The Pigeon Constant: A Mathematical Model of Head-bobbing in Pigeons

Abstract

This is a study of the motion of the “common pigeon”. Specifically, the formulation of a mathematical model to describe head movement and to link it to pigeon velocity. Previous studies have been made from a more biological point of view - focusing on the function of head bobbing rather than quantifying it. This paper is novel in that it seeks to produce a mathematical basis for the study of pigeon movement which may inform biological studies and provide food for thought. In doing so, this paper proposes the use of the “pigeon constant” which shall be used to hence provide a quantitative link to velocity. This pigeon constant refers to the fixed length through which pigeons appear to move their heads during motion at some fixed velocity. Whether this is unique to each bird in itself or varies as a function of velocity or acceleration remains to be explored and may form the basis of future research. Any implications of this pigeon constant or the factors it depends upon may be touched on briefly but is ultimately left in the hands of capable biologists.

Keywords: Pigeons, Necker, Head-bobbing, Pigeon constant