Vaulting 



V note: «-plane is mean 



ORIGIN 

 OFfi?C, 



WATER SURFACE 

 LINE IN CC-PLANE PARALLEL TO X-AXIS 



Fig. 1. Coordinate systems and nomenclature for member 



is assumed to be expressed as 



= - \ \ plT ds + C^U„ -^ J + C„U„w-'a„K) 

 J J '^ D nw nb m^ nw nb' 



(7) 



The first term is the resultant force obtained by integrating 

 over the surface of the body the pressure, p, which would exist 

 at that location if the body were nq^ present and is seen to be the 

 Froude-Krylov force. Note that n is the unit normal vector 

 directed out of the body into the fluid. 



The second term is called the drag force and is assumed 

 proportional to the relative normal velocity between the member and 

 the fluid. The third terra is called the added mass force and is 

 assumed proportional to the relative normal acceleration between 

 the member and the fluid. 



The first term and the first parts of the second and third 

 terms are seen to be dependent on the wave motion while the remain- 

 ing parts of the last two terms depend on the structure's rigid-body 

 motions. In order to evaluate these forces for the cylinder, we must 

 define two additional coordinate systems* The first, ox yz, is 

 associated with the member such that the x-axis lies along the 

 centerline of the member, the y-axis is directed generally upwards, 

 the z is defined to form a right-handed system. The second co- 

 ordinate system, oIt)^, is used to express the waves, and is so 

 defined that the 4-a~xis lies in the mean water surface and is positive 



1090 



