An Entropic Model for Assessing Avian Flight Formations

Abstract

Why do birds fly in well-defined formations? The observed formations of birds-in-flight are studied with a thermal model. Avian formation-flying is tested as a self-organization process. The maximum entropy production rate (MEPR) postulate is examined to determine its applicability to the observed V formation during the long-distance migration of large birds. A brief discussion of the principles of the rate of entropy generation maximization or minimization is first presented. The V formation is compared to other closely related, but distinctly different formations that can also be adopted by a flock. The thermodynamic analysis from the results of the model indicates that the V formation (named the SV formation in the article) is found to be the pattern that optimizes energy use for the flight duration. This is accomplished with savings in the formation's thermal energy output (heat) by the trailing birds. The MEPR postulate is found to hold for the V formation. The formation also provides for the highest comfort temperatures, perhaps thereby allowing for high altitude (low drag) flight levels to be accessed by the birds. The results of the model point to thermal awareness as a possible key driver for organization into a V formation. The thermal model appears to validate all the major experimental observations of avian formation flying. Regardless, without detailed thermal measurements to validate, and without a physical basis for the constant used in equation (C4d), it is not yet definitive that this thermal model is valid for avian flight formation. The analysis appears to indicate that the organization into patterns of live objects may follow the MEPR principle for self-organization in a manner previously noted for chemical and metallurgical processes.