Firing a shell converts chemical energy in the propellant charge into kinetic energy over the barrel length. Modelling the in-bore pressure as a half-sine along the travel distance and equating the work done to the shell's muzzle kinetic energy gives the peak chamber pressure needed to reach a chosen muzzle velocity.
P_max = (m · v0² · π) / (4 · A · L)
Exterior flight (quadratic drag):
dv/dt = -g·ĵ - (Cd·ρ·A)/(2m) · |v_rel|·v_rel
v_rel = v_shell - v_wind
The trajectory is integrated numerically at 50 Hz from the moment of firing until ground impact, so range, apex height, time of flight and impact velocity are all genuine outputs of the physics model, not lookups.
- Elevation angle — sets the launch angle of the barrel and initial velocity vector.
- Muzzle velocity — sets launch speed and, via the pressure formula above, the required chamber pressure.
- Crosswind — a lateral air-mass velocity that the drag term reacts against, curving the flight path.
- Standard Atm / Vacuum — toggles air density (1.225 kg/m³ vs 0), isolating the effect of drag on range.
- Fire — runs the integrator and animates the shell along the computed path.
Real proving-ground live-fire tests use radar and onboard telemetry to validate exactly these quantities — muzzle velocity, pressure, and impact data — against the ballistic model before a round is certified for service.