The initial formulation of the Doublet-Lattice Method has proven theoretically accurate for calculating the interference effects on arbitrary classes of oscillating nonplanar configurations with one known exception: nearly coplanar wing/horizontal-tail combinations. For this class of problems the integration of the kernel across the element loses accuracy. The reason for this loss of accuracy is explained, and a refined method for performing the required integration is presented. Numerical studies using wing-tail configurations are presented to illustrate how well the refined method works. Also a T-tail calculation is repeated to show that calculations using other configurations are unaffected by the refinement.
NomenclatureA, B, C= coefficients in parabolic approximations to kernel numerators; subscripts 1 and 2 refer to planar and nonplanar parts of kernel, respectively b r -reference semichord* is the rolling moment due to yaw of the horizontal stabilizer of Ref. 11 and Fig. 6 c -reference chord length D rs -normalwash factor; D 0rs is steady normalwash factor; D lrs and D 2rs are incremental oscillatory, planar, and nonplanar normalwash factors, respectively; D Prs is value of D lrs for z = 0 e = box semiwidth F -integral in Eq (17); F P is Mangier principal part for planar case /o = integral defined in Eq. (8) K = kernel function; KI and K 2 are factors in numerators of planar and nonplanar parts of kernel, respectively ® v (x) = modified Bessel function of argument x k r -reference reduced frequency, k r -a>b r /U M = Mach number TV= number of lifting surfaces Wj) = parabolic approximation to kernel numerator; P t and P 2 are approximations for planar and nonplanar numerators, respectively r = cylindrical radius from sending doublet S n = area of nth lifting surface S.P.( ) -denotes singular part of ( ) s = semispan T -direction cosine function; 7\ and T 2 are functions for planar and nonplanar parts of kernel, respectively, and T 2 * is modified value of T 2 U = freestream velocity #1 = parameter defined in Eq. (9) *o,y, z = Cartesian coordinate system transformed to midpoint of sending line and aligned with plane of sending box; £ is also vertical gap between near-coplanar parallel surfaces s = parameter defined in Eq. (31) y = dihedral angle \y r snd y s are dihedral angles of receiving and sending boxes, respectively, and y r = y r -y s is the relative dihedral angle between receiving and sending boxes A* s = centerline chord of sending box = spanwise coordinate, in the plane of an element = phase angle X s = sweepback angle of sending box i-chord line i/j = yaw angle to = circular frequency
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