HYDRODYNAMIC FORCES 



145 



for the latter indicated by the analyses of Ha\'elock and 

 Vossers have not diminished the discrepancy. Further 

 worlv is needed in four directions : Rechecic of tlie original 

 mathematical worlc (particularly in regard to physical 

 assumptions) ; experimental verification by oscillation of 

 cylindrical bodies; investigation of the effect of non- 

 linear damping on the mean value, Section 3.22; and 

 further investigation of the three-dimensional effect. 



In view of damping nonlinearity, the three-dimen.sional 

 investigation must also be made for a finite amplitude 

 of ship oscillations. The mathematically simple Hol- 

 stein-Havelock method of damping evaluation may pos- 

 sibly be extended to yield the damping of three-dimen- 

 sional bodies oscillating with finite amplitudes. 



In the foregoing projects, heaving and pitching were 

 kept directly in mind. Similar projects are recommended 

 for side-swaj'ing and for rolhng motions. Although the 

 basic techniciue was indicated by Haskind (1946) and 

 Ursell (1949a), derivations for the nonsymmetric mo- 

 tions were carried out to a lesser degree of completeness. 



Practical evaluation of Haskind's (1946) work has 

 been made in applying it to a Michell-type ship. An 

 advanced physio-mathematical project is recommended 

 in order to develop a mathematically defined family of 

 fines for whicli the Kotchin-Haskind II function can be 

 evaluated without resorting to Michell's assumptions. 



8.3 Measurements on Full-Size Ships. Measure- 

 ments made on full-size ships at sea involve responses of 

 a ship to the complex (irregular) sea whicli occurs in 

 nature. Tlrese will be discussed later in Chapters 3 and 

 5 in connection with ship motions and ship elastic re- 

 sponses. 



8.4 Slamming Pressures and Forces. The main 

 shortcomings of pressiu'e measurements in slamming, 

 both on models and on ships at sea, ha^-e been as follows: 



(a) Failure to distinginsh between the maximum pres- 

 sure causing local plate failure and the total force felt as 

 a slam and recorded in the bending stress amid.ship. 



(6) Failure to consider the extremely sharp peaks of 

 the pressure-distribution diagram, given theoretically by 

 Wagner's theory and observed experimentally. 



As an illustration of the former, in the work of M. A. 

 Todd (1954) and of Bledsoe (1956) effort was directed 

 only at determining the high pressures which were indi- 

 cated to be at the edge of the wetted area located at the 

 beginning of the bilge turn. These pressures were asso- 

 ciated with the maximum value of the total load re- 

 corded as slamming by an accelerometer. On the other 

 hand, maximum pressures causing bottom-plate damage 

 apparently occur in actual ships at an earlier instant of 

 impact, when the wetted width is very small and when 

 high pressures, resulting from too small a deadrise, are 

 present near the keel. While these pressures are high, 

 they cover a small area and the total force does not be- 

 come significant. In each research project on slamming 

 the two separate objectives, local pressure and total force, 

 must be clearly kept in mind. 



In connection with the second shortcoming (b), it 

 should be remembered that with a small angle of dead- 



rise, common in ship forms, the pressure peak is extremely 

 narrow and moves from keel to bilge extremely rapidly. 

 (The distance from keel to bilge is traversed in about two 

 thirds of the time it takes for this part of the bottom 

 to penetrate into water.) Therefore, reliable measure- 

 ments of these peak pressures on models are next to im- 

 po.ssible, both because of the physical diameter of a pres- 

 siu'e pick-up and of its freciuency response. The expand- 

 ing-plate theory also is not reliable in the matter of peak 

 pressure for a small deadrise, although it is apjsarently 

 reliable in respect to the total force. 



In experiments on ships at sea it Iras usually been pos- 

 sible to provide only a very limited number of pressure 

 gages, so that the probability of recording the peak pres- 

 sures is low. Gage readings depend to a large extent on 

 an accidental proximity to the pressure peak, so that the 

 real meaning of the record taken is uncertain. 



It is suggested, on the basis of the foregoing discu.ssion, 

 that a peak pressure is an academic concept to which 

 little attention need be paid. Instead it is recommended 

 that a convention be established for an area over which 

 a mean pressure is of interest. In practice this corre- 

 sponds to an area of a bottom plate between structural 

 supports. Instead of using point-pressure gages in 

 models and ships, a movable plate or a large-diameter 

 gage can be pro^dded, the total force on '\\'hich can be 

 measured by suitable small-deflection dynamometers. ^■' 

 Records of the total force exerted by water on such a 

 plate should be more systematic and more applicable to 

 design problems than measiu'ements by a few point- 

 pressure gages. In addition, it will be possible to ob- 

 tain comparable measurements by the same method on 

 a ship at sea and on a model in a towing tank. It should 

 be emphasized, howe\'er, that statement of the maximum 

 of the mean pressiu'e over an area is not suflieient. A 

 complete time history of the pressure is needed in order 

 to e^-aluate the elastic response of a structure. 



Theoretical research on ship slamming in waves is 

 recommended. The procedure of M. A. Todd (1954) for 

 computing the slamming force will apply once e\'aluation 

 is made of the relative position of ship and wa\'e and of 

 relative ship-water velocity. This subject will be dealt 

 with in Chapter 3. The project should be carried out 

 first for regular wa\'es and then for irregular ones. Study 

 should be made of a ship model for which towing tank 

 data on motions and instances of slamming are available. 



Condenseil List of Suggested Researcti Topics 



The following are given approximately in the order of 

 exposition in the monograph text. 



1 Evaluation of Added Masses should be undertaken 

 for sections characterized by: 



(a) The use of curved fines in conjunction with bilge 

 keels. Such sections are common in the middle part of 

 a ship's length. 



" In this connection attention is called to Oehi's (1958) work. 

 A gage 1 in. diam was used in the models, corresponding to 22 

 in. diam on a full-size ship. 



