Fig 1.
Still-frames showing flight path of H. pratti in tunnel: Wing marker points recorded and reconstructed to derive wing kinematics.
Fig 2.
Terminology used in the kinematic decomposition: The right and left wingtips each trace out a locus of points that are projected onto the vertical bisecting plane to determine the stroke plane angle.
Fig 3.
(a) Side view of the bat (view along the yb axis) showing the stroke plane and the body-fixed stroke plane coordinate system (xb, yb, zb), (b) view along the zb axis, looking directly at the stroke plane: the flap angle, ϕn, controls the location of the span line and varies with time, (c) view looking down the stroke plane, along the xb axis: the stroke plane deviation angle, θn, defines the position of the span line out of the stroke plane; a representative airfoil coordinate system, (xa, ya, za), is shown on the right wing, and highlighted in (d). The pitch angle, ψi,n, defines the rotation of the airfoil section about the span line, and varies along the span, ‘i’, as well as varies in time, ‘n’. The camber, Ci,j,n, defines the displacement of the airfoil away from the span line, and varies along the span, ‘i’, chord, ‘j’, and in time, ‘n’.
Fig 4.
Wing flexion as defined as displacement of the quarterchord from the span line: (a) along the za axis, (b) along the xa axis (refer Fig 3(d) for orientation information).
Fig 5.
Spanwise variation of pitch angle (ψ) at base reference state (time-invariant).
Fig 6.
(a) Flapping motion plotted for one flapping cycle (53ms to 182ms), with light-grey tiles representing the stroke plane (xb, yb) inclined at 53°, dark-grey surfaces representing the wings, tip trajectories traced by dots, and maroon arrows denoting direction of flight; (b) temporal evolution of flapping angle (ϕ), with shaded areas representing upstroke.
Fig 7.
(a) Combined flapping and stroke plane deviation plotted for one flapping cycle (53ms to 182ms), with light-grey tiles representing the stroke plane (xb, yb) inclined at 53°, dark-grey surfaces representing the wings, tip trajectories traced by dots, and maroon arrows denoting direction of flight; (b) temporal evolution of stroke plane deviation angle (θ), with shaded areas representing upstroke.
Fig 8.
Demarcation of inner (green) and outer (purple) wings based on the instantaneous locations of the left and right wrists, and the location of cutting planes.
Fig 9.
(a) Spanwise variation of pitch angle (ψ) for one flapping cycle (53ms to 182ms) with inset showing the definition of pitch angle with respect to stroke plane angle (β) for an airfoil chord line; (b) temporal evolution of ψ at mid outer and and inner wing sections.
Fig 10.
Temporal evolution of airfoil shape at mid-inner and outer sections on both wings over one flapping cycle (53 ms to 182 ms).
Fig 11.
Temporal evolution of chordwise camber at different airfoil sections along the span: (a) left wing, (b) right wing.
Fig 12.
(a) Spanwise variation of flexion over one flapping cycle (53ms to 182ms), (b) temporal evolution of maximum flexion.
Fig 13.
Comparison of force coefficients during bat flight (native kinematics) at three different Reynolds numbers (400, 1,200 and 12,000).
Fig 14.
Perspective view of background mesh (plotting every 5th grid line of the 30c × 16c × 16c domain) for fluid simulation enclosing the bat, with orthographic projections of top (18c × 16c), front (16c × 16c) and side (18c × 16c) views. The total cell count was 32 million.
Table 1.
Grid independence study.
Table 2.
Time-averaged forces over two flapping cycles (53ms to 324ms).
Fig 15.
Interpretation of αeffective (or α).
Fig 16.
Flapping motion: (a) Time variation of αeffective, (b) Forces evolution averaged over two flapping cycles (53ms to 324ms).
Fig 17.
Flapping motion (53 ms to 324 ms): 3D view of wing with pressure contours at y/c = 1.75 and y/c = -2, and isosurfaces of coherent vorticity (ωc = 5).
Fig 18.
Combined flapping and stroke plane deviation: (a) Time variation of αeffective, (b) Forces evolution averaged over two flapping cycles (53 ms to 324 ms).
Fig 19.
Combined flapping and stroke plane deviation (53 ms to 324 ms): 3D view of wing with pressure contours at y/c = 1.75 and y/c = -2, and isosurfaces of coherent vorticity (ωc = 5).
Fig 20.
Combined flapping, stroke plane deviation and pitching: (a) Time variation of αeffective, (b) Forces evolution averaged over two flapping cycles (53 ms to 324 ms).
Fig 21.
Combined flapping, stroke plane deviation and pitching (53 ms to 324 ms): 3D view of wing with pressure contours at y/c = 1.75 and y/c = -2, and isosurfaces of coherent vorticity (ωc = 5).
Fig 22.
Combined flapping, stroke plane deviation, pitching and cambering: Forces evolution averaged over two flapping cycles (53 ms to 324 ms).
Fig 23.
Effect of cambering on evolution of dorsal LEV during downstroke: wing surface colored by pressure, isosurfaces of coherent vorticity (ωc = 5): (a) without camber, (b) with camber.
Fig 24.
Combined flapping, stroke plane deviation, pitching, cambering and flexion: (a) time variation of αeffective, (b) Forces evolution averaged over two flapping cycles (53 ms to 324 ms).
Fig 25.
Effective angle of attack, αeffective, at mid-inner and mid-outer wing locations (top–without flexion, bottom–with flexion), with maroon arrows denoting flight direction, green arrows denoting the direction of the local relative flow velocity at the leading edge of each airfoil, and dashed lines denoting extensions of chord lines at each airfoil section.
Fig 26.
Combined flapping, stroke plane deviation, pitching, cambering and flexion (53 ms to 324 ms): 3D view of wing with pressure contours at y/c = 1.75 and y/c = -2, and isosurfaces of coherent vorticity (ωc = 5).