the crossflow is treated as a Helmholtz-type flow in which the Bobyleff results are used for 
estimating drag coefficients. Helmholtz flows are applicable only to steady-state conditions; 
so, it is assumed that the added mass for the fully wetted chine flow can be determined from 
Equation (3) using the value of the half-beam at the chine. In using the Shuford approach, 
it is assumed that the crossflow drag coefficient for a V-section is equal to the drag of a flat 
plate (C, , = 1.0) corrected by the Bobyleff flow coefficient approximated by cos 8, i.e. 
Coc = 1.0 cos 8 (5) 
The Bobyleff flow coefficient is the theoretical ratio of the pressure on a V-section to that 
experienced by a flat plate for a Helmholtz-type flow. 
The same approximation is used for estimating the drag coefficient for nonwetted chine 
sections, using the instantaneous value of the half-beam at the free surface. 
An additional force acting on the body is the buoyancy force f,,- This force is assumed 
herein to act in the vertical direction and to be equal to the equivalent static buoyancy force 
multiplied by a correction factor, i.e. 
fi =tee(A) (6) 
where A is the cross-sectional area of the section, and a is a correction factor. 
The full amount of the static buoyancy is not realized because at planing speeds the water 
separates from the transom and chines, reducing the pressure at these locations to atmospheric 
or less than the equivalent hydrostatic pressure. A greater reduction is realized in the 
buoyancy moment because of the corresponding shift in the center of pressure. Shuford4 
in his work on steady-state planing recommended a factor of one-half to obtain the correct 
buoyancy force. In the following computations, the buoyancy force was corrected by a 
factor of one-half, ie., a= 1/2. The buoyancy moment, computed as the static buoyancy 
force multiplied by its corresponding moment arm, was corrected by an additional factor of 
one-half to obtain the proper mean-trim angles. 
Equation (2) is a synthesis of several idealized flow conditions combined in an empirical 
manner. In all of these flows, it is assumed that the net relative movement of the fluid past 
the body is in an upward direction. This condition may not always be met in the case of 
unsteady planing in waves. Closer scrutiny will be required to determine what limitations 
will be imposed upon the problem as formulated and/or what modifications will be required 
to improve the formulation. 
