Side-on view of the same drag-augmented projectile physics as the 3D version, plus a horizontal wind term. The shell is a point mass launched at speed v0 and angle θ; gravity pulls it straight down while quadratic aerodynamic drag opposes its velocity relative to the moving air.
v_rel = v - v_wind
a = g + (-1/(2m)) * ρ * Cd * A * |v_rel| * v_rel
x(t+dt) = x(t) + v(t)·dt
v(t+dt) = v(t) + a(t)·dt (semi-implicit Euler, dt ≤ 0.02s)
g = 9.81 m/s² down, ρ = 1.225 kg/m³ (sea-level air), A ≈ 0.045 m² cross-section. A tailwind (positive) reduces the relative headwind drag and stretches the range; a headwind shortens it. Heavier shells resist deceleration better since drag scales with area, not mass.
- Muzzle velocity — initial speed v0 of each shot.
- Launch angle — elevation θ of the barrel above horizontal.
- Drag coefficient — 0 (vacuum parabola) to 1.0 (very draggy).
- Projectile mass — heavier rounds flatten the effect of air resistance.
- Wind — constant horizontal air velocity added to the drag term.
- Fire — launches a new shell; up to 6 trails are kept for comparison.
The view auto-zooms to fit the tallest and longest shot fired so far, so trails from very different settings stay comparable on one screen.