"Fundamental" Parameteric Geometry Representations for Aircraft Component Shapes

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.