▪ Abstract This article describes some of the fundamental ideas underlying methods for induced-drag prediction and reduction. A review of current analysis and design methods, including their development and common approximations, is followed by a survey of several approaches to lift-dependent drag reduction. Recent concepts for wing planform optimization, highly nonplanar surfaces, and various tip devices may lead to incremental but important gains in aircraft performance. Focusing on relatively high-aspect-ratio subsonic wings, the review suggests that opportunities for new concepts remain, but the greatest challenge lies in their integration with other aspects of the system.

DRAG DUE TO LIFT: Concepts for Prediction and Reduction

Introduction to shock-induced separation and its prevention by design and boundary layer control

The development of relaxation methods to calculate transonic flows is discussed. Rather accurate predictions can be made for a number of flows of interest using the transonic potential flow equation, which may be derived from the Euler equations for inviscid compressible flow by introducing the assumption that the flow is irrotational. Once the choice of a mathematical model has been settled, the numerical procedure for actually computing a solution contains two main elements: the construction of a discrete approximation which converges to the solution of the continuous problem in the limit as the mesh width is reduced to zero, and the solution of the resulting set of nonlinear difference equations by a convergent iterative scheme. The choice of an appropriate coordinate system and its influence on the accuracy of the discrete approximation is discussed. Several applications of the general method are described.

Transonic flow calculations

1. The feathers at the wing tips of most birds that soar over land separate both horizontally and vertically in flight to form slotted tips. The individual feathers in the slotted tips resemble the winglets used on the wing tips of some aircraft to reduce induced drag. 2. A wing that produces lift leaves a pair of vortex sheets in its wake. Wing theory shows that winglets can reduce the kinetic energy left in the vortex sheets, and hence the induced drag, by spreading vorticity both horizontally and vertically. 3. This paper describes the aerodynamic forces on a wing made of a base wing and different wing tips. The feathered wing tip was slotted and was made of four primary feathers from a Harris9 hawk (Parabuteo unicinctus). The Clark Y tip was unslotted and was made of balsa wood shaped to a Clark Y aerofoil. The balsa feather tip was slotted and was made of three balsa wood wings shaped like feathers. 4. The base wing in a wind tunnel at an air speed of 12.6 m s-1 generated upwash angles as high as 15° at the end of the wing when the angle of attack of the wing was 10.5°. The feathered tip responded to upwash by increasing its lift to drag ratio (L/D) by 107 %, from 4.9 to 10.1, as the angle of attack of the base wing increased from 4° to 14°. The L/D values of the balsa feather tip and the Clark Y tip increased by 49 % and 5 %, respectively, for the same change in angle of attack. 5. With the angle of attack of the base wing fixed at 13°, changing the angle of attack of the wing tip changed the drag of the base wing. The drag of the base wing increased by 25 % as the angle of attack of the Clark Y tip increased from 0° to 15°. The base wing drag decreased by 6 % for the same change in the angle of attack of the feathered tip. 6. The total drag of the wing with the feathered tip was 12 % less than that of a hypothetical wing with the same lift and span, but with tip feathers that did not respond to upwash at the end of the base wing. This value is consistent with wing theory predictions on drag reduction from winglets. 7. Wings with the tip and the base wing locked together had lift and drag that increased with increasing base wing angle of attack, as expected for conventional wings. Span factors were calculated from these data - a large span factor indicates that a wing has low induced drag for a given lift and wing span. The wing with the Clark Y tip had a span factor that decreased from 1 to 0.75 as the angle of attack of the base wing increased. Over the same range of angle of attack, the span factor of the wing with the feathered tip remained constant at 0.87. As the angle of attack of this wing increased, aerodynamic forces spread the feathers vertically to form slots. With fully formed slots, the wing had a higher span factor than the wing with the unslotted Clark Y tip. 8. Flow visualization with helium-filled bubbles showed that the addition of two winglets to the tip of a model wing spread vorticity both horizontally and vertically in the wake of the tip. 9. These observations taken together provide strong evidence that the tip slots of soaring birds reduce induced drag in the sense that the separated tip feathers act as winglets and increase the span factor of the wings.

Gliding birds: reduction of induced drag by wing tip slots between the primary feathers

On Making Things the Best-Aeronautical Uses of Optimization

Winglets, which are small, nearly vertical, winglike surfaces, substantially reduce drag coefficients at lifting conditions. The primary winglet surfaces are rearward above the wing tips; secondary surfaces are forward below the wing tips. This report presents a discussion of the considerations involved in the design of the winglets; measured effects of these surfaces on the aerodynamic forces, moments, and loads for a representative first generation, narrow body jet transport wing; and a comparison of these effects with those for a wing tip extension which results in approximately the same increase in bending moment at the wing-fuselage juncture as did the addition of the winglets.

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A design approach and selected wind tunnel results at high subsonic speeds for wing-tip mounted winglets

Comparisons have been made of the shock phenomena and drag-rise increments for representative wing and central-body combinations with those for bodies of revolution having the same axial developments of cross-sectional areas normal to the airstream. On the basis of these comparisons, it is concluded that near the speed of sound the zero-lift drag rise of a low-aspect-ratio thin-wing and body combination is primarily dependent on the axial development of the cross-sectional areas normal to the airstream. It follows that the drag rise for any such configuration is approximately the same as that for any other with the same development of cross-sectional areas. Investigations have also been made of representative wing-body combinations with the body so indented that the axial developments of cross-sectional areas for the combinations were the same as that for the original body alone. Such indentations greatly reduced or eliminated the zero-lift drag-rise increments associated with the wings near the speed of sound.

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A study of the zero-lift drag-rise characteristics of wing-body combinations near the speed of sound

An airfoil having an upper surface shaped to control flow accelerations and pressure distribution over the upper surface and to prevent separation of the boundary layer due to shock wave formulation at high subsonic speeds well above the critical Mach number. A highly cambered trailing edge section improves overall airfoil lifting efficiency.

Richard T. Whitcomb

Papers

A design approach and selected wind tunnel results at high subsonic speeds for wing-tip mounted winglets

A study of the zero-lift drag-rise characteristics of wing-body combinations near the speed of sound

Airfoil shape for flight at subsonic speeds

Fuselage shaping to reduce the strength of shock waves about airplanes at transonic and supersonic speeds

Apparatus for reducing exhaust gas pressure in internal combustion engines