Air density falls roughly exponentially with altitude, so drag — which scales
with density — weakens the higher the gun sits. A round fired from a mountain
position therefore reaches further than the same round fired at sea level. The
target-height difference also changes the effective angle of site, which shifts
the optimum elevation for a given range.
ρ(h) ≈ ρ₀ · exp(−h / 8500) (barometric approximation)
drag accel ∝ ρ(h) · v²
angle of site correction: elevation adjusts for Δheight / range
- Firing altitude — elevation of the gun position; higher altitude = thinner air = less drag = more range.
- Target height Δ — how much higher (+) or lower (−) the target sits than the gun.
- Launch angle — barrel elevation above the local horizontal.
The dashed comparison trail shows the same shot fired at sea level (ρ ≈ 1.225
kg/m³) for the same angle and velocity — the visible gap is entirely the effect
of altitude on drag.