Balloon Aerodynamics, Performance, and Weight & Balance
Buoyancy is the whole subject
A hot air balloon flies because the air inside the envelope is less dense than the air it displaces. Every performance and weight-and-balance question reduces to that relationship.
The physics
- Gross lift = (density of outside air minus density of inside air) x envelope volume.
- Inside density follows Charles's law: at constant pressure, density varies inversely with absolute temperature. Heating from 59 F (519 R) to 220 F (680 R) cuts density by about 24 percent.
- Controls: the burner adds heat (climb); the parachute valve or vent releases hot air (descend). There are no ailerons, elevator or rudder - the pilot controls vertical rate and chooses an altitude to find a wind direction.
- Weight and balance: empty weight plus fuel (propane about 4.2 lb per gallon) plus pilot, passengers, ballast and equipment must not exceed the manufacturer's maximum gross weight. Useful lift is gross lift minus empty weight and fuel.
- Ballast (sand or water bags) can be jettisoned to climb, but its weight must be planned into the load.
Worked example
Envelope volume 77,000 cubic feet. Outside air at sea level and 59 F is 0.0765 lb/ft3; inside temperature 220 F. Inside density = 0.0765 x (519 / 680) = 0.0584 lb/ft3. Lift per cubic foot = 0.0181 lb, so gross lift = 0.0181 x 77,000 = 1,394 lb. Subtract 450 lb of envelope, basket, burner and tanks for about 944 lb of useful lift. Three 180-lb adults, 40 lb of fuel and 20 lb of gear total 600 lb - comfortable on a cool morning. Recalculate at 95 F and a 4,000 ft field elevation and the outside density falls toward 0.062 lb/ft3, cutting the margin by hundreds of pounds.
Traps
Treating the maximum envelope temperature in the flight manual as a target rather than a limit; using volume instead of density in the lift calculation; and assuming the balloon has an airspeed - it moves with the air mass, so relative airflow appears only during climbs and descents.