Scaling trends of bird's alular feathers in connection to leading-edge vortex flow over hand-wing

Abstract

An aerodynamic structure ubiquitous in Aves is the alula; a small collection of feathers muscularized near the wrist joint. New research into the aerodynamics of this structure suggests that its primary function is to induce leading-edge vortex (LEV) flow over bird's outer hand-wing to enhance wing lift when manuevering at slow speeds. Here, we explore scaling trends of the alula's spanwise position and its connection to this function. Specifically, we test the hypothesis that the relative distance of the alula from the wing tip is that which maximizes LEV-lift when the wing is spread and operated in a deep-stall flight condition. To test this, we perform experiments on model wings in a wind tunnel to approximate this distance and compare our results to positional measurements of the alula on spread-wing specimens. We found the position of the alula on non-aquatic birds selected for alula optimization to be located at or near the lift-maximizing position predicted by wind tunnel experiments. These findings shed new light on avian wing anatomy and the role of unconventional aerodynamics in shaping it.

Figure 1

Spread-wing gliding posture used by birds to airbrake when executing a glide-assisted landing. Deflected lesser covert feathers implicate that the wings are operated at a deep-stalled flight condition. Protracted alula is labeled. Image taken by Kathleen Sue Sullivan.

Figure 2

Model alula induces apparent leading-edge vortex (LEV) with the alula’s distance from the wing tip controlling LEV lift. (a) Effect of angle of attack on the near surface flow structures outboard of the alula. The stall angle of the wing with no alula is approximately 22 deg. (b) Change in lift and drag coefficient relative to wing without an alula as a function of the alula’s root distance from the wing tip normalized by wing length. Inset figures are corresponding images of oil-patterns at labeled data points. Arrows indicate surface-footprint of apparent alula-induced LEV. Lift and drag increment rapidly increases as the alula is distanced further from the wing tip until drastically decreasing for alula distances for which the LEV is lost. = 1.5 wing is inclined to steady flow at angle of attack of 25 deg, $C_L=0.73$. The peak increase in lift coefficient due to the alula is approximately 13%. Figures adapted from Linehan and Mohseni.

Figure 3

Model alula induces and stabilizes leading-edge vortex (LEV) over outer portion of unswept wing in deep-stall flight condition. (a) Three-dimensional streamlines of time-averaged flow measured around a model wing with and without the alula. Streamlines originating at the wing’s leading-edge are colored black. Streamlines originating at the wing’s tip are colored magenta. Isosurfaces of spanwise flow are included in isometric views. = 1.5 wing at an angle of attack of 28 deg. Alula’s root is centered on the wing. (b) Corresponding contour slices of measured flow quantities. (I) Non-dimensional spanwise vorticity ${\omega }_y$ and velocity $v$ in streamwise-oriented planes at spanwise stations outboard of the alula. (II) Non-dimensional streamwise vorticity ${\omega }_x$ in spanwise-oriented planes along the chord of the wing. $c$ is the wing chord length, $b$ is the wing span, $U$ is the free-stream velocity, and $\alpha$ is the angle of attack.

Figure 4

Scaling of the alula’s root distance from wing tip $d$ as a function of spread wing length $L_w$. Scatter plots of $lo{g}_{10}\left(d\right)$ against $lo{g}_{10}\left(L_w\right)$ for (from left-to-right) all sampled bird species, core landbirds (as per Jarvis et al.), and waterbirds (following the ecological scoring of Jarvis et al., Fig. 1). The parentheses denote the 2.5% and 97.5% percentiles of the parameter estimate. The dotted line represents isometric scaling.

Figure 5

Scaling of the alula’s root distance from the wing tip $d$ as a function of spread wing length $L_w$ on birds selected for alula optimization. Scatter plots of $lo{g}_{10}\left(d\right)$ against $lo{g}_{10}\left(L_w\right)$ for (from left-to-right) Accipitriformes* and Strigiformes possessing broad-type wings, and Passeriformes possessing elliptical-type wings. The asterisk indicates the removal of Gyps fulvus. The parentheses denote the 2.5% and 97.5% percentiles of the parameter estimate. The dotted line represents isometric scaling.

Figure 6

Effect of wing shape on the approximate lift-maximizing relative position of the model bird alula. (a) The furthest normalized distance of the alula from the wing tip that maintains a stable LEV, ${(d/L_w)}_{max}$, as a function of aspect ratio, , for Zimmerman and rectangular wings at the test conditions as indicated. (b) Representative images of the = 3 rectangular and Zimmerman wing with an alula displaced increasingly farther from the wing tip. LEV is marked by arrows. The portion of the wing experiencing LEV flow and thus enhanced lift increases in area as the alula is distanced farther from the wing tip until a certain distance for which LEV is lost. ${(d/L_w)}_{max}$, is is as indicated. Angle of attack is 30 deg. Reynolds number is 75,000.

Figure 7

Lift-maximizing alula distance ratio predicts parameter estimates of the alula distance ratio on core landbirds selected for alula optimization. Distance of the alula’s root from the wing tip, $d$, as a function of spread-wing length, $L_w$, for landbirds, Passeriformes only, and Accipitriformes and Strigiformes only. The parentheses denote the” 2.5% and 97.5% percentiles of the parameter estimate. Schematics compare confidence intervals to the lift-optimal predicted value graphically.

Figure 8

Artist impression of the alula-induced LEVs on the spread wings of a bird executing a glide-assisted landing. The alula is located at the furthest distance from the wing tip that maintains LEV stability on the spread wing which magnifies the high-lift benefit of the alula when birds operate their wings in a deep-stall condition. The ability of the alula to reattach flow on the hand-wing enables the bird to maintain flight control despite the high-angle-of-attack condition. Consequently, large braking forces are generated that enable the bird to land over shorter distances with less landing force.

Figure 9

Measurements of the spanwise position of the alula on spread-wing specimens. Definition of $d$ and $L_w$ from a spread wing specimen. The distance of the alula’s root to the wing tip, $d$, is measured horizontally from the distal end of the longest primary feather to the leading-edge location where the lesser coverts and alula feathers intersect. The spread-wing length, $L_w$, is the horizontal distance measurement from the distal end of the longest primary feather to the intersection of the proximal edge of the shortest secondary feather with the adjacent tertiary feather.

Figure 10

Experimental S-DPIV setup in wind tunnel. The wing-alula model was suspended upside down in the test section via model adapter. Three-component velocity-field measurements were collected in closely-spaced streamwise data planes (2D–3C) by translating the wing-alula model in the cross-stream direction through a stationary vertically-oriented laser plane. These data planes were then time-averaged and subsequently stitched together to grant an approximation of the mean volumetric flow field around the wing-alula model (3D–3C).