Geometrical characteristics of noses and tails for parallel middle bodies

Abstract

Two-parameter geometric systems are developed for noses and tails attached to parallel middle bodies in terms of independent polynomials. A new parameter is introduced–the rate of change of curvature with arc length at the juncture with the parallel middle body. ‘Quadratic’ polynomials are considered for bodies of revolution and ‘square root’ polynomials for symmetric two-dimensional bodies. Permissible ranges of the two adjustable parameters are obtained for selected geometrical constraints such as the presence of inflection points.