Figure 1.

(a) Definition sketch of wing-tip kinematic parameters with respect to the laboratory-fixed frame of reference (x,y,z). This forms a right-handed coordinate system with the x-axis aligned opposite to the free-stream velocity vector and the z-axis pointing vertically downward. The solid green line marks the wing-tip path. The stroke plane angle (S) is defined as the angle between the z-axis and the projection onto the xz-plane of the line joining the wing-tip positions at the top and bottom of the stroke. The stroke amplitude (A) is defined as the angle between the lines joining the wing root to the wing tip at the top and bottom of the stroke. The deviation angle (D) is defined as the angle between the lines joining the wing root to the wing tip as the wing passes through the horizontal on the downstroke and the upstroke, respectively. (b) Definition sketch of the wing camber and the angle of incidence with respect to a frame of reference rotating with the wings (x,y_w,z_w). This axis system has the same x-axis as the laboratory-fixed frame, but rotates about this axis such that the line joining the wing root and tip always lies in the xy_w-plane. The local angle of incidence (angle a) was defined as the angle between the xy_w-plane and the line joining the leading and trailing edge parallel to the xz_w-plane. The local camber was defined as the ratio of the mid-chord height (c_h), measured parallel to the z_w-axis, to the chord length (c_l) parallel to the x-axis. Defining the camber and the angle of incidence with respect to this rotating frame of reference removes the effects of changing wing-tip elevation on these variables.