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- Temperature calculation

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

While calculating always use the temperature range stated in the flight manual for your baloon. Never exceed your maximum operating temperature!

These calculations ignore technical condition of the envelope, air humidity, its change with height, cylinders mass change caused by gas consumption, surface temperature inversions. Calculations are only relevant within the troposphere.

If you have any ideas or suggestions for improvement you can submit it here.

These calculations ignore technical condition of the envelope, air humidity, its change with height, cylinders mass change caused by gas consumption, surface temperature inversions. Calculations are only relevant within the troposphere.

**We recommend using this calculator for information purposes only!**If you have any ideas or suggestions for improvement you can submit it here.

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**%sunset%**Meteo as of

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`T`_{i} = (V * P * T_{o})/(V * P - M * R^{'} * T_{o})

Where

`T`_{o}

and `T`_{i}

– 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 [m^{3}];

`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:

`P`_{i} = P * h * g/R^{'} * (1/T_{o} - 1/T_{i})

Where

`P`_{i}

– 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/s^{2});

`R`^{'}

– gas constant of air (for dry air it is equal to 287 J/(kg*K));
`T`_{o}

and `T`_{i}

– 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:

`P`_{h} = P_{0} * exp(-(M * g)/(R * T_{0}) * h)

Where

`P`_{h}

– pressure at altitude h [Pa];
`P`_{0}

– 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/s^{2});

`R`

– universal gas constant (8.3143(H*m)/(mol*K));
`T`_{0}

– 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.