Each fragment falls through an exponential atmosphere ρ(h) = ρ₀e^(−h/H) (ρ₀ = 1.225 kg/m³, H = 7160 m) and decelerates under drag while gravity pulls it along the flight path:
dv/dt = g·sin(γ) − ½·ρ(h)·v²·Cd·A / m
dh/dt = −v·sin(γ)
Stagnation-point heating follows the Sutton–Graves approximation, then a lumped thermal-capacitance balance (heating in, blackbody radiation out) tracks the fragment's own temperature:
q = k·√(ρ/Rn)·v³ (k = 1.7415×10⁻⁴ SI)
m·c·dT/dt = q·A_front − ε·σ·A_surf·(T⁴ − T_amb⁴)
If T reaches the material's melting point the fragment demises (ablates away completely, real ADR guideline compliance). If it reaches h = 0 while still solid, it survives to ground impact and contributes a casualty area — the NASA-style expected footprint of a person struck by that debris:
A_c = π·(√(A_front/π) + r_person)², r_person ≈ 0.5 m
Expected casualties ≈ (ΣA_c / 1 km²) × population density
"Design for demise" swaps titanium and steel components (melting ~1650–1930 K) for aluminum and composite ones (melting ~750–930 K) so the same reentry heat pulse that leaves a legacy fuel tank intact instead burns it up completely — the real design principle behind the 25-year deorbit and post-mission-disposal guidelines cited across ESA and NASA debris-mitigation standards.
Note on this 2D version's defaults: the original 3D simulator's default sliders (28 cm, 18°) happen to sit in a region of this model's parameter space where neither the legacy nor the design-for-demise materials reach their melting point before impact — both fates come out "survived", so the toggle looked inert until you moved a slider. This build defaults instead to 8 cm / 45°, verified numerically (small ballistic coefficient plus a steep entry angle raises peak heating enough) to reliably demise the wheel and bus in design-for-demise mode while they still survive in legacy mode, so the comparison the tool is built around is visible immediately. The underlying physics is unchanged — it's a starting-parameter fix, not an equation fix.
Drag to pan the altitude view, scroll or pinch to zoom.