Arbitrary Sweep Research Articles

Modern Implementation and Evaluation of Lifting-Line Theory for Complex Geometries

A numerical lifting-line method (implemented in an open-source software package) is presented that can accurately estimate the aerodynamics of wings with arbitrary sweep, dihedral, and twist. Previous numerical lifting-line methods have suffered from grid convergence challenges and limitations in accurately modeling the effects of sweep, or have relied on empirical relations for swept-wing parameters and have been limited in their application to typical wing geometries. This work presents novel improvements in accuracy, flexibility, and speed for complex geometries over previous methods. In the current work, thin-airfoil theory is used to correct section lift coefficients for sweep, providing a more general closure to the lifting-line problem. A linearized solution is presented, which can be used as a rapid approximation for the full solution, or as an initial guess for the nonlinear system of equations to speed convergence. Sensitivities to model parameters are investigated, and appropriate recommendations for these parameters are given. Agreement with Prandtl’s classical lifting-line method is excellent in the case of straight wings. Comparison with experimental data shows that this method can reasonably predict lift, drag, and lift distribution for a range of wing configurations. The speed and accuracy of this method make it well-suited for preliminary design and optimization.

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.

Aeroelastic Analysis of Advanced Geometry Tiltrotor Aircraft

A tiltrotor model is formulated to predict the dynamics and aeroelastic stability of composite-coupled advanced geometry rotors. Advanced geometry rotor blades are modeled with arbitrary sweep, anhedral, pretwist and planform taper variation with span. The effect of advanced geometry blades on the tiltrotor response and whirl flutter stability in airplane mode is studied. Blade tip sweep and tip droop increase the flutter speed while forward tip sweep, tip anhedral and planform taper decrease it. Predicted wing beam mode damping correlates satisfactorily with test data.

Higher-order Bézier circles

Some remarks are given on a construction of a quartic full circle presented by Chou [Higher order Bézier circles. Computer-Aided Design, 1995, 27(4), 303–309]. His method is generalized to obtain rational Bézier circular arcs of arbitrary sweep angle and arbitrary even-degree. An arc of degree n = 2k is generated by elevating to the kth power in the complex plane a quadratic arc of circle. The resulting representation is symmetric and enjoys remarkable properties. Control points lie regularly spaced with respect to the angle swept by the arc. Their associated weights are given by a simple explicit formula, and are equal to the inverse of the distance between the control point and the centre of the circle.