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  • Print publication year: 2015
  • Online publication date: May 2018

Appendix A - Geometry for Aerodynamicists


Aerodynamicists control the flowfield through geometry definition and are always interested in possible geometric shapes that would be useful in design. This appendix provides the detailed definition of many of the classic shapes frequently specified in aerodynamics. It is not intended to be encyclopedic, but will provide a good starting point for where to obtain geometric definitions for aerodynamic shapes.

The NACA Airfoils

The NACA (National Advisory Committee for Aeronautics) airfoils were designed during the period from 1929 through 1947 under the direction of Eastman Jacobs at the NACA’s Langley Field Laboratory (now NASA Langley Research Center). Most of the airfoils were based on simple geometrical descriptions of the section shape, although the 6 and 6A series were developed using theoretical analysis and don’t have simple shape definitions. Although a new generation of airfoils has emerged as a result of improved understanding of airfoil performance and the ability to design new airfoils using computational methods, the NACA airfoils are still useful in many aerodynamic design applications. A number of references have been included to allow the reader to study both the older NACA literature and the new airfoil design ideas. Taken together, this literature provides a means of obtaining a rather complete understanding of the ways in which airfoils can be shaped to obtain desired performance characteristics.

Abbott, I.H., and von Doenhoff, A.E., Theory of Wing Sections, New York: Dover, 1959.
Patterson, E.W., and Braslow, A.L., “Ordinates and Theoretical Pressure-Distribution Data for NACA 6- and 6A-Series Airfoil Sections With Thicknesses from 2 to 21 and From 2 to 15 Percent Chord, Respectively,” NASA TR R-84, 1958.
Abbott, I.H., “Airfoils: Significance and Early Development,” AIAA Paper 80-3033, March 1980.
Jones, R.T., “Recollections from an Earlier Period in American Aeronautics,” Annual Review of Fluid Mechanics, Vol. 9, 1977, pp. 1–11.
Ladson, C.L., and Brooks, C.W., “Development of a Computer Program to Obtain Ordinates for the NACA 4-Digit, 4-Digit Modified, 5-Digit, and 16-Series Airfoils,” NASA TM X-3284, November 1975.
Ladson, C.L., and Brooks, C.W., Jr., “Development of a Computer Program to Obtain Ordinates for the NACA 6- and 6A-Series Airfoils,” NASA TM X-3069, September 1974.
Riegels, F.W., Airfoil Sections, London: Butterworths, 1961.
Whitcomb, R.T., “Review of NASA Supercritical Airfoils,” ICAS Paper 74-10, August 1974.
Harris, C.D., “NASA Supercritical Airfoils,” NASA TP 2969, March 1990.
Becker, J.V., “The High-Speed Airfoil Program,” in The High Speed Frontier, NASA SP-445, 1980.
Verhoff, A., Stookesberry, D., and Cain, A., “An Efficient Approach to Optimal Aerodynamic Design. I – Analytic Geometry and Aerodynamic Sensitivities,” AIAA Paper 93-0099, January 1993.
Stookesberry, D., Verhoff, A., and Cain, A., “An Efficient Approach to Optimal Aerodynamic Design. II – Implementation and Evaluation,” AIAA Paper 93-0100, January 1993.
Ventkataraman, P., “A New Procedure for Airfoil Definition,” AIAA Paper 95-1875, June 1985.
Ventkataraman, P., “Optimum Airfoil Design in Viscous Flows,” AIAA Paper 95-1876, June 1985.
Sadrehaghighi, I., Smith, R.E., and Tiwari, S., “Grid and Design Variables Sensitivity Analysis for NACA Four-Digit Wing-Sections,” AIAA Paper 93-0195, January 1993.
van Dam, C.P., “Recent Experiences with Different Methods of Drag Prediction,” Progress in Aerospace Science, Vol. 35, 1999, pp. 751–798.
Loftin, L.K., “Theoretical and Experimental Data for a Number of NACA 6A-Series Airfoils,” NACA TR-903, 1948.
Raymer, D.P., Aircraft Design: A Conceptual Approach, 5th Ed., Reston: AIAA, 2012.
Eppler, R., Airfoil Design and Data, Berlin: Springer-Verlag, 1990.
Bauer, F., Garabedian, P., and Korn, D., “A Theory of Supercritical Wing Sections with Computer Programs and Examples,” Lecture Notes in Economics and Mathematical Systems, Vol. 66, Berlin: Springer-Verlag, 1972.
Bauer, F., Garabedian, P., Jameson, A., and Korn, D., “Supercritical Wing Sections II, A Handbook,” Lecture Notes in Economics and Mathematical Systems, Vol. 108, Berlin: Springer-Verlag, 1975.
Bauer, F., Garabedian, P., and Korn, D., “Supercritical Wing Sections III,” Lecture Notes in Economics and Mathematical Systems, Vol. 150, Berlin: Springer-Verlag, 1977.
Krasnov, N.F., Aerodynamics of Bodies of Revolution, edited and annotated by D.N. Morris, New York: American Elsevier, 1970.
Handbook of Supersonic Aerodynamics, Vol. 3, Section 8, “Bodies of Revolution,” NAVWEPS Report 1488, October 1961.
Ashley, H., and Landahl, M., Aerodynamics of Wings and Bodies, Reading: Addison-Wesley, 1965, pp. 178–181.
Adams, M.C., “Determination of Shapes of Boattail Bodies of Revolution for Minimum Wave Drag,” NACA TN 2550, November 1951.
Liming, R., Practical Analytic Geometry with Applications to Aircraft, New York: MacMillan, 1944.
Williams, J.E., and Vukelich, S.R., The USAF Stability and Control Digital DATCOM, AFFDL TR-79–3032, 1979.
Lamar, J.E., and Alford, W.J., “Aerodynamic-Center Considerations of Wings and Wing-Body Combinations,” NASA TN D-3581, October 1966.
Hall, C.F., “Lift, Drag, and Pitching Moment of Low Aspect Ratio Wings at Subsonic and Supersonic Speeds,” NACA RM A53A30, 1953.
Boyd, J.W., Migotsky, E., and Wetzel, B.E., “A Study of Conical Camber for Triangular and Swept Back Wings,” NASA RM A55G19, November 1955.
Mason, W.H., “A Wing Concept for Supersonic Maneuvering,” NASA CR 3763, December 1983.
Mason, W.H., “SC3 – A Wing Concept for Supersonic Maneuvering,” AIAA Paper 83-1858, July 1983.
Hahn, A.S., “Vehicle Sketch Pad: A Parametric Geometry Modeler for Conceptual Aircraft Design,” AIAA Paper 2010-0657, January 2010.
Kulfan, B.M., “Universal Parametric Geometry Representation Method,” Journal of Aircraft, Vol. 45, No. 1, 2008, pp. 142–158.