Showing papers on "Lift-induced drag published in 2004"

The role of drag in insect hovering.

Abstract: SUMMARY Studies of insect flight have focused on aerodynamic lift, both in quasi-steady and unsteady regimes. This is partly influenced by the choice of hovering motions along a horizontal stroke plane, where aerodynamic drag makes no contribution to the vertical force. In contrast, some of the best hoverers– dragonflies and hoverflies – employ inclined stroke planes, where the drag in the down- and upstrokes does not cancel each other. Here, computation of an idealized dragonfly wing motion shows that a dragonfly uses drag to support about three quarters of its weight. This can explain an anomalous factor of four in previous estimates of dragonfly lift coefficients, where drag was assumed to be small. To investigate force generation and energy cost of hovering flight using different combination of lift and drag, I study a family of wing motion parameterized by the inclined angle of the stroke plane. The lift-to-drag ratio is no longer a measure of efficiency, except in the case of horizontal stroke plane. In addition, because the flow is highly stalled, lift and drag are of comparable magnitude, and the aerodynamic efficiency is roughly the same up to an inclined angle about 60°, which curiously agrees with the angle observed in dragonfly flight. Finally, the lessons from this special family of wing motion suggests a strategy for improving efficiency of normal hovering, and a unifying view of different wing motions employed by insects.

Plasma Flaps and Slats: An Application of Weakly Ionized Plasma Actuators

Abstract: The experimental validation of an application of weakly-ionized plasma actuators for improved aerodynamic performance of multi-element wings and wings with movable control surfaces is presented. Two spanwise arrays of plasma actuators, configured to produce a wall-jet effect, were applied on the suction surface of a two-dimensional NACA 0015 wing model, one at the leading edge and the other near the trailing edge to mimic the effects of a wing leading-edge slat and a trailing-edge flap, respectively. Flow control tests were conducted at chord Reynolds numbers, corrected for blockage, of 0.217 x 10 6 and 0.307 x 10 6 in a low-speed wind tunnel at the University of Notre Dame. The leading-edge-separation control resulted in an increase in both the maximum lift coefficient and the stall angle of attack and a lift-to-drag improvement of as much as 340%. An optimum frequency was found to exist for unsteady excitation of the leading-edge separation. Under this condition, the power to the actuator was estimated to be only 2 W. The trailing-edge actuator was found to produce the same effect as a plain trailing-edge flap. This included a uniform shift at all angles of attack of the lift coefficient and a shift toward higher lift coefficients of the drag bucket. In addition, there was a slight decrease in the minimum drag coefficient. The obvious advantages of this approach are its simplicity, as there are no moving parts, and its lack of hinge gaps, which add drag. An example of their use as ailerons for roll control produces a comparable roll moment coefficient to a sample general aviation aircraft.

Aerodynamic forces of revolving hummingbird wings and wing models

Abstract: A central challenge to the study of animal aerodynamics has been the measurement of forces generated by flapping wings. Relative to wings of other birds, hummingbird wings are of particular interest in that the smaller species operate in more viscous regimes (5000 < Re < 10 000) for which substantial drag and reduced lift:drag coefficients might be expected. Lift and drag forces were measured on mounted hummingbird wings and wing models spinning in continuous tipwise revolution about the wing base. Lift coefficients tended to increase as wing models became more realistic (i.e. with sharpened leading edges and with substantial camber). Lift:drag ratios of real wings were substantially higher than those of wing models, suggesting morphological contributions of feathers to lift enhancement and drag reduction. At Re= 5000, high values of the lift:drag ratio (8–16) at low angles of attack suggest that wings of hummingbirds are exceptionally good at producing lift.

Structure and induced drag of a tip vortex

Abstract: The three-dimensional flow structure of a tip vortex in the near wake of both a rectangular, square-tipped NACA 0015 airfoil and a high-lift cambered airfoil was investigated by using a seven-hole pressure probe at Re = 2.01 x 10 5 . Lift-induced drag was computed based on vorticity and was compared with force-balance data. For both the airfoils tested, the vortex strength reached a maximum immediately behind the trailing edge and remained nearly constant up to two chord lengths downstream. As the airfoil incidence increased, the increase in the lift force resulted in a basically linear increase in the vortex strength and the peak values of the tangential velocity and vorticity, whereas the vortex radius did not appear to have a clear dependence on the vortex strength. Depending on the airfoil incidence, the core axial velocity could be wake-like or jet-like. The normalized circulation within the inner region of the nearly axisymmetric tip vortex exhibited a universal, or self-similar, structure. The NACA 0015 airfoil, however, possessed smaller tangential velocities but similar vortex core diameters compared to those of a cambered airfoil

HELIPLAT: Design, aerodynamic, structural analysis of long-endurance solar-powered stratospheric platform

Abstract: This paper presents the design and manufacture of the first European Very Long-Endurance Stratospheric Unmanned Air Vehicle, HeliPlat® (HELIos PLATform). This vehicle is a monoplane with eight brushless motors, a twin-boom tail type and two rudders. A computer program has been developed to carry out the platform design. To minimize airframe weight, high modulus carbon fibre composite material has been used extensively. Airfoil coordinates and wing planform have been optimized in order to achieve the best possible aerodynamic efficiency by using integral panel/boundary-layer methods and also to obtain the minimum possible induced drag with respect to local Reynolds airfoil. To this effect, several wind-tunnel tests were carried out so as to compare the analytically predicted airfoil performances. After an initial configuration had been worked out, a scale technological demonstrator (wing span 24 m) was designed, manufactured, and tested under shear, bending, and torsion loads. Finite element analysis was also carried out in order to predict the static and dynamic behaviour of both the full-size and scale model versions of the HeliPlat structure. The preliminary static test resulted in a high correspondence.

Comparison of Predicted and Measured Formation Flight Interference Effects

Abstract: Results from a wind-tunnel test of two delta-wing aircraft in close proximity are presented and compared with predictions from a vortex lattice method. Large changes in lift, pitching moment, and rolling moment are found on the trail aircraft as it moves laterally relative to the lead aircraft. The magnitude of these changes is reduced as the trail aircraft moves vertically with respect to the lead aircraft. Lift-to-drag ratio of the trail aircraft is increased when the wing tips are slightly overlapped. Wake-induced lift is overpredicted slightly when the aircraft overlap in the spanwise direction. Wake-induced pitching and rolling moments are well predicted. A maximum induced drag reduction of 25% is measured on the trail aircraft, compared with a 40% predicted reduction. Three positional stability derivatives, change in lift and pitching moment with vertical position and change in rolling moment with lateral position, are studied. Predicted boundaries between stable and unstable regions were generally in good agreement with experimentally derived boundaries.

Aerodynamic and Aeroelastic Considerations of A Variable- Span Morphing Wing

Abstract: Morphing concepts for air vehicles such as unmanned air vehicles (UAVs) have been a topic of current research interest in aerospace engineering. A morphing wing is a bird-like wing that has the ability of adapting to obtain better flight performance. One concept of morphing is the variable-span morphing wing (VSMW) in which the wingspan is varied to accommodate multiple flight regimes. In the present study, the advantages and disadvantages of a VSMW for a cruise type missile are discussed. The aerodynamic characteristics and the range of this morphing wing are analyzed as its wingspan is changed. The results of the analysis demonstrate an improvement in the aerodynamic characteristics of the VSMW, in the form of a reduction in the induced drag, resulting in an increase in range. As further discussed, the VSMW also provides an alternative method of controlling the roll motions of a bank-to-turn cruise missile. Compared to conventional roll control the variable span method provides an increase in roll control authority. Unfortunately, the aeroelastic characteristics of the VSMW become worse because the wing-root bending moment increases due to the wingspan increase.

An Experimental Study of Drag Reduction Devices for a Trailer Underbody and Base

Abstract: *† th scale generic tractor-trailer model at a width-based Reynolds number of 325,000. The model is fixed to a turntable, allowing the yaw angle to be varied between ±14 o in 2 o increments. Various add-on drag reduction devices are mounted to the model underbody and base. The wind-averaged drag coefficient at 65 mph is computed for each configuration, allowing the effectiveness of the add-on devices to be assessed. The most effective add-on drag reduction device for the trailer underbody is a wedge-shaped skirt, which reduces the wind-averaged drag coefficient by 2.0%. For the trailer base, the most effective add-on drag reduction device is a set of curved base flaps having a radius of curvature of 0.91 times the trailer width. These curved base flaps reduce the wind-averaged drag coefficient by 18.8%, providing the greatest drag reduction of any of the devices tested. When the wedge-shaped skirt and curved base flaps are used in conjunction with one another, the wind-averaged drag coefficient is reduced by 20%.

Drag Prediction for Blades at High Angle of Attack Using CFD

Abstract: In the present paper it is first demonstrated that state of the art 3D CFD codes are capable of predicting the correct dependency of the integrated drag of a flat plate placed perpendicular to the flow. This is in strong contrast to previous 2D investigations of infinite plates, where computations are known to severely overpredict drag. We then demonstrate that the computed drag distribution along the plate span deviate from the general expectation of 2D behavior at the central part of the plate, an important finding in connection with the theoretical estimation of drag behavior on wind turbine blades. The computations additionally indicate that a tip effect is present that produces increased drag near the end of the plate, which is opposite of the assumptions generally used in drag estimation for blades. Following this several wind turbine blades are analysed, ranging from older blades of approximately 10 meter length (LM 8.2) over more recent blades (LM 19.1) around 20 meters to two modern blades suited for megawatt size turbines. Due to the geometrical difference between the four blades, the simple dependency on aspect ratio observed for the plates are not recovered in this analysis. The turbine blades behave qualitatively very similar to the flat plates and the spanwise drag distributions show similar tip effects. For the turbine blades this effect is even more pronounced, because the tapering of the blades makes the tip effect spread to a larger part of the blades. The findings are supported by visualizations of the wake patterns behind the blades.

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.

Cross flow vortex trap device and method for reducing the aerodynamic drag of ground vehicles

Abstract: An improved method and device for the reduction of aerodynamic drag and for improved performance of multiple component vehicles by reducing the pressure on the front face of the trailing vehicle or vehicle component by controlling the flow in the gap between the leading vehicle component and the trailing vehicle component. An improved method and device for generating a reduction in the drag force on a bluff face object moving through air. The apparatus consist of a plurality of forward extending surfaces that are positioned adjacent to one another on the forward facing surface of a bluff face object and are aligned parallel to the object center line and perpendicular to the local flow direction. The reduction in drag force results from the summation of a plurality of local reductions in drag force generated by the interaction of vortex structures emanating from the leading edges of the plurality of forward extending surfaces with the forward facing surface of a blunt face object. The objects and advantages also extend to other applications in which an object or vehicle is moving through either a gas or fluid.

Computational Modeling of the Unsteady Wake behind Gurney-Flaps

Abstract: The effect of small micro-tabs (Gurney-flaps) mounted at the lower trailing edge of a HQ17 airfoil has been studied using numerical simulation. The focus of attention has been placed on the unsteady flow structures in the wake of the Gurney-flap, as these are responsible for increased induced drag. At a Reynolds number of 106, the flow is investigated using steady and unsteady simulations based on the Reynolds-averaged Navier-Stokes equations (URANS) as well as Detached Eddy Simulations (DES). In order to reduce the occuring unsteady flow structures, further simulations have been performed using alternative trailing edge shapes. The results show that the unsteadyness can successfully be suppressed and the drag can be reduced substantially using advanced flap concepts.

Ideal Aerodynamics of Ground Effect and Formation Flight

Abstract: The theoretical induced-drag benefits are presented for ideally loaded wings flying in formation and ground effect. An optimum-downwash approach using a vortex-lattice implementation was used to study formations of wings loaded optimally for minimum induced drag with roll trim. An exact approach was also developed to examine the drag of elliptically loaded wings in formation. The exact approach allows for decomposition of the benefits by considering the mutual-interference contributions from different pairs of wings in a formation. The results show that elliptically loaded wing formations have nearly the same drag as optimally loaded wing formations. For a formation of planar wings, in or out of ground effect, the optimum lateral separation corresponds to a 10% span overlap of wing tips. At this optimum lateral separation, a formation of 25 elliptically loaded wings flying out of ground effect experiences an 81% drag reduction compared to 25 wings flying in isolation. For large formations, in or out of ground effect, multiple local optima are seen for the lateral separation. Large formations experience small additional benefits caused by ground effect even at relatively large ground clearances of four wing spans. The shape of vee formations, for equipartition of drag benefits, is found to be nearly independent of flight in or out of ground effect.

Analysis and design of wings and wing/winglet combinations at low speeds

Abstract: Numerical treatment in Prandtl lifting-line theory of the nonlinearity associated with a 2-D lift curve, when the local incidence is larger than the incidence of maximum lift, is proposed. It is shown that the use of an artificial viscosity term makes the solution unique and allows the iterative method to converge to a physically meaningful solution, that is in agreement with the exact solution for the test case. The design and analysis of winglets is presented. The winglets considered are small fences placed upward at the tip of the wing to improve the wing efficiency by decreasing the induced drag. The effect of yaw on a wing equipped with such optimal winglets indicates that they provide weathercock stability.

Effects of Auxiliary Lift and Propulsion on Helicopter Vibration Reduction and Trim

Abstract: This paper examines the vibration reductions caused by the introduction of auxiliary lift and propulsion, individually, as well as in combination, on a light [5800-lb (2640 kg)] helicopter with a four-bladed hingeless rotor, at flight speeds close to the maximum cruise velocity of the baseline helicopter. The changes in trim (vehicle orientations and control settings) because of auxiliary lift and propulsion are also examined in detail, and the fundamental mechanisms that produce the changes in trim and associated vibration reductions are identified. Based on results using a comprehensive aeroelastic analysis, it was concluded that auxiliary lift, alone, produces relatively small reductions in vibration. On the other hand, significant vibration reductions were obtained through auxiliary propulsion alone. A combination of lift and propulsion was most effective and reduced the vibration index by over 90%. It was also observed that auxiliary lift significantly reduces the main rotor thrust but increases the nose-down pitch attitude and tip-path-plane forward tilt to provide the required propulsive force. This increases the downwash through the rotor disk and requires a larger rotor longitudinal cyclic pitch input. In contrast, auxiliary propulsion that minimizes vibration produces little reduction in main rotor thrust, but results in a slightly nose-up pitch attitude (the auxiliary propulsion exceeds vehicle drag) along with a backward tilt of the tip-path plane. This decreases the downwash through the rotor disk and requires a smaller rotor longitudinal cyclic pitch input. A combination of auxiliary lift and propulsion minimizes vibration results in an even larger backward tilt of the tip-path plane and a net upwash through the rotor disk. The rotor collective pitch undergoes little change as a result of auxiliary lift, even though the main rotor thrust is decreased. In contrast, for auxiliary propulsion it decreases significantly even though the rotor thrust undergoes only small reductions. This counterintuitive observation is explained. The reduced downwash with auxiliary propulsion, or upwash with combined lift and propulsion, puts the rotor in a partial autorotation state, drastically reducing the induced drag, main rotor torque, and power. Auxiliary lift produces modest reductions in main rotor power, primarily because of a reduced profile drag associated with lower rotor loading. Because the rotor loading is lower with auxiliary lift than with auxiliary propulsion, but larger vibration reductions are produced with the latter, it can be deduced that vibration reductions are less a result of “unloading” of the rotor per se and more because of overall changes in trim, especially the reduction in longitudinal cyclic pitch (seen with auxiliary propulsion).

Toward blade-tip vortex simulation with an actuator-lifting surface model

Abstract: This paper presents a new method based on the imposition of velocity discontinuities to model °ow perturbation due to existence of vortical structures. The proposed method uses actuator disk and lift- ing line concepts in order to provide a framework of analysis that respects conservation laws for mo- mentum, energy and vorticity, which is not the case of classical actuator disk methods used in the wind industry. The °oweld is described by the Euler equations. In the proposed mathematical model, the attitude toward °ow determination is entirely linked to the vorticity structure of the °ow, which is modeled by velocity discontinuities. Results are produced for three basic problems of interest : 2D uniform vorticity distribution, actuator disk with uniform loading andnite wing with prescribed dis- tribution of circulation. These cornerstone prob- lems have shown that numerical method gives fairly precise values regarding °ow streamlines, lift and induced velocities predictions for all problems in- vestigated. Induced drag prediction for thenite wing problem could not be measured since proper grid-independent solution to this problem could not be attained.

Undercarriage flow control device and method for reducing the aerodynamic drag of ground vehicles

Abstract: An improved method and device for the reduction of aerodynamic drag and for improved performance of ground vehicles by increasing the pressure on the base area of a bluff-base ground vehicle or vehicle component by conditioning the undercarriage flow and controlling the discharge of the undercarriage flow into the trailing wake of a ground vehicle. The subject invention provides an improved method and device for generating a reduction in the drag force on a bluff-base object moving through air. The apparatus consists of aerodynamically shaped surfaces that are attached to the undercarriage of a vehicle between the base area and the aft most set of wheels. The surfaces are shaped and positioned such that they may be combined with the vehicle lower surface and the ground to form a nozzle with the smallest opening located at the aft end of the vehicle and the largest opening located forward of the smallest opening. The largest opening has a width that is equivalent to the width of the vehicle and has a height that is approximately equal to the distance between the vehicle lower surface and the ground. The smallest opening is located at the base of the vehicle and has an area and shaped opening to maximize the discharge of the undercarriage flow into the wake. The surfaces that comprise the invention are aerodynamically shaped to minimize separation of the flow passing through the device and on the outer surface of the device and at the same time, to increase the momentum for the flow passing through the device and to entraining additional air externally to the device. The reduction in drag force results from the increase in pressure acting on the base area of the vehicle. The increase in base pressure is a result of the increase in wake energy and reduction in the unsteady wake flow due to the addition of the high momentum undercarriage flow into the wake. The objects and advantages also extend to other applications in which an object or vehicle is moving through either a gas or fluid.

Low drag submerged asymmetric displacement lifting body

Abstract: Low drag underwater submerged lifting bodies which can be used as underwater displacement portions of a vessel whose main hull is at sea level are asymmetrical and have improved lift to drag ratios. The lifting bodies have outer surfaces whose shapes are defined in plan and elevation by generally parabolic curves which are different on opposite sides of the lifting bodies.

Numerical Winglet Optimization

Abstract: A method is presented to optimize the orientation of a winglet on a wing and include the effects of profile drag in addition to induced drag. The method use s the output from four potential -flow solutions in the Trefftz plane well behind the lifting surfaces. The four solutions are a baseline, an angle -of -attack increment, an increment in the root incidence of the winglet, and an increment in the tip incidenc e of the winglet. Results for the case studied show small differences in the root and tip incidences between an induced -drag -only solution and one with profile drag included. Nomenclature

Apparatus and method for reducing induced drag on aircraft and other vehicles

Abstract: A method and apparatus for varying the washout of a wing such that induced drag is minimized during a flight. The washout is varied pursuant to an optimized twist distribution that depends on the wing planform and an optimized twist amount which depends, at least in part, upon the operating conditions, including those parameters used to determine the lift coefficient. The optimum twist may be employed by geometric or aerodynamic twist, including full spanwise control surfaces used to simultaneously provide roll control, high-lift and minimum induced drag. The optimum twist may also be employed be twisting just a portion of the wing or the entire wing, either geometrically or aerodynamically.

Fundamental Study of Aerodynamic Drag Reduction for Vehicle with Feedback Flow Control

Abstract: The present paper deals with a fundamental study of aerodynamic drag reduction for a vehicle with a feedback flow control. As the first step, two-dimensional calculation was performed for a flow around a simplified vehicle model. The mechanism of unsteady drag was investigated in relation to the vortex shedding from the model. The location of the control flow nozzle was so determined that the control flow influences the drag most effectively. The key in designing the present feedback control is the definition of the output signal. Based on the physical consideration of the drag generation, the location of the output velocity measurement was changed within a limited region near the front windshield. A systematic calculation revealed that the output signal defined in a small region results in a significant drag reduction of 20% with respect to the case without control. The present feedback flow control is generally applicable to the drag reduction of the bluff body for which the drag is generated under the same mechanism of essentially two-dimensional vortex shedding.

Drag Minimization Through the Use of Mission Adaptive Trailing Edge Flaps and Fuel State Control

Abstract: The paper presents a methodology for minimizing total drag of a high-altitude, long endurance reconnaisance vehicle across its mission by optimal scheduling of flaps and fuel pumping. The methodology accounts for profile and induced drag and includes the effects to drag of trimming the vehicle. The use of conventional, rigidarticulating flaps are considered, in addition to conformal flaps which provide a smooth, continuous camber change and allow for flap twisting. Numerical results are demonstrated on a Lockheed Martin SensorCraft concept that is characterized by a 30 degree wing sweep, a fuel fraction of nearly 60 %, and a constant altitude cruise in which CL varies roughly from 0.5 to 1.2. The results have shown that significant reductions in drag can be achieved with optimal scheduling of flaps and fuel pumping. Drag predictions have been translated to mission range through integration of the Breguet range equation. Results show that between a 5 and 15 % increase in range can be achieved.

An Approach to Induced Drag Reduction and its Experimental Evaluation

Abstract: An approach to minimize the induced drag of an aeroelastic configuration by means of multiple leading and trailing edge control surfaces is investigated. A computational boundary-element model is c ...

Community Noise Considerations in Multidisciplinary Optimization for Preliminary Design of Innovative Configurations

Abstract: The paper proposes an approach for MDO/PD (Multi‐Disciplinary Optimization for Preliminary Design) of innovative aircraft configurations in the presence of aeroacoustics considerations. The specific innovative configuration of interest here is a box‐wing aircraft denoted as the Prandtl-Plane, which has, as a distinguishing feature, a low induced drag. Thus, one of the advantages is less noise at take-o. Hence here, as a very first step towards our long range goal, we apply the algorithm to the optimization of the Prandtl-Plane with the objective function modified by adding an empirical term representative of the take-o noise. The fact that the configurations are innovative requires that the formulation be first‐principle based, since in this case the designer cannot rely upon past experience. The mathematical model used is reviewed. The formulation is based upon an integrated modeling of structures, aerodynamics, aeroelasticity and flight mechanics developed primarily by the authors. The methodology is geared specifically towards MDO/PD for civil aviation. The emphasis here is on wing design ‐ the fuselage is assumed as given. The stress analysis is based on finite elements for beams, whereas the structural dynamics is based upon natural modes, which are evaluated by the same finite‐ element algorithm. For the aerodynamic analysis, a boundary‐element quasi‐potential‐flow method is used for both steady and unsteady aerodynamics. An elementary boundary layer model is used to include the steady viscous eects and estimate the drag. A reduced order model (ROM) for the unsteady‐aerodynamics forces is used in dynamic aeroelasticity. Numerical results on the optimized Prandtl-Plane configuration are included. It is shown how the addition of the community-noise term in the objective function aects the configuration and produces noise reduction.

Ideal Lift Distributions and Flap Angles for Adaptive Wings

Abstract: An approach is presented for determining the optimum flap angles and spanwise loading to suit a given flight condition. Multiple trailing-edge flaps along the span of an adaptive wing are set to either reduce drag in rectilinear flight conditions or to limit the wing bending moment at maneuvering conditions. For reducing drag, the flaps are adjusted to minimize induced drag, while simultaneously enabling the wing sections to operate within their respective low-drag ranges. For limiting wing bending moment, the flaps are used to relieve the loading near the wing tips. An important element of the approach is the decomposition of the flap angles into a distribution that can be used to control the spanwise loading for induced-drag control and a constant flap that can used for profile-drag control. The problem is linearized using the concept of basic and additional lift distributions, which enables the use of standard constrained-minimization formulations. The results for flap-angle distributions for different flight conditions are presented for a planar and a nonplanar wing. Postdesign analysis and aircraft-performance simulations are used to validate the optimum flap-angle distributions determined using the current approach.

Minimization of induced drag of elastic airplane

Abstract: The main purpose of this work is to develop an effectiv e procedure for computation and optimization of induced drag of an elastic airplane, as well as to consider different methods to realize drag optimum values. On the base of the standard panel method, the relations has been obtained that allows the matrix o f quadratic form for induced drag to be calculated simultaneously with the standard matrixes of influence for aerodynamic forces and moments. This approach makes it possible to reduce the task of induced drag minimization to the standard task of quadratic programming, and to simplify the optimization procedure essentially. Different methods of induced drag reduction for an elastic airplane are considered. Results of numerical analysis for a model of transport airplane are presented, and the problems of the practical realization of the induced drag reduction methods are discussed.