136 



THEORY OF SEAKEEPING 



than in the case of the simpler strip method (see con- 

 cluding paragraph of Section 6.oj. The primary value 

 of the advanced method lies in indicating general trends 

 which are not seen as easily in the strip method. 



One of the most important needs when using the strip 

 method (two-dunensional flow) is establishment of cor- 

 rections to account for the actual three-dimensional flow. 

 A beginning in this direction was made by Havelock 

 (195(i) and Vossers (1956) as shown by Figs. 17 and 18. 

 Ha\elock treated a submerged spheroid. A^osser's treat- 

 ment applied to a Michell ship and was made on the basis 

 of Haskind's methods, but no details of the process or the 

 exact ship model used have been published. Correction 

 coefficients were given for the entire ship. It is also 

 necessary to evaluate a correction for each strip for cal- 

 culation of the load distribution. Presumably this evalu- 

 ation can be obtained by differentiating Haskind's ex- 

 pressions for forces and moments with respect to ship 

 length. 



Haskind treated ships with affine sections. It would 

 be desirable to develop a similar treatment for ships with 

 full convex form amidships changing gradually to wedge 

 and hollow sections at the ends. This would correspond 

 to normal practical ships. Concei\-ably correction fac- 

 tors for conversion to three-dimensional flow would be 

 different for such forms from those obtained by Havelock 

 and Vossers for bodies with affine sections. 



Haskind and Riman experimented with a model, Fig. 

 24, wall-sided at the LWL, for which Michell's assump- 

 tions appear to be admissible. It would be desirable to 

 repeat the experiments for a model with V and concave 

 sections, thus distinctly violating Alichell's assumptions 

 at the load waterline. Such sections are common at the 

 stern of actual ships and appear at the bow of JMaier- 

 form ships. 



The projects outlined would make direct use of Has- 

 kind's material and do not call for ad\'anced mathe- 

 matical knowledge. A project on a higher level would 

 be to find a mathematical ship form for which the 

 Kotchin-Haskind //-function can be e\'aluated without 

 resorting to Michell's assumptions. This apparently is 

 a straightforward process for a submerged spheroid, and 

 conceivably a suitable mathematical definition could be 

 formulatecl for a surface ship which would bear a reason- 

 able resemblance to a normal practical form. 



The general derivations of Haskind have been applied 

 only to "longitudinal" or "symmetrical" motion of surg- 

 ing, heaving and pitching. The material also can be ap- 

 plied to combined rolling, yawing and side swaying. 



7 Forces Caused by Slamming 



As a definition of slannning the following cjuotations 

 from J. L. Kent (1949) can be used: 



"It is not an uncommon experience for ships to 'slam' 

 when labouring in a seaway. By slamming is meant the 

 series of blows delivered by the sea to the ship's structure 

 at irregular intervals and generally at the forward end 

 of the vessel. Each 'slam' causes a shudder to run 



through the ship, followed by a rapid vibi'ation of the 

 hull structure. If the magnitudes of these blows are 

 large, serious structural damage may occur and even 

 if the blows are small, the hull will be M-eakened by fa- 

 tigue, if slamming is frequent. 



"Damage to the hull structure by slamming has oc- 

 curred at the forward end of the ship only, in all cases 

 within the knowledge of the author. This damage was 

 situated between l/9th and 1/lOth of the ship's length 

 from the forward perpendicidar and occurred to the bot- 

 tom plating and floors a little to one side or the other of the 

 vertical keel. Damage to the vertical keel was not 

 shown, probably because of the great strength of this 

 ship's girder. 



"Wien slamming becomes severe, the experienced ship- 

 master invariably reduces speed, which immediately 

 eases or stops slamming. The author has never heard 

 of a ship slamming when drifting unpropelled in a sea- 

 wa3'. It would, therefore, appear that the hydro- 

 dynamic pressures on the hull, brought into existence by 

 the ship's forward motion through the water, play an 

 important part in creating slamming forces. 



"It was the author's experience that loaded vessels 

 did not slam with the same persistence or force as when 

 the same ships were in the light condition; and it is be- 

 lieved that this is the general experience of shipmasters. 



"It would appear that the ship and sea conditions con- 

 ducive to heavy shunming are: 



(1) Maximum heaving into and out of the water 



(2) Considerable height of ocean waves 



(3) Light draught 



(4) High ship speed 



(5) Shape of ship form forward 



(6) Irregular sea; i. e., two or more swells occurring 

 at the same time. 



(7) The blows delivered to the ship's hull will prob- 

 ably occur between l/8thand 1/lOth of the ship's length 

 aft of the stem." 



In this section attention will be concentrated on the 

 generation of hydrodynamic pressures and forces in the 

 process of slamming. Ship motions leading to slamming 

 will be discu.s.sed in Chapter 3. Towing-tank experi- 

 ments as well as observations on ships at sea ha\'e sho\vn 

 that the force in slamming is of the nature of an impulse 

 manifested by a high value of acceleration with a very 

 short duration. Only a small amount of the ship's ki- 

 netic energy is absorbed, and recorded traces of heaving 

 and pitching motions continue without perceptible 

 change. Oscillations initially excited by a slam are 

 superposed o\'er the strain records in ship bending, 

 which are continuous in the mean. These oscillations 

 appear to have the natural two-mode vibration frequency 

 of a ship. On a typical cargo ship at light draft the vi- 

 brations persist through 30 to 60 cycles, or between 15 

 and 30 sec. They are thus superposed o\'er se\^eral 

 cycles of the primarj' bending stress, which ha\e periods 

 of the order of 6 sec. 



7.1 Expanding Plate Theory in Landing Impact of 

 Seaplanes. While hj-drodynamic shocks can occur at the 



