A balloon cannot steer, but the wind blows in different directions at different heights. Heat the envelope to climb, cool it to sink, pick the right layer and drift to the green landing field.
The science
What you see. A 2 800 m³ pear-shaped envelope (the volume is measured from the Blender model) over a stylised English valley with a river, village and fields. The scene is artistic, not a survey of a real place.
Atmosphere. ISA troposphere: T = 288.15 − 0.0065 h, p = 101325 (T/288.15)^5.2559, ρ = p / (R T) with R = 287.05 J/(kg K).
Buoyancy. The mouth is open, so the hot air has the outside pressure and ρin = p / (R Tin). Lift Fb = V g (ρout − ρin) against the weight m g of structure, crew and fuel. Net force F = Fb − m g; the balloon rises if F > 0.
Heat balance. C dTin/dt = P − (k + kv·vent)(Tin − Tout) with C = ρinV cp + fabric; P = 8 MW · slider²; loss k = 9 kW/K and venting up to 40 kW/K are round model values. Fuel burns at P / (0.7 · 46 MJ/kg) (propane).
Vertical motion. meff dw/dt = F − ½ ρ Cd A w|w| with meff = m + ρinV + ½ρV (added mass), Cd = 0.45, A = πR2. Terminal rise speed for a surplus F is √(2F/(ρ Cd A)).
Wind layers. Speed u(z) = u10(z/10 m)0.2 (power law); direction veers clockwise with height, φ(z) = φ0 − Δφ tanh(z/600 m), like the Ekman turning of real winds [simplified, illustrative]. The balloon relaxes to the local wind with a 8 s lag. It has no horizontal control: all steering is choosing a layer.
Assumptions and gaps. One-node envelope temperature (no stratification), steady wind field, no thermals, no turbulence, no terrain-induced wind, rigid shape. Numbers are plausible round values, not a design tool. This is a virtual exercise: real ballooning needs a trained pilot, a weather briefing and clear landing sites.
Sources. International Standard Atmosphere; thermodynamics and buoyancy textbooks; general balloon-performance summaries [to verify against a named flight-manual source]. No data is quoted from a specific study.
Made with Blender models and Three.js.