An Aerodynamic Equation of State—Part I: Introduction and Aerospace Applications

Abstract

<div>In subsonic aircraft design, the aerodynamic performance of aircraft is compared meaningfully <i>at a system level</i> by evaluating their range and endurance, but cannot do so at <i>an aerodynamic level</i> when using lift and drag coefficients, <i>C_L </i> and <i>C_D </i>, as these often result in misleading results for different wing reference areas. This Part I of the article (i) illustrates these shortcomings, (ii) introduces a dimensionless number quantifying the induced drag of aircraft, and (iii) proposes an <i>aerodynamic equation of state</i> for lift, drag, and induced drag and applies it to evaluate the aerodynamics of the canard aircraft, the dual rotors of the hovering <i>Ingenuity</i> Mars helicopter, and the composite lifting system (wing plus cylinders in Magnus effect) of a YOV-10 <i>Bronco</i>. Part II of this article applies this aerodynamic equation of state to the flapping flight of hovering and forward-flying insects. Part III applies the aerodynamic equation of state to some well-trodden cases in fluid mechanics found in fluid-mechanics textbooks.</div>