Lift-induced drag

About: Lift-induced drag is a research topic. Over the lifetime, 2861 publications have been published within this topic receiving 41094 citations.

A theory of the jet flap in three dimensions

Abstract: The treatment of two-dimensional jet-flapped wings in incompressible flow by the methods of thin-aerofoil theory given by one of the authors (Spence 1956) has been extended to the case of a thin wing of finite aspect ratio which possesses a deflected jet sheet of zero thickness emerging with a small angular deflexion at its trailing edge. The restriction is imposed that the streamlines of the jet flow lie in planes perpendicular to the wing-span, transverse momentum-transport being thus excluded. As in classical theories, the downwash field is assumed to arise from elementary horseshoe vortices proportional in strength to the local lift distribution; a new feature is the ability of the sheet formed by these elements to sustain a pressure difference on account of the longitudinal flux of momentum of the jet within it. The induced downwash w i ( x, y ) in the plane z = 0 at intermediate distances x from the wing cannot be calculated, and is therefore replaced by an interpolation formula having the correct values U ∞ α i at the wing and U ∞ α i ∞ far downstream. To ensure that the errors so introduced are small the aspect ratio A must be large, its permissible minimum increasing with the jet momentum coefficient C J . Two methods of interpolating to w i ( x, y ), both of which lead within close limits to the same expression for C L , are discussed. They are chosen so as to allow the two-dimensional equation for loading, whose solution is known, to be used to calculate the loading in a streamwise section in three dimensions. The spanwise variation of loading could be calculated for arbitrary planforms and jet-momentum distributions, but the present paper is confined to the case in which the loading and downwash distribution depend only on x/c , where x measures distance from the leading edge and c ( y ) is the local chord. This is shown to require both c and the jet-momentum flux per unit span to be elliptically distributed, the deflexion τ and incidence a being constant over the span. The relation between the coefficients of induced drag and lift is then C D i = C (2) L /( πA + 2 C J ) induced drag being defined as the difference between the thrust and the (constant) flux of momentum in the jet. (The interpolations for induced downwash are not used in deriving this relation.) The ratio of C L to the value C (2) L which it would have in two dimensions is C L / C (2) L = { A + (2/π) C J } / { A + 2/π ) (∂ C (2) L /∂α) - 2(1+ σ)}, where ∂ C (2) L /∂α is the two-dimensional derivative of lift with respect to incidence, a known function of C J and σ = 1 — α i /(½ α i ∞ ). An expression for σ is found in terms of known quantities by equating the induced drag calculated from the detailed forces on the wing to that given above. The results have been compared with experimental measurements made on an 8:1 elliptic cylinder of rectangular planform at aspect ratios 2⋅75, 6⋅8 and infinity. Remarkably close agreement with observed values of C L is obtained in all cases, and the difference C D — C Di = C D 0 , say, between the total- and induced-drag coefficients, is virtually independent of the aspect ratio. C D 0 represents the effects of the Reynolds number, section shape and jet configuration, which are excluded from the present theory.

Effects of Sideslip on the Aerodynamics of Low-Aspect-Ratio Low-Reynolds-Number Wings

Abstract: The growing interest in micro aerial vehicles has brought attention to the need for an improved understanding of the aerodynamics of low-aspect-ratio wings at lowReynolds numbers. In this study, flat plate wings with rectangular and tapered planforms were fabricated with aspect ratios of 0.75, 1, 1.5, and 3, and the aerodynamic loading was measured at Reynolds numbers between 5 10 and 1 10. Surface tuft visualization was used to observe the interactions between the tip vortices and the leading-edge vortex. The tests were initially conducted at a sideslip angle of 0 and were then repeated for 10, 20, and 35 with and without winglets. Measurements made with a sixcomponent force balance showed that a decrease in aspect ratio caused an increase in stall and CLmax due to the nonlinear lift induced by the interacting flow on the upper wing surface. In addition, the detachment of tip vortices after stall leads to a sudden decrease in drag coefficient as the magnitude of the induced drag drops significantly. At increasing sideslip angles, the effects of the crossflow still contribute to an increase in lift but significantly reduce the pitching moment about the quarter-chord, thus decreasing the wing’s ability to recover from angle-of-attack perturbations. These results show that, while the effects of tip vortices and the leading-edge vortex complicate the flowfield around a low-aspect-ratio wing, particularly at increased sideslip angles, their impact tends to improve the aerodynamic performance.

Flight in Drosophila

Abstract: 1. The variation of the lift and drag of fruit-fly wings with angle of attack and velocity was compared with that of thin plates. 2. High drag and low ratios of lift to drag characterized these airfoils, the primary difference being the absence of stalling in the fly wings. 3. Flow photographs and determinations of stall point on thin plates suggested that the fly wing behaves as if encountering a Reynolds number below the actual value. 4. At positive angles of attack camber improved the aerodynamic characteristics of fly wings; at negative angles uncambered wings were superior. 5. The structural basis for the performance of fly wings and the relationship of their characteristics to their opening conditions are discussed.

Peak-Seeking Control for Drag Reduction in Formation Flight

Abstract: Formation flight is a known method of improving the overall aerodynamic efficiency of a pair of aircraft. In particular, one craft flying in the correct position in the vortex wake of another can realize substantial reductions in drag, with the amount of the reduction dependent on the relative positions of the two craft. This paper looks at such a pair, with one craft flying behind and to the side of the lead plane. The precise position of the second craft relative to the first to maximize the drag reduction is to be determined online, leading to a peak-seeking control problem. A new method of speak-seeking control, using a Kalman filter to estimate the characteristics of the drag reduction, is derived and discussed. A simple model of the two-plane formation using horseshoe vortices is defined, and the peakseeking controller is applied to this model. The method is demonstrated in simulation using this simplified model. S an airplane flies, it causes an upwash ahead of the wing and leaves a wake behind. This wake is characterized by the downwash behind the wing and by an accompanying upwash in the area on either side of the downwash region. By flying in the area of upwash, a second aircraft can gain a substantial efficiency boost because of the reduction in induced drag it will experience. This leads to the well-known fact that two aircraft flying in an appropriate formation can achieve overall efficiency much greater than were they flying separately. 1 This effect is analyzed using inviscid aerodynamic assumptions and lifting-line theory in Ref. 2, where it is noted that the effects were considered by Munk as early as 1919. The theory was put to test in actual aircraft by Hummel, 3 who established a fifteen per cent reduction on the second of a pair of civilian aircraft. Because of the gains in efficiency, formation flight has been investigated as a way of increasing the range and duration of autonomous aerial vehicles. In Refs. 4 and 5, formations of several aircraft are considered, with the object of creating a solar-powered formation that could cruise at high altitude for arbitrarily long times. In Ref. 4, decentralized controllers are derived for a formation of five highaspect-ratio craft and are shown to be capable of maintaining a prescribed formation despite the nonlinear, destabilizing moments induced on each plane by the aircraft ahead of it in the formation. The formation maintenance problem for a pair of F-16 class aircraft is considered in Ref. 6, though that paper relegates the rolling moments on the trailing craft to an inner-loop controller and considers only the lift and side force in designing an autopilot for the trailing plane. In this paper, only a pair of aircraft is considered. The two craft can be thought of as a leader and a follower. The leader flies straight

Wingtip-Mounted Propellers: Aerodynamic Analysis of Interaction Effects and Comparison with Conventional Layout

Abstract: Wingtip-mounted propellers installed in a tractor configuration can decrease the wing induced drag by attenuating the wingtip vortex by the propeller slipstream. This paper presents an aerodynamic analysis of the propeller-wing interaction effects for the wingtip-mounted propeller configuration, including a comparison with a conventional configuration with the propeller mounted on the inboard part of the wing. Measurements were taken in a low-speed wind tunnel at Delft University of Technology, with two wing models and a low-speed propeller. Particle-image-velocimetry measurements downstream of a symmetric wing with integrated flap highlighted the swirl reductions characteristic of the wingtip-mounted propeller due to wingtip-vortex attenuation and swirl recovery. External-balance and surface-pressure measurements confirmed that this led to an induced-drag reduction with inboard-up propeller rotation. In a direct comparison with a conventional propeller-wing layout, the wingtip-mounted configuration showed a drag reduction of around 15% at a lift coefficient of 0.5 and a thrust coefficient of 0.12. This aerodynamic benefit increased upon increasing the wing lift coefficient and propeller thrust setting. An analysis of the wing performance showed that the aerodynamic benefit of the wingtip-mounted propeller was due to an increase of the wing's effective span-efficiency parameter.