having the shortest intercepted segments between the parallels offers the greatest resistance to the atmosphere; and conversely, those having the longest intercepted segments offer the least resistance, and equal segments offer equal resistances. It will be seen that the intercepted segments of the paraboloidal near the apex are shorter than the corresponding segments of the ogival. And it will be seen on approaching the shoulder that the segments of the paraboloidal become equal to and after passing a certain point greater than the corresponding segments of the ogival. That is, the resistance offered by the paraboloidal is at first greater, then equal, and finally less, than that of the ogival. If then, the total resistance suffered by each can be computed, the relative efficiency of the two heads may be determined. Analytically, it may be shown that the corresponding segments are equal at some point, say E for the paraboloidal and F for the ogival, and the resistance suffered by each from the apex to this point and from this point to the shoulder of each com |