where d is depth of penetration, and @ is deadrise angle. 
Taking into account the effect of water pileup, the effective depth of penetration d, is, 
according to Wagner 
d, =7/2d 
e 
and 
b=d, cot 6 = m/2 d cot B 
where 77/2 is the factor by which the wedge immersion is increased by the pileup. Using this 
expression for the half-beam, the rate of change of sectional added mass becomes 
m, = kampb(n/2 cot B)d 
This expression is valid for penetration of the section up to the chine. When the immersion 
exceeds the chine, the sectional added mass is assumed to be constant, i.e., 
2 
may = koma plOme 
rh, = 0 
where Dee is the half-beam at chine. 
The submergence of a section in terms of the motions is given by 
h=z-r 
where z = Zo, - & sin 0+¢€ cos 0 
ia COS (kGee +£ cos @ +f sin 9) + wt} 
For wavelengths which are long in comparison to the draft and for small wave slopes, the 
immersion of a section measured perpendicular to the baseline is approximately 
Dial 
~ 
cos @ -ysin#@ 
where v = wave slope 
37 
