In the latter part of a paper on feather structure and biomechanics, I (Lingham-Soliar 2014) critiqued a paper by Nudds and Dyke (2010) on the inadequacy of feather rachis strength for flapping flight in Archaeopteryx. Subsequently, I received a few emails from one of the authors, essentially alleging that I had misrepresented the findings of Weiss and Kirchner (2010) with respect to the significance of the foam centre of the rachis. A written response by Palmer (2014) expressing similar views followed, to which I reply here (for references not listed see Lingham-Soliar 2014). Palmer says that the classical Brazier buckling formula for thin-walled circular tubes is a reasonable approximation for the calamus region of the rachis. However, most college textbooks on feather morphology plainly show that the calamus and the rachis are quite distinct structural components of the primary feather shaft. Thus, while the concept of the thin-walled, circular engineering tube may be a reasonable approximation for the calamus because it lacks a foam center, by default it would not be a reasonable approximation for the rachis, the structure investigated by Nudds and Dyke (2010), which has a foam center. For example, Azuma (2006, p. 37) describes the rachis as ‘‘a rectangular center filled with foam material and can more easily accommodate bending distortion than the quill [calamus].’’ Furthermore, Palmer refers to the calamus as the region subjected to the highest bending moment, and thus the most likely region to fail (a statement he makes without support or citation). Yet, regardless of whether it is true or not, it is irrelevant because of the quite distinctive structural environment and biomechanics of the calamus compared to the rachis. Just one condition (among many) is enough to show this, i.e., quite unlike the rachis it is completely embedded in the avian skin, which is a highly complex, hydraulic, skeleto-muscular apparatus that is subjected to a wide array of internal and external mechanical strains and stresses (Homberger and de Silva 2000; see their fig. 1). Palmer says that I had not taken the time to check what I had recommended as a more suitable formula based on Corning and Biewener (formula 5). I did take Corning and Biewener’s (1998) formula on trust, as one invariably does in respected publications. Nevertheless, the point I had made was based on a simple question of logic—the rachis possesses a medullary pith, and Corning and Biewener’s (1998) formula 5 allegedly allowed for a medullary pith (a foam sandwich structure; their formula 4 does not). However, Palmer (2014) claims, albeit without evidence, that formula 5 gives a failure bending moment almost an order of magnitude less than that given by the bare tube formula. Even if this is accepted, we have two choices: (1) it invalidates the sandwich principle in typical biological and engineering systems, or (2) formula 5 is faulty. Furthermore, Corning and Biewener’s formulae (p. 3059) use a Poisson ratio based on wool, i.e., ‘softer’, more ‘bendy’ (low modulus) a-keratin. Feathers comprise the stiffer (high modulus) b-keratin—this is important. However, a commentary is not the place to take this any further nor the appropriateness of the formulae used by Nudds and Dyke (2010). That study suffers from additional fundamental weaknesses. Palmer says I mislead by claiming that Weiss and Kirchner’s findings on the (2010) feather medullary foam shows a significant increase in mechanical efficiency (of Communicated by F. Bairlein.
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