Polynomials 



7 7 = rR(|) + k 1 K 1 (|)+Q(e) (1) 



where R(£) = 2£(£- l) 4 



K i a)=-t 2 «-l) 



Q«) = i-(£-i) 4 (4£ + i) 



Hemisphere 



r, = (2k-Z 2 )' (2) 



where | = x/Lg and 77 = 2y/D 



D is forebody maximum diameter 



Lg is forebody length 



x is axial distance from forward point 



y is forebody radius 



r is radius of curvature at £ = 



k, is rate of change of curvature at £ = 1 



where r = r- = -; r- ; k, - , 



4L e 1 ~ _/d 3 A _ 2L E /d J y 



djj\ D~ <y_x\ W/£ = , u \dx 



di7 2 /£ = \dy 



£ = 1 \ UA /x = L F 



2 



By selecting proper values of r and k, , various parent shapes can be derived. The values 

 of L £ and D then determine the shape of the particular forebody. Once values of r and kj 

 have been selected, the prismatic coefficient C p is uniquely determined and is given by 



E 



r *i 2 



C " E = T? - Ti5 + 1 (3) 



At x = L c , the slope ( — I and the curvature are set at zero, matching 



their corresponding values on the parallel middle body. The hemispherical shape is fixed 

 with L £ = D/2. At x = L £ the slope matches that of the parallel middle body; however, the 

 curvature does not. 



