cos 0) 
aoe {-M, cos 8 Z., - M, sin 6 nee + Q,6 + M, 0 (Zeg sin 6 - ets 
dw, A 
+ fm, a cos 0 ag- ['mw,0 sin 6 dé 
Q Q 
dw, vi dw, 
= V — si + —_ 
fm aE sin 6 dé A m,U DE cos 6 dé 
-UV - | Vm,dé - 2 
mM, fight i m, dé pf ca,cb¥ dé} cos 6 
+ [ apenct 
Q 
where M, = [mae 
Q 
and 
Q, = [meat 
Q 
This is essentially the form in which the integrals have been computed in the program. 
The rate of change of the sectional added mass in the third term of the integral 
expression is derived by relating it to the rate of change of depth of fluid penetration of the 
section. The added mass of a section is assumed to be equal to 
ma aka me pb? 
for which the time derivative is 
m, = k, tpbb 
where b is the instantaneous half-beam of the section, and k, is an added-mass coefficient, 
assumed to be constant. A value of k, = 1.0 was used in the computations contained in this 
report. For sections with constant deadrise, which is an imposed limitation of this work, 
the half-beam is related to the depth of penetration by 
b=dcotB 
36 
