THE COUPLING OF HEAVE AND PITCH DUE TO SPEED OF ADVANCE 
say, the linearized free surface condition, there would be 
additional terms expressing the effect of the surface dis- 
turbance. Meantime we shall simply assume that these 
terms are small, or at least that they do not affect appreciably 
the coupling effect which is under consideration. Taking 
(26) as it stands and calculating Z and M as in the previous 
sections, the values of k, and k’ will now be the usual values 
as if for motions in an infinite liquid. For the coupling 
terms, using (21) with (26), the vertical force upwards is 
—£rpae(1 +k) Uf [Qi (G)/Qs (&)] 
1 
[= 2 Benm@nary 
—trpae(I +k)Us(G— 1)? QY({) . 
Similarly for the additional moment we obtain the result 
—trpa@e(l + ky) UA[Q!(L)/Q! (L)] 
(27) 
1 
= 5 PS (1) Ph (w) dw 
—Airpa@e(l+k)Uh 
[3 (@ — 1)? Qt (Lo) — 4 QI (Lp)/Q! (fo)] 
In general, the coefficients of U b and UA in (27) and (28) 
are not equal numerically. For the case a/b = 10, they are 
(28) 
601 
It can easily be shown that as Cy > 1, we 
(2 — 1? Q) > —(@—-1) 
3 (22 — 1)? Q! (fo) — 4 QE (Lp)/Q! (Go) = + (G — 1) 
Thus for a long spheroid, with b/a small, 
approximate to 
nearly equal. 
have 
the equations 
\ . (29) 
(1) Haskinp, M. D.: “Oscillation of a Ship in a Calm Sea,” 
Bull. Acad. Sc. U.R.S.S. No. 1, p. 23 (1946); 
translated in Bull. No. 1-12, Soc. Nav. Arch. 
Mar. Eng., New York (1953). 
(2) Stoker, J. J., and Peters, A. S.: ‘““The Motion of a Ship, 
as a Floating Rigid Body, in a Seaway,” Rep. No. 203, 
New York University (1954). 
(3) WEINBLUM, G. P.: “Recent Progress in Theoretical 
Studies on the Behaviour of Ships in a Seaway.” 
(d+k)Mh—-4(1+kh)MU¢+epSh=0 
GQ+k)Is+40 +k)MUA+Memp=0 
References 
Interim Report, 7th Intl. Conf. Ship. Hydro., Oslo 
(1954). 
(4) Korvin-Kroukovsky, B. V., and Lewis, E. V.: “Ship 
Motions in Regular and Irregular Seas,” Tech. Mem. 
No. 106, Stevens Institute, New Jersey (1954). 
(5) Grim, O.: “Berechnung der durch Schwingungen eines 
SchiffskGrper erzeugten hydrodynamische Krafte,” 
Jahr. S.T.G., 47, p. 277 (1953). 
(6) Havetock, T. H.: “The Sinkage of a Ship at Low 
Speeds,” Zeit. f. Ang. Math. u Mech., 19, p. 202 (1939). 
