THE EFFECT OF SPEED OF ADVANCE UPON THE DAMPING OF HEAVE AND PITCH 
because extensive tables of these functions are available. With 
F = c/(g L)}, and with M, sinpt being the required part of 
the moment, we obtain finally 
a Mi/p BEg? L4Q = } B/L F-3 
[2 
A, B, sec3 8 Ay 
(1 + 4 B cos 6)? 372\ 4 F2 
0 
7/2 
a A, B, sec? 6 
(1 +4 B cos 6)t 3? 
0 
7/2 
a, A3 B; sec? 0 2 A3 
(1 — 4 B cos 6)! 3/7 \4 F2 
61 
— 9A 0.29 
sec bye LF2 d@0 
A 
(7 
_dA2 
sec ye aR "8 769 
— 93 oo 
sec) ¢ aR 9 
[2 
Ag B, sec? 6 
+/ (1 — 4B cos )6# 
61 
with 6, given by equation (7), B = p c/g, and 
Ay, Ap =1+28Bcosé + (1 +48 cos 0) 
B,, B, = (1 +48 cos A+ +1 
A3, Ay = 1 —2Bcos@ + (1 — 4 B cos 0)+ 
B;, By, = 1 + (4B cos)! | nay 
If we write g = p (B/z)?, it can be verified that when c = 0, 
equation (13) reduces to the result for this case which can be 
obtained directly, namely 
dA , 
3). ( me sec 6) ear? 79] “(13) 
m/2 
7M, /pgtBtL!Q=q3 ese TAG 5? cos 8) d6 (15) 
0 
620 
