Math Modeling of Propeller Geometry and Aerodynamics
Published April 20, 1999 by SAE International in United States
Annotation of this paper is available
A new implementation of the vortex step method for predicting subsonic propeller blade aerodynamic loading is described. The analysis, taking advantage of the classical work by Rankine, Betz, and Glauert, also accounts for the effects of an axisymmetric nacelle in both the vector boundary condition and Glauert velocity diagram. Wake-induced velocities are examined, including effects of wake extent and “observer” position. A certain “equivalence” is demonstrated for the classical results of Betz, Glauert, Goldstein and Theodorsen for the optimum-wake-induced velocities. The effects of wake continuity and rollup are studied, relative to a simple helical wake. Thrust loading calculations are compared to NACA wake-pressure-derived test data. Rationale and methods for geometry “math modeling” are shown and illustrated. Finally, geometric and aerodynamic models are integrated for the preliminary design of a new propeller.
“The propeller vortex sheet is fundamental to the understanding and calculation of the aerodynamic force distribution along the propeller blades.”
-- A.B. Bauer (25)
CitationBarnes, J., "Math Modeling of Propeller Geometry and Aerodynamics," SAE Technical Paper 1999-01-1581, 1999, https://doi.org/10.4271/1999-01-1581.
- Norris,J., “The Logic of Flight, the Thinking Man’s Way to Fly,” 11613 Seminole Circle,Northridge, CA 91326, ‘99
- Archer,R.D., and Saarlas,M., “An Introduction to Aerospace Propulsion,” Prentice-Hall, p. 68-108, 1996
- Rankine,W. , Trans. Inst. Naval Archit , V.6, p.13, 1865
- Froude,W. , Trans. Inst. Naval Archit. , V.30, p.390, 1889
- Betz,A., “Screwpropeller With Least Energy Loss,” Gottingen Reports, 1919
- Prandtl,L., “Applications of Modern Hydrodynamics to Aeronautics,” NASA RP 1050, 1979
- Hartman,E.P., and Feldman,L., “Aerodynamic Problems in the Design of Efficient Propellers,” NACA L-753 (ACR, Aug 1942)
- Glauert,H., “Elements of Aerofoil and Airscrew Theory,” Cambridge University Press, 1926
- Goldstein,S., “On the Vortex Theory of Screw Propellers,” Proceedings of the Royal Society, Series A, V.123, No.792, 1929 (doctoral thesis)
- Glauert,H. “Airplane Propellers,” Div.L,Vol .4, of Durand, “Aerodynamic Theory,” Dover reprint
- Theodorsen,T., “Determination ofthe Circulation Function and Mass Coefficient for Dual-Rotating Propellers,” NACA Report 775, ‘44
- Theodorsen,T. “Theory of Propellers. II, Method for Calculating the Axial Interference Velocity,” NACA Report 776, 1944
- Kaufmann,W., “Fluid Mechanics,” McGraw-Hill, p. 361,
- Crigler,J.L., “Application of Theodorsen’s Theory to Propeller Design,” NACA RM L8F30, 1948.
- Rankine,W., “On Plane Water Lines in Two Dimensions,” Phil. Trans. Roy. Soc., 1864
- Prandtl,L. and Tietjens,O.G., “Fundamentals of Hydro- and Aeromechanics,” p. 146, Dover, 1934
- Meyer,R.E., “Introduction to Mathematical Fluid Dynamics,” p. 30-31, Dover, 1971
- Milne-Thomson,L.M., “Theoretical Hydrodynamics,” p. 476-486, Dover, 1968
- Kaufmann,W., “Fluid Mechanics,” McGraw-Hill, p. 187,
- Mathews,C.W., “A Comparison of Experimental Subsonic Pressures on Several Bodies of Revolution,” NACA RM L9F28, 1949
- Chow,C.Y., “An Introduction to Computational Fluid Dynamics,” John Wiley & Sons, p.105-117, 1979
- Adkins,C.N., and Liebeck, R.H., “Design of Optimum Propellers,” AIAA 83-0190, 1983.
- AGARD CP-366,Aerodynamics & Acoustics of Propellers, 1984.
- Barnes,J. P., Semi-Empirical Vortex Step Method for the Lift and Induced Drag Loading of 2D and 3D Wings, SAE 975559, 1997.
- Bauer,A.B., “A New Look at Propeller Performance - From the Prandtl F-Factor to Vortex-Induced Downwash,” SAE 975560, 1997
- Bober, L.J., Mitchell,G.A., “Summary of Advanced Methods to Predict High-Speed Propeller Performance,” NASA TM X-81409, ‘80
- Bousquet, J.M., “Theoretical and Experimental Analysis of Highspeed Propeller Aerodynamics,”AIAA 86-1549
- Hall,K.C., and Pigott,S.A., “Power Requirements for Large-Amplitude Flapping Flight,” J.Aircraft, V.35, No.3, May-June, ‘98
- Keiter,I.D., “Impact of Advanced Propeller Tech. on Mission Characteristics of General Aviation Aircraft,”SAE 810584, 1981
- Larrabee,E.E., “Propeller Design for Motorsoarers,” NASA CR 2085, Part 1, 1979
- Qin,E.,., “Numerical Analysis of the Effect of the Propeller Slipstream on the Aircraft Flowfield,” J.Aircraft, V. 35,No.1,Feb‘98
- Roncz J.G., “Propeller Development for the Rutan Voyager,” SAE 891034, 1989
- Ribner H.S., “Wake Forces Implied in the Theodorsen and Goldstein Theories of Propellers,”J.Aircraft,V.35, No.6,Nov-Dec ’98
- Ribner H., and Foster S., “Ideal Efficiency of Propellers,”J.Aircraft,V.27, No.9, 1990
- LuomaA.A., “Critical Speeds and Profile Drag of the Inboard Sections of a Conventional Propeller,” NACA L-369 (ARR, 1941)
- Stack J. ,“Tests of Airfoils Designed to Delay the Compressibility Burble,”NACA Report 763, 1939
- Cleary,H.E., “Effects of Compressibility on Maximum Lift Coefficients for Six Propeller Airfoils,” NACA ACR L4L21A,1945
- Lindsey W.F.., Aerodynamic Characteristics of 24 NACA 16-Series Airfoils at Mach Numbers to 0.8, NACA TN 1546,1948
- Critzos, C.C., “Aerodynamic Characteristics of NACA 0012 Airfoil Section at Angles of Attack From 0° to 180°,”NACA TN 3361,1955
- Gilman J., “Wind-Tunnel Tests and Analysis of Three 3-Blade Propellers Differing in Pitch Distribution,NACA ARR L6E22,1946
- Weick F.E., “Aircraft Propeller Design ,”McGraw-Hill, p. 102, 1930
- Reid, E., Wake Studies of 8 Model Propellers,NACA 1040,1946
- Reid,E., The Influence of Blade-Width Distribution on Propeller Characteristics,NACA TN 1834,1949.
- not used.
- Rohrbach,C.,., “Evaluation of Wind Tunnel Perf. Tests of an Advanced 8-Bladed Prop to Mach 0.85,” NASA CR 3407, ‘78
- NystromP.A. , NASA TP 1662 (1980) for blade geometry
- Coe,P.L.,., “Low-Speed Wind-Tunnel Tests of an Advanced Eight-Blade Propeller,” NASA TM 86364, 1985
- Soderman,P.L., , NASA TP 3040 (1990) for blade geometry
- Dunham,D.M.,., “Low-Speed Wind-Tunnel Tests of Single and Counter-Rotation Propellers,” NASA TM 87656, 1986
- Soderman,P.T. , NASA TP 3040 (1990) for blade geometry
- Black,D.M.,., “Aerodynamic Design and Performance Testing of a Swept, 8-Bladed Propeller up to Mach 0.85,” NASA CR 3407, ’78
- Jeracki,R.J.,., “Wind Tunnel Performance of Four Energy Efficient Propellers Designed for Mach 0.8,” NASA TM 79124, ‘79
- Mikkelson,D.C., and Mitchell,G.A., “High-Speed Turboprops for Executive Aircraft - Performance and Test Data,” NASA TM 81482, ‘80
- Rohrbach,C. and Wainauski,H.S., “Aerodynamic Characteristics of an Advanced Tech. Propeller for Commuter Aircraft,” AIAA-81-1565
- Korkan,K.D.,., “A Theoretical and Experimental Investigation of Propeller Performance Methodologies,“AIAA 80-1240, 1980
- Stefko,G., and Jeracki,R., “Wind Tunnel Results of Advanced High-Speed Propellers, AIAA 85-1259, 1985.
- DeGeorge,C.L.,., “A Report on Initial Tests of the Large Scale Advanced Prop-Fan,” AIAA-86-1551.
- Jeracki,R.J., and Mitchell,G.A., “Low and High-Speed Propellers for General Aviation - Performance & Test Data,” SAE 811090, ‘81
- Barnes,J.P. , Math Modeling of Airfoil Geometry , SAE 961317, ‘96
- Chow,C.Y., “An Introduction to Computational Fluid Dynamics,” John Wiley & Sons, p. 309-320, 1979
- Photo of Vought F4U showing propeller tip vortices; U.S.Navy, “Introduction to Naval Aviation,” OPNAV 33-NY-85, p. 124
- Barnes,J. P., Non-Dimensional Characterization of Gear Geometry, Mesh Loss, and Windage, AGMA 97FTM11, 1997
- Cheney,W., and Kincaid,D., “Numerical Mathematics and Computing,” Brooks/Cole, p.220, 1985.