Figure 1.
(a) Experimental set-up. Flapper apparatus for measurement of aerodynamic forces and diagram of the bevel-geared flapper device moving the wing along three orthogonal Euler angles, namely the stroke amplitude ϕ, the deviation from mean stroke plane θ and angle of attack α. The wings were immersed in a tank of oil (46 cm × 41 cm × 152 cm) with walls sufficiently wide to ensure minimal edge effects (data not shown). Instantaneous forces and torques were measured by a sensor attached to the base of the wing model. (b) Sample kinematic plots for each trial. Top panel, angular velocity of the wing is constant throughout the stroke, from 0° to 180°. Middle panel, in all cases, the wing moves along a flat stroke plane with zero deviation from the mean stroke plane. Bottom panel, for each run, the angle of attack is kept at a constant value between −9 and 90° in steps of 4.5°. (c) Test wing: image of the wing attached with rigid carbon fibre leading edge. The wing length is 10 cm, and the maximal chord length 4.5 cm. (d) Measurement of the effective stiffness of the wings (not to scale). The micrometer stage moves the flexible beam along the pin direction and a movable stage adjusts the loading point on the wing. Pre-calibrated foil strain gauges wired in half bridge configuration (350 Ω each) and operating in their linear range measure the forces required to bend the wing through a given distance. Flexural stiffness was then calculated from the bending force and distance using equation (2.2). (e) Sample raw and average plots for three representative angles of attack (0°, 27° and 45°) and at three different stiffness values (PET-G06, Mylar007, Mylar005; see table 1). Top panels show drag coefficients (CD) and bottom panels lift coefficients (CL) as a function of time. In each case, the black line is the actual recorded, inertia-subtracted force and the smooth coloured line as follows: red = 0°, blue = 27°, yellow = 45°. (i,ii) Plots for the most rigid wing (PET-G06; EI ≈ 10−3). (iii,iv) Plots for wings of intermediate stiffness (Mylar007; EI ≈ 10−4). (iv,v) Plots for wings of low stiffness (Mylar005; EI ≈ 10−5).