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

In subsonic aircraft design, the aerodynamic performance of aircraft is compared meaningfully at a system level by evaluating their range and endurance, but cannot do so at an aerodynamic level when using lift and drag coefficients, C_L and C_D , 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 aerodynamic equation of state for lift, drag, and induced drag and applies it to evaluate the aerodynamics of the canard aircraft, the dual rotors of the hovering Ingenuity Mars helicopter, and the composite lifting system (wing plus cylinders in Magnus effect) of a YOV-10 Bronco. 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.