This paper presents a new approach to model the induction for wind turbines in yawed flow to find the effective angle of attack distribution along the blades. There is an inherent difficulty in determining the angle of attack required by aeroelastic codes as input to tabulated airfoil data. Unlike two-dimensional (2D) conditions where the angle of attack is the angle between the unperturbed flow and the airfoil chord, for the rotating blade, the incoming flow is bended because of rotation and affected by the induction of the blade circulation and the tip and root vortices, making the definition of the angle of attack uncertain.In this work, the analogy with 2D potential flows suggests that a coupling term between the unperturbed geometric angle of attack and the unitary velocity in the radial direction should be included to calculate the effective angle of attack seen by the blade strips. The model introduces two radially dependent interferences on the geometric angle, obtained from axial flow conditions that give the effective angle of attack under arbitrarily yawed flow conditions. The model gives a uniform treatment to the radial flows associated with yawed conditions or coned rotors and can be applied directly to calculate the effective angle of attack distribution on coned rotors in yawed flow. The accuracy of the method compares with results obtained from conventional or higher degree of complexity methods. The model can be incorporated into blade element momentum theory codes as an option to calculate angle of attack distributions.

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A quantitative model of the nonlinear motion leading to catastrophic yaw of finned missiles is presented. The coupled roll-yaw dynamics of the missile, acted on by the trim angle of attack due to slight configurational asymmetries, is represented by pitch, yaw, and roll equations of motion that include cubic aerodynamic coefficients and roll-orientation-dependent induced moments. The steady-state equilibrium points of the system are found and their stability is determined by linearization. The solutions are evaluated by comparison with numerical integration of the equations of motion, proving the capability of the model to predict catastrophic yaw.attack coefficient of the Magnus moment C Mq , C M _ = damping and lag coefficients of the pitch moment C M0 e i M0 = asymmetry moment coefficient C N = angle-of-attack coefficient of the normal force C N0 e i N0 = asymmetry force coefficient C = CSD=2m Cl i = induced roll moment coefficient Cl p = roll damping moment coefficient Cl = roll effectiveness moment coefficient D = reference length, missile diameter I x = axial moment of inertia I y = transversal moment of inertia k a = axial radii of gyration k t = transverse radii of gyration m = mass p = roll rate q d = dynamic pressurê r = dimensionless radial offset of the center of mass S = reference area, D 2 =4 s = dimensionless arc length u = X component of velocity V = speed of the missile v = Y component of velocity w = Z component of velocity , = angles of attack and sideslip = u=V = magnitude of the complex angle of attack, T = fin-cant anglẽ = complex transverse angular velocity in nonrolling axes, q irD=Ṽ = i angle of attack in nonrolling axes, ũ iw=V 0 = 0 i 0 static angle of attack in fixed axes at p 0 = I x =I y = roll angle ' = phase lag Subscripts e = steady state r = resonance Superscripts _ = differentiation with respect to t e = nonrolling axes