SahveiheVy Bentkowsky and Kerr 



the point In question and the center of the axis (- forward). This 

 integrcil can be evaluated at each step in the integration of a simula- 

 tion when the distribution of Z'^i^^i Is known but It proves both 

 cumbersome and time consuming. On the other hand, for a nearly- 

 cylindrical body such as a missile or the DSRV, test data has shown 

 that a fair representation of both the force and moment are obtained 

 when a constant value Is used for Z'y^iv^i from the nose of the vehicle 

 to the forward edge of the shroud, a distance Lg from the nose. 

 This then allows the value Z wlwl to be removed from the Integral 

 and sets the equality Z'wiwi = Z^iwl/Ls. Replacing the local normal 

 velocity w' by Its equivalent w + qX, the Integration 

 Z'wlwl Jbody (^ "^ qX)* U^w-qX) | dX still poses some problems because 

 of the absolute value signs. To accommodate these two Integrals 

 are formed depending whether the center of rotation, the point where 

 w' = 0, Is on or off of the body. Expressing the ratio of the distance 

 the center of the axis system Is off of the nose, L|, and the length 

 Ls as Kg = L|/Ls the center of rotation Is forward of the nose when 

 w/qLs < Ks and aft of the body when w/qLs > Kg - 1 and the value 

 w'|w' I can be replaced by (|w|/w)(w*) =( | w |/w)(w^ + 2wxq + x^q^) 

 and the Integration 





'-s''-l I I pL -L, 



w J.L, 



2 . -, _ . ..2_2v 



w' Iw' I dx = Z' „, i^^ \ (w^ + 2wxq + xV) dx 



results In three terms 



Ma" 



where 



C. WW +C q w +C,^-^-^q 



2 , 



C| - Lg Z^i^i 



Cg = Lg (1 - 2Ks)Zj,|^| 



C, = lJ/4(1 - 3K3 + 3Ka)Z', 



Iwl 



When the center of rotation Is on the body Kg^ w/qLg > Kg - 1 the 

 Integral must be divided Into two parts to account for the sign change 

 In w* 1 w' I at the center of rotation and 



z'.,«,_f'""wMwi dx=- z',,^M[r° w-^ dx - r ' w-^x] 



where the | q | /q Is used to denote the direction of force since the 

 local normal velocity forward of the center of rotation depends only 



1124 



