63 



APPENDIX 5 



GEOMETRICAL PROPERTIES 



The geometrical properties of sixth-degree polynomial forms can be 

 obtained from the following equations when the linear dimension is chosen: 



Diameter: d = t" t"" 3 



A 



Distance of maximum section from nose: X = ml [2] 



m 



Nose radius: R = —2" [3] 



Tall radius: R^ = -\ [k] 



Volume: V = C ^ [5] 



Longitudinal center of buoyancy: X = p— jxy^dx [6] 



p 



Volume moment of Inertia about the vertical axis through 

 the longitudinal center of buoyancy: 



_ v 



where x = y 



Surface area: S = ^J \ky^ '^Tsihi^fY^ 



[8] 



The integral in Equation [8] may be evaluated numerically using 

 Gauss's formula 



1 



J0(u)du = R^^(uJ + R^^^lUg) + ... + R^4>{\x^) [9] 







The numerical values of the u's and R's for n = 7 are: 



u^ = 0.02544604383 R^ = R7 = 0.06474248308 



U2 = 0.1292344072 



U3 = 0.247077^243 Rg = Rg = 0.1398526957 



u = 0.5 



u^ = 0.7029225757 R3 = Rg = 0.1909150253 



Ug = 0.8707655928 



u^ = 0.9745539562 R = 0.2089795918 



