Fig. 8. Comparison of time-averaged and instantaneous forces and their related dynamics. Three hypothetical flying animals of equal weight (mg) generate identical time-averaged forces but different instantaneous forces and flight dynamics over three stroke cycles. Solid black line, F_V-mg=0; broken blue line, F_V-mg=sin(2t); dotted red line F_V-mg=-sin(2t). Vertical velocity V(t) and trajectory Y(t) are determined from integration with initial conditions V(0)=0 and Y(0)=0. T, propulsive stroke duration. Figures are plotted using generic units.