Constructal law: Pleasure, golden ratio, animal locomotion and the design of pedestrian evacuation: Comment on “The emergence of design in pedestrian dynamics: Locomotion, self-organization, walking paths and the constructal law” by A. Miguel

Abstract

Antonio Miguel’s article [1] is a timely review of the research on pedestrian movement and its basis in a law ofphysics: the constructal law of design and evolution in nature [2–4].Here I make several additional connections between Miguel’s observations (shown in quotations) and the broaderconstructal-law field. To begin with, the “comfortable and desired” walking speed and “cooperativity” are perceivedas pleasant (attractive) because they are an integral part of the constructal design of animal locomotion. For humans,these feelings are of the same nature as the pleasure derived from beauty, and from understanding something easilyand fast, in order to get moving to safety and better life in general. This is why humans are attracted by images that fitin golden-proportion rectangles, because these shapes are scanned the fastest by the two eyes aligned on the horizontal[4,5].All these attractions are why animal locomotion is “guided locomotion”, with design–it is efficient, economical,safe, fast and purposefully straight. This is the constructal design of animal and human locomotion, and it is thecomplete opposite of Brownian motion. The constructal design of animal locomotion is much more complicated andperfected than the thermodynamics of balancing two work efforts, on the vertical (lifting weight) and the horizontal(getting the environment out of the way), which led to the discovery of the allometric relation between all animalspeeds, body frequencies and body mass [6–9].Second, the view of the movement of the body weight on one stiff leg as an “inverted pendulum” is equivalentto the view of walking and running as falling-forward locomotion [9–11]. The legs are the two spokes of the humanwheel from which the other spokes are missing, and which make the animal wheel the lightest wheel.The Froude number (Fr) is a concept from the mechanics of water waves, and the fact that walking has a con-stant Froude number and is no coincidence. The oneness of animal locomotion and water waves as a falling-forwardmovement was established based on the constructal law [9,10]. The value of the Fr constant speaks of falling-forwardmovement. To see this, consider the movement on one leg (a stick of body length