The longest recorded range is that given in 1888 by the 9.2-in. gun to a shot weighing 380 lb fired with velocity 2375 f/s at elevation 40°; the range was about 12 m., with a time for flight of about 64 sec., shown in fig. 2.
A calculation of this trajectory is given by Lieutenant A. H. Wolley-Dod, R.A., in the Proceedings R.A. Institution, 1888, employing Siacci's method and about twenty arcs; and Captain Ingalls, by assuming a mean tenuity-factor τ=0.68, corresponding to a height of about 2 m., on the estimate that the shot would reach a height of 3 m., was able to obtain a very accurate result, working in two arcs over the whole trajectory, up to the vertex and down again (Ingalls, Handbook of Ballistic Problems).
Siacci's altitude-function is useful in direct fire, for giving immediately the angle of elevation φ required for a given range of R yds. or X ft., between limits V and v of the velocity, and also the angle of descent β.
In direct fire the pseudo-velocities U and u, and the real velocities V and v, are undistinguishable, and sec η may be replaced by unity so that, putting y = 0 in (79),
| (88) tan φ = C | [ | I(V) - | ΔA | ] | . | ||
| ΔS |
Also
(89) tan φ - tan β = C [I(V) - L(v)]
so that
| (90) tan β = C | [ | ΔA | - I(v) | ] | , | ||
| ΔS |
or, as (88) and (90) may be written for small angles,