Flea beetles have a body length of 4 mm and are up to 2 mm in width. We filmed the jumping process for n = 33 flea beetle specimens, recording a total of 124 jumps. Figure 2a shows the complete trajectory performance of the flea beetle. Here, the flea beetle leaped from the horizontal platform, flew to the left, and landed on the ramp. We defined a successful landing as one in which the beetle landed on its leg. In Fig. 3a, colored arrow lines show the landing orientations and velocities. Each arrow represents a recorded trial. We can see the arrow lines are more densely distributed in the region of successful landing, corresponding to a net rotation of 90° or less. As shown by the first two pie charts in Fig. 3b, the success rates of live flea beetle were 85%, which is far greater than the 46% success rate of a dead beetle flipped through the air. For comparison, the third pie chart shows the 50% chance of the coin landing on head. Although the dead beetle keeps its wings unfurled, the near 50% success rate indicates that aerodynamics of is body alone are insufficient to enable successful landings. Motivated by the higher success rate for the live beetles, we seek to find active re-orientation strategies throughout the entire jumping processes, including takeoff, flight and landing.
In 124 videos captured from 33 flea beetle specimens, we only analyzed the videos in which the flea beetle lands on its legs. We categorized the jumping behavior into the following three modes, which we call wingless, semi-wingless, and winged. In the wingless mode, the flea beetle takes off simply by jumping (Fig. 2a, b). In semi-winged mode, the flea beetle takes off and deploys and flaps is wings in mid-air, conceivably to eliminate spinning, then lands with legs (Fig. 2c, d). In winged mode, the flea beetle takes off with wings assisted and sticks on the ramp (Fig. 2e, f). Rates of successful landing for the wingless, semi-winged and winged modes are 77% (54 out of 77 jumps), 92% (35 out of 38 jumps) and 100% (16 out of 16 jumps) respectively. These numbers are consistent with Brackenbury and Wang (1995), who also found a high correlation of successful landing with the use of wings.
Clearly, wing recruitment is beneficial for a successful landing. The winged takeoff had an initial velocity of 1.25 ± 0.24 m/s (16 samples in winged mode), which was lower than that of the wingless takeoff, namely 1.41 ± 0.28 m/s (108 samples in wingless and semi-winged) because of the air drag. Wingless takeoff generally creates ballistic motion consistent with the speed and angle of takeoff, similar to shooting a ball out of a cannon. The winged takeoff generates substantial lift, enabling the body to gains more than double the height of 78 mm, compared to the height with no wings (30 mm). The mean takeoff velocity in the wingless mode is 10% lower than that of semi-winged mode (1.57 ± 0.29 m/s, 38 samples). We conclude the beetle is more likely to deploy wings later if its initial velocity is higher. This makes sense if wings are used to reduce the speed of impact.
While flapping wings enable the flea beetle to reach greater heights, they also incur tradeoffs because wings increase air drag and require more energy compared with the wingless takeoff. The insect also slows down when it flings wings in midair, which effectively alleviated the impact force while landing. The takeoff time was independent of mode: it took 8 ± 1 ms for the flea beetle to take off (33 insects and 124 entire jumping processes). The takeoff angle for all modes was 45 ± 3°, as expected for maximizing the distance of travel. We now go into further detail about the body posture and behaviors the jump.
For the wingless mode in Fig. 2a, the flea beetle takes off from the horizontal platform, which we define as time t = 0. Nearly instantaneously from takeoff (t = 7 ms) it pitches backwards. Since we cannot see the antennae in the high-speed images, we presume that they are initially folded back during takeoff, as shown in the hand drawing in the figure. It is possible the rotation is too fast to resolve the antenna. At 43 ms, the flea beetle unfolds its antennae at 50 ms (Fig. 2a). Surprisingly that, the insect can rotate along two distinct axes, continuously pitch and roll 2 times until 79 ms (Fig. 2a). The flea beetle shows its right side to us with its body upright at 93 ms. To investigate the dual-axial rotation mechanism, we mapped the pitch and roll angles with respect to duration (Fig. S1, S2). For this trial, the total-accumulated pitch angle is -1494°, which means it turned 4.15 cycles. The accumulated roll angle ranges is -360°, which indicates that the flea beetle rolls one clockwise cycle about its body axis. It continues rotating and successfully lands at 157 ms.
For the wingless mode, (n = 77 samples) we found a persistent result that the flea beetle began to roll at \(t=49 \pm 4{\kern 1pt} {\text{ ms}}\) after takeoff, and roll around one cycle in either direction, with an average rotation speed of 7.2 deg /ms, which ensures that the flea beetle can accurately roll only one circle during flight (a roll angle magnitude of 353 ± 14°).
We now consider the semi-winged jump in Fig. 2b. The flea beetle begins with a wingless takeoff. It pitches and rolls from t = 0 to 42 ms. At 42 ms, the flea beetle orients almost horizontally with its right side to us. It continues the rotation from 42 ms to 75 ms. The wings unfold at 75 ms, which increases the moment of inertia and instantaneously eliminates the body rotation. The flea beetle flaps its wings and sticks a winged landing at 93 ms. The beetle pitches 2.14 cycles and rolls 360°, which helps it maneuver to a right position before landing. The wings deploy at 70 ms (Fig. S1), which stops rolling instantly. After 75 ms, the body only pitches a bit to regulate its position for a successful landing.
Lastly, we consider a winged jump. The flea beetle takes off with wings deployed, and flies directly to the vertical wall. The body does not rotate and then achieves a soft landing by its legs at 93 ms. Observing Fig. S2, we can see that the body over-pitches to -114°at 43 ms, and then corrects itself to the correct orientation of 90° to land on the vertical wall.
By zooming into the legs, we can see that takeoff forces are generated by straightening the back and possibly the front legs (Fig. 4a-d) actuated by the meta-femoral spring (Fig. 4f). The hindleg is almost fully extended at take-off, but the tarsus remains in contact with the ground throughout its length. Therefore, the displacement is made by only straightening of the femur-tibia joint (Fig. 4e). The high-speed images indicated that the body displacement during take-off is approximately 1 mm. After taking off, the kinetic energy of the body may be written as \({E_{kT}}(0)=M{v_i}^{2}/2\) and the rotational energy as \({E_{kR}}(t)=I\omega {(t)^2}/2\). Given the peak velocity \({v_i}=1.49{\text{ m/s}}\) and the peak angular velocity \(\omega =711{\text{ rad/s}}\), the average body mass \(M=4.16{\text{ mg}}\), and moment of inertia \(I=\frac{1}{2}M{r^2}=9.13 \times {10^{ - 13}}{\text{ kg}}\cdot {{\text{m}}^{\text{2}}}\), which r is the half of the body length, we arrived at the rotational energy as\({E_{kR}}(t)=162.8{ \mu J}\), occupying only 1.7% of the kinetic energy \({E_{kT}}(0)=9.5 \times {10^3}{ \mu J}\). As found by Brackenbury and Wang (1995), we also find that rotational energy is negligibe compared to the kinetic energy. By the law of energy conservation, the work done by the leg is equal to the kinetic energy \({F_{{\text{take off}}}}l={E_{kT}}(0)\), which l = 1 mm is the displacement of the leg during jumping. Thus, we infer the force applied by all the beetle legs is F = 9.5 mN, which is \(233\) times the beetle’s body weight.