# Design of a Hand-Launched Solar-Powered Unmanned Aerial Vehicle (UAV) System for Plateau
## 2 Conceptual Design Method
### Solar Energy Obtained during the Day  
In this paper, solar irradiance predicted model was used to estimate the solar irradiance. The solar energy obtained throughout the day can be calculated by solar irradiance model. Irradiance depends on many variables, such as geographical location, time, plane orientation, weather conditions, and albedo, which represents the reflection of ground [10]. In general, the total irradiance \(I_{tot}\) consists of direct irradiance \(I_{b}\) and scattering irradiance \(I_{d}\). The direct irradiance [10] is shown in Formula (5).  
\[\left\{\begin{array}{l}I=I_{0}\exp(-\frac{c_{s}\exp(-\frac{h}{h_{b}})}{\left[ \sin\left(\frac{a_{s}+a_{dep}}{1+a_{dep}/90}\right)\right]^{a_{s}+\frac{h}{h_{ b}}}})\\ I_{0}=G_{sc}[1+0.033\cos(360n_{d}/365)]\\ \alpha_{dep}=0.57+\arccos(R_{eth}/(R_{eth}+h))\end{array}\right. \tag{5}\]  
where \(G_{sc}\) is the standard solar radiation constant, taking 1367 \(W\!/\!m^{2}\). \(I_{0}\) is the solar irradiance outside the atmosphere on the \(n_{d}\) day of the year, \(c_{s}\) and \(s_{s}\) are both constants, taking 0.357 and 0.678, respectively. The \(h\) is the flight altitude of solar aircraft and \(\alpha_{dep}\) is the modified value relative to ground. \(R_{eth}\) is the radius of the Earth. The \(\alpha_{s}\) is determined by local latitude \(\varphi_{lat}\), solar declination angle \(\delta_{s}\), and solar hour angle \(\theta_{h}\). The relationship is shown in Formula (6).  
\[\left\{\begin{array}{l}\sin\alpha_{s}=\sin\varphi_{lat}\sin\delta_{s}+\cos \varphi_{lat}\cos\delta_{s}\cos\theta_{h}\\ \delta_{s}=23.45\sin\left(360\frac{n_{d}+284}{365}\right)\end{array}\right. \tag{6}\]  
in which the corresponding relationship between solar hour angle \(\theta_{h}\) and solar hour \(H_{s}\) is shown in Formula (7).  
\[\theta_{h}=15(H_{s}-12)\]Solar time in any region can be calculated by Formula (8).  
\[\left\{\begin{array}{l}H_{s}=H_{ct}+\frac{L_{st}-L_{ct}}{15}+\frac{E_{t}}{60}\\ E_{t}=0.0172+4.28\cos B-7.35\sin B-3.35\cos 2B-9.732\sin 2B\\ B=\frac{360}{365}(n_{d}-1)\end{array}\right. \tag{8}\]  
where \(H_{ct}\) is the local time. \(L_{st}\) is the standard longitude adopted by \(H_{ct}\). \(L_{ct}\) is the local longitude. \(E_{t}\) is the correction between \(H_{s}\) and \(H_{ct}\) caused by the revolution of earth. It is assumed that the scattering irradiance is omnidirectional and linearly proportional to the direct irradiance. Here, the proportionality coefficient is 0.08 [9]. The relationship between scattering irradiance and direct irradiance is shown in Formula (9).  
\[I_{d}=0.08I_{b}\exp\left(-\frac{h}{h_{s}}\right) \tag{9}\]  
The total solar irradiance considering latitude, altitude, and flight time is expressed as Formula (10).  
\[I_{tot}=I_{b}\sin\alpha_{s}+I_{d} \tag{10}\]  
The solar irradiance of Xi'an, China, on 27 May 2017 at an altitude of 400 m, simulated by the irradiance prediction model, is shown in the Figure 2a. The measured data in the figure was measured on 27 May 2017. For the parameters, such as the maximum irradiance, the corresponding time, and the time of the sun setting, the irradiance model fit well with the measured data. Figure 2b presents the measuring instruments of solar irradiance.  
Obviously, energy density captured by solar cells is the integral of irradiance with respect to time, in which energy density is the ratio of captured energy to solar cell area. Considering the actual laying area of solar cells \(A_{sc}\), packaging efficiency \(\eta_{cbr}\), electrical energy conversion efficiency \(\eta_{sc}\), maximum power point tracker (MPPT) efficiency \(\eta_{mpt}\), and weather influence factor, the solar energy captured by solar cells of the aircraft is shown in Formula (11).  
\[E_{sun\_tot}=\int I_{tot}(t)dtA_{sc}\eta_{turb}\eta_{sc}\eta_{cbr}\eta_{mpt} \tag{11}\]