The normal hydrodynamic force per unit length f, acting at a section, is treated as 
quasi-steady and is assumed to contain components proportional to the rate of change of 
momentum and the velocity squared (drag term), i.e. 
Pes all Gate: 2 
=~ |p (ma) + Ope bVv (2) 
where V is the velocity in plane of the cross section normal to the baseline 
m, is the added mass associated with the section form 
C,, . is the crossflow drag coefficient 
D,c 
p is the density of the fluid 
b is the half beam. 
For sections near the leading edge of the wetted length with nonwetted chine, the 
added mass is assumed to be defined in the same manner as during an impact which for a 
V-shaped wedge is given by 
m, =k, 7/2 pb? (3) 
where k, is an added-mass coefficient that may also include a correction for water pileup- 
k, is assumed to be 1.0 without pileup correction. 
The rate of change of momentum of the fluid at a section is given by 
io) 
dg 
dé 
D alee 
ay DS Pid eae (Ca De (4) 
where & is the body coordinate parallel to the baseline; see Figure 1. The last term on the 
right-hand side of Equation (4) takes into account the variation of the section added mass 
along the hull. This contribution can be visualized by considering the 2-D flow plane as a 
substantive surface moving past the body with velocity U = -dé/dt tangent to the baseline. 
As the surface moves past the body, the section geometry in the moving surface may change 
with a resultant change in added mass. This term exists even in steady-state conditions and 
is the lift-producing factor in low-aspect-ratio theory. 
The added mass of a section with fully wetted chines has not been developed to the 
same extent as the V wedge. In steady-state planing problems such as those of Shuford,* 
