The Insulating Properties of the Pelage of the North-American Porcupine (Erethizon dorsatum): The Influence of Quill-Like Structures on Heat Transfer

Abstract

Multifunctionality is characteristic of the hairy pelage of mammals, the key function of which is insulation. As a rule, mammalian fur can effectively insulate the body at a certain density of thin hair in it and sufficient thickness of the pelage in general [1]. The fulfillment of other functions (in particular, mechanical protection) may be related to changes in the pelage, as a result of which its structure becomes markedly different from the structure that may be regarded optimal from the standpoint of insulation. Apparently, more or less significant redistribution of roles between the insulating and defensive functions of the pelage took place in parallel more than once in the course of evolution of mammals. In particular, quill-like modifications of hair differing in the degree of modification occur in different taxa [2]. In extreme cases, the pelage turns into a strongly differentiated multilayer defensive formation consisting of a great number of various quills of a complex structure. Nevertheless, the functional aspects of these transformations have not been studied thus far. For example, it is unknown to which extent the presence of quills may affect the insulating properties of the pelage. Filling up this gap was the goal of this study, in which we performed quantitative estimation of the effect of the presence of quills on the insulating properties of the pelage using the North American porcupine ( Erethizon dorsatum L . ) as an example.Heat transfer within the pelage at temperatures lower than the thermoneutral zone characteristic of a certain individual may proceed in three ways: via thermal conductance, heat radiation, and convection [3]. Because convective heat losses, most likely, are small under natural conditions [3], the effectiveness of the pelage as an insulator is determined primarily by thermal conductance and heat radiation. In the absence of convection and evaporation, the total intensity of heat flux q through the pelage can be presented as a sum of two summands [4][5][6]:where q c is the heat flux via thermal conductance per se through air and hair, and q r is the heat flux via radiation. The heat flux through the pelage via thermal conductance cannot be lower than the flux through the still air layer whose thickness is similar to that of the pelage. At the same time, this flux cannot be greater than the heat flux through the area completely filled with keratin. The conductance quotient of keratin, according to indirect estimates [6][7][8], is greater than that of air approximately by an order of magnitude. Within the limits specified, q c increases linearly as the relative fraction of keratin in the area occupied by the pelage increases. Let us present fur as long solid cylinders; in this case, the relative fraction of keratin will be proportional to the product of hair density N by the squared diameter ( d ) of hair cross section: Nd 2 [5]. Thus, the dimensionless product Nd 2 , hereinafter designated as I h -c , may be regarded as a measure of the effect of pelage structure on the i...