Hot Air Balloon Buoyancy Experiment - 2D Altitude, Heat Balance and Wind-Layer Profile

Presets

Speed

Live readouts

Graphs

Numerical checks

running...

How to use

Pick a preset and watch the envelope heat up until the green lift arrow exceeds the red weight arrow. With autopilot on, the burner fires only when the climb rate is below what the target altitude needs. Try: (1) Hot day heavy load - lighter ambient air means much less lift per cubic metre; (2) Cold dawn, wind layers - climb above 1.2 km and the drift reverses; (3) switch autopilot to 0 and set the duty to see the burn-and-coast cycle; (4) raise the heat-loss coefficient and read the hover burner power in the readout. Space pauses, R restarts.

The science

Buoyancy. A hot-air balloon is open at the bottom, so the air inside is at the same pressure as outside; only its density differs. From the ideal-gas law:

rho = p M / (R T), F_lift = V g (rho_out - rho_in) - m g

With 15 C air outside and 100 C inside, each cubic metre carries about 0.28 kg, so a 2,800 m3 envelope lifts about 780 kg in total including its own fabric, basket and passengers.

Atmosphere. The outside state follows the International Standard Atmosphere: T(z) = T0 - 6.5 K/km * z, p(z) = p0 (T/T0)^(g M / (R L)) so lift drops with altitude and temperature.

Heat balance. The enclosed air (heat capacity rho V c_p) gains energy from the burner Q and loses it through the fabric surface A with coefficient k:

rho V c_p dT/dt = Q - k A (T - T_out)

Hovering needs the steady-state burner power Q = k A (T* - T_out), where T* makes the net lift zero.

Vertical motion. Newton's law with drag and added mass: (m + rho_in V + 0.5 rho_out V) dv/dt = F_lift - 0.5 rho_out C_d A_p v|v|

Checks. (1) ISA sea-level density 1.225 kg/m3; (2) textbook gross lift of a 2,800 m3 balloon at 100 C; (3) a separate time-stepped heat balance settles on the analytic hover temperature; (4) net lift is zero at that temperature.

Simplifications. Uniform envelope temperature (real balloons stratify), constant loss coefficient (no radiation/convection split), fixed drag coefficient, no turbulence, horizontal motion equals the local wind, burner power treated as continuous and convertible to air heat with 100% efficiency.