Flat- Faced Forebodies 



The curves connecting the flat face to the parallel middle body of the two flat-faced 

 shapes were developed, using both an elliptical contour and a contour derived from the 

 Granville two-parameter cubic polynomial. 3 The nondimensional elliptical contour offsets are 

 given by Equation (2), and the Granville cubic polynomial offsets are given by 



rj 3 =— K (£) + kj Kj^+Qtf) (4) 



and 



K (£) = 6£(£-D 4 



where now 





K 1 (£) = -|f 2 «-l) 3 





Q(£) = l-(£- 1) 4 (4| + 1) 



fc 



2y - D 



/T 1 * 



? - 



-x/L E and 7?- D _ ^ 



v 



/d 3 A _ (D " D F )3 /d 3 x\ 



W/| = o,r, = o 8Le Vdy 3 / x = oy = DF/2 



*i - 



./d 3 ^ _ 2L E /d 3 y\ 



Uv, =1 °- D Adx 3 ; x=LE 



where D p is the diameter of the flat face. 



For the Granville shape, the slope and curvature of the connecting curve match the slope and 

 curvature of the flat face and parallel middle body where the curves join, and the shape of a 

 parent body is determined by values assigned to k Q and kj . The values of L E and (D - D p )/2 

 then determine the contour of the particular forebody. The elliptical transition curve (non- 

 dimensional) is fixed, and variation in model forebody shape is a function of only L and 

 (D- D ]r )/2. The slopes match at the flat face and parallel middle body; however, the 

 curvatures do not. 



3 Granville, P.S., "Geometrical Characteristics of Flat-Faced Bodies of Revolution," NSRDC Report 3710 

 (Nov 1971). 



