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The Design and Testing of an Airfoil for Winglet on Low-Speed Aircraft

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The Design and Testing of an Airfoil for Winglet on Low-Speed Aircraft Extracting Energy from Atmospheric Turbulence with Flight Tests Chinmay K. Patel Acuity Technologies Inc. Menlo Park, CA 94025 USA [email protected] Hak-Tae Lee University of California, Santa Cruz Moffett Field, CA 94035 USA [email protected] and Ilan M. Kroo Stanford University Stanford, CA 94305 USA [email protected] Accepted by the XXIX OSTIV Congress, Lüsse-Berlin, Germany, 6 August – 13 August 2008 Abstract Birds frequently use the energy present in the atmosphere to conserve their energy while flying. Although en- ergy in the form of thermal updrafts is routinely used by pilots of full-scale and model sailplanes, the energy in atmospheric turbulence has not been utilized to its full potential. This paper deals with the design of simple control laws to extract energy from atmospheric turbulence. A simulation-based optimization procedure to de- sign control laws for energy extraction from realistic turbulence was developed, leading to about 36% average energy savings for a ‘bird-sized’ glider. Flight test results are presented to demonstrate the energy extraction concept and validate the predicted savings. The emergence of ultra-light sailplanes has opened up the possibility of utilizing this form of ‘gust-soaring’ for a class of manned sailplanes, and the concepts presented in this paper can serve as a background for understanding and applying the techniques to extract energy from atmospheric turbulence. Nomenclature t Time bref Reference span V0 Nominal aircraft speed cref Reference chord Vair Airspeed CD Coefficient of drag Vref Reference speed CDp Coefficient of parasite drag wg Vertical gust velocity CL Coeffienct of lift {x, z} Horizontal and vertical (positive down) inertial axes CLmax Maximum coeffienct of lift {u, w} Components of inertial velocity along {x, z} axes D Drag δflap Flap deflection E Total energy with respect to the atmosphere γ Flight path angle eAR Effective aspect ratio λ Wavelength of a sinusoidal gust g Acceleration due to gravity σw Intensity of vertical turbulence h Height He Total energy per unit mass with respect to an inertial Subscripts frame of reference f Final Kx Feedback gain, where x = 1, 2, 3, p, and d L Lift Introduction Lw Length scale of vertical turbulence For centuries, observers have been fascinated by the ability m Aircraft mass of certain birds to fly with little apparent effort. Numerous Sref Reference area accounts of birds soaring without flapping their wings, ranging from observations by Leonardo da Vinci to Octave Chanute,1, 2 TECHNICAL SOARING 100 VOL. 33, NO. 4 – October - December 2009 can be found in literature. Birds circling in thermals or using thrust. The figure also shows how energy can be gained by the ridge lift along a hill or an obstacle are popular examples of flying through a downdraft, by pulling negative g's. The con- advantageous use of atmospheric energy. Energy from up- cept remains valid even if a glider is flying through a lateral drafts due to thermals or ridge lift is often used successfully by gust and the bank angle is such that the glider executes a full-scale and unmanned gliders resulting in tremendous im- downwind turn, hence aligning the lift vector with the gust. In provements in their capabilities. general, when the lift vector of an aircraft is aligned such that In addition to thermal convection, birds also exploit the it has a component in the direction of the atmospheric wind, energy from wind shear and random gusts.3-5 Albatross, for positive work is done on the aircraft (and negative work on the example, are known to fly long distances over oceans, without gust). An alternative argument is that the downwash generated flapping their wings, by extracting energy from the atmos- by the glider reduces the magnitude of the gust. In Prandtl's pheric boundary layer over the ocean. The concept of using words, “One must attempt to equalize the fluctuations in the energy available in the atmosphere has often attracted the at- wind.”18 tention of aircraft designers and pilots. The energy present in Earlier work by Lissaman and Patel19 presented the deter- the motion of air, if converted to the energy of an aircraft, ministic case of optimal control laws in sinusoidal vertical could lead to energy savings and improved performance. gusts. Using a non-dimensionalized problem formulation, they The flight of albatross in the oceanic boundary layer has developed control inputs that enabled a glider with a maximum been studied by several authors.6-9 Dynamic soaring in the lift to drag ratio of 20 to sustain a neutral energy cycle in a shear layer on the leeward side of ridges has become very sinusoidal gust with amplitude of 15-20% of the glider's cruise popular with model aircraft enthusiasts. Proximity to terrain speed. A simple sinusoidal control schedule was also shown to and pilot workload have been the deterrents in applying such a yield good results, indicating the possibility of using simple technique to full-scale sailplanes, along with the fact that wind control techniques for energy extraction from turbulent shear naturally available within atmospheric boundary layer gusts.19, 20 The following sections, which build on the work of may not be sufficient to provide a significant benefit. The Kroo and Patel,21 present a method to determine optimal con- flight speeds of many birds and small Unmanned Aerial Vehi- trol laws for energy extraction from random vertical gusts. A cles (UAVs), however, are comparable to atmospheric fluctua- description of an autonomous UAV and the results of a flight tions and the energy present in time-dependent atmospheric test demonstration are also presented. fluctuations is a much larger fraction of the total power re- The control law developed here is based on controlling the quired for flight of these small vehicles. Light sailplanes may lift of the airplane in response to the gust encountered. This also obtain observable benefits. concept is applicable to manned as well as unmanned air- Reduction in the drag of an airplane flying through a verti- planes. However, the effectiveness of this concept applied to cally fluctuating freestream has been reported10, 11, 12 The use manned airplanes needs further investigation. Furthermore, it of well-designed control laws could lead to significant energy is not clearly understood whether the methodology developed savings and the possibility of sustained flight using energy in this paper is similar to the techniques used in a few available extraction techniques. Energy gain from random wind gusts accounts of soaring in turbulence,13, 14 and whether human pi- and turbulence has been studied to some extent but not demon- lots can reliably implement the control law using basic sensors, strated in flight tests using formally determined control algo- such as a variometer. rithms.9, 11, 12 Pilots of a new class of ultra-light sailplanes have discovered some of the benefits achievable from carefully con- Control Law Design trolled flight through atmospheric fluctuations, also referred to Unlike the deterministic case of a sinusoidal vertical gust, as microlift soaring.13-17 Since this form of soaring does not energy extraction from realistic turbulence requires control require circling in thermals or specific terrain conditions, as in laws that perform well over a variety of random gusts. Meas- slope soaring, it improves cross-country performance. This urements taken at low altitudes in the Earth's boundary layer paper explores the problem of designing simple control laws to have shown that the von-Karman or Dryden wind turbulence extract energy from vertical turbulence. Results presented in spectra are representative of natural turbulence.20, 22, 23 In the this paper show that subtle changes in airplane lift coefficient, present formulation, the ‘frozen gust’ assumption was used, based on easily available sensors, are all that is needed for ex- and the power spectrum of the gust was assumed to follow the tracting energy from atmospheric fluctuations. The concepts Dryden Power Spectral Density (PSD) function. The gusts and results presented here can also be extended to lateral gusts. were modeled as a function of the x (spatial) co-ordinate only. Figure 1 illustrates how a component of the lift vector acts The gust profiles were generated by superposing a set of sinu- as an effective thrust when a glider flies through a vertical soids with amplitude corresponding to their relative contribu- 20, 24 gust. The glider flies through a gust of amplitude wg at speed tion to the gust intensity and a random phase angle. V0. Vectors L and D denote the lift and drag forces, respec- The aircraft was modeled as a point-mass glider flying tively. Since lift acts perpendicular to the local wind, the lift through a vertical gust. A control law for the coefficient of vector is tilted forward and its component acts as an effective lift, CL, was designed to minimize the energy loss as the glider VOL. 33, NO. 3 – October - December 2009 101 TECHNICAL SOARING traveled a fixed horizontal distance. Results are shown for The coefficient of lift at a particular instant is determined gusts generated using the Dryden PSD, and the performance of as a function of the gust velocity, the deviation from a refer- the optimized control laws is compared over a sinusoidal gust. ence airspeed, Vref, and a fixed component. The first term in The equations of motion are presented in Eq. 1. In spite of Eq. 4 is directly related to the angle of attack of the glider. The being the simplest representation, the point-mass model cap- second term is a feedback based on the ratio of the glider's tures the primary physics required for this analysis. airspeed to the reference airspeed.
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