New radius of curvature formulae and their applications

Abstract : The shape of a surface influences reflectance properties; therefore, shape is one factor among many which determines how difficult it is to 'see' a surface-laid mine from the air. The shape of the surface can be locally characterized using the radius of curvature concept. A survey of the literature showed no systematic radius of curvature treatment which displayed explicit formulae for calculating radius of curvature in three dimensions and which emphasized applications of this concept. In this report a new and physically motivated definition for radius of curvature is given and from this definition the well-known and some hitherto unknown radius of curvature formulae are derived. The problem of computing radius of curvature in three dimensions for curves known at discrete points is solved and applied to the problem of measuring one parameter characterizing enemy aircraft maneuverability from radar data. Other applications include: the design of a device for measuring road or railroad track radius of curvature, the design of a device for checking highspeed roads for proper banking and a technique for the use of curvature concepts in the design of a land navigational system. (Author)