Vehicle & Trajectory
Breakup triggers when q = ½ρv² ≥ q*. Post-breakup: fragments generated stochastically if enabled.
What these inputs mean
- m₀: total mass at interface (~120 km).
- A: reference cross-section; sets drag and heating collection area.
- CD: drag coefficient; 2.0–2.2 typical for blunt tumbling shapes.
- Rn: effective nose radius for stagnation heating; smaller ⇒ hotter.
- v₀: interface speed; ~7.6–7.9 km/s for LEO.
- h₀: initial altitude of integration start.
- γ: flight-path angle; positive is downward. Small positive is shallow.
- Δt: integrator time step.
- q*: breakup threshold dynamic pressure (Pa) where structure fragments.
- L/D: simple lift model (0 = ballistic).
Materials & Mass Fractions
Fractions should sum ≈ 1.0; model normalizes them.
What these inputs mean
- Fractions approximate bulk materials. Used to split ablation energy draw and yields.
- Electronics+Cu covers wiring, boards, connectors.
- CFRP/epoxy drives soot yield when pyrolyzed.
Thermochemistry (effective heats of ablation)
Convective heating via Sutton–Graves: q̇ = k √(ρ/Rn) v³ with k ≈ 1.7415×10⁻⁴ (SI, Earth).
What these inputs mean
- Habl: effective energy to remove 1 kg (sensible + phase + chemistry).
- ηabl: fraction of convective heating that goes into the structure (vs air).
Stochastic Breakup & Risk
Risk proxy Ec ≈ (Σ Acas)·(Pop/LandArea)·fland. Global-average only — use ground-track population for formal work.
What these inputs mean
- Stochastic breakup: splits remnant mass into lognormal fragments.
- kA: converts fragment mass to area (∝ m2/3).
- Acas: casualty area per surviving fragment footprint.
- fland: fraction of ground track over land.
Environmental Yields & Chemistry
NOₓ ≈ kNOx·(convective heat to air) with Gaussian altitude weighting (peak set by NOₓ altitude peak). O₃ proxy uses alumina/titania surface area × uptake rate over a window.
What these inputs mean
- kNOx: proportionality from energy to air → NOx formed (tunable).
- hNOx: altitude where NOx formation is most efficient in this proxy.
- κ: ozone loss proxy rate per unit particle surface area.
- Window: integration duration for the proxy effect.
Assumptions: 1-DOF along-path dynamics; exponential density; constant Sutton–Graves k; stochastic breakup allocates mass via lognormal; survivor threshold 250 g; simplified NOₓ & ozone proxy parameters are user-tunable—treat as first-order estimates.
Key Events
Totals
How to read these
- Burned/Residual mass: change in vehicle mass due to ablation; residual may impact.
- Al₂O₃, TiO₂, SS‑ox, Cu/CuO, Black C: total particulate/oxide yields across all layers.
- NOₓ: proxy estimate formed in heated air along the path.
- Surface area: specific surface in stratosphere/mesosphere — larger can enhance heterogeneous chemistry.
- O₃ loss proxy: ozone-equivalent mass lost via proxy uptake over the window.
Layer Depositions
| Layer | Al₂O₃ (g) | TiO₂ (g) | SS-ox (g) | Cu/CuO (g) | Black C (g) | NOₓ (g) |
|---|
How to read this
- Shows where in the atmosphere materials and NOx are deposited or formed.
- Stratospheric burdens are most relevant for ozone chemistry; mesospheric for noctilucent cloud seeding.
Risk & Chemistry Proxies
How to interpret
- Surviving fragments: pieces ≥ ~0.25 kg assumed to reach ground.
- Casualty expectation Ec: global-average expected casualties per reentry (use ground‑track models for missions).
- Common standard: Ec < 1×10⁻⁴ for compliance.