Flexural stiffness of feather shafts: geometry rules over material properties

Abstract

SUMMARYFlight feathers of birds interact with the flow field during flight. They bend and twist under aerodynamic loads. Two parameters are mainly responsible for flexibility in feathers: the elastic modulus (Youngʼs modulus, E) of the material (keratin) and the geometry of the rachises, more precisely the second moment of area (I). Two independent methods were employed to determine Youngʼs modulus of feather rachis keratin. Moreover, the second moment of area and the bending stiffness of feather shafts from fifth primaries of barn owls (Tyto alba) and pigeons (Columba livia) were calculated. These species of birds are of comparable body mass but differ in wing size and flight style. Whether their feather material (keratin) underwent an adaptation in stiffness was previously unknown. This study shows that no significant variation in Youngʼs modulus between the two species exists. However, differences in Youngʼs modulus between proximal and distal feather regions were found in both species. Cross-sections of pigeon rachises were particularly well developed and rich in structural elements, exemplified by dorsal ridges and a wellpronounced transversal septum. In contrast, cross-sections of barn owl rachises were less profiled but had a higher second moment of area. Consequently, the calculated bending stiffness (EI) was higher in barn owls as well. The results show that flexural stiffness is predominantly influenced by the geometry of the feathers rather than by local material properties.

Light Like a Feather: A Fibrous Natural Composite with a Shape Changing from Round to Square

“…These are circular throughout the entire shaft length 8, 20. Flight feathers from other flying birds, e.g., condor (Figure 2d), pigeon,6 barn owl,2 pelican, and seriema,21 show a similar change in shape factor; this is demonstrated by the squareness along the shaft length, the measured average radii of curvatures of different cortical regions, and the ratios of those radii over the entire cortical size, as plotted in Figure 3 . At the calamus (positions 1 and 2), the dorsal, dorsal–lateral corner, and lateral regions exhibit comparable radius of curvature; ratios of each radius of curvature over the local dorsal–ventral distance are all close to 0.5, both indicating the circular cross sectional shape.…”

“…Flight feathers of volant birds, upon encountering aerodynamic forces, aid the generation of thrust and lift, and primarily bend and twist 2, 3. The central shaft provides the main mechanical support.…”

“…An increase of axially aligned keratin molecules toward the tip within the feather rachis was reported 17; circumferential, axial fibers, and crossed‐fibers were observed by selectively degrading the matrix proteins 18. A few studies used nanoindentation to obtain the local modulus and hardness of feathers by indenting in limited or unspecified locations 2, 19, 20…”

Nanomechanical properties of bird feather rachises: exploring naturally occurring fibre reinforced laminar composites

“…The b-keratin fibres are relatively stiff compared to the inter-fibre matrix and so the output values will vary depending on the material within the interaction volume. Previous work by Bachmann et al [15] used nanoindentation to investigate the innermost laminae of the rachis of T. alba and C. livia (T Bachmann 2014, personal communication). Evidence from this study means it is likely that the mechanical differences reported Bachmann et al [15] between feathers are caused by extrinsic differences in fibre orientation rather than a change in the mechanics of the intrinsic properties of the constituent b-keratin.…”

“…Previous work by Bachmann et al [15] used nanoindentation to investigate the innermost laminae of the rachis of T. alba and C. livia (T Bachmann 2014, personal communication). Evidence from this study means it is likely that the mechanical differences reported Bachmann et al [15] between feathers are caused by extrinsic differences in fibre orientation rather than a change in the mechanics of the intrinsic properties of the constituent b-keratin. Modulus values reported after larger tissue bending tests [15,25,26] are not comparable to our study because they test the structure as a whole and therefore incorporate all the laminae.…”