Induced Drag Coefficients Research Articles

The estimation of applicability concerning the methods for calculation of asimple wing with wingtips inductive resistance during the flight near the earth surface

One of the problems in the hovercrafts design is to dtermine the aerodynamic charactreistics of the wing near the earth surface. In this article, 4 methods for calculating the induced drag coefficient Cxi of a simple airfoil with an end plate at different relative heights were considered. Four methods of induced drag coefficient determination were considered for different relative flight’s heights. Calculations were performed according to the Phillips, Wieselsberge, Panchenkov-Surzhik, Mantle methods for the TsAGI-876 wing profile. The calculated values of induced drag coefficients were compared with the experimental wind tunnel’s data at the Central Aerohydrodynamic Institute.

Aerodynamic Interaction Effects of wingtip-Mounted Propellers

The study presents an aerodynamic analysis of the propeller–wing interaction effects for the wingtip-mounted propeller configuration. The influence of the initial parameters of the propellers, such as the radius, the pitch angle as well as the direction of rotation on the models aerodynamic characteristics, in particular, on the wing span-efficiency factor and the induced drag was determined. In this research a computational simulation of the wingtip flow field was implemented using two different computational models with two different Reynolds numbers.Flow field simulations over computational models with different combinations of initial parameters were performed by means of the computational aerodynamic methods (the panel-vortex method of symmetric peculiarities). The simulation showed a significant positive effect on the aerodynamic characteristics of the computational models due to wingtip-vortex attenuation and swirl recovery by the propeller slipstreams. Analysis of the wing performance pointed out that the aerodynamic benefit of the wingtip-mounted propeller was due to an increase of the effective span-efficiency parameter of the wing.The induced drag coefficients and wing span-efficiency factors of the computational models for different combinations of given initial parameters, such as propellers radius and pitch angles, as well as the direction of rotation are obtained. The dependences between the given initial parameters and the studied aerodynamic characteristics of the computational models are determined. It is established that the character of these dependencies is identical for both computational models with two different Reynolds numbers. The analysis of the obtained dependencies indicates that when the propellers pitch angle φ changes, the highest efficiency zone is observed, that is characterized by the maximum value of the derivative dλef/dφ. The range of expedient change of the propellers pitch angle is determined, as a consequence.The most of the results are presented by diagrams for both computational models. The results obtained are of practical significance and will be useful for the aircraft design, performed according to the studied aerodynamic scheme.

Effects of aspect ratio on the hydrodynamic performance of full-scale rectangular otter board: Numerical simulation study

In the present work, the hydrodynamic characteristics of full-scale rectangular otter board were studied by numerical simulation, including the effects of aspect ratios (AR), flow distribution around the otter board, induced velocity, induced angle of attack (AOA), effective AOA and induced drag coefficient. It was demonstrated that the otter board had a critical AOA of 40° (when the stall appeared) and induced AOA of 3~10°. The maximum induced drag coefficient was 0.185, which is a great contribution to the total drag coefficient. The otter board exhibited better performance when the AR was set to 0.5, and higher AR had a smaller critical AOA (the stall happened earlier). The maximum lift coefficient decreased with an increasing AR, while the maximum lift-to-drag ratio increased. The induced drag coefficients showed similar trends across ARs, initially rising with an increase of the AOA, and then dropping. The flow distribution around the otter board showed that the wing-tip vortex was fully developed at the AOA of 40°, and the AR can affect the development of the wing-tip vortex.

Aerodynamic comparisons of flexible membrane micro air vehicle wings with cambered and flat frames

Flexible membrane wings at the micro air vehicle scale can experience improved lift/drag ratios, delays in stall, and decreased time-averaged flow separation when compared to rigid wings. This research examines the effect of frame camber on the aerodynamic characteristics of membrane wings. The frames for the wings were 3D printed using a polymer-based material. The membranes are silicone rubber. Tests were conducted at Re ∼50,000. Aerodynamic force and moment measurements were acquired at angles-of-attack varying from −4 to 24°. Additionally, digital image correlation data were acquired to assess time-averaged shapes of the membrane wings during wind tunnel tests. An in-house program was developed to average the deflection plots from the digital image correlation images and produce time-averaged shapes. Lifting-line theory based on the time-averaged shapes was then used to calculate theoretical lift and induced drag coefficients, showing that the time-average shape of the membrane under load contributes extensively to the aerodynamic performance. The results show that introducing camber to the frames of membrane wings increases aerodynamic efficiency.

Formation of vortices on a tubercled wing, and their effects on drag

Wake surveys of 2 swept NACA 0021 wings were conducted at angles of attack of 0°, 3°, 6°, 9°, and 12°. One wing had a smooth leading edge and the other had a tubercled leading edge. Sweeping the tubercled wing resulted in one vortex in each vortex pair being at least 4 times stronger than the other. There was little difference between the strength of the wingtip vortices of either wing at 3°. From 6° onwards tubercles reduced the strength of the wingtip vortex. The tubercle troughs tended to produce local maxima and minima in the profile and induced drag coefficients, respectively. The converse was true over the peaks. The change in the profile, induced, and total drag coefficients primarily arose from over the wingspan; there was little contribution from the wingtip region.

What supports an aeroplane? Force, momentum, energy and power in flight

Some apparently confusing aspects of Newton’s laws as applied to an aircraft in normal horizontal flight are neatly resolved by a careful analysis of force, momentum, energy and power. A number of related phenomena are explained at the same time, including the lift and induced drag coefficients, used empirically in the aviation industry.

Numerical analysis of multiple, thin-sail geometries based on Prandtl’s lifting-line theory

Solutions obtained from a numerical method based on Prandtl’s lifting-line theory, valid for multiple lifting surfaces with arbitrary sweep, are obtained for a number of rigid wing and sail geometries. The results are compared against solutions obtained using established vortex-lattice methods, and computational fluid dynamics solutions to the Euler equations. For the case of an untwisted, rectangular wing, numerical lifting-line, vortex-lattice, and Euler solutions were all in reasonable agreement. However, the numerical lifting-line method was the only method to predict the constant ratio of induced-drag coefficient to lift coefficient squared, which has been predicted from the analytic solution and confirmed by well established experimental data. Results are also presented for a forward-swept, tapered wing. Additional results are presented in terms of lift and induced-drag coefficients for an isolated mainsail, and mainsail/jib combinations with sails representative of both a standard and tall rig Catalina 27. The influence of the nonlinear terms in the lifting-line solution appears minimal, with the exception of mainsail results when considering jib/mainsail combinations.

Time-Area-Averaged Momentum Stream Tube Model for Flapping Flight

This paper formulates a time-area-averaged momentum stream tube model to provide the useful functional relations for the cruise velocity, power, and propulsive efficiency in forward flapping flight. This model is a direct generalization of the classical actuator disk theory by taking into account the effects of the unsteadiness and spatial nonuniformity of velocity in a momentum stream tube. It is found that the functional relation for the time-areaaveraged power required in flapping flight is almost the same as that given by the classical lifting-line theory for a fixed wing. The flapping span efficiency is introduced, and its physical meaning and significant role in the power relationareinterpreted.The flappingpropulsiveefficiencyisrelatedtothe flappingspanefficiency,normalizedtotal fluctuating kinetic energy, and wing aspect ratio. The use of this model to fit the collected data for birds allows estimating the flapping span efficiency, parasite, and induced drag coefficients and propulsive efficiency. Nomenclature A = effective area of actuator disk or cross-section area of momentum stream tube Ab = circular area of a diameter of wingspan AR = wing aspect ratio b = wingspan CDPara = parasite drag coefficient

A Lifting-Line Analysis of a Cavitating Hydrofoil in Uniform Shear Flow

An existing lifting-line theory for. a non-cavitating hydrofoil in uniform shear flow is applied to both partial- and super- cavitations in the same condition. A lifting-line equation is derived from an assumption holding two-dimensional at any spanwise position and from a solution of ordinary differential equation with variable coefficient. A method in the theory to obtain local cavity length, in which a solution of the lifting-line equation is used, is also applied. The hydrofoil for numerical examples is flat in section, rectangular in planform, and 5 degrees in attack angle. Effects of a main stream shear parameter, aspect ratio and cavitation number on local lift coefficients, total lift coefficients and induced drag coefficients for force characteristics, and on local cavity, length for cavity characteristics are clarified.

A Lifting-Line Theory and a Critical Shear Parameter of a Wing in Uniform Shear Flow.

A lifting-line theory of a wing in uniform shear flow is presented and also a critical shear parameter where aerodynamic characteristics abruptly change is found by obtaining analytical expressions of the characteristics. The governing equation with respect to potential function defined by Karman is derived and reduced to two ordinary differential equations by separation of variables. A general solution is obtained by linearly combining the fundamental solutions of the ordinary differential equations. An induced attack angle is derived from the general soultion and a condition of far downstream. A relation of a lift force to an effective attack angle is described by the Taylor series expansion in a vicinity of geometrical attack angle. From the induced attack angle and the lift force, a lifting-line equation is obtained, and solved by Gaussian elimination method. Effects of shear parameter and aspect ratio on the local lift, total lift and induced drag coefficients are clarified through some numerical calculations.

Flight Motion of a Continuously Elastic Finned Missile

Abstract : The motion of elastic finned projectiles has been analyzed by various approximate theories. In this report the exact equations of small amplitude motion are derived for a symmetric missile. The aerodynamic and elastic symmetries are used to allow the use of complex variables to describe the lateral motion in a non-rotating coordinate system. Although the resulting equations are both ordinary and partial differential equations, frequencies and damping rates of free oscillations are obtained from an ordinary differential equation with boundary conditions. Equations for a permanently deformed bent missile are derived, and an ordinary differential equation for the forced motion of a bent missile is obtained. Sample calculations for a finned projectile with a fineness ratio of 20 show resonant motion at the aerodynamic frequency as well as at each elastic frequency. The nonlinear roll moment associated with a bent missile is computed and the location of possible spin-yaw lock-in is determined. The flight motion of an elastic missile is shown to be the sum of two elliptical motions: a low frequency pitching motion and a higher frequency flexing motion. The induced drag coefficients for both motions are computed as functions of the missile's elasticity.

Experimental and nonlinear vortex lattice method results for variouswing-canard configurations

Experimental measurements of the aerodynamic characteristics of five close-coupled wing-canard configurations up to moderately high angles of attack are used to evaluate the ability of the nonlinear vortex lattice method (NLVLM) to calculate the aerodynamic characteristics of such configurations. The longitudinal aerodynamic coefficients, the rolled-up vortex trajectories, and the pressure distributions are compared for the five wing-canard configurations, as well as for the three wing planforms for which experimental data is available. The investigation includes the effects of varying the canard deflections and the canard positions relative to the wing of the various configurations. The lift- and induced-drag coefficients which are evaluated by the NLVLM for the wing-canard configurations are found to be in good agreement with the experimental data up to the angle of attack of 20-25 deg. The NLVLM works even better for wings alone in that the pitching moment can also be well-predicted. Therefore, this tool can potentially be used in the by analysis process employed during the preliminary design for wing-canard configurations. Nomenclature AR = aspect ratio b - wing span, mm CD = induced-drag coefficient based on wing planform area CL = lift coefficient based on wing planform area Cm = pitching moment coefficient based on wing area and wing root chord Cp = pressure coefficient when Ap is the lifting

On the vortex wake of an animal flying in a confined volume

When an animal flies near a boundary, the airflows it generates interact with that boundary. These interactions may have a significant effect on flight performance, as measured by quantities such as the energy rate to sustain flight, or the circulation of the vortices bound on the wing or shed in the wake (or, equivalently, by the lift and induced drag coefficients). The problem of hovering and slow flight within a confined volume is considered by a theoretical model based on helicopter practice, and by flow visualization experiments. The wake takes the form of a strong recirculating flow within the volume, and because of this recirculation the boundaries appear to cause a large reduction in the induced power required for sustained flight, even when their distance from the animal is several times greater than the wingspan. The correction factor relative to ideal momentum jet theory is greater than for the hovering ground effect, forward flight ground effect, or wind tunnel wall interference problems at comparable distances. The flow pattern that develops in the presence of floor and wall interactions in hovering or slow flight includes a large-diameter vortex ring trapped underneath the animal; this vortex ring is conjectured to be analogous to that below a helicopter in slow descending flight in the 'vortex ring state’. Performance measurements for animals in hovering flight within a confined volume may underestimate power for free hovering by a significant margin. Comparable boundary effects may also be important in confined forward flight. Because of speed-related changes in the wake, and the rise in induced power at lower speeds, the appropriate correction to total mechanical power is dependent on air speed, becoming progressively greater as speed reduces. Some wind tunnel measurements of total metabolic power have produced the apparently anomalous result that power is independent of flight speed within measurement error. These observations may be explained - at least in part - by boundary effects caused by interaction between the wake and the walls of the wind tunnel.

Effects of nonplanar outboard wing forms on a wing

It is possible for a constant span to obtain better aerodynamic performance from a wing with a nonplanar outboard wing form than from a wing with a planar outboard form, despite the added drag from the increased wetted area. Furthermore, the semispan rolling-moment characteristics indicate the lower wing-root bending moment for some nonplanar configurations. These conclusions are based on an experimental and computational investigation of the aerodynamic characteristics of planar and nonplanar outboard wing forms. Seven different configurations - planar rectangular, nonplanar rising arc, nonplanar drooping arc, planar sheared, sheared with dihedral, sheared with anhedral, and planar elliptical - were investigated for two different spans. Flow-visualization photographs indicate that there are three vortex systems associated with the sheared forms. The lower induced drag coefficients of nonplanar wings are believed to accrue from the movement of vorticity away from the center-of-span line, resulting, in some instances, in induced efficiencies higher than that of a planar elliptical wing. Flow surveys indicate that the effective span, as determined by the location of the tip vortex, might not be a sufficient yardstick of the induced performance of a nonplanar wing.

A method for flight-test determination of propulsive efficiency and drag

A flight-test method is described from which propulsive efficiency as well as parasite and induced drag coefficients can be directly determined using relatively simple instrumentation and analysis techniques. The method uses information contained in the transient response in airspeed for a small power change in level flight in addition to the usual measurement of power required for level flight. Measurements of pitch angle and longitudinal and normal acceleration are eliminated. The theoretical basis for the method, the analytical techniques used, and the results of application of the method to flight-test data are presented. Flight-test data showed performance parameters measured with a standard deviation of about 0.8% for propulsive efficiency, 0.3% for parasite drag coefficient, and 8% for the airplane efficiency factor, e.

Low-speed aerodynamic characteristics of wings with sweep discontinuities

It has been shown that, using the concept of a discrete vortex filament shedding, Weissinger’s method can be modified to determine the span-wise loading for wings with a sweep discontinuity. The sweep discontinuity is modelled by the introduction of a discontinuity in the equivalent vortex pattern chosen to replace the wing. The total lift, induced drag, pitching moment coefficients and span-wise location of the centre of pressure have been found for a few wing geometries using De Young and Harper’s procedure. An increase in the outboard sweep shifts the maximum load position outboard besides decreasing the overall lift and induced drag coefficients. High suction peaks appear at the pivot.

A New Approach to Animal Flight Mechanics

ABSTRACT The mechanics of lift and thrust generation by flying animals are studied by considering the distribution of vorticity in the wake. As wake generation is not continuous, the momentum jet theory, which has previously been used, is not satisfactory, and the vortex theory is a more realistic model. The vorticity shed by the wings in the course of each powered stroke deforms into a small-cored vortex ring; the wake is a chain of such rings. The momentum of each ring sustains and propels the animal; induced power is calculated as the rate of increase of wake kinetic energy. A further advantage of the vortex theory is that lift and induced drag coefficients are not required; estimated instantaneous values of these coefficients are generally too large for steady state aerodynamic theory to be appropriate to natural flapping flight. The vortex theory is applied to hovering of insects and to avian forward flight. A simple expression for induced power in hovering is found. Induced power is always greater than simple momentum jet estimatés, and the discrepancy becomes substantial as body mass increases. In hovering the wake is composed of a stack of horizontal, coaxial, circular vortex rings. In forward flight of birds the rings are elliptic; they are neither horizontal nor coaxial because the momentum of each ring balances the vector sum of parasite and profile drag and the bird’s weight. Total power consumption as a function of flight velocity is calculated and compared for several species. Power reduction is one of the major factors influencing the choice of flight style. A large body of data is used to obtain an approximate scaling between stroke period and the body mass for birds. Together with relations between other morphological parameters, this is used to estimate the variation of flight speed and power with body mass for birds, and on this basis deviations from allometric scaling can be related to flight proficiency and to the use of such strategies as the bounding flight of small passerines.

A vortex theory of animal flight. Part 2. The forward flight of birds

The vortex wake of a bird in steady forward flight is modelled by a chain of elliptical vortex rings, each generated by a single downstroke. The shape and inclination of each ring are determined by the downstroke geometry, and the size of each ring by the wing circulation; the momentum of the ring must overcome parasitic and profile drags and the bird's weight for the duration of a stroke period. From the equation of motion it is possible to determine exactly the kinematics of the wing-stroke for any flight velocity. This approach agrees more readily with the nature of the wing-stroke than the classical actuator disk and momentum-jet theory; it also dispenses with lift and induced drag coefficients and is not bound by the constraints of steady-state aerodynamics. The induced power is calculated as the mean rate of increase of wake kinetic energy. The remaining components of the flight power (parasite and profile) are calculated by traditional methods; there is some consideration of different representations of body parasite drag. The lift coefficient required for flight is also calculated; for virtually all birds the lift coefficient in slow flight and hovering is too large to be consistent with steady-state aerodynamics.A bird is concerned largely to reduce its power consumption on all but the shortest flights. The model suggests that there are a number of ways in which power reduction can be achieved. These various strategies are in good agreement with observation.

Vortex lattice prediction of subsonic aerodynamics of hypersonic vehicle concepts

The vortex lattice method introduced by Lamar and Gloss (1975) was applied to the prediction of subsonic aerodynamic characteristics of hypersonic body-wing configurations. The reliability of the method was assessed through comparison of the calculated and observed aerodynamic performances of two National Hypersonic Flight Research Facility craft at Mach 0.2. The investigation indicated that a vortex lattice model involving 120 or more panel elements can give good results for the lift and induced drag coefficients of the craft, as well as for the pitching moment at angles of attack below 10 to 15 deg. Automated processes for calculating the local slopes of mean-camber surfaces may also render the method suitable for use in preliminary design phases.

A theory of the jet flap in three dimensions

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.