Analysis Code for High Altitude Balloons - FedOA - Università degli ...
Analysis Code for High Altitude Balloons - FedOA - Università degli ...
Analysis Code for High Altitude Balloons - FedOA - Università degli ...
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ACHAB: <strong>Analysis</strong> <strong>Code</strong> <strong>for</strong> <strong>High</strong> <strong>Altitude</strong> <strong>Balloons</strong> Chapter 3<br />
The Mean Anomaly (MA) can be determined as follows:<br />
MA<br />
= 2π<br />
Day<br />
number<br />
DaysPerYear<br />
where DaysPerYear is the total number of days in a year <strong>for</strong> the considered planet<br />
(<strong>for</strong> Earth = 365) and Day number is the number of the balloon flight day starting from<br />
perihelion (<strong>for</strong> Earth, perihelion occurs on January 2).<br />
The true anomaly (TA) can be approximated by the following equation provided that<br />
the orbital eccentricity is small:<br />
5<br />
TA ≈ MA + 2esin<br />
2<br />
4<br />
2 ( MA)<br />
+ e sin(<br />
MA)<br />
The solar irradiance flux at the top of the atmosphere is related to the position of the<br />
planet (Earth) along its orbit around the Sun:<br />
I<br />
1367.<br />
5 ⎡1+<br />
ecos<br />
=<br />
( ) 2<br />
TA<br />
Sun 2<br />
2<br />
R ⎢<br />
⎣ 1−<br />
e ⎥ [W/m<br />
AU<br />
⎦<br />
2 ]<br />
For Earth: R = 1 and e = 0.<br />
016708.<br />
The constant 1367.5 [W/m 2 ] is the nominal<br />
AU<br />
value of the solar constant 32 .<br />
At the balloon altitude Z, the direct solar irradiance is equal to the product of its<br />
value at the top of the atmosphere and the atmospheric transmittance:<br />
I = I τ<br />
SunZ<br />
Thus the direct solar flux acting on the balloon is:<br />
Sun<br />
SunZ<br />
Sun<br />
⎤<br />
atm<br />
q = I [W/m 2 ]<br />
35
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