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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

Mean axes provide the usual reference in maneuvering and dynamic response analyses of flexible vehicles. Attached or structural axes have also been used because the flexibility characteristics of the structure are only determined for a restrained structure. If the structural axes are employed, a relationship is required for the orientations of the structural axes relative to the mean axes, since the equations of motion determine the orientations of the mean axes. If this relationship is not considered, as it has not been in a number of publications, the solution to the equations of motion of the structural axes is not invariant with the choice of support configuration used in the calculation of the structural flexibility influence coefficients and is, therefore, incorrect. This relationship and the correct equations of motion for the structural axes are presented, and the correctness of the formulation is demonstrated numerically in studies of longitudinal maneuvering of an example forward-swept-wing airplane at constant forward velocity. Although the paper assumes constant airspeed in the basic developments, it concludes with discussions of aeroelastic speed derivatives and aeroelastic effects on drag. The paper assumes quasisteady equilibrium of the structure with its applied loads throughout. Nomenclature A= aeroelastic deflection amplification factor a = flexibility, a F is free-body flexibility a s = amplitude of motion of support reference point #0 = airfoil two-dimensional lift curve slope B = aeroelastic load amplification factor b = reference span C = generalized aerodynamic force coefficient: C/ is inertial value, C q is angular rate value, C a is incidence and control surface value, C^ is incidence rate value, C 0 is initial value C e = experimental control point force coefficient C h = complex oscillatory aerodynamic influence coefficient C hs = static aerodynamic influence coefficient C m = aerodynamic pitching moment coefficient C z = aerodynamic normal force coefficient c =mean aerodynamic chord c f = local lift curve slope EI X