Unifying constructal theory for scale effects in running, swimming and flying

Area of Science:

• Physics
• Biomechanics
• Zoology

Background:

• Traditionally, running, flying, and swimming are viewed as fundamentally different forms of locomotion.
• Differences in animal morphology and movement mechanisms (e.g., limbs vs. body undulations) support this view.

Purpose of the Study:

• To demonstrate that a single physics theory can describe all forms of animal locomotion.
• To explain observed scaling laws in animal movement using an optimization principle.

Main Methods:

• Applied the principle of minimum useful energy (exergy) destruction to model animal locomotion.
• Analyzed the balance between vertical energy loss (body weight) and horizontal energy loss (friction).

Main Results:

• Derived established relationships between speed, frequency, and body mass (M(b)¹/⁶ and M(b)⁻¹/⁶).
• Predicted universal features like the Strouhal number and force-mass proportionality in animal motors.
• Identified conditions (Reynolds number > 30) for undulating swimming and flapping flight.

Conclusions:

• Animal locomotion, like turbulent fluid flow, is an optimized intermittent movement.
• Constructal theory provides a unified framework for understanding movement across biological and physical systems.