6.4 Mayevski’s Analytical Form of the Drag Model
The Krupp firing tests which generated the first table of values for G 1 (u) took place in 1881. General Mayevski fitted an analytical expression to the tabulated drag function data, forming what is referred to mathematically as a piecewise continuous analytical expression for the drag function. This mathematical expression was used by Col. James Ingalls of the U.S. Army to compute the first ballistics tables which he published in 1893. These tables were updated in 1917. They include the Sand T functions.
The analytical expression which Mayevski chose was the following:
In this expression k is an index that denotes a velocity subrange. Mayevski separated the total velocity range of 0 to 3600 fps into seven subranges, and then found a value of A and a value of nfor each of these subranges. The bullet muzzle velocity will fall in one subrange with index k , and as long as u remains in that subrange the drag function is calculated from (6.4-1) using the values of A k and n k for that subrange. When u decreases to the boundary between that subrange and the next lower one, then drag is computed from the same equation, but with the new values A k+1and n k+1 .
The specific values of A k and n k found by Mayevski are now only approximately correct becauseG1(u) has been redetermined several times through the years as instrumentation and computational technologies have improved. Table 6-1 lists the values of G 1 (u) which are most current to our knowledge. Table 6-2 shows the velocity subranges and corresponding values of A kand n k used by us. We use nine subranges to cover velocities from 0 to 4400 fps.