A fired projectile follows Newton's second law under gravity and, in the real atmosphere, aerodynamic drag opposing its velocity relative to the air.
m·dv/dt = m·g + F_drag + F_wind
F_drag = -½·ρ·Cd·A·|v_rel|·v_rel
- Muzzle velocity / angle — set the initial velocity vector at the instant of firing.
- Crosswind — couples into drag on the relative velocity, deflecting the shell's horizontal range.
- Air density — scales drag directly; thinner air (higher altitude) flattens the drag-vs-vacuum gap.
- Air toggle — "Vacuum" removes drag and wind coupling entirely, giving the textbook parabola with range v²·sin(2θ)/g, drawn as a dashed reference curve.
Real-world relevance: fire-control computers for artillery solve exactly this kind of drag-coupled trajectory (plus Coriolis effects at long range) to convert a desired target distance into a gun's elevation and azimuth.