David J. Willis

Quantifying the complexity of bat wing kinematics

Body motions (kinematics) of animals can be dimensionally complex, especially when flexible parts of the body interact with a surrounding fluid. In these systems, tracking motion completely can be difficult, and result in a large number of correlated measurements, with unclear contributions of each parameter to performance. Workers typically get around this by deciding a priori which variables are important (wing camber, stroke amplitude, etc.), and focusing only on those variables, but this constrains the ability of a study to uncover variables of influence. Here, we describe an application of proper orthogonal decomposition (POD) for assigning importances to kinematic variables, using dimensional complexity as a metric. We apply this method to bat flight kinematics, addressing three questions: (1) Does dimensional complexity of motion change with speed? (2) What body markers are optimal for capturing dimensional complexity? (3) What variables should a simplified reconstruction of bat flight include in order to maximally reconstruct actual dimensional complexity? We measured the motions of 17 kinematic markers (20 joint angles) on a bat (Cynopterus brachyotis) flying in a wind tunnel at nine speeds. Dimensional complexity did not change with flight speed, despite changes in the kinematics themselves, suggesting that the relative efficacy of a given number of dimensions for reconstructing kinematics is conserved across speeds. By looking at subsets of the full 17-marker set, we found that using more markers improved resolution of kinematic dimensional complexity, but that the benefit of adding markers diminished as the total number of markers increased. Dimensional complexity was highest when the hindlimb and several points along digits III and IV were tracked. Also, we uncovered three groups of joints that move together during flight by using POD to quantify correlations of motion. These groups describe 14/20 joint angles, and provide a framework for models of bat flight for experimental and modeling purposes.

Wing structure and the aerodynamic basis of flight in bats

Powered, flapping flight has evolved at least four times in the Animal Kingdom: in insects, birds, pterosaurs, and bats. Although some aspects of flight mechanics are probably common to all of these lineages, each of the four represents a unique solution to the challenges of maneuverable flapping flight at animal length scales. Flight is less well documented and understood for bats than birds and insects, and may provide novel inspiration for vehicle design. In particular, bat wings are made of quite flexible bones supporting very compliant and anisotropic wing membranes, and possess many more independently controllable joints than those of other animals. We show that the mechanical characteristics of wing skin play an important role in determining aerodynamic characteristics of the wing, and that motions at the many hand joints are integrated to produce complex and functionally versatile dynamic wing conformations.

A Computational Framework for Fluid Structure Interaction in Biologically Inspired Flapping Flight

Although there are many examples of successful flapping flight in nature, engineers and scientists have had difficulty achieving high performance levels using flapping wing designs. In this paper a computational framework to design and analyze flapping flight for Micro Aerial Vehicle size scales is presented. This computational framework exploits a series of different geometric and physical fidelity level representations. The tools considered are wake only methods(HallOpt), lifting line methods(ASWING), panel methods (FastAero) and high order discontinuous Galerkin methods for solving the Navier Stokes equations(3DG). Using this suite of tools, both design oriented explorations as well as analysis of animal flight can be performed. In this paper we present the framework in its current state and illustrate its use by examining several characteristic problems.

Whole-body kinematics of a fruit bat reveal the influence of wing inertia on body accelerations

SUMMARY The center of mass (COM) of a flying animal accelerates through space because of aerodynamic and gravitational forces. For vertebrates, changes in the position of a landmark on the body have been widely used to estimate net aerodynamic forces. The flapping of relatively massive wings, however, might induce inertial forces that cause markers on the body to move independently of the COM, thus making them unreliable indicators of aerodynamic force. We used high-speed three-dimensional kinematics from wind tunnel flights of four lesser dog-faced fruit bats, Cynopterus brachyotis, at speeds ranging from 2.4 to 7.8 m s–1 to construct a time-varying model of the mass distribution of the bats and to estimate changes in the position of their COM through time. We compared accelerations calculated by markers on the trunk with accelerations calculated from the estimated COM and we found significant inertial effects on both horizontal and vertical accelerations. We discuss the effect of these inertial accelerations on the long-held idea that, during slow flights, bats accelerate their COM forward during ‘tip-reversal upstrokes’, whereby the distal portion of the wing moves upward and backward with respect to still air. This idea has been supported by the observation that markers placed on the body accelerate forward during tip-reversal upstrokes. As in previously published studies, we observed that markers on the trunk accelerated forward during the tip-reversal upstrokes. When removing inertial effects, however, we found that the COM accelerated forward primarily during the downstroke. These results highlight the crucial importance of the incorporation of inertial effects of wing motion in the analysis of flapping flight.

The Numerical Simulation of Flapping Wings at Low Reynolds Numbers

Although there are many examples of successful apping ight in nature, the design of e cient apping wings for human designed vehicles has been an elusive goal. One of the main obstacles encountered is the multi-dimensional design space. In order to e ciently search the design space one must rely on e cient models that allow the rapid evaluation of the proposed designs and at the same time are able to capture the critical subtleties of the ow. An e ective strategy to accomplish these two requirements is the use a multidelity simulation capability. In this paper, we analyze apping ight for Micro Aerial Vehicle size scales at two di erent levels of delity: an inviscid panel method code (FastAero), and a high-order discontinuous Galerkin method for solving the Navier-Stokes equations (3DG). One of the objectives of this paper is to examine and establish the limits of validity for each approach.

Multifidelity Approaches for the Computational Analysis and Design of Eective Flapping Wing Vehicles

task. Several computational results are presented illustrating the versatility of the computational methods which are presented. The computational investigations explore top-down and bottom-up philosophies to enhance the understanding of flapping flight physics, force production and energetics. The results which are discussed range from simple two dimensional prescribed motions, to three-dimensional aerodynamics simulations of geometrically accurate bat flight.

Comparing Aerodynamic Models for Numerical Simulation of Dynamics and Control of Aircraft

Stability and control derivatives are routinely used in the design and simulation of aircraft, yet other aerodynamics models exist that can provide more accurate results for certain simulations without a large increase in computational time. In this paper, several aerodynamics models of varying fidelity are coupled with a six degrees of freedom rigid body dynamics simulation tool to model various geometries under a number of different initial conditions. The aerodynamics models considered are: stability derivatives, strip theory methods, quasi-steady vortex lattice methods, and unsteady panel methods. Through dynamic simulations using a virtual wind tunnel, differences between the various aerodynamics models are examined. The simulations that were examined were primarily concerned with the short period mode in the longitudinal direction. Initial examinations were performed on single-surface geometries and showed good agreement between all models. The follow-up simulations of conventionaland canard-type aircraft configurations showed variations due primarily to the inclusion of a wake model for domain vorticity in the vortex lattice and unsteady panel methods. Although dynamics are considered, the simulations performed did not show unsteady aerodynamics effects causing significant differences in short-period responses. This suggests that the quasi-steady approaches traditionally considered are adequate for the majority of stability and control simulations. The use of unsteady panel methods is only required when reduced frequencies increase to the point where Theodorsen’s lag function contributes significantly to the aerodynamic behavior. This would be the case for high frequency forced flapping flight, but is generally not the case for aircraft.

A Numerical Exploration of Parameter Dependence in Power Optimal Flapping Flight

A computational framework for analyzing and designing efficient flapping flight vehicles is presented. Two computational tools are considered: a Betz Criterion code proposed by Hall et. al., and an accelerated, unsteady, potential flow solver. The parameters considered in this paper are: the flapping frequency, the flapping amplitude in both up-down and forward-aft directions, and the addition of a mid-wing hinge for articulated flapping flight. The flapping kinematics are represented using harmonics. Three numerical experiments are examined for the flapping flight analysis. The first experiment involves sweeping through a basic flapping flight parametric design space. The second experiment minimizes flight power at a given flight condition using a quasi-Newton optimization. The third experiment demonstrates the conversion of the problem from a wake only analysis to a 3-D flapping wing geometry.

Aeromechanics in aeroecology: flight biology in the aerosphere

The physical environment of the aerosphere is both complex and dynamic, and poses many challenges to the locomotor systems of the three extant evolutionary lineages of flying animals. Many features of the aerosphere, operating over spatial and temporal scales of many orders of magnitude, have the potential to be important influences on animal flight, and much as marine ecologists have studied the relationship between physical oceanography and swimming locomotion, a subfield of aeroecology can focus attention on the ways the biology of flight is influenced by these characteristics. Airflows are altered and modulated by motion over and around natural and human-engineered structures, and both vortical flow structures and turbulence are introduced to the aerial environment by technologies such as aircraft and wind farms. Diverse aspects of the biology of flight may be better understood with reference to an aeroecological approach, particularly the mechanics and energetics of flight, the sensing of aerial flows, and the motor control of flight. Moreover, not only does the abiotic world influence the aerospheric conditions in which animals fly, but flying animals also, in turn, change the flow environment in their immediate vicinity, which can include the air through which other animals fly, particularly when animals fly in groups. Flight biologists can offer considerable insight into the ecology of the aerial world, and an aeroecological approach holds great promise for stimulating and enriching the study of the biology of flight.

A Quadratic Basis Function, Quadratic Geometry, High Order Panel Method.

Most panel method implementations use both low order basis function representations of the solution and flat panel representations of the body surface. Although several implementations of higher order panel methods exist, diculties in robustly computing the self term integrals remain. In this paper, methods for integrating the single and double layer self term integrals are presented. The approaches are conceptually simple and robust. The paper considers quadratic basis functions to represent the solution, while the geometry of the body is approximated using piecewise parametric quadratic patches. Increased convergence rates are demonstrated for cases where the quadratic basis functions on quadratic curved panels are used. The quadratic panel method converges at a rate proportional to the cube of the panel side length (or NP 3 2, where NP is the number of panels).