Monarch butterflies migrate approximately 4000 km from the northern United States or Canada to central Mexico to hibernate, a migration pattern unmatched by any other species of their kind. Such a long journey seems strange at first: Butterflies are the only flying creatures with short, wide and large wings in proportion to their bodies. But more than just flying high enough to catch favorable wind currents may have contributed to this success.
Lepidoptera, which means “scaly wings” in Greek, is the scientific classification used for butterflies and moths. Butterfly wings may contain more than a million microscopic scales covering both sides. Although the shape of the flakes varies, they normally have a thickness of 0,1 mm. In addition to keeping the insects dry, the scales also give them their distinctive color pattern that helps them avoid predators, control temperature, and attract mating attraction. Additionally, its microgeometry can reduce skin friction friction by up to 45%.
Insect wing designs vary greatly, and size plays an important role in flight efficiency. Smaller winged insects such as flies (200 Hz) use higher wing flapping frequencies, while larger insects such as monarchs (10 Hz) use lower frequencies. Most butterflies, including monarchs, fly only a few meters above the ground, but during migration monarchs have been observed rising to altitudes of more than 1 km, from which they glide for kilometers on wind currents. When flying close to the ground and flapping their wings, they can fly at up to 5 m/s, which is about half the speed of the world's fastest man, Usain Bolt.
As part of a project we carried out in 2017, researchers examined the wing flapping movements and trajectories of monarch butterflies, first with their scales open and then with their scales closed. First, the experiment disproved the idea that an insect needs scales to fly. More importantly, after gently removing the scales attached to the wing, similar to bird feathers, a butterfly's weight decreased by only 9,5% on average.
However, in one study involving 11 specimens and more than 200 flights, removing scales reduced a monarch's climbing efficiency by an average of 32%. The washers have a special and beneficial design that creates small chambers that improve the aerodynamics of the wing.
Flight Aerodynamics of Butterflies
The figure shows the four basic forces acting on a butterfly during flapping flight: lift (L), counterweight (W), thrust (T), and drag (D). Wings produce three of these: lift, thrust and drag. In order for the insect to climb, its lifting and pushing power must be greater than its weight and dragging power. Additionally, air in contact with the wings applies pressure and shear stress to the wings, which is the only way the wings get net lift, thrust, and drag.
As the insect flies, a leading-edge vortex is created by the air passing over each wing. Low pressure is created inside the vortex by the rotating flow, and the resulting pressure difference across the wing produces both lift and thrust. Shear stress is the main cause of drift.
Different flight patterns of butterflies were detected in 2020 by Christoffer Johansson and Per Henningsson using slow-motion cameras and flow measurements. They discovered that the end of the upstroke, where the flexible wings interlock and squeeze the trapped air between them, is when the most thrust is produced. Three-dimensional, complex and irregular airflow are all possible. In glider flight, skin friction or shear stress caused by viscous air moving over the wing accounts for almost half of the total drag force. The energy left behind in wake vortices, also known as induced drag, is another important factor.
The glide ratio of monarchs is conservatively estimated to be 4:1. Skin friction during gliding flight can account for 10% or less of lift, to say the least. Butterflies fly inefficiently due to their low aspect ratio wings, at least when compared to a Boeing 17, which has a glide ratio of about 1:747. If there were a way to reduce skin friction, monarchs could maneuver through the air with much less resistance with their lightweight bodies and large wings.
Butterflies Friction with Air
What causes skin friction on a butterfly's wing is the development of a laminar boundary layer, a region of smooth viscous flow with a velocity difference between the wing and the surrounding air. In fluid mechanics, the so-called no-slip condition states that the air velocity along the wing must coincide with the wing surface. However, the presence of scale-created microcavities changes how air interacts with the wing surface.
In the spaces below the scales, the Reynolds number (ratio of inertial forces to viscous forces) is less than 10 due to the small size of the scales and the viscous air flow above them. Due to the low Reynolds number, the flow is steady and orderly. If the Reynolds number increases, the flow will begin to become unstable. My group was able to recreate this low Reynolds number flow in the laboratory by replacing the air with high-viscosity mineral oil and the scales with fabricated plates that tripled the size of the scales. Using cavity wall angles between 22° and 45°, biologically inspired models of the scale surface were investigated.
As the liquid flows over the gaps in the flakes transverse to the rows of flakes, small eddies are captured. These small air wheels are independent of the external flow and virtually merge with the wing surface. When this occurs, external flow has the potential to jump over the surface, partially overriding the no-slip requirement. Laboratory results have shown that for the low Reynolds number flow encountered by a butterfly's scales in flight, there is a reduction in skin friction drag of at least 26% and up to 45% compared to a smooth surface.
According to our latest findings, when the void Reynolds number is significantly higher than 10 (80 or more), the positive effect disappears as the flow in the small vortex becomes disordered and merges with the external flow above it. Therefore, the small scales on a butterfly's wings perfectly accommodate the insect's typical flight speeds. If the flakes were significantly larger, they would produce a larger gap Reynolds number and lose the flow control mechanism that increases flight efficiency.
Source: Physics Today
📩 14/09/2023 10:03