which is Colonel Sladen's formula, employed in plotting ordinates of a trajectory.
At the vertex A, where y = H, we have t = t′ = ½T, so that
(33) H = ⅛gT2,
which for practical purposes, taking g = 32, is replaced by
(34) H = 4T2, or (2T)2.
Thus, if the time of flight of a shell is 5 sec., the height of the vertex of the trajectory is about 100 ft.; and if the fuse is set to burst the shell one-tenth of a second short of its impact at B, the height of the burst is 7.84, say 8 ft.
The line of sight Ox, considered horizontal in range table results, may be inclined slightly to the horizon, as in shooting up or down a moderate slope, without appreciable modification of (28) and (29), and y or PM is still drawn vertically to meet OB in M.
Given the ballistic coefficient C, the initial velocity V, and a range of R yds. or X = 3R ft., the final velocity v is first calculated from (29) by
(35) S(v) = S(V) - X/C,
and then the time of flight T by