# Albatross-Like Utilization of Wind Gradient for Unpowered Flight of Fixed-Wing Aircraft
## 5 Simulation Results and Discussion
### Discussion of Criterion for Unpowered Climbing
#### 5.1.4 Minimum Gradient and Environmental Effects  
According to the inequality in Equation (31), the minimum gradient for climbing \((G_{w})_{min}\) can be readily determined as follows:  
\[\left(G_{w}\right)_{\text{min}}=\left(\sqrt{\frac{gp}{2}}\right)\left(\sqrt{ \frac{s}{m}}\right)\left[\left(C_{L}{}^{2}+C_{D}{}^{2}\right)^{\frac{1}{4}}h(L /D)\right] \tag{55}\]  
This promises to facilitate the choice of appropriate parameters and locations for dynamic soaring, and indicates the dependency of the aircraft on the wind field.  
The gravitational acceleration \(g\) and air density \(\rho\) vary little near the earth's surface. However, the situation is quite different near space and on other planets. The near space altitude is higher than that at which traditional aircrafts fly, but lower than that at which traditional aircwheicles usually orbit. It ranges between 20 and 100 km above sea level. The effects of gravity gradually weaken and the air thins with increasing altitude, as indicated in Figure 10. The data presented in the figure were obtained using the International Standard Atmosphere model [47]. The lower values of \(g\) and \(\rho\) lower the minimum gradient near space, relaxing the required wind field for climbing. An advantage of near space is that the wind field has a steady gradient, especially between 40 and 60 km above sea level (Figure 11). The horizontal wind data in Changsha (28\({}^{\circ}\)11'49\" N, 112\({}^{\circ}\)58'42\" E) presented in Figure 11 were obtained by the MATLAB function atmoshwm07 using the Naval Research Laboratory Horizontal Window Model [48]. [PERSON] et al. [49] attempted to use the wind shear at the bottom of near space to achieve high-altitude long-endurance flight.  
Let us consider a flight at an altitude of 50 km above sea level. The air density at this altitude is very low at approximately \(10^{-4}\) kg/m\({}^{3}\), compared to 1 kg/m\({}^{3}\) at sea level. There is, however, little change in the gravitational acceleration. From Equation (35),  
\[\frac{\left(G_{w}\right)_{\text{min}}\mid_{50\text{ km above sea level}}}{\left(G_{w}\right)_{\text{min}}\mid_{\text{at sea level}}}=\sqrt{\frac{\left(g\rho\right)_{50\text{ km above sea level}}}{\left(g\rho\right)_{\text{at sea level}}}}\approx 0.01\]  
Figure 10: Variations in the air density and gravitational acceleration with the altitude.  
This indicates that the minimum gradient for climbing at an altitude of 50 km is 1% of that near the earth's surface. Climbing at the high altitude thus requires a relatively weak wind gradient, implying the potential for dynamic soaring over a large area.  
NASA [50; 51], ESA [52], and JAXA [53] are considering using a fixed-wing aircraft for the exploration of Mars. Early in the 1970s, NASA built and tested the Mini-Sniffer [54], which had a wingspan of 6.7 m. The Sky-Sailor [45; 52] is an ultra-lightweight solar autonomous model aircraft designed by the Autonomous System Lab of EPFL under a contract with ESA, for scientific missions to Mars. The NUDT also developed a prototype solar aircraft for Mars exploration (Figure 12).  
The exploitation of a wind shear on Mars may be a possible approach to extending the flight endurance of Mars exploration aircrafts. The gravitational acceleration on Mars is less than 4/9 of that on Earth, and the atmosphere is also much thinner (Figure 13). The minimum gradient for sustainable  
Figure 11: Variations in the wind speed and heading with altitude in Changsha (28\({}^{\circ}\)11\({}^{\prime}\)49\({}^{\prime}\)N, 112\({}^{\circ}\)58\({}^{\prime}\)42\({}^{\prime}\) E) obtained by the MATLAB function atmoshwm07 using the Naval Research Laboratory Horizontal Window Model.  
Figure 12: Prototype solar aircraft developed by NUDT.  
climbing on Mars is thus considered to be smaller than that on Earth. In addition, the wind field on Mars significantly varies with the altitude [55], which is also favorable to climbing. The data presented in Figure 13 were obtained using the standard Mars-GRAM 2005 [55].