Microscopic scales enhance a butterfly’s flying efficiency

Flying efficiency drives the diversity of wing shapes in insects, and size is an important factor. Higher flapping frequencies are used by smaller winged insects, such as flies (200 Hz), and lower frequencies by larger insects, such as monarchs (10 Hz). Most butterflies, including monarchs, fly within a few meters of the ground, though monarchs have been observed during migration to reach altitudes of more than 1 km, where they can glide for miles in the wind currents. When cruising near the ground and flapping their wings, they can reach speeds of up to 5 m/s—about half the speed of Usain Bolt, the fastest human on record.

In 2017 Nathan Slegers and I worked with colleagues to analyze the flapping motion and trajectory of monarch butterflies, first with their scales intact and then with the scales removed. For one thing, the experiment disproved the myth that scales are essential for the insect to fly. More importantly, gently removing the scales, which are anchored to the wing much as bird feathers, decreased a butterfly’s weight by an average of just 9.5%.

Yet in a study of more than 200 flights by 11 specimens, the removal decreased a monarch’s mean climbing efficiency—defined as the total change in kinetic and potential energy achieved by the butterfly per flap—on average by 32%. The scales impart a unique, advantageous geometry: They are angled upward and form microscopic cavities that improve the wing’s aerodynamics.

As shown in figure 1, the four fundamental forces on a butterfly in flapping flight are the lift (L), which counters the weight (W), and the thrust (T), which counters the drag (D). Three of them—lift, thrust, and drag—are generated on the wings. To climb, the insect’s lift and thrust must be greater than its weight and drag. Furthermore, the only ways by which net lift, thrust, and drag are imparted to the wings are through the pressure (normal force per unit area) and shear stress (tangential viscous force per unit area) of air in contact with the wings.

As the insect flies, air passing over each wing—either during its downward stroke or while gliding motionless—produces a leading-edge vortex, shown in figure 2a. The swirling flow generates low pressure inside the vortex, and the resulting pressure difference across the wing generates both lift and thrust. The drag primarily arises from the shear stress.

In 2020 Christoffer Johansson and Per Henningsson used slow-motion cameras and flow measurements to discern a butterfly’s distinct flight patterns. They found that the thrust is largely produced at the end of the upstroke, when the flexible wings clap together and press out the air trapped between them. The airflow can become complex, unsteady, and three-dimensional. The shear stress, or skin friction, of viscous air passing over the wing makes up about half the total drag force during gliding flight. The other major contributor comes from the swirling energy, known as induced drag, left behind in wake vortices.

A conservative estimate of the monarchs’ glide ratio—the ratio of lift to drag force—is 4:1. A modest estimate for the skin friction during gliding flight could be around 10% of the lift. With their wings’ low aspect ratio, butterflies are inefficient flyers, at least compared with a Boeing 747, whose glide ratio is around 17:1. A mechanism to reduce the skin friction would allow monarchs to move their lightweight bodies and large wings through the air with significantly less resistance.

The skin friction on a butterfly’s wing comes from the formation of a laminar boundary layer, a region of smooth viscous flow with a velocity difference between that of the wing and the surrounding air. Along the wing, the velocity of the air must match that of its surface—the so-called no-slip condition in fluid mechanics. But the presence of microcavities formed by the scales alters how the air interacts with the wing surface.

Because the scales are so small and the airflow over them is viscous, the Reynolds number—the ratio of inertial forces to viscous forces—is less than 10 in the cavities under the scales. At such a low Reynolds number, the flow is steady and smooth. Were the Reynolds number to increase, instabilities in the flow would emerge. My group replicated that low Reynolds number flow in the lab by replacing air with high-viscosity mineral oil and scales with manufactured plates, which increased the size of the scales 300-fold. We tested bioinspired models of the scale surface using cavity wall angles between 22°and 45°.

When the fluid passes over the scales’ cavities transverse to the rows of scales, small vortices become trapped, as shown in figure 2b. Those minuscule wheels of air essentially become part of the wing surface and are independent of the outer flow. The outer flow can then skip over the surface—the so-called roller-bearing effect—thereby negating to some extent the no-slip condition. For the low Reynolds number flow experienced by a butterfly’s scales during flight, lab results revealed a reduction in skin-friction drag of at least 26% and as high as 45%, compared with that over a smooth surface. (See figure 2a.)

Our latest results show that when the cavity Reynolds number is increased well above 10 (to 80 or more), that beneficial effect disappears—the skin friction drag increases—because flow in the small vortices becomes unsteady and mixes with the outer flow above it. A butterfly’s tiny scales thus function precisely for the flight speeds that the insect usually experiences. Were the scales much larger, they would generate a higher cavity Reynolds number, and the flow-control mechanism that boosts flight efficiency would be lost.

Amy Lang is a professor of aerospace engineering and mechanics and directs the Bio-inspired Flow Control Laboratory at the University of Alabama in Tuscaloosa.