Full length articleA lightweight, biological structure with tailored stiffness: The feather vane
Graphical abstract
Introduction
The complex design of the modern feather evolved during the Late Jurassic period along with the advancement of aerial locomotion [1]. This unusual integument derived from less sophisticated filaments used for sexual selection and (or) thermoregulation in dinosaurs [2], [3]. Contemporary bird feathers, composed exclusively of β-keratinous material, are extremely specialized and diverse and range from bristles (analogous to whiskers in mammals) to downy feathers [4].
The flight feather consists of a main shaft (rachis and calamus, Fig. 1a), and a feather vane composed, sequentially, of barbs that branch from the rachis (Fig. 1b) and barbules that branch from barbs (Fig. 1c). Flight feathers must be lightweight and able to sustain aerodynamic loads without excessive flexure/torsion and damage. One of the ways feather components conform to these constraints is by having a sandwich structure, consisting of a solid shell and cellular core. Their dense exterior is composed of layers of ordered fibers in a matrix material which form a biological composite laminate on the micro-scale. According to a study by Lingham-Soliar et al. [5], both the barb and rachis have fibers oriented in the axial direction along dorsal and ventral sides with thin crossed-fibers in the lateral walls.
Within the feather vane, barbs form a highly ordered lattice where they interlock with adjacent barbs via barbules to produce a tightly woven structure. On a given barb, proximal barbules have a grooved structure while distal barbules have four to five tiny microhooks (hooklets) along their length (Fig. 1d) [6], [7]. Hooked barbules interlock with the neighboring barb’s grooved barbules to form a “Velcro-like” connection that can be separated and re-zipped [8]. This enables repair of the damaged areas by re-hooking the hooks to grooves.
The innovation of the interlocking feather vane is credited as the essential element which makes flight possible in birds [9], [10] as it allows for a compact and cohesive structure for aerodynamic efficiency [11]. The air transmissivity of the feather is a function of how tightly connected barbs are, and birds preen themselves daily to re-zip their feather vanes [12]. Similarities in the barb structure and interlocking mechanism across bird species are demonstrated in Fig. 2, where feathers of the razor-billed curassow (Mitu tuberosum), house sparrow (Passer domesticus), and California seagull (Larus californicus) are shown. Since these structures are similar in nearly all flying birds [6], structural deformation concepts can be generalized to apply to most feathers.
While barbules are an essential part of the feather vane, barbs make the greatest contribution to its stiffness as they are its most rigid component. For this reason we chose to study the flexural behavior of the barb. Qualitative observations have been made regarding this behavior, but there is a surprising lack of quantitative data and detailed analysis of their flexure behavior, the mechanisms used by barbs to avoid being permanently deformed, and the reason for their evolution to an unusual asymmetrical shape. In this paper we answer these questions through experimental procedures and theoretical analysis.
Section snippets
Test specimens
Feathers of an adult razor-billed curassow (Mitu tuberosum) were obtained postmortem and stored at ambient conditions. Feathers from the left wing within a total length range of 31–34 cm were used in experiments. To prepare the specimens for mechanical testing, barbs were cut from the trailing side of each feather, within the middle section of the rachis (between 45% and 80% of the total feather length). The ends of the barbs (on average approximately 25% of total barb length) were attached to a
Elastic modulus of the barb’s foam-filled center
To create a theoretical model of the deflection behavior of a barb, one first has to determine the elastic modulus of its foam-filled core. This was calculated using the Gibson and Ashby [13] equations. The foam cells inside the barb were modeled as close-celled hexagonal prisms. From geometrical measurements of SEM images, the relative core/shell density ratio was found to be 0.152. This value, along with other geometrical parameters, was used to find the foam’s relative elastic modulus:
Materials characterization
The cross sections of untested feather barbs show that closer to the rachis the barb is highly asymmetric; it becomes smaller and more symmetrical towards the tip (Fig. 4a), as previously observed by Proctor et al. [6]. Foam core cells were found to be most homogeneous in size at the tip and most diverse in size between the rachis and the center of the barb (Fig. 4b–d). Perhaps a larger total area of foam allows nature to create cells of varying size, with larger cells at the interior of the
Conclusions
The morphology of the feather vane was investigated and the flexural behavior of un-zipped and zipped barbs was quantitatively measured for the first time. The following significant enhancements of our understanding were accomplished:
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When loaded in cantilever orientation, un-zipped barbs deflect in the y-direction and then twist due to their asymmetry. By twisting the barb becomes less stiff with respect to its y-axis and therefore its maximum resistive force occurs before the maximum
Acknowledgements
This work is supported by the University of California San Diego Materials Science Program and the AFOSR MURI (AFOSR-FA9550-15-1-0009). We would like to thank Andy Kietwong and Kyle Adriany for helpful discussion and Paulina Villegas and David Moncivais for image data gathering.
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