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A low-speed investigation was made in the 6- by 6-foot curved-flow test section of the Langley stability tunnel to determine the effects of change in profile and aspect ratio on the pitching derivatives of triangular wings. The effects of aspect ratio on the pitching derivatives of a series of modified triangular wings, obtained by cutting various portions from the tips of a basic triangle, also were determined. Values of the damping-in-pitch parameter (Cmq) obtained for the triangular and modified triangular wings were one-fifth to one-tenth as large as the value expected for a typical airplane.
Planform effects on low speed aerodynamic characteristics of triangular and modified triangular wings
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Triangular Bernstein-Bezier patches are an alternative to the standard rectangular ones. They are maps of triangular domains into R cubed, where the patches are described by control nets similar to the rectangular case. One difference in the definition of surface normals at the patch corners: rectangular patches have inherent problems with so-called degenerate corners, i.e., edges collapsing into one point. Triangular patches do not have these problems. Since triangular shapes arise rather frequently in the design of complicated surfaces (e.g., interior car body panels), it seems that for such surfaces triangular patches are a promising addition to the usually employed rectangular patches. Another major application is the formulation of interpolants to solve the scattered data problem: here Bernstein-Bezier patches provide a very powerful tool; they can be used to discover new schemes as well as to discover new properties of existing methods.
We discuss the use of triangular elements in the spectral element method for direct simulation of incompressible flow. Triangles provide much greater geometric flexibility and are better conditioned and more accurate than quadrilateral elements when small angles arise. We employ a family of tensor product algorithms for triangles, allowing triangular elements to be handled with comparable arithmetic complexity to quadrilateral elements. The triangular discretizations are applied to the Poisson equation and are validated. The triangular discretizations are then applied to the incompressible Navier-Stokes equations, and a laminar channel flow solution is given. The new triangular spectral elements can be combined with standard quadrilateral elements, yielding a general and flexible high order method for complex geometries in two dimensions.
A method is derived for calculating the lift and the drag due to lift of point-forward triangular wings and a restricted series of sweptback wings at supersonic speeds. The elementary or "supersonic sources" solution of the linearized equation of motion is used to find the potential function of a line of doublets. The flow about the triangular flat plate is then obtained by a surface distribution of these doublet lines. The lift-curve slope of triangular wings is found to be a function of the ratio of the tangent of the apex angle to the tangent of the Mach angle. As the apex angle approaches and becomes greater than the Mach angle, the lift coefficient of the triangular wing becomes equal to that of a two-dimensional supersonic airfoil at the same Mach number. The drag coefficient due to lift of triangular wings with leading edges well behind the Mach cone is shown to be close to that of elliptically loaded wings of the same aspect ratio in subsonic flight. The resultant force on wings with leading edges outside the Mach cone, however, is shown to act normal to the surfaces and thus an induced drag equal to the lift times the angle of attack is obtained.
A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.
Solution adaptivity is discussed first from a general perspective and then from the specific viewpoint of triangular meshes. The use of a general connectivity triangular mesh is emphasized. The development of monitor surfaces and their geometric properties is discussed. Mesh point movement is addressed, as is the dynamic restructuring of the connectivity pattern among moving modes. Changes in the number of mesh nodes to obtain suitable refinement for a physical simulation is examined, and the use of locally regular structures to offset the data structure limitation of a general connectivity triangular mesh and thus to obtain an enhanced range of application is considered. To illustrate the basic features of the adaptive triangular mesh strategy, an application to the study of plasma equilibrium is briefly considered.