Fig. 3. Typical changes in tail midline shape during a tail beat illustrated by one individual. On the left are coordinates for the midline taken from a dorsal view and the curves that approximate their shape. The numbers at the end of the curves specify the corresponding time (t) in terms of the tail-beat cycle. The curvature profiles corresponding to these curves are shown on the right. (A,B) t=0.03 tail-beat cycles (shown in black), is within the first half of the tail beat (t<0.5) and tail motion is directed towards the right side of the body. At this moment, the section of the tail anterior to the inflection point (s<s_i) bends concave-right with a curvature equal to _CR, and positions posterior to the inflection point (s>s_i) are bent concave-left with a curvature of _CL. t=0.57 tail-beat cycles (shown in red) is within the second half of the tail beat (t>0.5), and the tail is moving towards the left side of the body. Tail curvature is equal to _CL anterior to the inflection point (s<s_i) and to _CR posterior to the inflection point (s>s_i). (C,D) Tail motion shown at 4ms intervals (roughly 0.03 tail-beat cycles) for the first half of a tail beat (t<0.5), when the tail is moving towards the right side of the body. Note that the magnitude of curvature in both directions (_CL and _CR) changes with time. (E,F) The motion during the left-directed, second half of the tail beat (t>0.5) shown at 4ms intervals. Again, curvature in both directions varies with time.