Alt 0 mNet lift 0 kgBallonet 0 %Superpressure 0 PareadyFPS 0

Drag to orbit, wheel or pinch to zoom. X-ray: yellow = lifting gas, blue = ballonet air. The cells are drawn as ellipsoids sized from the live gas and air volumes (volumes exact, shapes schematic).

Airship Envelope Lab: Lifting Gas, Ballonets and Superpressure

Climb through the standard atmosphere and watch the gas expand, the ballonets empty, the relief valve open and the fabric carry the pressure.

Flight

Gas, loading and envelope (Reset applies fill, gas, loading)

Weather

Live readouts

Net lift (kg) vs altitude for the current gas

Ballonet share of the envelope (%) vs altitude

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom.
"Target altitude" is the height the pilot flies to (climb 4 m/s of simulated time). The ship stops climbing where static lift runs out, and a descent always uses elevators (dynamic lift), shown as the angle needed.
Gas, fill, purity, payload, ballast and hot-air temperature take effect on Reset. Superpressure, superheat, weather and X-ray act live.
Gas that is vented through the relief valve is gone: descend again and you are heavier than you started.

The science

Atmosphere. ISA troposphere: T = 288.15 + ΔISA − 0.0065 h, p = 101325 (1 − 0.0065 h/288.15)^5.2559, ρ = p/(287.05 T). Valid to 11 km.

Lifting gas. Ideal gas inside the envelope at p + Δp and T + superheat: ρ_g = (p + Δp) M_g / (R T_g). At sea level, ISA, that gives a lift of 1.056 kg/m³ for pure helium and 1.14 kg/m³ for hydrogen (hydrogen is flammable; it is shown here as a physics comparison only).

Ballonets. The envelope always displaces V_max. The gas mass is fixed, so its volume V_g = m_g/ρ_g grows as the ambient pressure falls; air ballonets give way (V_b = V_max − V_g) so the envelope pressure stays at Δp. Net lift m_net = ρ_air V_g − m_g − m_{structure+payload+ballast+fuel}, constant while ballonet air remains. At the pressure height the ballonets are empty (V_g = V_max); above it the relief valve vents gas and lift falls with air density. Closed-form ceiling (no superheat, Δp = 0): ρ* = m_s / (V_max(1 − M_g/M_a)).

Hot air. An open-mouthed envelope has no ballonets: lift = (ρ − ρ_hot) V_max with ρ_hot = p M_a/(R (T + ΔT)). Hot air gives about 0.21 kg/m³ at +60 K, one fifth of helium.

Superpressure and fabric. For a cylinder of radius r, Laplace's law gives hoop tension per unit length T_h = Δp r and axial T_a = Δp r / 2. Safety factor = fabric strength / T_h. The nose stays rigid only if the internal overpressure exceeds the dynamic pressure q = ½ ρ v² (rule of thumb Δp ≳ 1.2 q).

Dynamic lift. To hold altitude while statically heavy or light, elevators produce L = ½ ρ v² S_ref · 0.02 · α[°], S_ref = V^2/3; the angle needed is displayed.

Simplifications. Ellipsoid envelope 60 × 18 m (10 179 m³), uniform gas temperature (ambient + superheat), instant relief valve and blowers, ballonet air at ambient density, no drag/mass dynamics in the climb (fixed 4 m/s), fixed masses (structure 5200 kg, fuel 300 kg), illustrative fabric strengths. Not a design tool. Models built with Blender, scene by Three.js.