This is not a textbook parabola. The gun throws a 76 mm round at a drag
coefficient of 0.28, and at these speeds air drag takes a bite of the same order as gravity, so a
vacuum range formula lands hundreds of metres wrong. The computer instead runs the round through
the game's own integrator, the same 1/240 s steps and the same constants, and searches for the
launch condition that puts it through the target's altitude at the target's range.
- Muzzle velocity is not an energy sum. The launch is integrated at two microsecond
steps down the 3 inch bore, 120 cm barrel: compressible flow out of the 10 L receiver through the
2 inch valve as it opens over 3 ms, an energy balance on the gas behind the projectile, static
breakaway then running friction on a tight pressure fit, atmospheric back pressure, and the
weight component along an inclined barrel. That last term is why the elevation you dial changes
the muzzle velocity you get, and why the chamber never reaches reservoir pressure.
- The station. Air density is read at the round's real height above sea level the whole
way up the arc, from the site elevation, altimeter setting, temperature and humidity you enter.
Between a cold day at sea level and a hot one high up, the same solution moves the fall of shot
by more than a hundred metres, so copy these four numbers off the game's atmosphere panel before
you trust anything below.
- Two arcs. Range peaks near 41 degrees and falls away either side, so a reachable
target has a flat low arc and a lofted high arc. The low arc is faster and flatter, the high
arc drops nearly vertically and is far less fussy about range error.
- Wind is a vector, applied to the round's airspeed rather than bolted on as a range
offset, and it strengthens with altitude exactly as the game strengthens it: 35 percent stronger
at 450 m and up. Give it as a speed and the bearing it blows from, the way the game reports it,
and the computer resolves it onto your gun target line itself.
- Lay off. Whatever blows across the line pushes the round off it, so the gun is laid
off the target bearing by the angle that walks the drift back onto the target. Laying off rotates
the gun line, which changes the wind's own components and swings the target off the new line, so
it is solved in the target line frame and iterated to a fixed point. The answer is the bearing to
dial on the plan view, not the bearing to the target.
- Gusts cannot be predicted, only bounded. The gust window is where the round lands
if the gust happens to sit at full tail or full head for the whole flight.
- Snapping. The game's controls move in 1 psi and 0.1 degree steps, so the solution is
rounded to what you can actually dial in and the residual miss is reported honestly.
What it does not know: the terrain between you and the target. The solution puts the
round through the target's altitude at the target's range. If a ridge stands in the way, take the
high arc. It also cannot know the gust, only bound it.
Checked against the gun. Ten fire missions read straight off the game panel, solved here,
dialled in and fired: ten compounds destroyed, worst miss 1.7 m on a 50 m target, flight times
matching prediction to seven thousandths of a second, over ranges from 202 to 688 m and stations
from 75 to 1304 m.