This tool estimates the probability of a mid-air collision between a high-altitude balloon and passing aircraft using a sweep-area model.
Model assumptions & calculation method
Sweep-area approach: Each aircraft is modelled as sweeping a cylindrical volume through the study airspace. The cylinder’s radius equals the aircraft’s projected cross-sectional equivalent radius plus the balloon radius; its length equals speed × exposure time.
Study volume: The horizontal study area (entered in km²) is converted to square metres and multiplied by the aircraft’s cruise altitude to yield a prism volume Vtot.
Aircraft density: For each class, the “# Aircraft” field is interpreted as the average number of aircraft simultaneously present below that cruise altitude. Density is ρ = count / Vtot (m⁻³).
Typical mission time split: We assume aircraft spend 50% of mission time at cruise altitude and 50% distributed across climb and descent below their cruise altitude. Collision exposure is scaled by these fractions. Float exposure above an aircraft class’s cruise altitude is taken as zero.
Exposure time: The balloon spends tasc = h / vasc and tdesc = h / vdesc within the altitude region up to each aircraft class’s cruise altitude; both are scaled by 50% to reflect that only the non‑cruise portion of aircraft time overlaps. Float exposure is: (i) zero if the float band lies entirely above the aircraft cruise altitude; (ii) equal to 50% of float duration if the float band includes the cruise altitude; and (iii) for float entirely below cruise, equal to 50% of float duration multiplied by the fractional altitude overlap (band height ÷ cruise altitude).
See-and-avoid: A user-specified “see-and-avoid” percentage scales the expected collisions, representing the fraction of encounters that are avoided through ATC, pilot visual avoidance, NOTAMs, etc.
Collision probability: Expected collisions λ = ρ × sweep-volume × (1 − avoid). We assume Poisson statistics, so P = 1 − e^{−λ}. Probabilities across independent aircraft classes are combined via the product of survival probabilities.
This explanatory section is for transparency only and does not constitute certification of the tool’s accuracy.
