Velocity

Is rate of motion; the relation of motion to time, measured by the number of units of space pa ed over by the moving body in a unit of time, usually the number of feet in a second. The velocity of a projectile, at any point of its flight, is the space in feet pa ed over in a second of time, with a continuous, uniform motion. Initial velocity is the velocity at the muzzle of the piece; remaining velocity is the velocity at any point of the flight; terminal velocity is the velocity with which it strikes its object; and final velocity of descent in air, is the uniform velocity with which a projectile moves, when the resistance of the air becomes equal to the accelerating force of gravity. The initial velocity of a projectile may be determined by the principles of mechanics which govern the action of the powder, the resistance of the projectile, etc., or by direct experiment. The instant that the charge of a fire-arm is converted into gas, it exerts an expansive effort which acts to drive the projectile out of the bore. If the gaseous ma be divided into elementary sections perpendicular to its length, it will be seen that, in their efforts to expand, each section has not only to overcome its own inertia, but the inertia of the piece and projectile, as well as the inertia of the sections which precede it. The tension of each section, therefore, increases from the extremities of the charge to some intermediate point where it is a maximum. The pre ure on all sides of the section of maximum density being equal, it will remain at rest, while all the others will move in opposite directions, constantly pre ing against the projectile and piece, and accelerating their velocities. As the projectile moves in the bore, the space in which the gases expand is increased, while their density is diminished; it follows that the force which sets a projectile in motion in a fire-arm varies from several causes: (1st) It varies as the space behind the projectile increases, or as the velocity regarded as a function of the time; (2d) It varies throughout the column of gas for the same instant of time; and (3d) It varies from the increasing quantities of gas developed in the succe ive instants of the combustion of the powder. See Initial Velocity . The motion of a body falling through the air will be accelerated by its weight, and retarded by the buoyant effort of the air, and the resistance which the air offers to motion. As the resistance of the air increases more rapidly than the velocity, it follows that there is a point where the retarding and accelerating forces will be equal, and that beyond this the body will move with a uniform velocity, equal to that which it had acquired down to this point. The buoyant effort of the air is equal to the weight of the volume displaced, or P d D ; in which P is the weight and D the density of the projectile, and d the density of the air. When the projectile meets with a resistance equal to its weight, we shall have, P ( 1 - d D ) = A p R 2 v 2 ( 1 + v r ) ; (15) in which the weight of the displaced air is transferred to the first member of the equation. As the density of the air is very slight compared to that of lead or iron, the materials of which projectiles are made, d D may be neglected. Making this change, and substituting for P , 4 3 p R 3 D , the expre ion for the final velocity reduces to v 2 ( 1 + v r ) = 4 3 R D A . (16) The resistance on the entire projectile for a velocity of 1 foot, is A p R 2 ; dividing this by P g , or the ma , we get the resistance on a unit of ma . Calling this 1 2 c we have, 1 2 c = A p R 2    P g , or 2 g c = P A p R 2 . Substituting for P its value in the equation of vertical descent, we have, 2 g c = v 2 ( 1 + v r ) ; from which we see that v depends only on c ; but c = 2 3 R D g A (17) hence, the final velocity of a projectile falling through the air is directly proportional to the product of its diameter and density, and inversely proportional to the density of the air, which is a factor of A . The expre ion for the value of c shows that the retarding effect of the air is le on the larger and denser projectiles. To adapt it to an oblong projectile of the pointed form, the value of D should be increased (inasmuch as its weight is increased in proportion to its cro -section), while that of A should be diminished. It follows, therefore, that for the same caliber an oblong projectile will be le retarded by the air than one of spherical form, and consequently with an equal and perhaps le initial velocity, its range will be greater.