## 6 Atmospheric Gaseous Losses Profile for Aircraft-Stratospheric Basestation (SB) Link
### Complete Flight Profile Scenario  
In this communication scenario, an aircraft has the complete flight stages as shown in Figure 6. From takeoff to landing in a complete flight, the aircraft passes three main stages including climbing, cruise and descending. A typical civil flight has cruise altitudes ranging from 33,000 to 40,000 ft (10-12 km) high. The climbing and descending ground distance ranges from 100 to 250 km according to the cruise height. Figure 9 demonstrates the flight geometry model during the three phases where the ground elevation angle is \(\alpha_{g}\) at the airport. The flight starts/ends at a distance \(d_{gx}\) and the aircraft reaches the cruise height \(h_{cr}\) at an elevation angle \(\alpha_{cr}\). In the climbing/descending stage, the aircraft hasan altitude \(h_{p}\) and elevation angle \(\alpha_{p}\). Assuming also that the climbing/descending inclination angle is \(\alpha_{cl}\), then the ground distances measured from an airport during takeoff and climbing/descending stages are obtained as follows respectively:  
\[d_{gSB}=\frac{h_{s}}{\tan\!\left(\alpha_{g}\right)} \tag{24}\]  
and,  
\[d_{gcr}=\frac{h_{p}}{\tan\!\left(\alpha_{cr}\right)} \tag{25}\]  
Also, the starting cruise elevation angle is given by:  
\[\alpha_{cro}=\tan\!\left(\frac{h_{s}-h_{p}}{\tan\!\left(\alpha_{g}\right)}- \frac{h_{p}}{\tan\!\left(\alpha_{cr}\right)}\right) \tag{26}\]  
where during cruise stage, the cruise elevation angle is given by:  
\[\alpha_{cro}\leq\alpha_{cr}\leq 90^{\circ} \tag{27}\]  
The atmospheric losses will vary with the aircraft height where it is expected to have lower losses in the cruise stage while severe losses impact the communication performance during the climbing/descending periods. Fortunately, for passengers during climbing/descending periods, it is not allowed to engage in activities and they must stay fastened. The most active period of broadband services will, therefore, during cruise stage. The flowchart shown in Figure 10 can be followed when we calculate the atmospheric gaseous attenuation. The main factors affecting this attenuation is the aircraft altitude and the elevation angles which define the atmospheric thickness in the troposphere which affects the communication link. The impact of frequency on the atmospheric attenuation is described for each set of frequencies (i.e., FR'1 and FR'2) where there is an expected big difference in performance between the two sets. As a case study to investigate the atmospheric losses for this scenario, assume that the \(\alpha_{g}=2^{\circ}\) which results  
Figure 9: Geometrical model for calculation of atmospheric attenuation profile during flight. in ground distance of approximately 508 km between the aircraft and SB. If the climbing/descending ground distance is assumed to be 200 km and the cruise height is 11 km, then the resulting flight atmospheric attenuation profile is displayed for the set of FR'1 frequencies (i.e., @ 3.5, 6, and 10 GHz) in Figure 11a. The effect of atmospheric attenuation especially during the cruise stage is less than 0.1 dB at f = 10 GHz which is negligible compared to a maximum of 2 dB loss during the takeoff stage at the same frequency. This is because at cruise heights, the aircraft is almost above the troposphere where the air density and temperature provide very low atmospheric attenuation and the three frequency attenuation curves converge to the same values indicating almost frequency-independent atmospheric attenuation in this frequency range. At the minimum distance between aircraft and SB, where the SB is at the zenith position of the aircraft, the atmospheric attenuation is very small and can be neglected. Figure 10: Atmospheric attenuation calculation flowchart during flight. Figure 11: _Cont._  
The atmospheric attenuation is added to the free space path loss which is given by:  
\[L=\left(\frac{4\pi d_{c}f}{c}\right)^{2} \tag{28}\]  
where \(f\) is the signal frequency and \(c\) is the speed of light.