Dimensionally and Physically Proper Lift, Drag, and Thrust-Related Numbers as Figures of Merit: Normalized Lift, Drag, and Thrust, , , and
Publication: Journal of Aerospace Engineering
Volume 30, Issue 3
Abstract
Textbooks state that the lift, drag, and thrust coefficients , , and , 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, , normalized drag , and normalized thrust, , 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 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 (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 of the blades of the record-breaking quadcopter AeroVelo Atlas is presented and compared with its lift coefficient as calculated by the AeroVelo group.
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Acknowledgments
The author is grateful to contributions and support by C. Anderson, J. Canal, J. Calabretta, C. Hiemcke, H. Posnansky, C. Rimoldi, and B. Voogd.
References
Abbott, I. H., and von Doenhoff, A. E. (1959). Theory of wing sections: Including a summary of airfoil data, Dover, New York.
Andersonrson, J. D. (1997). History of aerodynamics, Cambridge Aerospace Series, Cambridge, U.K.
Anderson, J. D. (2002). The Airplane: A history of its technology, AIAA, Reston, VA, 127–128.
Anderson, J. D. (2011). Fundamentals of aerodynamics, McGraw Hill, 5th Ed., New York, 34–40.
Bachmann, T. W. (2010). “Anatomical, morphometrical and biomechanical studies of barn owls’ and pigeons’ wings.” Ph.D. dissertation, RWTH Aachen Univ., Aachen, Germany.
Burgers, P. (2016). “Comparison of the average lift coefficient and normalized lift for evaluating hovering and forward flapping flight.” Aerospace, 3(3), 24.
Burgers, P., and Alexander, D. E. (2012). “Normalized lift: An energy interpretation of the lift coefficient simplifies comparisons of the lifting ability of rotating and flapping surfaces.” PLoS ONE, 7(5), .
Dudley, R., and Ellington, C. P. (1990). “Mechanics of forward flight in bumblebees—I: Kinematics and morphology.” J. Exp. Biol., 148, 19–52.
Friend, E. L., and Sefic, W. J. (1972). “Flight measurements of buffet characteristics of the F-104 airplane for selected wing-flap deflections.”, NASA Flight Research Center, Edwards, CA.
Halliday, D., and Resnick, R. (1981). Fundamentals of physics, 2nd Ed., Wiley, Hoboken, NJ, 186.
Harris, C. D., McGhee, R. J., and Allison, D. O. (1980). “Low-speed aerodynamic characteristics of a 14 percent thick NASA phase 2 supercritical airfoil designed for a lift coefficient of 0.7.”, NASA Langley Research Center, Hampton, VA.
Hoerner, S. F. (1965). Fluid dynamic drag, Hoerner Fluid Dynamics, Bricktown, NJ, 3–16.
Lentink, D., and Dickinson, M. H. (2009). “Biofluidynamic scaling of flapping, spinning and translating fins and wings.” J. Exp. Biol. 212, 2691–2704.
Loftin, L. K. (1985). “Quest for performance: The evolution of modern aircraft.”, NASA, Washington, DC, 491–494.
McCormick, B. W. (1979). Aerodynamics, aeronautics, and flight mechanics, Wiley, Hoboken, NJ, 349–359.
Moran, J. M., and Shapiro, H. N. (1988). Fundamentals of engineering thermodynamics, Wiley, Hoboken, NJ.
Munk, M. M. (1923). “General biplane theory.”, National Advisory Committee for Aeronautics, Washington, DC.
Prandtl, L. (1921). “Applications of modern hydrodynamics to aeronautics.”, National Advisory Committee for Aeronautics, Washington, DC.
Raymer, D. P. (1999). Aircraft design: A conceptual approach, 3rd Ed., AIAA Education Series, Reston, VA.
Reid, E. G. (1924). “Test of rotating cylinders.”, National Advisory Committee for Aeronautics, Langley Aeronautical Lab, Langley Field, VA.
Seifert, J. (2012). “A review of the Magnus effect in aeronautics.” Prog. Aerosp. Sci., 55, 17–45.
Soderman, P. T., and Aiken, T. N. (1971). “Full-scale wind tunnel tests of a small unpowered jet aircraft with a T-tail.”, NASA Ames Research Center, Moffett Field, CA.
Taylor, G. K., Nudds, R. L., and Thomas, A. R. L. (2003). “Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency.” Nature, 425(6959), 707–711.
Tinetti, A. F. (2011). “Equivalent longitudinal area distributions of the B-58 and XB-70-1 airplanes for use in wave drag and sonic boom calculations.”, NASA Langley Research Center, Hampton, VA.
Torenbeek, E. (1976). Synthesis of subsonic airplane design, Delft University Press, Rotterdam, Netherlands.
Vogel, S. (1988). Life’s devices: The physical world of animals and plants, Princeton University Press, Princeton, NJ.
Yip, L. P. (1985). “Wind tunnel investigation of a full-scale canard-configured general aviation airplane.”, NASA Langley Research Center, Hampton, VA.
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© 2016 American Society of Civil Engineers.
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Received: Nov 24, 2015
Accepted: Jul 11, 2016
Published online: Oct 27, 2016
Discussion open until: Mar 27, 2017
Published in print: May 1, 2017
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