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Dynamic Soaring is a flying technique which extracts energy from an environment where wind gradients form, with the potential to increase the endurance of small unmanned vehicles. The feasibility to use dynamic soaring flight is questioned here; it requires the identification of energy-extraction mechanisms as well as accurate understanding of the way energy-harvesting performances are governed by trajectory constraints, vehicle characteristics and environment conditions. A three-dimensional energy-neutral trajectory is derived out of a specified optimization problem. Characteristic phases of flight are evidenced out of an overall closed trajectory. Simplified equations are used to evidence the physics behind energy transfers. Finally, overall energy-harvesting balance is studied through local variations of total energy along the path. 1. NOMENCLATURE χ = position along the east direction, m m = vehicle mass, kg y = position along the north direction, m Etot = total energy, earth related, J z = height, m Vair = airspeed, m/s Vi = inertial speed, m/s tf = final time, s γi = inertial flight path angle, rad dt = time step, s ψi = inertial azimuth angle, rad γair = air-relative flight path angle, rad CL = lift coefficient ψair = air-relative azimuth path angle, rad φ = bank angle, rad CLmax = maximum lift coefficient CDi = ith drag polynomial coefficient Nt = number of time discretization nodes b = span, m Wi = wind component along direction i, m/s S = wing area, m2 u* = wind friction velocity, m/s ρ = air density, kg/m3 hR = wind reference height, m g = gravitational acceleration, m/s2 z0 = surface roughness length, m L = lift, N ztip = wing tip clearance, m D = drag, N 2. INTRODUCTION 2.1 Long Endurance UAV flight Long-endurance flight is acknowledged to be a key factor of UAV utility [1]. Without any human beings on board, endurance is only limited by fuel capacity. However, in the domain of small-sized UAVs, the limited mass and volume challenge the energy storage. Besides, the smaller size comes with reduced aerodynamic efficiency by flying at lower Reynolds number and the scaling effect does not play in favour of long endurance. Innovative solutions are therefore approached in order to enable longer range and autonomy for small-sized UAVs. Research on fuel-cell propulsion for long endurance UAV is particularly active as their high energy density potential enables to outclass hydrocarbon or electric-powered systems. Recently, the Ion Tiger performed a flight of 48h using only 500g of liquefied hydrogen to feed its fuel-cell [2]. However, although fuel-cells provide high specific energy together with high power, their size and volume can only be constrained to a limited level. On Ion Tiger, the fuel-cell system only (fuel cell, fuel tank, regulator, cooling) weights 5.5 kg [3] with neither fuel nor propulsion system. Moreover, the need for heat transfer area increases the size of the fuselage. In order to achieve a maximum lift over drag ratio of 17, Ion Tiger has a wingspan of up to 5.15 meters, for a practical payload of 2.3 kg and an overall mass of 16 kg. Another option for improving endurance is to seek for energy from the surrounding environment. Studies about long endurance vehicles have mainly focused on using solar power to maintain a vehicle aloft all round the clock, with the shortage of solar exposition during the night being balanced by the excess of power received throughout daylight and stored into potential energy. The Qinetiq Zephyr paved the way by performing a two-week-long flight in 2010 and the Boeing Solar Eagle project aims at staying aloft for up to five years at altitudes above 60,000 ft. Another approach is static soaring, where energy is gained by flying through a mass of rising air, either due to pockets of warm air or to wind-slope deflections. It requires detecting sparsely distributed zones of rising air and adopting an appropriate trajectory management. Several studies investigated autonomous thermal soaring for UAV and were faced with the challenge of flying through the constrained volume of thermals. 2.2 The Albatross Legacy The technique this paper is going to focus on is called dynamic soaring. It consists in extracting energy from the wind, in an environment where vertical gradients of horizontal wind are formed. This flying technique is directly inspired by the flight of albatrosses. Those singularly massive seabirds take advantage of wind gradients which forms at the interaction between air and sea to fly for thousands of kilometres with hardly a flap of their wing [4, 5]. Since the first observations of albatrosses by Lord Rayleigh in the late XIXth century [6], the enthusiasm for dynamic soaring has grown bigger [7, 8]. Energy-Harvesting Mechanisms for UAV Flight by Dynamic Soaring Figure 1. Wandering Albatross (Diomedea Exulans) brushing the surface with wingtips. Copyright Klaus Berre kbphoto.dk. Little was known about their flight until impressive travel performances were revealed by a satellitetracking experience conducted in 1990 which showed that tagged specimens could travel more than 800 kilometres a day [9]. Albatross geographical distribution in Fig.2 shows a widespread presence, although rather limited to southern oceans, especially for great albatrosses of the gender Diomedea, like the Wandering Albatross, Diomedea Exulans, which can weigh up to 13kg. Many albatross species are actually endemic to a specific island and they anyway have very sparse colonies, secluded on remote islands such as Crozet, Amsterdam or Kerguelen. Their wide distribution is therefore the result of singular travel abilities which carries them all over southern oceans. However their presence is strictly out of tropical regions, with the only exception being the Chatam Albatross seen in orange on Fig.1. This first analysis has to be completed by a study at Fig. 3 which shows the annual estimate of global wind strength. The correlation between wind strength and albatross presence is significant, with albatross species being reported in every zone of average wind velocity above 9 m.s-1, except North Atlantic, and reciprocally very little albatross presence outside of those areas. Although the wind strength can not explain in itself the distribution of albatrosses around the globe, it highlights the assertion that V. Bonnin, E. Benard, J.-M. Moschetta and C. A. Toomer Figure 2. Satellite tracking locations of albatrosses and petrels, from [10]. All coloured-locations represent albatross species, the Wandering Albatross is shown in bright red. Figure 3. Estimate of wind velocity (m.s-1) at 50m, average over a 10-year period [11]. albatrosses use a wind-related phenomenon to propel themselves effortlessly around the globe. It should also be mentioned that the North Pacific Albatross species, which range from US west coast to Japan east coast, are among the lightest albatrosses, with a weight not exceeding 4.5 kg [4], while the Great Albatross species, including Wandering Albatross, are the heaviest and do not venture outside of areas of average wind velocity of 9 m.s-1and above. All observations of inflight albatrosses mention very little wing-flapping and biological analysis of their morphology concluded that they were not adapted to flapping flight, with long high-aspect-ratio wings and thin flight muscles [5]. The peculiarity of albatross flight technique hence does not rest upon a particular kinematic of their wings but upon specific trajectories of a fixed-wing vehicle, that are therefore potentially transposable to the domain of small fixed-wings-UAVs. Figure 4. Overall dynamic soaring pattern and principles, from [17]. The wind profile given in the figure is not realistic but just depicts the significance of the zone of wind shear. The basic idea behind this soaring technique is to cross layers at different windspeeds in a welldefined way, such that the manoeuvres entail a local increase in airspeed for the vehicle [6]. This cyclic pattern is simplified on Fig.4, with the albatross crossing a shear region in a repetitive motion. Albatross have in this way been observed to perform repetitive patterns, although of more intricate variations, in the first 15-20m above the surface. Several numerical studies focused on building a model of dynamic soaring applied to UAV flight [12-14]. However, the nature of energy-harvesting mechanisms has been controversial and still suffers from a lack of consistency. Pennycuick uses his observations on the field to demonstrate that albatrosses gain their energy out of gusts created by flow separation over waves [17]. Sachs and Deittert showed through numerical studies that classic wind-shear soaring over a flat ocean surface can provide conditions for sustainable dynamic soaring flight. Deittert provides a methodology that uses differential flatness, and computes trajectories for a 3m-wingspan vehicle which lift over drag ratio is evaluated at 33.4, seem rather high for a vehicle of that size. Sachs then highlighted that the energy gain comes from the upper turn from windward to leeward and he made use of albatross in-flight measurements to support his claim [16]. Richardson describes how the different energy-extraction theories are not mutually exclusive but could rather be combined during dynamic soaring flight, although no further analysis supports this claim [17]. This background of studies underlines that energy-harvesting mechanisms involved in dynamic soaring are multiple and not trivial. This paper aims at providing a clear picture of the physics involved in the energy-extraction mechanisms, in the case of wind-shear soaring. Indeed, for the sake of simplicity, our numerical model would be based on the assumption of a flat surface. Moreover, this paper would also take advantage of powerful numerical resolution tools to produce flight models of dynamic soaring and to investigate which variables govern the energy-harvesting process. The first part would expose the methodology followed to derive dynamic soaring trajectories. Then, closed trajectory results would be extrapolated, energy extraction mechanisms would be explained and their contribution to the overall energy harvesting process would be determined. 3. METHODOLOGY 3.1 Equations of Motion Equations of motion of a point-mass model flying through a wind environment are derived in this section. Kinematics are observed from an earth-based inertial reference frame R0 oriented along the North and East direction as shown in Fig. 5. The inertial speed Vi, defined in Eq.1a, is oriented with azimuth and flight path angles with respect to R0, as presented in Fig. 5, defining a Ri reference frame so that the inertial speed is oriented along xi, in the same direction. The airspeed is then oriented with respect to R0 using also a set of azimuth and elevation angles and the lift is oriented by the bank angle φ, as shown in Fig. 6. Moreover the wind is supposed to be unidirectional, coming from the north only. This is introduced in Eq. 1c. Figure 5. The orientation of the inertial speed with respect to the reference frame R0. Figure 6. Orientation of the airspeed and of aerodynamic forces, with respect to the reference frame R0.