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Phenomena which affect a solar balloon

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 :

principe d'Archimède"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 :

atomes 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 :

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.

 Air temperature
 Mass of one cubic meter of air  Difference between masse of air
at 15°C
 0°c   1,292 kg/m3   +67 gr 
 15°C   1,225 kg/m3   0 gr 
 25°C   1,184 kg/m3   -41 gr 
 70°C   1,029 kg/m3   -196 gr 
 100°C   0,946 kg/m3   -279 gr 
 15°C   0,835 kg/m3   -390 gr 

Other important considerations for a solar balloon :

rayonnement du soleil

Useful jargon :

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


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