Micro-structures, nanomechanical properties and flight performance of three beetles with different folding ratios

Beetle flying attitude

Figure 2 shows a flapping cycle of the three beetles obtained using a high-speed camera. The flapping frequency of each beetle was calculated by measuring the time required for one flapping cycle. The flapping period of P. brevitarsis was 11 ms, and the flapping frequency was 90 Hz. For A. chinensis, the values were 22 ms and 45 Hz, respectively, and for T. dichotomus, the values were 23 ms and 43 Hz, respectively.

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Figure 2: (A), (B), and (C) show one flapping cycle of P. brevitarsis, A. chinensis, and T. dichotomus, respectively.

The wingtip path of the upstroke almost overlapped with the wingtip path at the beginning of the downstroke in one flapping cycle. The reason for this is that the beetles needed to rapidly increase the vertical lift at the beginning of the upstroke [37]. The flapping amplitude of the hind wings of P. brevitarsis during flight was smaller than that of A. chinensis and T. dichotomus, which means that the higher flapping frequency was needed [38]. Also, it was found that the flapping amplitude of the elytra of the three beetles will vary with the flapping angle of the hind wings, and the elytra will flap almost synchronous with the hind wings. A similar phenomenon was found in dung beetles (Heliocopris hamadryas), whose elytra contributed to produce lift [39]. In addition, the hind wings of beetles twist to a certain extent during flight. The rotational lift is an important factor affecting the aerodynamics of the beetle [30].

Hind wing unfolding and folding morphology

The hind wings of the three beetles were folded in a V-shape when they were not in flight (Figure 3). For P. brevitarsis, A. chinensis, and T. dichotomus, body weight, body and extented hind wing lengths are increasing and are positively correlated (Table 1). In contrast, the flapping frequency is decreasing. Folding ratio, aspect ratio (i.e., the ratio between square of the wingspan and wing area), and the wing loading (i.e., the weight of the beetle divided by the wing area) of the three beetles were calculated. The folding ratio of A. chinensis was the smallest (0.34), and those of P. brevitarsis and T. dichotomus were similar (0.44 and 0.42, respectively). Aspect ratio and wing loading show an opposite trend.

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Figure 3: (A), (B), and (C) show hind wings of P. brevitarsis, A. chinensis, and T. dichotomus, respectively. (A1) and (A2), (B1) and (B2), and (C1) and C2 show the extended and folded hind wings of P. brevitarsis, A. chinensis, and T. dichotomus, respectively. (A3–A7), (B3–B7), and (C3–C7) show cross-sectional morphologies of costal “C”, media posterior “MP”, the posterior end of “C”, wing membrane, and anal posterior “AP” of the three beetles, respectively.

Folding angle and folded states of the hind wings of three beetles are shown in Figure 3. The folding angle of the hind wings of P. brevitarsis is close to 120° (Figure 3A2), and the folding angle of the hind wings of T. dichotomus is close to 90° (Figure 3C2). The hind wings of A. chinensis overlapped when folded (Figure 3B2), and the folded length of the hind wings was smaller than the folded length of the other two species. Comparing the folding sites of the hind wings of the three beetles, the costal (C) and the media posterior (MP) of the hind wings of P. brevitarsis and T. dichotomus both were found to be folded, while the C of the hind wings of A. chinensis was found to be less folded, and the MP was not folded at the folding sites at all. This could be the reason for the folding ratio of the hind wings of A. chinensis being smaller.

Figure 3A3–A7, Figure 3B3–B7, and Figure 3C3–C7 show cross-sectional morphologies of different wing veins of the hind wings of three beetles at the same position obtained using SEM. The images show that the cross-sectional shapes are all nearly elliptical, while all were basically hollow, similar to blood vessels. This structure provides support for the beetles in spreading their hind wings or during flight [40]. Comparing the cross sections of different wing veins of the hind wings of the same beetles, the diameter of the C (Figure 3A3) was found to be larger than that of the MP (Figure 3A4) and the cubitus anterior (CuA) (Figure 3A7). Also, the diameter of the posterior end of the C (Figure 3A5) was smaller than that of the anterior end (Figure 3A3). Additionally, the wall thickness of the hind wing veins on the dorsal side was thicker than that on the ventral side. This was also found in the Asian ladybeetle (Harmonia Axyridis) [41]. Thicker wing veins are good for sustaining greater forces and preventing the hind wings from being damaged [42].

Nanomechanical analysis of the hind wings

Nanomechanical test results are shown in Figure 4. The nanomechanical properties of the hind wings of the three beetles change according to the same trend. The maximum values of the reduced Young’s modulus, Er, were all measured at test point II (the end of the costal) and were 6.530, 7.652, and 6.645 GPa for P. brevitarsis, A. chinensis, and T. dichotomus, respectively. The higher Er helps the beetle to resist external forces and prevents wing damage [43]. The values of Er and hardness H of cubitus anterior, anal posterior, and wing membrane were smaller than those of the costal and media posterior. It was also found that the Er of costal of P. brevitarsis was smaller than those of A. chinensis and T. dichotomus, which possibly affected the deformation ability of the hind wing. Thus, the lift-to-drag ratio of P. brevitarsis was relatively large.

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Figure 4: Nanomechanical test results of the anterior of the costal (I), the end of the costal (II), media posterior (III), cubitus anterior (IV), anal posterior (V), and wing membrane (VI).

Influence of wind speed, folding ratio, aspect ratio, and flapping frequency on the lift-to-drag ratio

The wind tunnel test results of the three beetles at wind speeds of 1.0, 1.5, 2,0, 2.5, and 3.0 m/s are shown in Figure 5. With increasing wind speed, the lift-to-drag ratios of all three beetles show a decreasing trend (Figure 5A). When the wind speed increased, the drags of the beetles also increased, while the lift did not change significantly. At low wind speeds (<2.0 m/s), the drag on the beetle was small and the lift was relatively stable. Thus, the lift-to-drag ratio was higher than that at higher wind speeds (≥2.0 m/s). In addition, the lift-to-drag ratio of P. brevitarsis is obviously different from that of A. chinensis and T. dichotomus. It is significantly higher at low wind speeds and becomes gradually similar to the lift-to-drag ratio of the other two beetles at high wind speeds. For all three beetles, fluctuations of the lift-to-drag ratio were obvious at low wind speeds. At 1 m/s wind speed, the range of fluctuation of the lift-to-drag ratio was 10.5–16.0 for P. brevitarsis, 2.2–6.0 for A. chinensis, and 3.0–4.8 for T. dichotomus. At high wind speeds, the range of the lift-to-drag ratios gradually decreased and stabilized. For P. brevitarsis, although the downward trend of lift was not obvious (at low wind speed) (Figure 5B), the lift-to-drag ratio still rapidly descended. The reason for this is that, when the insect size decreased, the wing speed decreased (due to reduced wing length), while the wing drag increased (due to increased air viscosity) [44]. In addition, P. brevitarsis with a higher folding ratio was significantly affected by wind. Its peak lift force with increasing wind speeds appeared earlier than that of the other two beetles. This led to a larger decline of its lift-to-drag ratio compared to the other two beetles. So for P. brevitarsis, the effect of wind was greater than for the other beetles because of its small size. Considering only aspect ratio, wing area, or flapping frequency, the change trends of the lift-to-drag ratios of three beetles were not consistent. However, it was found that the lift-to-drag ratios of three beetles at low wind speeds varied directly with their folding ratio.

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Figure 5: Aerodynamic characteristics of the three beetles. (A), (B), and (C) show the average lift-to-drag ratio, average aerodynamic force at different wind speeds, and the transient force curves of the three beetles (flapping time period of 0.2 s), respectively.

The aerodynamic force at different wind speeds of the three beetles is shown in Figure 5B. It was found that the thrust of the beetles at different wind speeds was greater than their lift (except for A. chinensis). The lift of T. dichotomus was the biggest because its wing area was much larger than that of the other beetles. When the wind speed increased, the lift of three beetles wing in flapping motion first showed an increasing trend; but when the wind speed reached a certain value, the lift decreased. The drag increased with the wind speed. The order of the lift force peak values with increasing wind speeds was P. brevitarsis, T. dichotomus, and then A. chinensis. It was consistent with their folding ratio. A possible reason is that when the wind speed reaches a certain threshold, the hind wings would undergo passive deformation reducing the wing area, which results in decreased lift. A higher folding ratio of hind wings leads to easier deformation with increasing wind speed (Figure 6).

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Figure 6: Schematic diagram of passive deformation of the hind wings of the three beetles.

When the wind speed reached a certain value (Figure 5B) and the wings were flapping, lift and drag increased at the same time. At this time, the beetle could change its flight speed and obtain more lift or thrust to improve the flight efficiency and reduce the energy loss. When the wind speed reached a larger value, the lift decreased and the drag increased, and the aerodynamic performance of beetles was poor. At this time, continuing to maintain the original flight attitude and relying on the ability of the beetles to resist the wind causes insufficient lift to fly. Thus, at wind speeds greater than 2.0 m/s, there was no thrust for P. brevitarsis and A. chinensis. This means that, although the two beetles were flapping their hind wings, there was no forward movement. In nature, beetles could change lift, drag, and the moment of body rotation by changing the flight speed and the angle of attack to fly stably in different incoming flows and reduce energy consumption.

The transient force curves of the three beetles for a flapping time period of 0.2 s are shown in Figure 5C. The trends of lift and thrust curves of the three beetles show some convergence. As the lift of the beetle increases, the thrust also increases. In addition, the peak of lift and drag produced by T. dichotomus was the largest, up to 80 and 140 mN, respectively. Although P. brevitarsis is the smallest beetle, its peak lift and thrust were greater than that of A. chinensis. When the beetle is exposed to the wind force during flight, the hind wings undergo backward bending and passive deformation at the folding points, which directly decreases wing area (Sw) and body frontal area (Sb), which is helpful to reduce the profile drag and parasite drag (Figure 6).

The total drag on a beetle is equal to the sum of three aerodynamic components, as D = Dind + Dpro + Dpar, where the components are induced drag Dind, profile drag Dpro, and parasite drag Dpar. Dind represents the cost of generating lift, Dpro is the drag of the wings and Dpar is due to skin friction and the drag from the body form [45]. It was found that the wingspan b and Sw of the hind wings decrease simultaneously when passive deformation occurs. This changes the aspect ratio, b2/Sw, and Dind = 2L2/πρb2v2). Thus, the drag reduction mainly comes from Dpro = 0.5ρv2SwCDpro and Dpar = 0.5ρv2SbCDpar, in which CDpro and CDpar are the dimensionless drag coefficient and the body drag coefficient, respectively. It might also be the reason for the high lift-to-drag ratio of P. brevitarsis at wind speeds lower than 2.0 m/s. The largest reduction of Sw and Sb led to the largest reduction in total drag compared to the other two beetles.

A multifactor analysis of variance was performed regarding the influence of folding ratio and wind speed on the lift-to-drag ratio. The results are shown in Table 3 (significance level is 0.05). The significance of the effect of the folding ratio and wind speed on the lift-to-drag ratio was less than 0.05, indicating that both folding ratio and wind speed would affect the lift-to-drag ratio of beetles. In this test, at low wind speeds (<2.0 m/s), the higher folding ratio was found to yield a better lift-to-drag ratio. With the increase of wind speed, the lift-to-drag ratio gradually decreased, and the effect of the folding ratio on the lift-to-drag ratio was no longer obvious.

Table 3: Tests of between-subjects effects.

Source Type III sum of squares df Mean square F Sig. Partial eta squared corrected model 481.580a 14 34.399 20.324 0.000 0.905 intercept 513.760 1 513.760 303.543 0.000 0.910 folding ratio 94.102 2 47.051 27.799 0.000 0.650 wind speed 234.388 4 58.597 34.621 0.000 0.822 folding ratio × wind speed 153.090 8 19.136 11.306 0.000 0.751 error 50.766 30 1.693 – – – total 1046.116 45 – – – – corrected total 532.356 44 – – – –

aR2 = 0.905 (adjusted R2 = 0.860).

There is a correlation between aerodynamic forces and aspect ratio. Increasing the aspect ratio increases the average aerodynamic loads, and a smaller aspect ratio prevents the airflow from separating at the top and bottom [46]. Using butterfly wings as a prototype to design bionic wings with different aspect ratios and through wind tunnel tests and numerical simulations, it was found that a higher aspect ratio of bionic wings leads to a higher lift-to-drag ratio [19]. The three-dimensional effect of flow is weakened with increasing aspect ratio, which increases the aerodynamic coefficient [47]. Based on beetle hind wing models with different geometries, the average lift force was found to increase with increasing aspect ratio in a certain range [12]. Compared with the other two beetles, P. brevitarsis had a larger range of variation. This might be because the large aspect ratio of the wing yields a greater wing flexibility [48].

The flapping frequency of P. brevitarsis, A. chinensis, and T. dichotomus were 90, 45, and 43 Hz, respectively. It was found that P. brevitarsis had a higher flapping frequency and lift-to-drag ratio than the other beetles. The flapping frequencies of A. chinensis and T. dichotomus were similar. Especially, at low wind speeds, a higher flapping frequency yields a better lift-to-drag ratio. A bionic flexible FWMAV was tested in a wind tunnel to explore the effects of different flapping frequencies and aspect ratios on the aerodynamic performance. The flapping frequency played a crucial role in lift generation. Higher flapping frequencies yielded more lift. Also, a wing with a higher aspect ratio could significantly increase the lift [49]. For low flapping frequencies, the lift change is not obvious, but for high flapping frequencies, the lift increase is obvious [50]. The flapping frequency was found to affect inertial acceleration and aerodynamic pressure, thus affecting inertial force and aerodynamic force; with the increase of flapping frequency, their increment was relatively consistent [51]. For a four-wings FWMAV, the lift was increasing linearly with the flapping frequency [52]. Also, the increase in flapping frequency improves the thrust of the flapping [53].

Research on the living environments and living habits of the three beetles found that P. brevitarsis mostly live in farmland and loose soil, and the environmental conditions are relatively humid. Adults come out at night and have a strong flying ability. P. brevitarsis also has a strong migratory ability, moves quickly, and generally flies approximately 50 m [54-56]. A. chinensis lives mostly inside trunks of trees or in small closed forests, feeding on young leaves and bark [57]. T. dichotomus often lives in areas with well-developed forestry and thick trees und conditions native to a forest, feeding on the sap that flows from the surface of the bark. During the day, they mostly rest in shady and humid environments such as soil and move more in the evening hours [58,59]. Compared with the other two beetles, the living environment of P. brevitarsis is more open and offers a better flying environment. Long-term living habits improved its flying ability with better aerodynamic characteristics. Due to the narrow living environment, the flight performance of A. chinensis and T. dichotomus is not as good as that of P. brevitarsis. A study of the wing loading of the three beetles revealed that P. brevitarsis had the smallest wing loading of 19.85 g/dm2 matching its fast-moving nature. The wing loading of A. chinensis was 21.22 g/dm2, and the wing loading of T. dichotomus was 32.87 g/dm2. A lower wing loading leads to a better maneuverability [60]. Additionally, the wing loading affected the overload capacity of the aircraft, that is, the smaller the wing loading, the greater the overload of the aircraft [61]. Both P. brevitarsis and A. chinensis had smaller wing loadings, but P. brevitarsis had a higher lift-to-drag ratio, which might be due to higher folding ratio, aspect ratio, and flapping frequency. Although lift and drag of P. brevitarsis were more obviously affected by the wind speed, its excellent flight performance provides input for improving the maneuverability of MAVs.

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