last changed : 01/10/2003

The air being a perfect gas , it's volumetric mass is given by the formula where :

• rho is the volumetric mass of the air at altitude z (kg/m³),
• P is atmospheric pressure at altitude z (Pascal Pa),
• M is la molar mass of the air   M = 28,9644 kg/kmol
• R is the perfect gas constant   R = 8314,32 J/K.kmol
• t° is the temperature at altitude z (°Kelvin).
  t°K (Kelvin) = t°C (Celsius) + 273,15      Example : 293,15°K = 20°C

Simplifying (R : M = 287,053), that leave :
Example : At sea level and with an atmospheric pressure of 1013,25 hPa, when the temperature is 15°C (288,15°K),
the volumetric mass of the air is about : 101325/(287,053 x 288,15) = 1,225 kg/m³

Therefore, the volumetric mass masse varies with the atmospheric pressure and air temperature.

Atmospheric pressure variation with altitude :

The atmospheric pressure at some point correspond to the weight of the air column above this point. The lower layers of the atmosphere bears the weight of all the upper layers all the way up to the vacuum of space. The atmospheric pressure decrease with altitude at a rate of about 1 per thousand every 8 meters.

Temperature variation with altitude

according to the International Standard Atmosphere :
- In the troposphere (at our latitudes : from the ground up to 11000m - 36.000 ft), the temperature decrease at a rate of 6,5°C per km. This variation of temperature with the altitude is called standard atmosphere temperature gradient.
- At the beginning of the stratosphere (at our latitudes : from 11000m up to 20000m - 65.600 ft), the temperature remain constant at -56,5°C or -69,7°F or 216,6°K.

(see the computer)

- when a dry air mass (without water vapor) rise in adiabatic way (without exchange of heat with the outside media ), it will goes through lower and lower pressure. This will tend to make it expand and so cool down. This decrease of temperature with altitude is the dry adiabatic gradient. It is - 9,77°C/km. So a dry air mass rising in an adiabatic way will cool down faster than the outside air. This will stop it's ascension pretty fast.
but...
- the ascending solar balloon still pickup the sun energy : it even get stronger with altitude. It is around 1000W per m² at ground level and 1320 W per m² in the vacuum of space.
- the ascending solar balloon loose less heat : because the air get less dense, there are less thermal exchange between the heated envelope heated by the heat radiation from the sun and the outside air surrounding the balloon.
- the outside temperature decrease quite fast.
So the temperature differential between the inside and the outside increase with altitude.
Some measures have been performed by R.Rochte - USA - 22 June 2003. Around 15000m, the temperature differential reached 69°C.

Lift possibility Variations with the volume :

Of course more the balloon is inflated more load it can lift : lift gr/m³ x volume m³.
When the altitude increase, the atmospheric pressure decrease. The hot air contained in the balloon will expend of 1 per thousand every 8 m !
As long as the balloon has not reached it's maximum volume, an increase of altitude will produce an increase in volume. After the hot air leaks by the inferior opening.
(this is because of that the small helium balloon explode very fast when released.)

The lift possibility increase with the volume : total aerostatics force = aerostatics force per m³ x volume m³

In this movie, the variations are exaggerated !

Lift possibility Variations with altitude :

When the altitude increase the air become thinner : The volumetric mass of the air decrease of de 1 per thousand every 8 m (a little bit less than 1 per thousand because the air becomes cooler). So the volumetric mass differential also decrease.

The measures made by R.Rochte - USA - 22 June 2003 shows that the lift as decreased from 85 gr/m³ ground level down to 50-55 gr/m³ at 15000m.
The lift capacity decrease with the altitude increasing.

Lift possibility Variations with the weather :

The atmospheric pressure varies with the local weather conditions (low pressure, high pressure, etc.). When the atmospheric pressure increase (anti cyclone), the volumetric mass of the outside increase. The differential of volumetric mass increase also. The lift ability increase with a situation of high pressure.

Lift possibility Variations with the albedo:

When the quantity of reflected solar energy increase the solar balloon receive more light. The inner temperature increase. So the lift possibility is better on snow. And lower above water.
There is still an experimental study to conduct to check this.

Lift possibility Variations with the outside temperature :

At some defined altitude, if the ambient air becomes cooler, the temperature differential increase, the volumetric mass differential increase, the aerostatics force increase and so does the lift possibility. So the best results are obtained during the winter !
This variation is quite important. A 4m (13 ft) diameter balloon (36m³) lift around 2 kg during summer and more than 3 kg with outside temperatures under 0°C.

Variations of the vertical speed :

The vertical speed (usually m/sec in Europe) is dependent of the difference between the aerostatics force and the weights of the envelope and its flight load. The stronger this force the higher the vertical speed within the air mass (weather a climbing air mass or a descending air mass !).
(the balloon can have a different vertical speed relative to the ground...).