Allocating Section Thickness and Camber for Transonic Wing Design

Abstract

The ability to empirically allocate the spanwise distribution of thickness across a wing during the earliest phases of conceptual design is extremely useful. Quantitative statistical design for system optimization studies requires a reliable allocation process, directly traceable to a final loft. In choosing the local section thickness ratio of a wing, there are multiple considerations which are at first, somewhat unintuitive to make. For each strip, from root to tip, the allowable wing thickness as well as the necessary camber and incidence depends broadly upon the local lift the strip must sustain as well as the design Mach number for the incoming flows. The difficulty in developing a concise technique or equation to simultaneously determine thickness and camber stems from a cross-coupling of common design variables. A statistical study of potential flow solutions lead to develop a technique which the reader may use to supplant the Korn Equation, choosing specific rather than generalized theoretically attainable airfoils to meet specific lift and critical Mach number conditions. Subtle, yet important, non-linearities were found in the coupling between allowable thickness, critical Mach number and design lift coefficient. Nomenclature CL = Lift CoefficientCL max = Maximum Lift Coefficient CL des = Design Point Lift Coefficient Cp = Dimensionless Pressure Coefficient = (P-P  )/q Cp* = Dimensionless Pressure Coefficient corresponding to the Sonic Condition L/D = Lift-to-Drag Ratio M = Mach number M cr = Critical Mach Number (where flow first goes sonic) M des = Design Mach Number M dd = Drag Divergence Mach Number (where pressure drag losses due to shock formation become significant) P = Pressure q = Dynamic Pressure t/c = Wing Section Thickness-to-Chord Ratio V = Velocity  = Angle of Attack (degrees)  = Prandtl-Glauert Factor  = Potential  = Specific Heat Ratio of Air (typically 1.4)

Hybrid Laminar Flow Control Optimizations for Infinite Swept Wings

“…In such a way, the coefficient matrix of the interpolating equation is a sparse band matrix, which improves computational efficiency to some extent. The details of the RBF dynamic mesh method based on the radial basis function with compact support are shown by Kady and Takahashi [40]. The interpolating function of the RBF dynamic mesh method based on the compact support radial basis function is described as…”