An alternative approach to induced drag reduction

    Nikolaos Kehayas   Affiliation


Induced drag constitutes approximately 40% of the total drag of subsonic civil transport aircraft at cruise conditions. Various types of winglets and several non-planar concepts, such as the C-wing, the joined wings, and the box plane, have been proposed for its reduction. Here, a new approach to induced drag reduction in the form of a combination of an elliptical and an astroid hypocycloid lift distribution is put forward. Lift is mainly generated from high circulation in the center part of the wing and fades away along the semi-span towards the wing tip. Using lifting line theory, the analysis shows that for fixed lift and wingspan the combined lift distribution results in an induced drag reduction of 50% with respect to the elliptical distribution. Due to its wing planform the combined lift distribution leads to a 51.5% higher aspect ratio. If structural constraints are placed, then the higher aspect ratio may affect wing weight. Although any substantial increase of wing weight is not envisaged, further study of the matter is required. Zero-lift drag and lift-dependent drag due to skin friction and viscosity-related pressure remain unaffected. The proposed lift distribution is particularly useful in a blended wing-body design.

Keyword : drag reduction, induced drag, drag due to lift, vortex drag, lifting line theory, lift distribution

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Kehayas, N. (2021). An alternative approach to induced drag reduction. Aviation, 25(3), 202-210.
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Nov 10, 2021
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Allison, E., Kroo, I., Sturdza, P., Suzuki, Y., & Martins-Rivas, H. (2010). Aircraft conceptual design with natural laminar flow. In Proceedings of the 27th International Congress of Aeronautical Sciences (pp. 1–9). Nice, France.

Anderson, J. D. (1984). Fundamentals of aerodynamics. McGraw-Hill.

Cavallaro, R., & Demasi, L. (2016). Challenges, ideas, and innovations of joined-wing configurations: a concept from the past, an opportunity for the future. Progress in Aerospace Sciences, 87, 1–93.

Chattot, J.-J. (2006). Low speed design and analysis of wing/winglet combinations including viscous effects. AIAA Journal of Aircraft, 43(2), 386–389.

Demasi, L. (2006). Induced drag minimization: a variational approach using the acceleration potential. AIAA Journal of Aircraft, 43(3), 669–680.

Demasi, L., Monegato, G., Cavallaro, R., & Rybarczyk, R. (2019). Optimum induced drag of wingtip devices: the concept of best winglet design. In AIAA SciTech Forum (pp. 1–48). San Diego, California.

Frediani, A., & Montanari, G. (2009). Best wing system: an exact solution of the Prandtl’s problem. In G. Buttazzo & A. Frediani (Eds.), Variational analysis and aerospace engineering (pp. 183–211). Springer.

Glauert, H. (1947). The Elements of aerofoil and airscrew theory (2nd ed.). Cambridge University Press.

Howe, D. (2000). Aircraft conceptual design synthesis. Professional Engineering Publishing Limited.

Jones, R. T. (1950). The spanwise distribution of lift for minimum induced drag of wings having a given lift and a given bending moment. NASA TN-2249.

Kehayas, N. (1998). The blended wing-body configuration as an alternative to conventional subsonic civil transport aircraft design. In Proceedings of the 21st International Congress of Aeronautical Sciences (pp. 1–7). Melbourne, Australia.

Kehayas, N. (2006). A powered lift design for subsonic civil transport aircraft. In Proceedings of the 25th International Congress of Aeronautical Sciences (pp. 1–10). Hamburg, Germany.

Kehayas, N. (2011). Propulsion system of a jet-flapped subsonic civil transport aircraft design. AIAA Journal of Aircraft, 48(2), 697–702.

Kroo, I. (2001). Drag due to lift: concepts for prediction and reduction. Annual Review of Fluid Mechanics, 33, 587–617.

McMasters, J., & Kroo, I. M. (1998). Advanced configurations for very large transport airplanes. Aircraft Design, 1(4), 217–242.

Munk, M. M. (1923). The minimum induced drag of aerofoils. NACA TR-121.

Pate, D. J., & German, B. J. (2013). Lift distributions for minimum induced drag with generalized bending moment constraints. AIAA Journal of Aircraft, 50(3), 936–946.

Phillips, W. F., Hunsaker, D. F., & Joo, J. J. (2019). Minimizing induced drag with lift distribution and wingspan. AIAA Journal of Aircraft, 56(2), 431–441.

Prandtl, L. (1921). Applications of modern hydrodynamics to aeronautics. NACA TR-116.

Prandtl, L. (1924). Induced drag of multiplanes. From Technische Berichte, Vol. III, No. 7. NACA TN-182.

Prandtl, L. (1933). Uber Tragflugel kleinster induzierten Winderstandes. Zeitschrift fur Flugtechnik und Motorluftschiffart, 24(11), 305–306.

Scardaoni, M. P. (2020). A simple model for minimum induced drag of multiplanes: could Prandtl do the same? Aerotecnica Missili & Spazio, 99(3), 233–249.

Simmons, G. F. (1992). Calculus gems: brief lives and memorable mathematics. McGraw-Hill.

Taylor, J. D., & Hunsaker, D. F. (2020a). Minimum induced drag for tapered wings including structural constraints. AIAA Journal of Aircraft, 57(4), 782–807.

Taylor, J. D., & Hunsaker, D. F. (2020b). Numerical method for rapid aerostructural design and optimization. In AIAA Aviation 2020 Forum (pp. 1–20). Virtual Event.

Torenbeek, E. (2013). Advanced aircraft design. Conceptual design, analysis and optimization of subsonic civil airplanes. Wiley.

Whitcomb, R. T. (1976). A design approach and selected windtunnel results at high subsonic speeds for wing-tip mounted winglets. NASA TN-D-8260.

Wolkovich, J. (1985). The joined wing: an overview. In AIAA 23rd Aerospace Sciences Meeting (pp. 1–17). Reno, Nevada.