The math, lift tables, and build details behind hydrogen gas balloons of the type flown in the Coupe Aéronautique Gordon Bennett — the world's oldest and most prestigious distance race.
A Gordon Bennett balloon is a gas-tight sphere of roughly 1,000 m³ filled with hydrogen, launched at dusk and flown for days. Pilots win not on speed but on distance, which makes it a game of careful arithmetic: every gram of ballast and every cubic metre of valved gas is finite. Below is the physics, the practical rules of thumb, the construction, and the safety — with the actual equations and the numbers the sport uses.
Lift is just Archimedes' principle: a balloon rises by the weight of the air it pushes aside, minus the weight of everything aboard (gas included).
Gross lift (Archimedes):
Fb buoyant / gross lift force • ρair air density • ρgas lifting-gas density (same P, T) • g = 9.80665 m/s² • V envelope volume
Net lift (equation of motion) — what's left to carry crew, basket, instruments and ballast:
The key insight: lift depends on the density difference, not the ratio. That is why hydrogen beats helium by only ~8% even though it is half as dense — both are already tiny next to air.
At STP (sea level, 59 °F / 15 °C, 29.92 inHg):
| Gas | Density | vs. air |
|---|---|---|
| Air | 1.29 g/L | — |
| Helium | 0.179 g/L | ~14% |
| Hydrogen | 0.090 g/L | ~7% |
FAA gross-lift factors (ISA sea level), and the total for a 1,000 m³ envelope:
| Gas | per m³ | × 1,000 m³ |
|---|---|---|
| Helium | 2.329 lb | 2,329 lb |
| Hydrogen | 2.513 lb | 2,513 lb |
| Ammonia (NH&sub3;) | ~1.17 lb | ~1,166 lb |
Lift tracks air density, which follows the ideal-gas law ρ ∝ P / T. Scale the sea-level value by the pressure and temperature ratios to get lift anywhere.
LSL sea-level lift • P ambient pressure (inHg) • T absolute temp in Rankine (°F + 459.67); metric: use mb/1013.25 and K/288.
| Altitude | Hydrogen | Helium |
|---|---|---|
| Sea level (59 °F) | 2,513 lb | 2,329 lb |
| 25,000 ft (−30 °F) | 1,128 lb | 1,045 lb |
FAA tables assume a fully filled envelope, no superheat, and >99% pure gas. Real superheat shifts these numbers upward during the day.
The whole sport lives in this trade: valve gas to descend, drop ballast to climb. Conserving both is how you fly far enough to win.
At the pressure ceiling, below 18,000 ft MSL (FAA Ch. 11):
| Change | Effect on lift |
|---|---|
| Pressure ↓ 1 inHg | −80 lb |
| Ambient + gas temp ↓ 3.3 °F | +16 lb |
| Drop ~64 lb ballast | +1,000 ft |
A "quick-fill" launch happens once there is enough gas to make ~100–150 lb of net lift, at which point the apex is released.
Day: the sun heats the gas (superheat) → the balloon wants to rise → the pilot valves gas off the top to hold altitude.
Night: the gas cools → the balloon sinks → the pilot drops ballast (sand or water) to stay aloft.
Every cycle costs gas and ballast, both finite. The winning strategy minimises both — ballast conservation sets how many nights you can survive, and therefore how far you fly.
A gas balloon is a sphere, so the geometry is simple — and the 1,000 m³ cap is what keeps the race about piloting, not equipment.
For the 1,000 m³ class:
Real reference: the Cameron GB1000 measures ~13.3 m across the envelope equator and ~19.4 m tall from basket runner to valve.
1,000 m³ = 35,315 ft³ is the maximum envelope volume permitted in major FAI Category AA competition, with a ~5% construction / measurement tolerance.
The cap has been in place since the 1983 revival of the race, specifically to equalise lift across competitors so the contest is decided by weather reading and piloting skill rather than who brought the biggest balloon.
A gas-tight sphere with a valve at the top and an appendix at the bottom — the basic anatomy has barely changed in 150 years, but the materials have.
The Cameron GB1000 departs from the open appendix: it uses a totally sealed envelope so the hydrogen never contacts air during flight, keeping it pure (which preserves lift).
In place of the open tube it uses a servo-driven pressure-relief mechanism that pulls the valve line to vent hydrogen at the top when the balloon reaches its ceiling.
Hydrogen is the best lifting gas and the most dangerous. The handling discipline is what makes it routine.
| Property | Value |
|---|---|
| Flammable range in air | 4–75% |
| Most violent (stoichiometric) | ~29% |
| Autoignition temp | ~500–571 °C |
| Required purity | >99% |
That 4–75% window is far wider than methane (5–15%) or propane (2–10%). The FAA notes even a 25% H&sub2; / 75% air mix will sustain an existing flame. Impurities also directly cut lift.
Hydrogen's saving grace: it rises and disperses extremely fast, so an open-air escape is rarely serious — the danger is confinement and ignition sources.
Compiled from primary and authoritative references; figures cross-checked against the underlying physics.
Educational reference only. The physics here is sound, but always cross-check against manufacturer data, current FAA guidance, and an experienced gas pilot before building or flying. Looking for the calculators? See Balloon Builder Tools.