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.

On the far wake and induced drag of aircraft

Abstract: A set of matched asymptotic expansions is proposed for the flow far behind an aircraft, with the primary purpose of identifying lift, thrust and drag, particularly induced drag, in a unified manner in integral statements of the momentum equation. The fluid in the far wake is inviscid and incompressible, and variations of total pressure are allowed, as are vortex sheets. A notable feature is that the Trefftz-plane approximation is not invoked; instead the wake is taken as fully rolled-up, and the analysis proceeds without the assumption of light loading. Attention is paid to the absolute convergence of integrals over infinite domains and handling of discontinuities. The expansion includes a sink term, which appears new, so that the mass flux through a transverse plane is non-zero, as is the flux of mechanical energy. The lift can be formally attributed to the velocity induced by the bound vortex of the wing, which is at odds with some treatments, although consistent with Prandtl's analysis over a ground plane. The drag contains the integral of ρ(v2 + w2 − u2)/2, as in many treatments of the subject, u being the perturbation velocity along the wake. The negative sign for u2 appears paradoxical on two counts, one of which is resolved here. First, its very presence instead of the + sign, which would lead to the perturbation kinetic energy and therefore a compelling explanation of induced drag, is explained by the longitudinal energy flux. This energy, the integral of ρu2, is continuously provided by the unsteady starting-vortex system and was deposited earlier by the aircraft. Second, it appears that negative drag could be predicted by this equation. This is shown to be impossible, because of inequalities between the integrals of (v2 + w2) and of u2, but the proof is valid only if the vorticity is of only one sign on each side. A general proof of positivity has not been derived, because of nonlinearities, but neither has a counter-example.

Variable-complexity aerodynamic optimization of an HSCT wing using structural wing-weight equations

Abstract: A new approach for combining conceptual and preliminary design techniques for wing optimization is presented for the high-speed civil transport (HSCT). A wing-shape parametrization procedure is developed which allows the linking of planform and airfoil design variables. Variable-complexity design strategies are used to combine conceptual and preliminary-design approaches, both to preserve interdisciplinary design influences and to reduce computational expense. In the study, conceptual-design-level algebraic equations are used to estimate aircraft weight, supersonic wave drag, friction drag and drag due to lift. The drag due to lift and wave drag are also evaluated using more detailed, preliminary-design-level techniques. The methodology is applied to the minimization of the gross weight of an HSCT that flies at Mach 3.0 with a range of 6500 miles.

Numerical method to calculate the induced drag or optimum loading for arbitrary non-planar aircraft

Abstract: A simple unified numerical method applicable to non-planar subsonic aircraft has been developed for calculating either the induced drag for an arbitrary loading or the optimum aircraft loading which results in minimum induced drag. The method utilizes a vortex lattice representation of the aircraft lifting surfaces coupled with the classic equations and theorems for computing and minimizing induced drag. Correlation of results from the numerical method with non-planar solutions obtained from other more complex theories indicates very good agreement. Comparison of the induced-drag computations using the numerical method with experimental data for planar and non-planar configurations was also very good.

Supercritical airfoil drag reduction by passive shock wave/boundary layer control in the Mach number range .75 to .90

Abstract: Airfoils operating in the transonic region are subject to large increases in drag due to shock wave/boundary layer interactions. The concept of passive shock wave/boundary layer control seeks drag reduction by placing a thin cavity with a porous top surface at the airfoil chordwise position where a shock wave would normally occur. The higher pressure behind the shock wave circulates flow through the cavity to the lower pressure ahead of the shock wave. The effects from this circulation prevent boundary layer separation and reduce entropy increases through the shock wave. In this investigation this concept is studied at a freestream Mach number range of .75 and .90. The Mach number distributions over the model, the wake impact pressure surveys used to determine profile drag and schlieren photographs for 2.8 percent porosity and solid airfoil cases are presented and compared. Results indicate that the profile drag coefficient can be reduced by as much as 40 percent through the use of this passive drag control system.

Vorticity cancellation at trailing edge for induced drag elimination

Abstract: Wing tip vortices are evident from airliner vapor trails, and helicopter blade slap. Elliptically loaded high aspect ratio tapered wings have minimum induced drag but cannot eliminate it. Different methods are disclosed herein, for upper and lower surface boundary layers to cancel their opposing vorticity upon shedding from the trailing edge, thereby eliminating wake vorticty, induced drag and associated noise. This requires wing-rotor-propeller or fan blades with a platform designed for uniform bound circulation and with boundary layer control near the tip. In addition this requires special techniques to counter span-wise pressure gradients, such as tip circulation control blowing or an upwind small propeller or wind turbine on each tip. These techniques can eliminate wake vorticity with its induced drag, noise, flying on the backside of the power curve and the option for asymmetric loading by pneumatic means to eliminate need for cyclic pitch control or conventional ailerons.