**1. Introduction**

The contour feathers of birds are well-known to serve a variety of functions ranging from intraspecific signaling to such physical qualities as thermal insulation [1], water repellency [2] and resistance to impact [3]. They are arranged on the bird's body in an overlapping fashion like shingles on a roof with the dorsal aspect of their distal one-third exposed to air or water. This outer part of the contour feather has the patterned structure seen in pennaceous feathers with barbs extending from the rachis, each sprouting barbules of which the distal ones have hooks that catch upon the curled, proximal barbules of the barb next more distal [4]. These structural details confer to the plumage the properties of water repellency, resistance to water penetration and resistance to forceful impact. The overall pattern is essentially the same for all regions of the body surface, but differs by location for some species. For instance, a marked difference in barb diameter and spacing was observed for the head, breast and abdominal feathers of Blue Swallows *(Hirundo atrocaerulea*) affecting the water repellency and water resistance of these regions to cope with the swallow's specific habit of foraging along misty mountain slopes [5].

Water birds that swim, dive or plunge can be expected to show adaptations in their contour feathers, compatible with their foraging niches, that are absent in land birds that have no interaction with open water as indeed they do [6]. They show a water repellency and a resistance to water penetration in their contour feathers that vary with the family's specific behavioral patterns. Surface feeders tend to have a predominantly water repellent body plumage whereas those of divers and plungers are more resistant to water penetration and forceful impact.

Birds that swim and dive will also benefit from reduced drag for their locomotion in water, a consideration that applies less to waders and shore birds and not at all to land birds. Viscous drag in water is dependent on the surface microstructure of the distal one-third of the contour feather, but also on the shape of its surface in contact with water, an aspect of feathers that has so far received little or no attention. Drag in air, such as in flight, on the other hand, has been the topic of several studies.

That the shape of the surface area in contact with water varies among bird families has been noticed in the course of previous studies. It was seen to be nearly circular in land birds with a length-to-width ratio (L/W) of approximately 1.0, but oblong with an L/W of about 4 in penguins (*Spheniscidae*), the most aquatic of families. Birds less intimate with open water showed intermediate values for L/W.

In this chapter, we consider the interface between the distal one-third and flowing water to calculate viscous drag for feather shape geometry. Assuming the flow to be parallel to the long axis of the feather, i. e. zero angle of attack, we can derive the total drag coefficient (DC), composed of viscous pressure and frictional drag, from the computational and experimental results of studies on model ship hulls of varying length-to-diameter ratios using solutions to the Reynolds-averaged Navier– Stokes Equations [7]. For the relationship between drag coefficient and L/W, we then find

$$\text{DC} \left( \mathbf{10^{-3}} \right) = \mathbf{4.071} \,\mathrm{e^{-0.0595L/W}} \tag{1}$$

**41**

*Viscous Drag Reduction and Contour Feather Geometry in Water and Land Birds*

The measurements on contour feathers were performed on abdominal feathers as these are considered to be most representative of interaction with water. The primary source of feathers was the same as used for earlier studies which included water bird species from 11 orders and, for comparison, land bird species from 9 orders [10]. The species entered in this study are compiled in **Table 1**, using English names and taxonomic sequence suggested by Handbook of the Birds of the

The length and the width of the closed pennaceous portion of the contour feathers of the 48 water birds and twelve land birds in this study were measured to the nearest millimeter using a traveling microscope with the mid-part of the vane taken for the width. At least three feather specimens of each species were examined. The drag coefficients, listed in **Table 1**, were calculated from L/W values using the

Grouping the bird species according to their interaction with open water can be achieved by assigning them to foraging niches as proposed by Pigot et al. [12], using a standardized protocol for foraging niche delimitation. Following this procedure, a total of thirty niches has been identified for all of the approximately 10,000 bird species of the world. Of these six major foraging niches were categorized as Aquatic with two more chosen by us to accommodate the 48 water bird species of this study. The twelve land bird species could be grouped into two niches: Ground Feeding and

All statistical analyses were conducted using the R statistical computer software (version 3.6.0). In addition to the foraging niches proposed [12] for aquatic birds (group 1) and land birds (group 2), four more analyses were performed using the values of L/W and DC for both land and aquatic bird species (consisting of the various foraging niches) categorized as the following independent variables: aquatic versus land birds (group 3), swimmers versus land birds (group 4), waders versus land birds (group 5) and swimmers versus waders (group 6). These groupings can be visualized in the context of a phylogeny in **Figure 1** and **Table 4**. Phylogenetic trees comprising of 60 bird species representatives of the independent groups were obtained from www. birdtree.org [13]. A total of 1000 trees were generated and a representative tree was constructed using the *maxCladeCred* function from the *phangorn* package

The degree of group aggregation was determined in order to establish if the ANOVA methodology would be affected by the association between the independent variable, i. e. foraging niche and the phylogeny. Group aggregation was performed by calculating phylogenetic variance–covariance using the *vcv.phylo* function from the *ape* package (version 5.3), which was followed by performing a two-block partial least squares analysis using the *two.b.pls* function from the *geomorph* package (version 3.2.1). The degree of group aggregation was estimated by the proximity of the R-value to either 1 or 0, where values equal to or larger than 0.6 were considered strong aggregation. Significant group aggregation was considered

In order to determine if the foraging niches for aquatic and land birds as well as the other independent variables, explain feather microstructure while accounting for phylogenetic relationships, a phylogenetic ANOVA (*procD.pgls* function from the *geomorph* package), conventional ANOVA (*aov* function) and non-parametric (*kruskal.test* function) equivalent approaches were followed. Significance among all

*DOI: http://dx.doi.org/10.5772/intechopen.96994*

**2. Methods**

World [11].

above equation.

Aerial/Sally.

(version 2.5.3).

for *p*-values <0.05.

analyses were accepted for *p*-values <0.05.

for values of L/W less than 7 which is within the range of feather geometry. The equation predicts that oblong shapes of the tips of contour feathers reduce drag facilitating swimming and diving, whereas a more circular shape would cause an increase in frictional drag. A similar reasoning could be applied to the shape of the area that the body of a swimming bird has in contact with water. If this area is assumed to be elliptical, a drag coefficient for body surface area in contact with water could be determined using the same equation.

In order to establish if niche-specific adaptations in feather microstructure exist among bird species, various statistical approaches should be considered. Generalized least squares estimation of coefficients for linear models have been commonly used to investigate traits within phylogeny [8, 9]. However, statistical inaccuracies due to high type I errors are widespread without accounting for the evolutionary relationships. A more appropriate approach, described by Adams and Collyer (2018), incorporates phylogeny under a Brownian motion model of evolution while performing ANOVA. This phylogenetic-ANOVA approach offers additional advantages by accounting for group aggregation within phylogeny which could influence results and overall conclusions.

Our hypothesis is that water birds have contour feathers that exhibit in their shapes adaptations to reducing viscous drag according to their interaction with open water.

*Viscous Drag Reduction and Contour Feather Geometry in Water and Land Birds DOI: http://dx.doi.org/10.5772/intechopen.96994*
