INTRODUCTION 



When the David Taylor Model Basin became interested in making stud- 

 ies of the hydrodynamical behavior of streamline bodies of revolution, it was 

 decided that such work could be most satisfactorily accomplished with families 

 of bodies of revolution for which certain parameters could be systematically 

 varied. Accordingly, prior to the testing, a program to establish a procedure 

 for the development of such families was initiated. 



It was determined that the best approach would be to define these 

 families by a general mathematical equation. The main advantages of the use 

 of a mathematical expression over the empirical or "fairing by eye" method 

 are: The geometry of the body can be precisely defined, fairness between 

 given offsets is assured, and the geometrical parameters can be directly and 

 accurately varied. 



A search of the literature reveals that various methods for obtain- 

 ing mathematical definition of forms have been tried but generally only for 

 application to single forms rather than to families of forms. Among these 

 have been combinations of known analytical curves such as an ellipse with a 

 parabola, an ellipse with a hyperbola, etc.,-"-'^ polynomials of various de- 

 grees,^ '^ and trigonometric series. 



The polynomial method was selected as the basis for the development 

 described herein since it appeared to have distinct advantages in ease of han- 

 dling and furthermore because of its ready application to hydrodynamical prob- 

 lems such as computations of theoretically derived pressure distributions. 

 It provides a simple method for evaluating the constants in the general equa- 

 tion once a given set of parameters has been selected, and supplies data for 

 readily computing the offsets of a wide variety of forms. 



THE GEOMETRIC PARAMETERS 



Of the various geometric properties that may be employed to char- 

 acterize the shape of an elongated body of revolution, it has been convenient 

 to choose, for practical reasons, the following primary quantities to define 

 the body; 



I is the length. 



d is the maximum diameter. 



X is the distance of the maximiom section from the nose, 

 m 



R is the radius of curvature at the nose, 

 o 



Eeferences are listed on page 6k. 



