A projectile in moving a given distance through the air displaces or thrusts aside a definite number of its particles, and an equal number of like particles are forced by the pressure of gravity into the space vacated by the projectile.
As friction may, with the smooth surfaces and limited dimensions of projectiles, be wholly neglected, a very slight addition to the values of the constant representing the form will be ample in any case save for rough turned or cast shot such as the old spherical shot; and for reasons that will appear as we proceed, friction will not for the present be considered in computing the resistance to elongated projectiles.
I shall use the symbol ? to designate all modifications of form, or resistance to the head.
I have computed values of ? for various forms of head used in modern artillery and small arms, and these values I have finally adopted as best for practical use.
We have, for the three forms of head—
? = .625 for the flat head,
? = .375 for the hemisphere,
? = .263 for the ogival of 12 calibres.
Formula (1) may, for practical computations with the 8-inch projectile, be conveniently shortened as follows: The area displaced is 50 square inches, and with air of a density of 534.22 grains per cubic foot (Bashforth), equal to 13.1032 cubic feet of air to the pound, the 8-inch projectile will displace one pound of air in each 37.74 feet of flight, or one 37.74th of a pound, in moving one foot; and since dividing the Vel. by 37.74 is equivalent to multiplying it by the weight displaced in moving one foot, the operation can be further simplified by also dividing by 2g at the same time, or 37.74 X 64.4 = 2430.