Colloquium: Miniature insect flight

Many of the existing winged-insect species are extremely small (wing $\text{length}\approx 0.3–4\mathrm{mm}$); they are referred to as miniature insects. Yet, until recently much of our knowledge about the mechanics of insect flight was derived from studies on relatively large insects, such as flies, honeybees, hawkmoths, and dragonflies. Because of their small size, many miniature insects fly at a Reynolds number ($\mathrm{Re}$) on the order of 10 or less. At such a low $\mathrm{Re}$, the viscous effect of the air is substantial: A miniature insect moves through the air as a bumblebee would move through mineral oil. The great importance of viscosity for miniature insects means that their flight relies on physical mechanisms that are different than those exploited by large insects. These differences range from the nature of the wing stroke to the structure of the wings, with some insects even using porous (bristled) wings to fly. Over the past decade, much work has been done in the study of the mechanics of flight in miniature insects: novel flapping modes have been discovered and new mechanisms of aerodynamic-force generation have been revealed; progress has also been made on fluid-mechanics-related flight problems such as flight power requirements and flight dynamic stability. This Colloquium reviews these developments and discusses potential future directions.

Figure 1

Comparison between a typical miniature insect (a small wasp Encarsia formosa) and a medium size insect (a drone fly Eristalis tenax, which is the same size as a honeybee). Note that most of the smallest insects use bristled wings.

Figure 2

(a) Stroke diagram showing the wing-tip trajectory (projected onto the symmetrical plane of the insect; the black curve) of the drone fly Eristalis tenax, a relatively large insect. A black dot defines the wing-root location on the insect body. (b) Motion of a section of the wing and definition of aerodynamic lift and drag, with dots marking the leading edge.

Figure 3

(a) Lift and (b) drag coefficients of a drone fly in a flapping period. Adapted from [42]. (c) Sketch of the LEV on a flapping wing.

Figure 4

(a) Stroke diagram showing the wing motion of E. formosa. The dashed curve indicates the wing-tip trajectory (projected onto the symmetrical plane of the insect); the black lines indicate the orientation of the wing at 20 temporally equidistant points, with dots marking the leading edge; and the black dot defines the wing-root location on the insect body. (b) Wing motion at dorsal stroke reversal showing the fling. $R$ is the wing length. Adapted from [9].

Figure 5

Aerodynamic forces. (a)–(d) Vertical force, horizontal force, lift, and drag of a wing. (e) Diagram showing the wing position, velocity vector, and force vector at various times in one stroke cycle (side view). (f) Back view of the wing in fling motion, represented as the wing section at $0.7R$, and the corresponding velocity vector and force vector. Blue arrow, velocity; red arrow, force. Adapted from [9].

Figure 6

Idealized wing kinematics (represented by a sections of the wing). The dot represents the leading edge of the wing, and the downstrokes and upstrokes are shown separately. The solid red arrows indicate the direction and relative magnitude of the dimensionless drag ($C_{\mathrm{D}}$) during each downstroke or upstroke, and the solid blue arrows indicate the direction and relative magnitude of the dimensionless lift ($C_{\mathrm{L}}$). The solid axes on the right indicate the net $C_{\mathrm{D}}$ and $C_{\mathrm{L}}$ during a flapping cycle. The directions of the dimensionless vertical ($C_{\mathrm{V}}$) and dimensionless horizontal forces ($C_{\mathrm{H}}$) always face the same way with respect to the global frame (the dashed arrows). (a) A vertical, drag-based stroke uses only $C_{\mathrm{D}}$ to produce $C_{\mathrm{V}}$. (b) A tilted, hybrid stroke uses both $C_{\mathrm{L}}$ and $C_{\mathrm{D}}$ to produce $C_{\mathrm{V}}$. Adapted from [32].

Figure 7

Top diagram: wing-tip trajectory (projected onto the symmetrical plane of the insect) of a fruit fly ($R=3\mathrm{mm}$), which is a relatively large miniature insect. Bottom diagram: wing-tip trajectory of a small wasp ($R=0.5\mathrm{mm}$), which is a typical miniature insect. Middle diagrams: conjectured wing-tip trajectories for insects with sizes in between.

Figure 8

Stroke diagrams showing the wing motions of the insects. The solid curve indicates the wing-tip trajectory (projected onto the symmetrical plane of the insect); black lines indicate the orientation of the wing at various times in one stroke cycle, with dots marking the leading edge; a black dot defines the wing-root location on the insect body; and the purple arrow represents the velocity of the wing at the radius of gyration. Adapted from [46].

Figure 9

Sketch of the bristled wing of a small beetle Paratuposa placentis plotted according to the photograph taken by [22].

Figure 10

Stroke diagrams showing the wing motions of Paratuposa placentis. The solid curve indicates the wing-tip trajectory (projected onto the symmetrical plane of the insect); black lines indicate the orientation of the wing at various times in one stroke cycle, with dots marking the leading edge; a red dot defines the wing-root location on the insect body. Adapted from [22].

Figure 11

Wing-tip trajectories and direction of aerodynamic force and wing velocity. Cyan arrows show aerodynamic force, magenta arrows show wing-tip velocity, and yellow disks show dorsal surface orientation of the wing at nine time instants. Opaque and transparent curves correspond to the right and left wings, respectively. Adapted from [22].

Figure 12

Mass-specific powers in cases of 0% and 100% elastic energy storage for 16 species of insects. Adapted from [43].

Figure 13

Relationship between $t_d$ and $m$ of 12 species of insects. Adapted from [44].