Triangular Wing Research Articles

Self-similar problems of the dynamic bending of infinite nonlinearly elastic beams

Soc. London, A195, No. 1041 (1948). 3. R. Ya. Tugazakov, "Nonstationary problem of the sudden motion of a wedge and a cone at suband supersonic velocities," Uchen. Zapiski TsAGI, ~, No. 1 (1973). 4. V. V. Titarenko, "Nonlinear analysis of the flows initiated by sudden motion of a wedge," Prikl. Mekh. Tekh. Fiz., No. 3 (1976). 5. M. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic, New York (1968). 6. H. Routh, Mechanics of Fluids [Russian translation], Stroiizdat, Moscow (1967). 7. L. Prandtl and O. Tietjens, Applied Hydroand Aeromechanics, edited by Jacob Den Hartog, Dover (1934). 8. G. Batchelor, Introduction to Fluid Dynamics, Cambridge Univ. Press (1967). 9. A. A. Nikol'skii, "On the "second" form of ideal fluid motion around a streamlined body (investigation of separated vortex flows)," Dokl. Akad. Nauk SSSR, !16, No. 2 (1957). i0. L. I. Sedov, Mechanics of Continuous Medium [in Russian], Vol. 2, Nauka, Moscow (1973). Ii. S. M. Belotserkovskii and M. I. Nisht, Separated and Unseparated Ideal Flud Flow around Thin Wings [in Russian], Nauka, Moscow (1978). 12. H. K. Cheng, "Remarks on nonlinear lift and vortex separation," J. Aero. Sci., 21, No, 3 (1954). 13. G. G. Sudakov, "Analysis of the separated flow around a small-span slender triangular wing," Uchen. Zapiski TsAGI, ~, No. 2 (1974). 14. G. M. Arutyunyan and L. V. Karchevskii, Reflected Shocks [in Russian], Mashinostroenie, Moscow (1973).

Transonic Flows Past Nonaxisymmetric Slender Shapes- Classical Equivalence Rule Analysis

An assessment of .the classical transonic equivalence rule is provided. Extensive comparisons of theoretical results are made with data obtained in conventional transonic tunnels for various slender bodies, as well as a thin triangular wing of unit order aspect ratio. Results are reported for surface and flowfield pressure distributions at Mach numbers throughout and beyond the transonic range for both nonlifting and lifting conditions. Particular attention has been paid to wind tunnel interference effects through use of an interesting alternative to the classical homogeneous wall condition, whereby experimentally measured flowfield pressures are imposed as an outer boundary condition. The comparisons with experiment display good agreement, including the region near shock waves, and indicate that the classical equivalence rule approximation remains effective for certain threedimensional aerodynamic configurations over a broad range of geometries and flow conditions.

Normal force of a flat triangular wing in a supersonic flow

On the basis of an analysis of the results of numerical calculations for flow conditions with a forward shock wave attached to the leading edges, the dependence of the coefficient of the normal force of a flat triangular wing on the parameter $$K = \sqrt {M^2 - 1} $$ sinα is obtained in a wide range of change in the angle of attack, the angle of sweepback, and the Mach numbers.

Errata: Remarks on Thin Airfoil Theory

Fig. 3 Angles of attack for vanishing leading-edge singularity and for zero lift. References E., High-Speed Aerodynamics, Pergamon Press, London/New York/Paris, 1956, pp. 619-624. 2 Holla, V. S. and Krishnaswamy, T. N., Conically Cambered Triangular Wings, Journal of the Aeronautical Society of India, Vol. 22, May 1970, pp. 94-107. Bera, R. K., Slender Delta Wings with Conical Camber, Journal of Aircraft, Vol. 11, April 1974, pp. 245-247. Evvard, J. C., Effects of Yawing Thin Pointed Wings at Supersonic Speeds, NACA TN 1429, 1947. Hancock, G. J., Note on the Extension of Evvard's Method to Wings with Subsonic Leading Edges Moving at Supersonic Speeds, Aeronautical Quarterly, Vol. VIII, 1957, pp. 87-102. Wagner, B., Untersuchungen uber konische Uberschalltragflachen mit Unterschallvorderkanten, Institut fur Flugtechnik, T. H. Darmstadt, Rept. No. 8/75, 1975.

Application of a gradient-projection method to minimum weight design of a delta wing with static and aeroelastic constraints

A structural optimization algorithm based on gradient-projection is presented. The algorithm is applied to minimum-weight design of a delta wing subject to multiple constraints. Examples are provided for the following sets of constraints: stress and minimum-gage; flutter and minimum-gage; stress, flutter and minimum-gage. Analytical expressions are employed for evaluating constraint gradients, which are calculated only for active constraints. Due to nonlinearity of the constraints, the optimization algorithm incorporates constraint tolerances and provides for returning to the constraints if they are violated. For a triangular wing having 10 design variables and subject to stress, flutter (supersonic) and minimum-gage constraints a 44% weight reduction was obtained in 6 design steps; a 59% weight reduction was obtained in 17 steps.

Minimum induced drag of ground effect wings

Kida and Miyai's theory, which treats theoretically the problem of the minimum induced drag of nonplanar ground effect wings, is refined and extended. The gap clearance between the wing tip and the ground is assumed to be so small that the method of matched asymptotic expansions may be used. Except for this restriction, this method has a remarkable flexibility in wing front-view geometry. The theory is applied to some typical cases such as semielliptic, rectangular, and triangular ground effect wings over flat surface and a flat plate in a rectangular guide way. Special attention is concentrated on the two limiting cases with very high and low front views. Kida and Miyai's errors are corrected.

Linear problem for triangular and V-shaped wings

Linear problem for triangular and V-shaped wings

Estimation of aerodynamics for slender bodies alone and with liftingsurfaces at alpha's from 0 deg to 90 deg.

Expressions are derived, according to a method developed by the author (1972), for bodies in which the cross-sectional shape (but not necessarily the area) is constant along the longitudinal axis. For the more general case of a body alone or with lifting surfaces where the cross-sectional shape varies along the length, a similar procedure is suggested. The specific case for an elliptic cone with a triangular wing is considered, and formulas for winged elliptic cross sections are developed. For the limited test conditions shown, the agreement between computed and experimental results is very good.

Calculation of the supersonic flow around conical bodies

A finite-difference scheme [1, 2], proposed previously for calculating spatial supersonic flows, which is written in spherical coordinates, is applied to the calculation of the supersonic flow around various conical bodies: circular, elliptic and almost pyramidal cones, triangular and V-shaped wings and combinations of a triangular wing and a circular cone. The solutions describing the corresponding conical flows are developed in the build-up process along the radial coordinate. The difference scheme used is direct, which enables us to perform the calculation without the isolation of internal shock waves, which are generated, for example, by the leeward (shady) side of the cones at fairly large angles of attack. At the same time the calculation of a leading shock wave, the isolation of which is advisable, does not require the inclusion in the computer program of any supplementary algorithm, since allowing for shock waves (rather, the interaction of two uniform supersonic flows) constitutes one of the elements of the difference scheme mentioned.

Strong viscous interaction on triangular and slipping wings

The flow past triangular slipping wings is considered in strong viscous interaction conditions. It is shown that the solution of each of the problems discussed is not unique. The condition is obtained which has to be satisfied by the solution on the axis of symmetry of a triangular wing of infinite dimensions. The class of self-similar flows in the boundary layer of a thin triangular wing is found.

Wing of given volume with maximum lift/drag ratio in hypersonic flow

Results are presented of the numerical solution of the problem of a triangular wing of given volume having maximum aerodynamic efficiency in hypersonic flow. In calculating the aerodynamic characteristics of lifting bodies in hypersonic viscous gas flow it is often assumed that the pressure coefficient on the surface of the body is given by the Newton law [1, 2], while the friction coefficient is constant. These assumptions make i t possible to formulate the variational problem of bodies with optimal characteristics as the problem of the extremal value of a functional which can be expressed explicitly. However, even for simple problems the Euler equations will be nonlinear partial differential equations whose solution can be obtained only in certain particular cases. Therefore the additional assumption is usually made that the wing is slender, which makes it possible to solve certain simple variational problems with the aid of the analytic methods. But this assumption restricts severely the class of permissible wing forms and does not permit obtaining a complete picture of the dependence of the aerodynamic characteristics of the optimal bodies on the various parameters. The numerical method of local variations [3], used in the following, makes it possible to solve certain variational problems without imposing any limitations on the relative dimensions of the wings. Let us assume that the pressure coefficient Cp on the ~,ing surface (Fig. 1) is given by the Newton law with a modifying factor N(M co), the friction Coefficient cj = const and the upper and lower surfaces of the wing are given by the respective functions Yi Y* (x, z) and Y2 = Y2( x, z). We use the dimensionless variables ~ = x/b0, = y /V • z = 2 z / l . Here b0, l, and V are, respectively, the width span, and volume of the wing. Then the wing drag and lift coefficients and the wing volume are given by the functions (bars over letters are dropped)

The problem of supersonic flow over the lower surface of a triangular wing

In formulating the problem we make no assumption of smallness of the angle of attack; the attached three-dimensional compression shock which arises under the lower surface of the wing may be of arbitrary intensity, and in form is assumed to differ little from a plane shock; a finite yaw angle is allowed. We consider linear supersonic conical flow which is realized, with the exception of a characteristic linear dimension, in the portion of space bounded by the shock, the plane of the wing, and the surface of a disturbance cone with vertex at the discontinuity of the supersonic leading edge and which is a disturbance of the uniform flow behind the plane shock wave.

Wing of simple planform in a sharp-edged gust

The entry of a wing into the zone of a sharp-edged gust is considered in the linear formulation. The case is studied when the wing velocity is supersonic and its edges satisfy the supersonic flow condition. The gust intensity is considered to be variable, and its edge may move into the undisturbed medium. Equations in finite form are obtained for the forces and moments for a rectangular wing of infinite span, and also for triangular wings with positive and negative sweep, for the case when the gust intensity varies linearly. Sudden envelopment of the wing and penetration of the wing into a gust whose edge is fixed relative to the undisturbed medium are considered.

Some exact solutions of the problem of super- and hypersonic gas flow about a yawed wing with fence

Individual examples are known of bodies of three-dimensional form for which it is possible to construct the solution of the flow problem, for example, bodies of star-shaped (polygonal) cross section [1, 2], or bodies of revolution (cone, ellipsoid) at an angle of attack, and so on. The role of such individual solutions is important in clarifying the characteristic features of the three-dimensional flow about bodies. The application of the hypersonic method of small perturbations [3], which reduces the problem of three-dimensional flow to the problem of the unsteady motion of a gas in two dimensions, and also the use of one of the known families of exact solutions of the two-dimensional problem on unsteady motion [4] make it possible to study the flow about a yawed wing with a tip plate in a hypersonic flow in certain particular cases. In the present paper, we construct a more general class of threedimensional bodies of thi s type (combinations of a yawed or triangular wing with tip plate directed parallel to the free stream) for which it is possible to construct simple exact solutions of the supersonic and hypersonic flow problem without use of the method of small perturbations. In a particular case, these solutions describe the flow about two mutually intersecting yawed wings. The example of flow about these bodies reveals an interesting phenomenon of strong interference at high velocities, when, as a result of the interference, local pressures are developed which far exceed the pressures on the isolated wing. w 1. Let us consider a supersonic gas flow about a portion of a triangular (or sweptback) wing similar to that shown in Fig. 1, with thefreestream directed opposite to the x coordinate axis.

Supersonic flow past triangular wings with ribs on their surface: PMM vol. 31, no. 6, 1967, pp. 1050–1056

Various types of partitions are a common feature of lifting surfaces. These partitions can take the form of stiffening ribs, deflectors for preventing secondary flows or flow separation, etc. The presence of partitions has a marked effect on the character of flow and on the values of the aerodynamic parameters. Flow past such wings cannot be computed in the general case. Wings of a special type are amenable to simple solution, however, and this will be considered below. One special case of interaction between a partition and an infinite wing is also considered in [1].

Calculation of the flow past plane triangular wings at large angles of attack

Calculation of the flow past plane triangular wings at large angles of attack

Strong interaction between the boundary layer and the inviscid flow past a triangular wing

Strong interaction between the boundary layer and the inviscid flow past a triangular wing

FACTORS AFFECTING LIFT-DRAG RATIOS AT MACH NUMBERS FROM 5 TO 20

Yawed-cone working charts and an engineering method are presented and used to calculate lift-drag ratios of flat-top conical wing-body arrangements at Mach numbers from 5 to 20. Viscous interaction effects are considered, but bluntness effects are neglected. Correlations of wind-tunnel data in the range 0.1 is the freestream Reynolds number based on body length. Doubleand singletype shock patterns, transition from one pattern to the other, and the variation of inner-shock position with angle of attack are described. Lift-drag ratios are calculated at selected flight design points for flat-top, conical body arrangements with triangular and hyperbolic wing planforms. The hyperbolic wing arrangement offers a potential L/D benefit at Mach 5 but not at Mach 10 or above.

The numerical solution of the problem of the flow about the lower surface of a triangular wing in a supersonic stream

The numerical solution of the problem of the flow about the lower surface of a triangular wing in a supersonic stream

Numerical solution of the problem of flow round the upper surface of a triangular wing by a supersonic stream

Numerical solution of the problem of flow round the upper surface of a triangular wing by a supersonic stream