Tiny flying insects of body lengths under 2 mm use the `clap-and-fling' mechanism with bristled wings for lift augmentation and drag reduction at chord-based Reynolds number ($Re$) on $\mathcal{O}$(10). We examine wing-wing interaction of bristled wings in fling at $Re$=10, as a function of initial inter-wing spacing ($\delta$) and degree of overlap between rotation and linear translation. A dynamically scaled robotic platform was used to drive physical models of bristled wing pairs with the following kinematics (all angles relative to vertical): 1) rotation about the trailing edge to angle $\theta_\text{r}$; 2) linear translation at a fixed angle ($\theta_\text{t}$); and 3) combined rotation and linear translation. The results show that: 1) cycle-averaged drag coefficient decreased with increasing $\theta_\text{r}$ and $\theta_\text{t}$; and 2) decreasing $\delta$ increased the lift coefficient owing to increased asymmetry in circulation of leading and trailing edge vortices. A new dimensionless index, reverse flow capacity (RFC), was used to quantify the maximum possible ability of a bristled wing to leak fluid through the bristles. Drag coefficients were larger for smaller $\delta$ and $\theta_\text{r}$ despite larger RFC, likely due to blockage of inter-bristle flow by shear layers around the bristles. Smaller $\delta$ during early rotation resulted in formation of strong positive pressure distribution between the wings, resulting in increased drag force. The positive pressure region weakened with increasing $\theta_\text{r}$, which in turn reduced drag force. Tiny insects have been reported to use large rotational angles in fling, and our findings suggest that a plausible reason is to reduce drag forces.

Aerodynamic interaction of bristled wing pairs in fling

Abstract Most of the smallest flying insects use bristled wings. It was observed that during the second half of their upstroke, the left and right wings become parallel and close to each other at the back, and move upward at zero angle of attack. In this period, the wings may produce drag (negative vertical force) and side forces which tend to push two wings apart. Here we study the aerodynamic forces and flows of two simplified bristled wings experiencing such a motion, compared with the case of membrane wings (flat-plate wings), to see if there is any advantage in using the bristled wings. The method of computational fluid dynamics is used in the study. The results are as follows. In the motion of two bristled wings, the drag acting on each wing is 40% smaller than the case of a single bristled wing conducting the same motion, and only a very small side force is produced. But in the case of the flat-plate wings, although there is similar drag reduction, the side force on each wing is larger than that of the bristled wing by an order of magnitude (the underlying physical reason is discussed in the paper). Thus, if the smallest insects use membrane wings, their flight muscles need to overcome large side forces in order to maintain the intended motion for less negative lift, whereas using bristled wings do not have this problem. Therefore, the adoption of bristled wings can be beneficial during upward movement of the wings near the end of the upstroke, which may be one reason why most of the smallest insects adopt them. 

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Aerodynamics of two parallel bristled wings in low Reynolds number flow

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Effects of stroke deviation on the aerodynamics of the smallest flying insects

All previous studies on the aerodynamics of bristled wings in miniature insects are based on continuum flows. However, the diameter of the bristle is very small, and the diameter-based Knudsen number (Kn) is approximately between 0.03 and 0.11, indicating that the flow around the bristle is in the slip-flow regime and rarefaction effect will be present. To investigate how the rarefaction will affect the aerodynamic force and flow field of the bristled wing, we calculated and analyzed the flow around a model bristled wing under two conditions: the continuum flow and the slip flow. The following is shown. Within the range of Kn considered in this study (0.01 ≤ Kn ≤ 0.1), the rarefaction has a very small effect on the aerodynamic force of the bristled wing: it decreases the aerodynamic force by less than 0.5% compared with that of the continuum flow. However, the rarefaction has a significant effect on the contributions of the viscous tangential and normal stress terms to the aerodynamic force: in the continuum flow, the force contribution of the viscous tangential stress is 50.7% and that of the viscous normal stress is zero, whereas in the slip flow, e.g., at Kn = 0.08, the contribution of the viscous tangential stress is only 37.7% and that of the viscous normal stress is 12.9% instead of zero; this is because the rarefaction-induced slip velocity in the slip flow changes the normal derivative of the velocity on the bristle surface compared with that of the continuum flow. Since the rarefaction has only a slight effect on the aerodynamic force, the results on the aerodynamic force of the bristled wing obtained based on continuum flows in previous studies are very good approximations to the correct results.

Rarefaction effect on the aerodynamics of bristled wings in miniature insects

Miniature insects must overcome significant viscous resistance in order to fly. They typically possess wings with long bristles on the fringes and use a clap-and-fling mechanism to augment lift. These unique solutions to the extreme conditions of flight at tiny sizes (<2 mm body length) suggest that natural selection has optimized wing design for better aerodynamic performance. However, species vary in wingspan, number of bristles (n) and bristle gap (G) to diameter (D) ratio (G/D). How this variation relates to body length (BL) and its effects on aerodynamics remain unknown. We measured forewing images of 38 species of thrips and 21 species of fairyflies. Our phylogenetic comparative analyses showed that n and wingspan scaled positively and similarly with BL across both groups, whereas G/D decreased with BL, with a sharper decline in thrips. We next measured aerodynamic forces and visualized flow on physical models of bristled wings performing clap-and-fling kinematics at a chord-based Reynolds number of 10 using a dynamically scaled robotic platform. We examined the effects of dimensional (G, D, wingspan) and non-dimensional (n, G/D) geometric variables on dimensionless lift and drag. We found that: (1) increasing G reduced drag more than decreasing D; (2) changing n had minimal impact on lift generation; and (3) varying G/D minimally affected aerodynamic forces. These aerodynamic results suggest little pressure to functionally optimize n and G/D. Combined with the scaling relationships between wing variables and BL, much wing variation in tiny flying insects might be best explained by underlying shared growth factors.

Interspecific variation in bristle number on forewings of tiny insects does not influence clap-and-fling aerodynamics.

Flight-capable miniature insects of body length (BL) < 2 mm typically possess wings with long bristles on the fringes. Though their flight is challenged by needing to overcome significant viscous resistance at chord-based Reynolds number (Rec) on the order of 10, these insects use clap-and-fling mechanism coupled with bristled wings for lift augmentation and drag reduction. However, inter-species variation in the number of bristles (n) and inter-bristle gap (G) to bristle diameter (D) ratio (G/D) and their effects on clap-and-fling aerodynamics remain unknown. Forewing image analyses of 16 species of thrips and 21 species of fairyflies showed that n and maximum wing span were both positively correlated with BL. We conducted aerodynamic force measurements and flow visualization on simplified physical models of bristled wing pairs that were prescribed to execute clap-and-fling kinematics at Rec=10 using a dynamically scaled robotic platform. 23 bristled wing pairs were tested to examine the isolated effects of changing dimensional (G, D, span) and non-dimensional (n, G/D) geometric variables on dimensionless lift and drag. Within biologically observed ranges of n and G/D, we found that: (a) increasing G provided more drag reduction than decreasing D; (b) changing n had minimal impact on lift generation; and (c) varying G/D produced minimal changes in aerodynamic forces. Taken together with the broad variation in n (32-161) across the species considered here, the lack of impact of changing n on lift generation suggests that tiny insects may experience reduced biological pressure to functionally optimize n for a given wing span. SUMMARY STATEMENTIntegrating morphological analysis of bristled wings seen in miniature insects with physical model experiments, we find that aerodynamic forces are unaffected across the broad biological variation in number of bristles.

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Truc T. Ngo

Papers

Interspecific variation in bristle number on forewings of tiny insects does not influence clap-and-fling aerodynamics.

Inter-species variation in number of bristles on forewings of tiny insects does not impact clap-and-fling aerodynamics