Earth reference: a conventional aerodynamic wing assisted by helium gas cells. Select another gas where its usable local supply and engineering properties justify it. The reference values are editable examples; an optimum requires validated geometry, loads, costs and supply.
Screening only — 99% project feasibility is not demonstrated.
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ρ = pM/(RT); V = LĀf; gross lifting mass = (ρambient − ρgas)V; aerodynamic lift Laero = ½ρambient v²SCL; combined net vertical force = gross lifting mass × g + Laero − (structure + payload) × g. Required additional vertical support = max(0, −combined force).
Relative airflow supplies aerodynamic lift; at zero airspeed conventional wing lift is zero in this model. Airfoil coefficients, gusts and stall require separate aerodynamic validation. Cable-supported stationary structures may use the calculated support deficit; this value is a vertical force, not cable tension.
Equal gross lift requires Vgas/VHe = (ρambient − ρHe)/(ρambient − ρgas). At equal length this is the section-area factor. A geometrically similar section scales linearly by √factor. Envelope mass must be re-entered after resizing.
Material strength, creep, wind loads, gas containment, leakage, moorings and full-scale tests remain engineering inputs. Hydrogen and methane require fire-control provisions appropriate to the surrounding atmosphere. No gas-assisted lift is available in a vacuum.
Supply priority: 1 = preferred, 9 = last. Enter a site-specific preference after checking gas quantity, separation effort and delivery. Defaults express the Earth design preference, not measured abundance. A gas must supply enough lift at the actual pressure and temperature.
Earth: helium is an established industrial lifting gas with limited recoverable supply; hydrogen can be produced but requires energy and fire controls; biomethane supply depends on sustainable feedstock and upgrading. Nitrogen is abundant in air but provides only a small lifting difference in Earth air. On Mars its heavier surrounding atmosphere allows a larger density difference, while the low pressure strongly reduces lift per cubic metre.
Hydrogen and helium are observed in Jupiter and Saturn; these observations do not establish a recoverable supply for a surface settlement. Exoplanet resource quantities and extraction routes remain unknown until measured. In an H₂-dominated atmosphere helium can be heavier than the surroundings and unsuitable for buoyant lift.
Qualify site supply, structure and airfoil before treating this as an optimum.
Choose a yield per tonne of fresh material or enter a measured site value. The following ranges are supplied by the publisher, not independently validated measurements: cattle slurry 15–25; pig slurry 12–18; solid manure 45–65; municipal biowaste 70–100; food/fat waste 110–250+; sewage sludge 15–25; grass/clover 70–95; maize 100–115 m³ CH₄/t. Here, calculations explicitly assume these volumes are normal cubic metres. Actual reporting conditions must be checked.
Delivered methane = tonnes × yield × (1 − loss fraction). Its heating value is not electricity output. Gas consumed as fuel no longer provides lift. Digestate storage, upgrading losses, lifecycle energy and land-use effects require a separate emissions balance.
CO₂ + 4H₂ → CH₄ + 2H₂O. Full conversion of the CO₂ fraction of 50–65% CH₄ raw biogas would raise methane amount by about 1.54–2.00×, conditional on sufficient hydrogen, conversion and separation; not free energy or an automatic near-doubling.
The EU target is 35 billion m³ biomethane/year by 2030, not an achieved output. The supplied German and global quantities are not labelled current observations here. Use dated primary sources.
99% remains a requested acceptance target, not a computed project success probability. Representative independent reliability tests and engineering qualification are required.