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Albatross-Like Utilization of Wind Gradient for Unpowered Flight of Fixed-Wing Aircraft

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Albatross-Like Utilization of Wind Gradient for Unpowered Flight of Fixed-Wing Aircraft applied sciences Article Albatross-Like Utilization of Wind Gradient for Unpowered Flight of Fixed-Wing Aircraft Shangqiu Shan * ID , Zhongxi Hou and Bingjie Zhu College of Aerospace Sciences and Engineering, National University of Defense Technology, Changsha 410073, China; [email protected] (Z.H.); [email protected] (B.Z.) * Correspondence: [email protected]; Tel.: +86-137-8729-3515 Received: 3 September 2017; Accepted: 12 October 2017; Published: 14 October 2017 Abstract: The endurance of an aircraft can be considerably extended by its exploitation of the hidden energy of a wind gradient, as an albatross does. The process is referred to as dynamic soaring and there are two methods for its implementation, namely, sustainable climbing and the Rayleigh cycle. In this study, the criterion for sustainable climbing was determined, and a bio-inspired method for implementing the Rayleigh cycle in a shear wind was developed. The determined sustainable climbing criterion promises to facilitate the development of an unpowered aircraft and the choice of a more appropriate soaring environment, as was demonstrated in this study. The criterion consists of three factors, namely, the environment, aerodynamics, and wing loading. We develop an intuitive explanation of the Raleigh cycle and analyze the energy mechanics of utilizing a wind gradient in unpowered flight. The energy harvest boundary and extreme power point were determined and used to design a simple bio-inspired guidance strategy for implementing the Rayleigh cycle. The proposed strategy, which involves the tuning of a single parameter, can be easily implemented in real-time applications. In the results and discussions, the effects of each factor on climbing performance are examined and the sensitivity of the aircraft factor is discussed using five examples. Experimental MATLAB simulations of the proposed strategy and the comparison of the results with those of Gauss Pseudospectral Optimization Software confirm the feasibility of the proposed strategy. Keywords: unpowered flight; dynamic soaring; wind gradient; energy extraction; micro fixed-wing unmanned aerial vehicle 1. Introduction An aircraft usually consumes a large amount of energy during flight. There is, however, the question of whether an aircraft can fly indefinitely without carrying a power source. This might be realizable if a method could be developed for the aircraft to continuously extract energy from its environment. A wind field in which the wind gradient varies with the altitude is known to contain a large amount of energy [1–3]. In addition, albatrosses have been observed to soar for long periods without flapping their wings [4–7]. Lord Rayleigh was perhaps the first to discuss the problem relevant to albatrosses soaring in a horizontal but non-uniform wind field [8]. This type of flight involves the extraction of energy from a wind gradient and is referred to as dynamic soaring. The phenomenon of dynamic soaring has attracted the interest of many scholars. The technique utilized by an albatross to obtain extra airspeed for soaring is referred to as the Rayleigh cycle [9] and is illustrated in Figure1. Idrac [ 10] showed that wind speed increases with the altitude, which generally occurs over the sea where albatrosses fly. Different researchers have observed birds to understand their soaring mechanics [11–13], and theories regarding their utilization of wind gradient have been developed. Wood [14] used a two-dimensional model to investigate two types of complete soaring flight cycles in a logarithmic wind velocity profile. Hendriks [15] Appl. Sci. 2017, 7, 1061; doi:10.3390/app7101061 www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1061 2 of 25 Appl. Sci. 2017, 7, 1061 2 of 25 obtainedthree‐dimensional a three-dimensional mass point mass dynamics point dynamicsequation for equation obtaining for non obtaining‐diving non-divingflight. In addition, flight. In addition,Denny Denny[16], Taylor [16], Tayloret al. et[17], al. [and17], andLiu Liuet al. et al.[18] [ 18analyzed] analyzed the the energy energy transformation transformation in in wind-gradient-basedwind‐gradient‐based flight flight from from a a physics physics viewpoint. viewpoint. FigureFigure 1. An1. An albatross albatross flying flying over over the the sea sea to to obtainobtain extra airspeed. airspeed. Because Because the the wind wind speed speed below below the the wavewave is nearly is nearly zero zero and and the the wind wind above above the the wavewave has a certain speed, speed, the the wind wind can can be be considered considered to to comprisecomprise two two layers layers with with a wind a wind shear shear between between them. them. Suppose Suppose that thethat initial the initial airspeed airspeed of the of albatross the is 17albatross m/s in is the 17 wind m/s in layer the belowwind layer the wave. below Ifthe the wave. wind If speed the wind above speed the waveabove isthe 7 m/swave higher is 7 m/s than thathigher below than the wave,that below when the the wave, albatross when faces the thealbatross wind andfaces crosses the wind the windand crosses shear betweenthe wind the shear lower between the lower and upper wind layers, the airspeed would suddenly increase to 24 m/s. This and upper wind layers, the airspeed would suddenly increase to 24 m/s. This sudden gain in speed is sudden gain in speed is due to the lack of time for the albatross to change its ground speed. due to the lack of time for the albatross to change its ground speed. With the development of computer science, the use of numerical algorithms has become a popularWith the approach development to determine of computer the optimal science, trajectory the use of under numerical a wind algorithms gradient. has Zhao become [19,20] a popularused approachNPSOL, to a numerical determine optimization the optimal software, trajectory to underminimize a wind the dynamic gradient. soaring Zhao cycles [19,20 of] unpowered used NPSOL, a numericalaircraft and optimization powered aircraft. software, Sachs to [21,22] minimize also the solved dynamic the optimal soaring control cycles problem of unpowered of dynamic aircraft andsoaring powered and aircraft. computed Sachs the minimum [21,22] also shear solved wind the strength optimal under control certain problem conditions. of dynamic Deittert soaring et al. [23] and computedutilized the the differential minimum flatness shear wind property strength to determine under certainthe optimal conditions. trajectory Deittert for cross et‐country al. [23] flight. utilized theKaushik differential et al. flatness [24] used property the GPOPS to determine‐II optimal the control optimal software trajectory for for trajectory cross-country computation. flight. There Kaushik et al.have [24 been] used several the GPOPS-II other studies optimal on the control optimization software of dynamic for trajectory soaring computation. [25–29]. There have been severalRecent other studies improvements on the optimization were achieved of in dynamic the practical soaring application [25–29]. of dynamic soaring. Lawrance et Recental. [30,31] improvements proposed an algorithm were achieved for determining in the practicalthe flight direction application for the of dynamicquickest energy soaring. Lawranceharvest. etLangelaan al. [30,31 et] proposedal. [32] and an Rodriguez algorithm et foral. determining[33] proposed the a method flight directionfor estimating for the the quickestwind field for trajectory design. Liu et al. [34] presented a nonlinear model of a predictive control strategy energy harvest. Langelaan et al. [32] and Rodriguez et al. [33] proposed a method for estimating for trajectory determination for energy extraction. Barate et al. [35] controlled a simulated glider the wind field for trajectory design. Liu et al. [34] presented a nonlinear model of a predictive based on a set of Takagi‐Sugeno‐Kang fuzzy rules to exploit wind gradient energy. Although these control strategy for trajectory determination for energy extraction. Barate et al. [35] controlled a contributions improved the sophistication of the concept of dynamic soaring, this was accompanied simulated glider based on a set of Takagi-Sugeno-Kang fuzzy rules to exploit wind gradient energy. by a more complicated practical implementation process. In contrast, Gao et al. [36] and Yang [37] Althoughproposed these a simple contributions method improvedfor generating the sophistication a guidance strategy of the conceptfor autonomous of dynamic dynamic soaring, soaring. this was accompaniedThis involved by the a more division complicated of the Rayleigh practical cycle implementation into four sections, process. the characteristics In contrast, Gao of which et al. [were36] and Yangdetermined [37] proposed by simple a simple equations. method Gao for and generating Liu [38] also a developed guidance strategya dynamic for soaring autonomous plan in dynamicwhich soaring.the Dubins This involved path was the used division to improve of the Rayleighthe computational cycle into fourefficiency. sections, They the showed characteristics that dynamic of which weresoaring determined could be by achieved simple using equations. modern Gao technology. and Liu However, [38] also developed their strategy a dynamic has the shortcoming soaring plan of in whichinvolving the Dubins numerous path control was used parameters, to improve which the computationalmakes practical efficiency.implementation They showedcumbersome. that dynamic soaringIn could the present be achieved study, using we followed modern technology.the
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