Aerodynamic Effects of Elevating Motion on Hovering Rigid Hawkmothlike Wings K. B. Lua, * Y. J. Lee, † T. T. Lim, ‡ and K. S. Yeo § National University of Singapore, Singapore 117576, Republic of Singapore DOI: 10.2514/1.J054326 Flapping of an insect wing can be broadly separated into sweeping, elevating, and rotational motions. The sweeping motion generates forward velocity, and the rotational motion imposes an appropriate angle of attack; both are vital to lift generation. However, the purpose of elevating motion in insect flight remains unclear. In this paper, the aim is to better understand the effects of elevating motion to lift generation and vortex structure development when rigid wings are subjected to three-dimensional simple harmonic motion and hovering hawkmoth flapping motion. Both experimental and numerical techniques are used, and results show that, among the different types of simple harmonic motions considered here, only figure-of-eight motions at a relatively low midstroke angle of attack (25 deg) outperform flapping motions without elevating motion. In this case, lift is enhanced by approximately 11% with insignificant cost to hovering efficiency. The lift enhancement could be attributed to rapid growth of the leading-edge vortex, due to an increase in instantaneous angle of attack when the wing elevates downward during midstroke. For the hawkmoth motion, a small elevating motion has minimal aerodynamic effects, whereas a large one causes reduction in lift due to detachment of the leading-edge vortex from the wing surface. Generally, elevating motion affects lift and power coefficients via four mechanisms: alteration of instantaneous angle of attack, introduction of radial force component, wake capture, and early shedding of leading-edge vortex. Although elevating motion confers a significant lift enhancement to specific sets of flapping-wing kinematics, it is generally detrimental to flight performance. Nomenclature C D = drag coefficient  C D = average drag coefficient C L = lift coefficient  C L = average lift coefficient C P = power coefficient  C P = average power coefficient  c = mean chord length, m F D = drag force, N F L = lift force, N F N = normal force acting on the wing, N FM = figure of merit f = flapping frequency, s −1 l = length of path traced by the wing at the location of the second moment of wing area for one flapping cycle M α = moment about rotating axis, N · m M θ = moment about elevating axis, N · m M φ = moment about sweeping axis, N · m n α = frequency of rotating motion, s −1 n θ = frequency of elevating motion, s −1 n φ = frequency of sweeping motion, s −1 P = aerodynamic power, W p = pressure, Pa q = dynamic pressure, Pa R = wing span measured from wing tip to center of rotation, m R tip = wing span measured from wing tip to wing base, m Re = Reynolds number ^ r 2 = dimensionless second moment of area of wing S = surface area of wing, m 2 T = flapping period, s t = time, s t  = t∕T, nondimensional time U ref = reference velocity, m∕s α = angle of attack, deg _ α = rotational angular velocity, rad · s −1 α I = instantaneous angle of attack, deg α M = midstroke angle of attack, deg β = rotational motion amplitude, deg Θ = elevating motion amplitude, deg θ = elevating angle, deg _ θ = elevating angular velocity, rad · s −1 ν = kinematic viscosity, m 2 ∕s ρ = density, kg∕m 3 Φ = sweeping motion amplitude, deg φ = sweeping angle, deg _ φ = sweeping angular velocity, rad · s −1 I. Introduction I N RECENT decades, there has been growing interest in flapping- wing micro air vehicles (MAVs). This is motivated by potential civilian and military applications [1–3]. Flying insects are known to be excellent fliers, and they can perform much better than human inventions such as fixed-wing aircraft or helicopters in terms of maneuverability and agility. These unique features have inspired engineers to design a MAV that mimics flapping-wing kinematics of insects in an attempt to replicate their superior flight capability. The flapping motion of an insect wing can be broadly separated into sweeping, elevating, and rotational motions [4,5]. The sweeping motion generates forward wing velocity, which is required for lift generation, and the rotational motion imposes an appropriate angle of attack and helps to enhance lift generation during upward pitching motions [6–9]. One frequently asked question is whether elevating motion, defined as motion deviating from the mean stroke plane, is vital for lift generation and efficiency. It is not clear if insects execute elevating motion to improve aerodynamic performance or merely as unintentionally concomitant of their deforming anatomy. Received 7 March 2015; revision received 9 September 2015; accepted for publication 6 November 2015; published online 20 May 2016. Copyright © 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal and internal use, on condition that the copier pay the per-copy fee to the Copyright Clearance Center (CCC). All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the ISSN 0001- 1452 (print) or 1533-385X (online) to initiate your request. *Research Assistant Professor, Department of Mechanical Engineering, 9 Engineering Drive 1, Block EA, 07-08. † Graduate Student, Department of Mechanical Engineering, 9 Engineering Drive 1, Block EA, 07-08. ‡ Professor, Department of Mechanical Engineering, 9 Engineering Drive 1, Block EA, 07-08. § Associate Professor, Department of Mechanical Engineering, 9 Engineering Drive 1, Block EA, 07-08. Article in Advance / 1 AIAA JOURNAL Downloaded by NATIONAL UNIVERSITY OF SINGAPORE on May 22, 2016 | http://arc.aiaa.org | DOI: 10.2514/1.J054326