Ballistic Trajectory & Interception Lab
Calculate high-arc ballistic flight kinetics, radar horizon detection limits over Earth’s curvature, and surface-to-air interceptor engagement corridors for regional missile defense.
Engagement Profile & Trajectory
Radar acquired target at T+88s. Fire-control solution achieved at T+113s. PAC-3 MSE interceptor launches at T+505s and neutralizes warhead in terminal re-entry phase at altitude 21.4 km with a 18-second residual safety corridor.
Physics & Ballistic Principles
Sub-orbital ballistic missiles follow a Keplerian elliptical path bounded by the Earth's gravitational potential well ($g = 9.81\text{ m/s}^2$) and atmospheric friction layers.
- Boost Phase (0–85s): Solid or liquid propellant motors accelerate the missile through the troposphere and stratosphere to burnout velocity ($V_{bo} = 1.8\text{ to }3.5\text{ km/s}$).
- Midcourse Exo-atmospheric Phase: The payload arcs outside the Karman line (100+ km), where aerodynamic drag is zero. Apogee altitude is determined by launch angle and velocity.
- Terminal Re-entry Phase: As the warhead re-enters atmospheric density ($<40\text{ km}$), extreme shock heating and deceleration occur before ground impact.
Radar Horizon & Interception Corridor
Radar cannot see through the curve of the Earth. A ground radar detects an inbound missile only when the missile climbs above the geometric line-of-sight horizon:
D_horizon ≈ 3.57 · (√h_radar + √h_target) [km]
Early Warning Radars placed forward or airborne (AEW&C) dramatically widen the intercept window by acquiring the boost/apogee vector earlier, leaving ample seconds for battery battle management and hit-to-kill terminal release.
How does the PAC-3 vs. THAAD engagement envelope differ?
Patriot PAC-3 MSE operates primarily in the high-endoatmospheric terminal envelope (altitudes 15 km to 36 km) utilizing active millimeter-wave guidance and solid rocket attitude control motors for direct hit-to-kill impact. THAAD (Terminal High Altitude Area Defense) operates in both upper endo-atmospheric and exo-atmospheric layers (40 km to 150 km) using infrared homing, destroying threats before they penetrate the lower atmosphere.
What creates an "Engagement Breach" or Missed Intercept?
If reaction delays exceed the available window, or if the missile passes outside the interceptor's kinematic ceiling (e.g. attempting to engage an exo-atmospheric apogee with an endo-atmospheric missile), or if the interceptor cannot reach the flight path before ground impact, the status reflects a breach.