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The Aerodynamics of Compliant Membrane Wings Modeled on Mammalian Flight Mechanics

Ricardo Galvao*, Emily Israeli*. Arnold Song†, Xiaodong Tian‡, Kristin Bishop§,

Sharon Swartz** and Kenneth Breuer†† Brown University, Providence RI 02912, USA

Mammalian flight is characterized by several features unique and distinct from the flight of both insects and birds. One such feature is the use of thin compliant wings as the lifting surface. Motivated by this, we present experimental results on the aerodynamics of compliant membrane wing models of low aspect ratio, performed at low Reynolds numbers, ranging from 30,0 to 100,0. Lift and Drag coefficients are measured over a range of angles of attack from -5 to 60 degrees. In addition the deformation of the wing due to aerodynamic loading is directly measured using a stereo photogrammetric method. Results indicate that the compliant wings' deformation increases with both angle of attack and that deformation scales with dynamic pressure until the onset of stall at which point inertial scaling fails. Stall on compliant wings occurs at higher angles of attack and is gentler than on a similar wing in which the membrane does not deform. Unsteady membrane vibrations are also measured and characterized.

Nomenclature

Cij = lift/drag (i) transformation coefficient for lift/drag load cell pair (j) CD = drag coefficient

CL = lift coefficient c = chord

Fx = drag acting on wing Fz = lift acting on wing Re = Reynolds number

∆Vx = drag load cell pair voltage differential

∆Vz = lift load cell pair voltage differential x = streamwise coordinate y = spanwise coordinate z = altitude coordinate

I. Introduction

Low Reynolds number, low aspect ratio (LAR) aerodynamics is an area of increased research activity, driven in large part by the recent interest in micro-sized aircraft design1, 2 as well as the growth of quantitative studies of flight in insects, birds and bats. LAR wings composed of thin and very flexible membranes are unique to flying and gliding mammals, such as bats, flying squirrels and sugar gliders3, 4 and these animals exhibit extraordinary flight capabilities with respect to maneuvering and agility that are not observed in other species of comparable size. Birds, which are have been studied extensively,4-6 have relatively rigid wings with limited motion, while insects, which fly at much lower Reynolds numbers, are typically characterized by rigid wings moving with a relatively simply

* Undergraduate Student, Division of Engineering † Graduate Student, Division of Engineering ‡ Research Scientist, Department of Ecology and Evolutionary Biology § Graduate Student, Department of Ecology and Evolutionary Biology ** Associate Professor, Department of Ecology and Evolutionary Biology †† Professor, Brown University, Division of Engineering, Box D Providence RI 02912, Senior Member, AIAA.

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36th AIAA Fluid Dynamics Conference and Exhibit5 - 8 June 2006, San Francisco, California AIAA 2006-2866

Copyright © 2006 by Kenneth Breuer. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

articulated flapping motion7. Bats, on the other hand, have an extremely high degree of articulation in the wing (the elbow, wrist and finger joints). More relevant to the current investigation is the fact that the wing surface in bats and other flying mammals is unusual in that it is composed of a thin wing consisting of a highly anisotropic, compliant skin membrane (Fig. 1). This observation suggests that a potentially useful feature for engineered maneuverable micro flight vehicles might be the incorporation of flexible wing membranes as lifting surfaces.

aerodynamic performance of MAVs

An additional feature (and complication) of mammalian flight is the fact that they operate in a highly unsteady fashion and at an intermediate Reynolds number regime where many complex aerodynamic phenomena, such as transition to turbulence and laminar separation, are both present and hard to predict. Although this area of aerodynamics has not been studied extensively, there are some notable exceptions in recent years2, 8, 9. These studies have investigated LAR wings and airfoils at low Reynolds numbers in an attempt to better understand the

be less suited to the low-Re regime associated with MAVs

As an example of an initial inquiry to understand MAV aerodynamics, Shyy and coworkers8 used a computational analysis of ‘low Reynolds airfoils’ to ascertain the effect of thickness and camber, as well as generating pressure surface profiles. Well-known airfoils: the NACA0012 and CLARK-Y were investigated, and compared with the performance of specially designed low-Re wing sections over a range of Re (~7.5 x 104 to 2.0 x 106) and angles of attack. The low-Reynolds airfoils are characterized by highly cambered profiles, low area, and sharply angled leading and trailing edges (the UF airfoil is also quite a bit thinner than the other airfoils in the assessment). The authors concluded that increased camber and reduced thickness airfoils have more favorable liftto-drag ratio as Re number decreases, while the conventional airfoils, i.e. NACA0012 and CLARK-Y, were found to

Figure 1. Examples of mammalian flight. The sugar glider on the left can perform controlled glides at high angles of attack over distances of 100 meters. The unique wing morphology of bats (right) include their skeletal structure and thin wing membranes.

On the experimental front, recent studies by Mueller and coworkers have specifically examined LAR thin/flat/cambered-plate wings10 and several planforms of LAR wings9 over a range of Reynolds numbers, Re = 70,0 to 200,0. Both studies explore the behavior of aerodynamic force coefficients, mainly lift and drag, as well as range efficiency (lift-to-drag ratio) and power efficiency (CL3/2/CD) with respect to aspect ratio and Re dependence. Torres and coworkers suggest that the large non-linearities in the lift curves for wings with aspect ratios less than 1.25 are due to wing tip vortices. These flow structures contribute to an increased maximum lift,

CLmax, and the delay of stall to a larger angle of attack. The interaction of the wingtip vortices with the flow over the lifting surface for LAR wings is analogous to the delta wing, which has vortex lift at high angles of attack.

A strong thrust in the recent research on MAVs focuses on designs that employ membrane wings that have variable-camber or an adaptive-wing structure1, 2. This is desirable for several reasons, and yet a detailed analysis of the complexities that compliance adds to the aerodynamic characteristics of a flexible membrane wing does not appear to be been fully pursued. One motivation for the utilization of flexible membrane wings is to mimic the aeromechanics of natural flyers such as bats because MAVs operate in a similar flight parameter space as these biological flight systems, i.e. flying at low Re with LAR wings. As the evolution of MAV design progresses, little basic science research has attempted to develop a model of the interplay of aerodynamic contributing to the better performance of flexible membrane flyers. The adaptive nature of the membrane wing may give MAVs the potential to mimic the extraordinary flight agility of bats. The morphing capability of the wing structure is the product of the interaction between fluid and structural capabilities. Recently, Shyy2 has reviewed the recent computational and experimental work relating to MAV research. He also discusses the development of computational techniques to assess the flow structure associated with LAR, low Reynolds wings and the generation of optimization techniques for MAV wing shape. The structural deformation or dynamics of the flexible membrane greatly contributes to the aerodynamic forces over the wing and the wing performance. Clearly, in looking to nature’s flyers as inspiration, MAV designers have recognized the potential of flexible membrane wings to achieve improved agility and efficiency.

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wing motions

The study of the full complexity of mammalian flight is challenging but is nevertheless underway3, 1. However, a significant challenge in working with live animals (and something that is somewhat unfamiliar to the traditional aerodynamics community), is the requirement that the testing must be accomplished in a safe and humane manner, and furthermore, that it is difficult, if not impossible, to isolate unique contributions that different characteristics of an animal's morphology contribute to its overall aerodynamic performance. To address these issues, we have thus embarked on a systematic study with an attempt to isolate different morphological features present in mammalian flight, and to explore the role that each plays. The current study focuses on the effects of thin membrane wings on aerodynamic performance and the present manuscript, which is the first step in this direction, has two goals: firstly to characterize the aerodynamic performance of compliant membrane wings and secondly to explore the dynamics of the membrane as it is subjected to aerodynamic loads. To accomplish this, we describe the design, fabrication and testing of simple "canonical" membrane wings with low aspect ratio. The wing is tested in a low-speed wind tunnel over a range of (low) Reynolds numbers and angles of attack. Both lift and drag forces are measured for four wing configurations. In a separate but overlapping series of experiments, we have measured the three-dimensional shape of the wing as it deforms while subject to aerodynamic loading. This is accomplished using high-speed, stereo photogrammetry which allows us to measure not only the static deflection of the wing but also the onset of unsteady I. Experimental Procedure

measures 61.0 cm by 61.0 cm

All experiments were conducted in the low-speed, low-turbulence wind tunnel at Brown University. The wind tunnel is a closed-return facility in which free stream velocities are controlled by a constant speed variable angle axial fan. The test section

A. Flexible wing models

A compliant membrane wing was designed and manufactured for the experiments. The rectangular wing is composed of a compliant latex membrane held between two stainless steel posts located at the leading and trailing edges (Fig. 2). The posts measure 6.0 cm in height and are secured to an aluminum mounting plate designed to attach to the force balance which is mounted on the test section ceiling. At either end of wing, the membrane material is inserted through a slit aligned with the centerline of the post then secured using spring steel clamps. With the clamps in place, the leading and trailing edges are approximately parabolic in shape with a maximum thickness of 3.7 m. The fully assembled wing measures 12.9 cm (chord, c) by 5.9 cm (half-span, b), giving a half-wing aspect ratio of

0.46. We should note that the assembly technique did not carefully control the tension in the wing membrane, only adjusting it so that it seemed taut, but not stretched, in its default position (in absence of aerodynamic forces). As a result, direct comparisons between wings of different membrane materials are taken to be merely qualitative, since the results will depend, not only on the wing membrane material, but also on the pre- tension of the wing with no aerodynamic loading.

Figure 2. Photograph of the flexible wing model. The trailing edge spring clamp has been removed for clarity. The dot array is tracked by the photogrammetry system.

B. Lift and Drag Measurements

The wing is mounted upside down on a gimbaled, two-axis force balance for measurement of lift and drag (Fig. 3). The platforms are aligned to be orthogonal so as to decouple the two horizontal components of the aerodynamic forces, each of which is measured using a pair of load cells. The entire force balance assembly is mounted to a turntable which allows

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Figure 3. Schematic of the wind tunnel configuration. The wing hangs down into the test section, mounted on a two-axis gimbal. Lift and drag are measured from the output of four load cells, each attached to an orthogonal axis of the force balance adjustment of the angle of attack. The orientation of the orthogonal force platforms is fixed with respect to the chord line of the wing as the angle of attack is varied. The load cells are pre-loaded so that, as the aerodynamic force increases, the output of one load cell increases while the output of the other decreases. Thus, the applied load is determined from the difference between the two load cell readings, an arrangement that minimizes common-mode noise due to the vibrations of the apparatus. Voltages were acquired using a 16-bit A/D system sampling at 4 kHz and averaging over 50 seconds. Although this can ultimately allow unsteady force measurements, this was not attempted in the current series of experiments.

The force balance measures the applied moment about a center bearing. Assuming that the lines of action of the aerodynamic forces intersect the mid-span of the wing, we can then recover the lift and drag acting on the wing. The wing deflection measurements presented later in this paper support the validity of this assumption. However, planned improvements to force balance apparatus will allow future experiments to simultaneously measure the aerodynamic forces and the center of pressure.

At any given speed and angle of attack, the forces in the chordwise and cross-chord directions may be found from a linear combination of the four load cell voltages. Nominally, two load cells will contribute equal and oppositely to each component of force. However, each load cell has slightly different gain, and a slight misalignment between the axes of the force balance and the axis of the wing is unavoidable. For this reason we utilize the voltage differentials, ∆Vx and ∆Vz, of both load cell pairs in the determination of both Fx (drag) and Fz (lift). This can be expressed in matrix form:

x xz x x zx z z z

The coefficient matrix is determined from a series of measurements performed by applying static forces in both the streamwise and spanwise directions. For calibration, the applied forces in the lift and drag coordinate directions ranged from 0.98 to 4.95 N. These calibration measurements were then converted to a series of linear weights using a generalized linear regression based on a singular value decomposition (SVD) of the over-constrained linear system:

(2) xz x x xi z i xixz xz zzx z x i zi zi

V FC i V FC where the number of calibration measurements is denoted by N. However, we can decompose the matrix of measured voltages, denoted here as A, via SVD

Let the dimension of voltage matrix, A, be of dimension m x n. We define S to be a m x n diagonal matrix of the singular values of the original matrix A. U and V are then defined to be matrices of dimensions m x m and n x n, respectively, which have orthogonal columns so that

V I (3)

We can write Eq. (2) as where c and f are the vectors containing the transformation coefficients and applied forces respectively. Solving for c,

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