"Fundamental" Parameteric Geometry Representations for Aircraft Component Shapes

TLDR

Aircraft component geometries such as nacelles, bodies, and airfoils are continuous but non‑analytic due to infinite nose slopes and large curvature variations, requiring many coordinates to describe them. The study formulates a general mathematical framework to enable a fundamental geometric transformation technique for airfoils, axisymmetric bodies, and nacelles. The technique introduces a simple analytic shape function that directly controls key parameters (leading‑edge radius, trailing‑edge boattail angle, aft thickness) and a class function that generalizes the method to a wide range of geometries. The shape and class functions provide a unified, versatile approach for describing arbitrary 2D and 3D geometries, as demonstrated by multiple examples.

Abstract

The mathematical description of a nacelle, body or airfoil having a round nose and pointed aft-end is a continuous but non-analytic because of the infinite slope at the nose and the corresponding large variations of curvature over the surface. Consequently, a large number of coordinates are typically required to describe the geometry. The general mathematical formulation necessary to describe an airfoil, axisymmetric body or nacelle, is defined in order to develop a fundamental geometric transformation technique. This method includes the introduction of a simple analytic and well behaved shape function” that describes the geometry. The “shape function” provides the ability to directly control key geometry parameters such as leading edge radius, trailing edge boattail angle, and closure to a specified aft thickness. A class function is defined that generalizes the method for a wide variety of geometries. The shape function and class function methodology provides a unified approach for describing rather arbitrary 2D and 3D geometries. Examples of using this approach to produce a variety of 2D and 3D geometries are shown to illustrate the versatility of this new methodology.