Figure 1.
Light micrographs of the whirligig beetle.
(A) Dorsal view of the beetle, demonstrating the overall shape. (B) Ventral view of the beetle showing the fore, middle and hind legs. (C&D) Micrographs of dissected middle right (C) and left (D) legs. (E&F) Micrographs of dissected hind right (E) and left (F) legs. Measurements of leg length (Lh and Lm) and area (Sh− and Sm−) were made from micrographs of dissected legs. The scale bars are 1 mm.
Figure 2.
Diagram demonstrating how each parameter was calculated.
(A) Top-down view of the body showing key parameters for swimming. (B&C) Side view of the body on the surface of water (indicated by blue line) showing both the maximum and minimum position of the legs during a leg beat when diving. In all of the above diagrams, the hind legs are indicated by the subscript h, while the middle legs are indicated by the subscript m. Using this notation, the length of the hind legs is Lh, etc. The direction of motion of the beetle is indicated by an arrow showing the forward velocity (Uy). The dashed line in B&C indicates the submerged portion of the beetle. All other parameters designations are listed in Tables 1–3.
Figure 3.
The SEM micrographs of the legs of Gyrinus.
(A) SEM micrograph of the middle leg showing the folded swimming laminae. On the middle leg, the laminae are predominately on the outer surface. (B) SEM micrograph of the hind leg demonstrating the presence of laminae on both the inner and outer surface of the rowing blade. (C) SEM micrograph showing the significantly altered morphology of the foreleg. (D) Image of the point of attachment of a leg. The inset demonstrates the location of the micrograph relative to the beetle's body, with the area analyzed highlighted by the red box. SEM micrographs were used to measure the length (Llaminae) and width (Wlaminae) of the laminae for calculation of the effective are of the hind (Sh+) and middle legs (Sm+) with laminae extended. In all micrographs, the scale bar = 100 µm.
Table 1.
Parameters obtained from micrographs.
Figure 4.
The sequence of one hind leg stroke.
In frames 1–5, only the hind leg is visible, with the middle leg emerging in frame 6. In frames 6–10 it is possible to observe the beating of both legs. During the course of one leg stroke, the effective area of the legs decreases in the horizontal plane, indicating that the effective area for forward propelling increases.
Table 2.
Swimming parameters obtained from high-speed video analysis.
Figure 5.
Time-lapse images of the diving process.
This image shows the complete diving process, from the 83 ms pre-diving to the 89 ms diving process. To illustrate the diving motion, images captured every 17 ms are overlaid onto each other to show the complete diving motion.
Table 3.
Diving parameters obtained from high-speed video analysis.
Figure 6.
Net forward trajectories from swimming simulations.
As indicated above each frame, the beating patterns that generated a true linear path were those where the right and left middle legs (mr+ml), hind legs (hr+hl), and hind followed by middle legs (hr+hl, mr+ml) beat simultaneously. In these three cases, the total distance traveled was equal to Δy. For the other three cases where the middle right and left legs (mr, ml) and the hind right and left legs (hr, hl) beat alternately, and the simultaneous beating of the hind legs followed by the beating of a middle leg (hr+hl, mr, hr+hl, ml) the net forward distance traveled was calculated from a line between the start and end point. Numerical analysis of these trajectories is shown in Table 4.
Table 4.
Analysis of forward trajectories.
Figure 7.
Circling trajectories from swimming simulations.
The circular trajectories obtained from the swimming simulations are illustrated above. Based on the simulations, only three beating patterns stabilized to form a consistent circular trajectory, the middle right leg only (mr), the middle right followed by the hind right (mr, hr), and the middle right followed by the simultaneous beating of the hind legs (mr, hr+hl). The other beating patterns analyzed produced unstable trajectories, resulting in trajectories not observed in nature. Numerical analysis of the circular swimming trajectories is shown in Table 5.
Table 5.
Analysis of circling trajectories.
Figure 8.
Results from the diving simulations.
Simulation results of diving with different initial conditions. The initial values of forward speed (0.17 m/s), angular velocity of the body (−333°/s), tilt angle of the body (7°), striking speed of the hind legs (0.18 m/s), and striking speed of the middle legs (0.14 m/s), were varied ±30% to determine the effect on the diving trajectory. Each of these terms was varied ±30%, with the other terms held constant, to determine their effects on the overall trajectory. The values generated the closest diving trajectory as observed in the experimental studies was with an initial speed of 0.17 m/s, angular velocity of −333°/s, tilt angle of −7°, hind leg speed of 0.18 m/s, and middle leg speed of 0.14 m/s.