Fig 4.

Time variation of the components of added-mass lift $F_{{\kappa }_{\mathrm{\text{I}}}}^{(2)}$ for the (a) hawkmoth and (b) fruit fly over one flapping cycle. Surface contours of added-mass lift $F_{{\kappa }_{\mathrm{\text{I}}}}^{(2)}$ at instants corresponding to peak values in the flapping cycle for the (c) hawkmoth and (d) fruit fly. Chord-lines at a few instances with black and green vectors corresponding to $d\vec{U}/dt$ and $-\widehat{n}(\Delta {\Phi }^{(2)})$ respectively where ΔΦ⁽²⁾ is the difference in scalar Φ⁽²⁾ on the two sides of the wing, are also shown. Note the supination and downward movement of the wing in early upstroke. During this time, the vectors corresponding to $d\vec{U}/dt$ and $-\widehat{n}(\Delta {\Phi }^{\mathrm{\text{(2)}}})$ are pointing in similar directions so that their dot-product generates a positive (upward) lift force, creating a net positive centripetal acceleration reaction contribution during upstroke. Scaling of various components of lift with Reynolds numbers for the (e) hovering hawkmoth and (f) fruit fly. The black, green, red and cyan lines represent total, vortex-induced, added-mass and viscous components of lift, respectively.