Calculation of the temperature inside the envelope of a hot air balloon

Weather conditions:

atmospheric pressure in the flight area
Specify the pressure in the flight zone
average temperature in the flight area
°С
Specify the ambient temperature in the flight area

Balloon:

according to the balloon specs
m3
Specify the volume of the envelope
according to the Flight Manual of your balloon
°С
Specify the maximum temperature inside the envelope
from the inlet
m
Specify the height of the balloon
including the mass of halyards, carabiners and air intake
kg
Specify the mass of the envelope
including the mass of pipes
kg
Specify the weight of the burner
Including altimeter, uncoupling, stands, covers, fire extinguisher, spare rope, first aid kit and documents
kg
Specify the weight of the basket together with the equipment
including gas, covers, plugs and straps
kg
Specify the mass of gas cylinders

Load:

just use the scale :)
kg
Specify your weight in equipment
check with passengers :)
kg
Specify the total weight of passengers
computer, cameras, batteries, food
kg
Specify the weight of additional equipment
  • Let's take off ???
  • Start temperature:
    temperature inside the envelope at the specified parameters

    -

  • Takeoff weight:
    the mass of the loaded balloon at the time of takeoff

    -

  • Temperature inside the envelope:
    at the chosen height

    -

  • Pressure inside the envelope:

    -

  • Flight altitude:
    above launch point
    Specify the planned flight altitude
  • Click on the "CALCULATE" button
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The temperature inside the balloon is calculated by the formula:
Ti = (V * P * To)/(V * P - M * R' * To)
Where To and Ti – respectively stand for the temperature of the outside or ambient air and the temperature inside the envelope [K];
V – is the volume of the envelope of the hot air balloon [m3];
P – is for ambient pressure [Pa];
M – full load [kg];
R' – gas constant of air (for dry air it is equal to 287 J/(kg*K)).

The excessive pressure is calculated by the formula:
Pi = P * h * g/R' * (1/To - 1/Ti)
Where Pi – pressure inside the balloon [Pa];
P – ambient pressure [Pa];
h – the height of the envelope, measured from the inle [m];
g – free fall acceleration (9.807 m/s2);
R' – gas constant of air (for dry air it is equal to 287 J/(kg*K));
To and Ti – respectively stand for the temperature of the outside or ambient air, and the temperature inside the enclosure [K].

The dependence of pressure on altitude is calculated by the barometric formula:
Ph = P0 * exp(-(M * g)/(R * T0) * h)
Where Ph – pressure at altitude h [Pa];
P0 – pressure at the height of the starting point [Pa];
M – molar mass of air (0.02896 kg*mol);
g – free fall acceleration (9.807 m/s2);
R – universal gas constant (8.3143(H*m)/(mol*K));
T0 – temperature at the height of the starting point [K];
h – height above launch point [m].
A decrease in temperature by 6.5° is taken into account for every 1000 m of rise.