HYDRODYNAMIC FORCES 



149 



ments on a free floating body with a suitable analysis of 

 the coupled motion are therefore suggested. 



In both types of tests just suggested the added masses 

 and damping moments are to be obtained as real and 

 imaginary parts of the total hydrodynamic moment. 



26 Scale Effect on Damping in Roll is very uncertain 

 and conflicting data have been gi\'en by various e.xperi- 

 menters. Presence of the squared term in equation (31) 

 as well as T. B. Abell's (1916; Section 5.34) measure- 

 ments indicate a large viscous effect. A scale influ- 

 ence is therefore to be expected. On the other hand, 

 Watanabe and Inoue (1958) demonstrated identical 

 damping values for a ship and its model. Specific I'e- 

 search to evaluate the scale effect is therefore needed. 

 This can best be done by sectional damping measure- 

 ments indicated under project 25; larger model sections 

 can be used in these tests than would be practical in the 

 same tank with a complete ship model. 



27 Speed Effect on Damping in Roll is large as is 

 indicated by Figs. 22 and 23 and as is well known from 

 experience with ships at sea. It is known, however, only 

 qualitatively and theoretical and experimental research 

 for its quantitative evaluation are needed. Figs. 22 and 

 23 give, of course, quantitative data for particular 

 models. The word "quantitative" was used in the 

 previous sentence in the sense of generalized quantitative 

 data suitable for use in ship design. 



(a) Theoretical approaches to the evaluation of sec- 

 tional damping do not indicate the probabilit.v of a large 

 speed effect. It appears to the author, therefore, that 

 these effects stem from (i) the forward (leading) edge of 

 bilge keels, (ii) the bow sections of the hull adjacent to 

 the stem. Theoretical analyses (at least crude ones) of 

 the action of these ship parts can be made by analogy 

 with the evaluation of damping of airplane surfaces. 

 This can be found in many books on aeronautical engi- 

 neering. 



The local water flow at the stem of a ship probafily 

 can be estunated by assuming it to be two dimensional 

 (in horizontal planes) and applying the Schwartz-Christof- 

 fel transformation. The instantaneous obliquity of the 

 flow is given by the vectorial addition of the forward ship 

 velocity and the lateral velocity of an element of the 

 stem caused by ship rolling and a given depth of the ele- 

 ment below the axis of rotation. 



(6) The following experimental projects ou the speed 

 effect on damping in roll are suggested : (i) The relati\'e 

 contribution of the bilge keel's leading edge can be esti- 

 mated by a successi\'e shortening of bilge keels, cutting 

 away the leading edge while retaining the position of the 

 trailing edge; (ii) in experiments on the bare ship models, 

 the eft'ect of the entrance angle on the damping increase 

 with speed is to be evaluated. 



It is probable that the damping can be expressed em- 

 pirically by a polynomial in speed with a first term inde- 

 pendent of speed. It may be hoped that this first term 

 can be evaluated by the strip method on the basis of 

 Ursell's (1949a) or possibly Grim's (1956) material. 



The subsequent speed-dependent terms may be e\'alu- 

 ated by the theoretical analysis suggested under sub- 

 project (a). Thus a complicated physical relationship 

 may possibly be replaced by a smnmation of assmned 

 simple ones, and a crude theory may provide sufficient 

 guidance for the generalization of empirical data. 



28 Measurements of Pressures in Slamming Impact 

 are needed. Pressures should be measured in the process 

 of normal slamming in waves rather than in artificial 

 conditions. The author con.siders the measurements of 

 peak-point pressures neither reliable nor necessary for 

 engineering purposes. He suggests instead the measure- 

 ment f)f a mean pressure over an area typical of the un- 

 supported area of bottom plating in actual ships. Ochi's 

 (1958) use of 1-in-diam gages on models corresponding 

 to 22 in. on a ship, appears to be a good example. It is 

 emphasized that the time history of pressure growth and 

 decay is needed. The data are to be u.'ed in computing 

 the elastic response of a ship structure, and this requires 

 knowledge of the time pattern of the pressure appli- 

 cation. 



2Q Impact Characteristics of a Plate on a Rippled 

 Water Surface should l)e evaluated both theoretically 

 and experimentally. Theoretically, the problem of plate 

 impact on a single crest of a wave of a certain steepness 

 (up to the limiting case of 120 deg included angle) may 

 be tractable. The results can be generalized by statis- 

 tical methods to apjily to the impact on a sea surface of a 

 typical spectrum. Flat-plate and V-shaped sections of 

 small deadrises may be considered. 



30 Total Impact Force in Slamming should also be 

 measured experimentally. The measurement (or rather 

 estimate) can be obtained from simultaneous accelera- 

 tions in heaving and pitching. This will give the magni- 

 tude and the position of the impact force. This method 

 of force evaluation is applicable to ships at sea as well 

 as models in towing tanks. A complete time history is 

 required. The very short duration of the impact makes 

 it necessary to pay utmost attention to the sensing and 

 recording equipment. Because of uncertainty in the 

 elastic response of a model, it is suggested that accelerom- 

 eters be located near the estimated force position and 

 be well secured to a solid block supporting the bottom 

 of the model in the impact area. Measiu'ements made 

 in regular waves may be used to pro\'ide the easiest corre- 

 lation with a theory. Measurements in iri-egular waves 

 will correspond to actual shijj behavior at sea and also will 

 be useful in connection with a statistical evaluation of 

 slamming at sea. The results of this project are expected 

 to be used in the evaluation of ship bending moments 

 taking the elastic response into account. This will be 

 discussed in Chapter 5. Tests should be conducted at 

 several values of draft and trim, corresponding to the 

 range of these values used at sea. 



31 Slamming Impact of Ship Sections of Low Section 

 Coefficient must be evaluated theoretically and experi- 

 mentally. Such ship sections are typical for bow sec- 

 tions of fast ships such as destroyers, cruisers, and air- 

 craft carriers. With a sharp deadrise at the keel, the 



