Walk through the convolution that turns a trajectory and a population field into Individual Risk and Expected Casualties. Toggle the stages below to progressively layer the inputs onto the map. All parameter edits at the bottom apply live.
The trajectory is sampled every 1 s by computeTrajectory()from a 2-stage burn model parameterised by site, azimuth, target altitude, and stage timings. Risk integration is performed on every 5th sample — 38 waypoints in total.
At each sample point, the dispersion of a vehicle-failure debris cloud is modelled as a 2-D Gaussian with standard deviation σ = max(5 km, h × 0.025). We use the 3σ disc as the practical casualty footprint.
The map circles you see at stage 2 are exactly these footprints. Their union is the “debris corridor” — the support of the kernel that we'll convolve against the population field next. Higher altitudes yield wider but thinner kernels because Pdebris(h) ∝ exp(−h / 200).
Population density ρ(lat, lon) is sampled from Statistics Canada's 2021 Census Dissemination Area polygons. The map renders every DA whose centroid falls inside the launch circle (100 km) or the downrange corridor band (±50 km cross-track). Hover a polygon to see its density and resident count.
The corridor population above is the convolution of the corridor mask with the DA polygons (a polygon-in-polygon aggregation). The per-sample table below shows the other convolution — the dispersion kernel against ρ(x, y) — which yields Ec and IR.
Stage 4 paints each sample's 3σ disc on the map with a colour stop driven by its exposed population ρᵢ · A₃σ. Cool blues mean the kernel landed on empty terrain (or open ocean); warm reds mean it overlapped a populated DA. Hover any disc to see the multiplication breakdown; the centroid label gives the scalar value used by the table below.
Each table row evaluates the integrand at one sample. Reading left to right you can see every factor of Ec = Σᵢ Pdebris(hᵢ) · Pcas | deb(σᵢ) · ρᵢ · A₃σ(σᵢ) multiplied out, with the ★-marked row dominating the IR maximum.
Edits apply live to every section above. Out-of-range values are clamped on submit.
Per-launch probability of catastrophic vehicle failure. Drives every downstream debris term.
Industry initial-flight reliability ≈ 98% — Transport Canada Space Launch Risk Methodology §4.2.
Average number of casualty-producing fragments resulting from a vehicle break-up.
FAA AC 431.35-2B Appendix A; small-launch class typically 40–80 pieces.
Effective lethal-debris footprint per fragment. Combines fragment cross-section with person projection.
FAA AC 431.35-2B §A.3; tuned for liquid-propellant first-stage break-up.
Vertical projected area of a standing person, used inside casualty-area derivation.
FAA RCC 321-17 Annex A — accepted standard 0.5 m².
exp(-h / h₀) attenuation of debris-reach probability with vehicle altitude — higher break-ups disperse before reaching ground.
Empirical fit to NASA-CR-2002-211867 ground-debris distribution data; default 200 km.
Ground-impact 1σ dispersion as a fraction of altitude. σ = max(5 km, alt × factor). Larger factor = wider but thinner footprint.
Range-safety Monte-Carlo fits; 0.025 is typical for solid 1st-stage debris.
Multiplier applied to IR and Ec when ≥60% of the ground track is over open ocean. Reflects negligible population density.
Transport Canada §6.5 — overflight-of-uninhabited-area allowance.
Maximum allowable Individual Risk for any member of the public per launch event.
CSAA/Transport Canada §5.3 — equivalent to 1×10⁻⁶.
Maximum allowable Expected Casualty count summed across the affected population per launch event.
CSAA/Transport Canada §5.4 — equivalent to 1×10⁻⁴.
Advanced Mode is intended for sensitivity analysis only. Regulatory submissions must use the Transport Canada–approved default values.