Figure 1. Key variables and validation results.

(A) Schematic defining the variables used to parameterize the kinematics and deformation of the wing in the current study. () and () are lab and wing-attached coordinated frames respectively. The wing shape and position at the middle of downstroke (gold) and upstroke (aqua) are shown. The red dot identifies the leading-edge and is the cambered shape associated with the wing surface at one spanwise location in both wing positions. The local camber is defined as the ratio of maximum camber ( in the figure) to the local chord length (, which is the straight line joining the leading and trailing edge of ). The angle-of-incidence (AoI) is defined as the angle between and the plane. (B) Simulation result for the observed butterfly wing (OBW) in forward flight showing streaks mimicking smoke traces and vortical structures at early downstroke. (C) Vanessa cardui with its brightly colored wings. Center-of-masses (CoMs) for different parts of the butterfly are marked. Point 1: abdomen; Point 2: whole body; Point 3: head and thorax; Point 4: hind wing and Point 5: fore wing. (D) Comparison of the lift force predicted by the simulation and the experimentally estimated value. The error-bars indicate the uncertainties in the experimental estimate.