Air density falls exponentially with altitude, so a shell fired from a mountain firebase (or in thinner high-altitude air) experiences less drag and flies noticeably farther than the same shot at sea level.
ρ(h) = ρ0 · e^(−h/H), H ≈ 8500 m
F_drag = ½·ρ(h)·v²·Cd·A
range(h) > range(0) as ρ(h) < ρ0
- Firing altitude — elevation of the gun position; higher altitude → thinner air → less drag.
- Muzzle velocity — initial shell speed.
- Launch angle — elevation angle of the barrel.
- Sea-level reference toggle — overlays a dashed trajectory computed at ρ0 for direct comparison.
Real use: Mountain and high-altitude artillery units apply exactly this density correction in their firing tables — the same charge and angle used at sea level would fall short at altitude if uncorrected in reverse, and travels farther when firing FROM altitude.