Understanding and Prediction of Ship Motions 



Attempts were subsequently made to correct this situation by reformulating 

 the perturbation problem. In particular, the Peters-Stoker assumption that the 

 ship beam can be used as the sole characteristic small parameter is open to 

 question; the amplitude of the incident waves is a small quantity which is quite 

 independent of beam. A multiple -parameter perturbation scheme takes care of 

 this problem theoretically, but it does not lead to practicable results. The the- 

 ory for motions of a thin ship still stands in this unsatisfactory condition. 



There seem to be at least two logical ways out of this predicament. We 

 must have at least one small parameter associated with the hull geometry, in 

 order that the ship travelling at finite speed may cause only a very small dis- 

 turbance. (This is necessary for any linearization to be valid.) We could try to 

 select this small parameter so that the damping due to vertical motions is in- 

 creased in size by an order of magnitude. Such a result is realized, for exam- 

 ple, in a flat- ship theory. But there are at least two objections to this; first, 

 the practical solution of the flat- ship approximation is very difficult, involving 

 a two-dimensional integral equation, and, second, the original difficulty would 

 pop up again in consideration of horizontal modes of motion, namely, in surge, 

 yaw, and sway. 



The second logical escape is to use a small parameter which leads to no 

 resonance at all in the lowest order non-trivial solution. This is accomplished 

 by assuming that the ship is both shallow and narrow, i.e., slender. Then it can 

 be shown that the inertia becomes an order of magnitude smaller than in the 

 thin- ship theory, whereas the damping order of magnitude is unchanged. But 

 slender body theory for ships also has its problems. In particular, a theory for 

 ship motions should be part of a general theory which includes steady transla- 

 tion as a special case. We now know that slender body theory in fact gives poor 

 results for the wave resistance of a ship in steady motion. 



Nevertheless, slender body theory appears promising for predictions of 

 ship motions. I shall only outline the ideas involved, for, if I presented the de- 

 tailed modern theory as it stands in the published literature, I would be out-of- 

 date before this morning session is over. The following speakers will present 

 some of the evidence which suggests the promise of the approach. 



It is obvious that much remains to be done in the theory of ship motions. 

 There is still a problem of developing a logical approach which gives answers 

 agreeing with experiments. Furthermore, most of my discussion relates only 

 to motions in the longitudinal plane of the ship; we have barely begun to attack 

 the corresponding problems involving yaw, sway, and roll. 



SHIP MOTIONS IN CONFUSED SEAS 



It has long been recognized that the sea is a complicated thing, but it was 

 only with the war-time and post-war development of random noise theory that 

 the means became available for providing a realistic description of it. 



The kind of statistical description to be employed in describing the sea de- 

 pends on the specific aspect of the ship motions problem which happens to be of 



