last changed : 25.08.2008

Gravitation or terrestrial attraction : Very useful for getting back down to the ground !

Weight is the vertical downward force which Earth's gravitation exerts upon a body, proportional to its mass. P = m . g.
The principal factor is the mass of the warm air contained in the envelope. Mass of one cubic meter of warm air at 35°C : about 1.145 kg.
Example : There are 1735 cubic meters of warm air in a 14.5 meter diameter balloon ... The mass is more than 2 metric tons ! . To this must be added the masses of the envelope (polyethylene+adhesive tape+load tapes), plus the load circle, the harness and its support lines, any ballast, the pilot and parachute, and of any flight accessories.

The principle of Archimedes :

"Any body immersed in a fluid experiences a force opposed to its weight of magnitude equal to the weight of the fluid which it displaces". This principle was formulated by Archimedes more than twenty centuries ago ! . It is the archimedean buoyancy.
In this case, the displaced fluid is air at the ambient temperature. The body immersed in this fluid is the balloon !
Since the warm air inside the balloon is lighter than the ambient air, the resultant force is a vertical upwards force : the aerostatics force or "lift". The lift is about 0,8 Newton per cubic meter (i.e. 80 grams per cubic meter).
In a stable atmosphere, if this force is greater than the weight of the balloon's envelope and its load, the balloon will rises !
In a stable atmosphere, if this force is just equal to the weight of the balloon's envelope and its load, the balloon will remain at a stable altitude !

Volumetric mass and temperature differential :

Volumetric mass is the mass per cubic meter or the quantity of matter mass per cubic meter. The volumetric mass of air at 15°C is 1.225 kg/m³. A balloon made of black plastic film inflated with dry air absorbs enough solar energy to raise its interior temperature significantly. The hot air expand and this reduces the volumetric mass of the warm air within the balloon quite substantially (there is less air molecules per volume unit). Thus this bubble of warm air rises because it is lighter than ambient.

At sea level and at atmospheric pressure of 1013 millibars (hecto Pascal's or 29.92 in.hg.) we can note :

• mass of one cubic meter of ambient air at 15°C : 1,225 kg
• mass of one cubic meter of warm air at 35°C : 1,145 kg
• difference between these masses : 80 grams per cubic meter of air, which produces an aerostatics force or lift (according to International Standard Atmosphere - ISA).
• If the temperature differential increase the aerostatics force will increase also. This way a solar balloon 4m (13 ft) diameter has lifted a load of more than 3 kg with -8°C ambient while it usually lift 2 kg during the summer.

For more information, volumetric mass of helium is 0,176 kg/m³. The Volumetric mass difference with ambient air (the lift) is about 11 Newton per cubic meter (i.e. 1,1 kg per cubic meter) ! but it is very expensive and leak easily.

Other important considerations for a solar balloon :

• Heat radiation from the sun : his is more intense when the atmosphere is thin (at altitude) and when the sun's rays fall perpendicularly upon the receiving surface. Outside the atmosphere it amounts to 1,360 W/m² (the solar constant), and on the ground to about 1,000 W/m² (when the sun is overhead and the sky is clear). The average strength of solar radiation over the year, day and night, all weathers) is from 120 to 260 W/m².
• Reflected solar radiation : Depending upon the type of soil and the cloud conditions (if you're above them they are a very good reflector), a fraction of the solar radiation is reflected upwards. Albedo is the proportion of reflected solar radiation : ice, fresh snow - 0.6 to 0.8 ; bare soils and deserts - 0.3 to 0.4 ; forests and agricultural areas - 0.1 to 0.15 ; water - 0.05 to 0.1 ; above clouds - stratus 0.4, cumulus 0.8. The albedo of black polyethylene is very near zero, which means that it absorbs all the solar radiation and reflects none.
• Thermal transmission : This is the heat exchange of the envelope to the outside air or inside air.
• Inside heat convection : Local differences in temperature close to the envelope surface cause local air density variations, which generate circulation movements, and these tend to mix the air so that the air temperature is equalized.
• Outside heat convection : Local differences in temperature close to the envelope surface cause local air density variations, which generate upward circulation movements.
• Effects of porosity of the polyethylene (negligible) and of losses through the envelope.
• Heat loss through the base (load circle) and through the top of the envelope (through the valve).

Useful jargon :

• Archimedean buoyancy or archimedean force : the weight of the ambient air displaced by the balloon.
• Aerostatics force or lift : this is a vertical force, directed upwards, equal to the difference between the archimedean buoyancy and the weight of the hot air contained in the balloon. It varies to the volume of the envelope, the temperature differential, the altitude, the pressure, etc.
• The weight of a solar balloon : This is the sum of the weights of the air contained in the envelope, the envelope itself (polyethylene+adhesive tape + load tapes), the load circle, the seat and its support lines, the ballast, the pilot and his equipment, his parachute, and the flight accessories (instrumentation).
• Empty weight : this is the weights of the envelope (polyethylene+adhesive tape+load tapes), of the load circle, of the seat and its support lines.
• Effective useful flight load : The weight of everything the balloon is carrying : pilot, parachute, ballast, and flight accessories.
• Maximum useful load : this is the maximum load that the balloon can carry in optimum conditions : volume at maximum, etc.

CNES-Education has a very detailed large teaching web site about helium balloons (in French) at https://www.cnes.fr/