Dimensionally and Physically Proper Lift, Drag, and Thrust-Related Numbers as Figures of Merit: Normalized Lift, Drag, and Thrust, ηL, ηD, and ηT

Abstract

Textbooks state that the lift, drag, and thrust coefficients CL, CD, and CT, are numbers that must be dimensionally proper (i.e., dimensionless) for their use in comparing different data sets. This paper posits that for the meaningful comparison of different data sets, numbers must be dimensionally and physically proper. The physical propriety is satisfied by expressing the number as a ratio of work and the energy available at an aerodynamic system during the generation of lift, drag, or thrust. The aerodynamic systems addressed in this paper are aircraft, propellers and lift rotors, cylinders in Magnus effect, and flapping wings. This paper introduces the normalized lift, ηL, normalized drag ηD, and normalized thrust, ηT, numbers that are dimensionally and physically proper and can evaluate the ability of generating lift, drag, and thrust of these aforementioned systems and compare this ability between different systems. These numbers are shown to act like the thermal efficiency η in thermodynamics as they represent the ratio of work exerted onto the surrounding flowfield and the kinetic energy available at the system, are associated with a maximum value ηmax (that may exceed 1) and can be read on a stand-alone basis. Their common mathematical format facilitates crosspollination between engineering, biomechanics, and biology. A numerical calculation of the normalized lift ηL of the blades of the record-breaking quadcopter AeroVelo Atlas is presented and compared with its lift coefficient CL as calculated by the AeroVelo group.