Force Measurements of a Flapping Wing with Two Angular Degrees of Freedom and Bio-Inspired Kinematics

Abstract

This paper presents preliminary results of an experimental investigation of the aerodynamics of rigid and flexible flapping wings with bio-inspired kinematics. We consider rigid and isotropic flexible wings undergoing two degrees of freedom periodic motions of the flapping angle and the pitch angle. The wing models are thin flat plates with Zimmerman elliptical planform of aspect ratio 7.2. We present comparisons of two bio-inspired kinematics derived from the hawkmoth kinematics along with a purely sinusoidal motion. The experiments are conducted at conditions relevant to biological flight, properly scaled for water tests, which are Reynolds number of 7100 and a reduced frequency of 0.21 based on flow properties at the 75% span location. The performance of the flapping motions is compared between the differing motions and between flexible and rigid wings. Time resolved phase-averaged force measurements show the development of two force peaks during the flapping cycle for the bio-inspired kinematics and a single peak for the sinusoidal kinematic. These features are not strongly influenced by wing flexibility. Propulsion efficiency is characterized by the measured figure of merit for each case and it is found that flexibility improves performance in terms of both thrust and efficiency compared to rigid wings. Nomenclature = swept areaflat plate bending stiffness /12 1 [N·m] E = Young's Modulus [Pa] f = frequency [Hz] k = reduced frequency ref ⁄ = lift [N] ref = reference length = figure of merit ideal ⁄ = power [W] = dynamic pressure ½ = half span [cm] % = 75% of the half span = Reynolds number = wing planform area = thrust [N] ⁄ = phase of motion = thickness = reference velocity = pitch angle = pitch amplitude = kinematic viscosity = Poisson's ratio Π = effective stiffness = fluid density Φ = stroke amplitude (peak to peak)

Force generation of bio-inspired hover kinematics

“…The force generation, propulsion efficiency and flow evolution are measured and reported. These results complement related work on the effects of flapping reported by Morrison et al 8 and Yeo et al…”