240 



THEORY OF SEAKEEPING 



0.4 



0.2 



0) 



F'0.224 



E 

 O 



[^ 0.3 

 w 



a: 0.2 _ 

 io.IL 



F-0.IB9 



0.G 



0.8 



X/L 



1.4 



Fig. 2 Comparison of calculated and experimentally measured 

 resistance of Weinblum's (1932) No. 1097 ship model in waves 

 at three Froude numbers, F (from Hanaoka, 1957 NSMB Symp.) 



per ton of displacement. Tankers and bulk cargo 

 carriers fall into this category. 



Nevertheless, certain broad conclusions can be made 

 on the basis of the data just outlined. Over a pre- 

 dominating part of its time at sea a large and long ship 

 will encounter waves not exceeding three ciuarters of the 

 ship's length. The pitching and heaving motions will be 

 small and the increase of resistance will be governed by 

 the formulas (1), (3) and (4). The small mean angle of 

 entrance, a, is indicated as beneficial, and will be ob- 

 tained by the use of U-type sections. I^arge tankers 

 and large fast liners, such as SS United States, should 

 have, therefore, U-sections at the bow and waterplane 

 lines as fine as the block coefficient permits. 



As an extreme opposite, small cargo ships can be con- 

 sidered. Over a large proportion of their operating time 

 these ships will meet the waves of the length eciual to 

 ship's length. Furthermore, these waves can be ex- 

 pected to be steep, i.e., to have small \/h ratios. Pitch- 

 ing and heaving motions are expected to be large and 

 they will cause large increase of resistance. The use of a 

 pronounced V-form of bow sections or of Maier form can 

 be expected to decrease the amplitude of motions and 

 thereby to reduce the resistance. This observation 

 gives the rational explanation to the widespread use of \'- 

 forms in the small ships engaged in the trade between 

 English, Scandmavian, and North European ports. 

 &eitner (1939) has already called attention to these 

 characteristics of the bow forms. 



A modern general cargo ship represents a case inter- 

 mediate between two extreme ones just considered. A 



wide variety of bow forms is, therefore, found in practice. 

 A moderate to pronounced "\'-form appears to be pre- 

 vailing in Europe while the current tendency' in the 

 I'nited States is towards U-form, as exemplified by 

 DTMB Series 60 (F. H. Todd, 3-1953). The towing- 

 tank experiments of Kempf (1935) and of Lewis and 

 Numata (3-1956) showed that a pronounced V-form is 

 advantageous for ships of this type in adver.se weather. 

 The large mean entrance angle in ca.se of V-sections, 

 howe\-er, increases the resistance in fair weather. The 

 choice between U and V-sections hinges, therefore, on 

 whether the emphasis is placed on the fair or on the 

 rough-weather (jperations. In this connection it is of 

 interest to observe that Kempf at an early date estab- 

 lished a practice to test ship models in waves while the 

 recent development of Series 60 at the David Taylor 

 Model Basin was based entirely on smooth water tests. 



2.3 Towing-Tank Tests for Resistance in Waves. 

 Towing-tank tests for resistance in waves are conducted 

 for a wide range of ship speeds and wa\"e sizes. These 

 latter often exceed (relatively to the model) the waves 

 found at .sea. The subject of model testing is placed, 

 however, under Section 2 (on resistance in moderate 

 seas) because only in moderate seas the resistance deter- 

 mines a ship's speed. In higher seas a ship's speed is 

 go\erned by considerations of safety of a ship and its 

 cargo, and not by the resistance. This subject will be 

 treated in Section 3. 



2.31 Methods of testing and presenting test results. 

 The resistance and speed of a ship in wa\'es are usually 

 represented in one of two forms corresponding to two 

 methods of towing-tank testing. The first one corre- 

 sponds to the early practice of Kent and Kempf who made 

 tests in large towing tanks. The mean speed of a model 

 was controlled by the speed of a towing carriage. Kempf 

 introduced the method of towing a model by a weight 

 and a towing cord which were installed on the main 

 carriage. The model was towed, therefore, with a con- 

 stant force and it was free to surge about the mean speed 

 of the main carriage. This sy.stem was adopted later by 

 the Da\-idson Laboratory of the Stevens Institute of 

 Technology (3-E. V. Lewis, B. V. Kor-vin-Ivroukovsky), 

 by the Delft Shipbuilding Laboratory (3-Gerritsma) 

 and by University of California (3-Paulling).'' The 

 results of tests are expressed by curves of the resistance 

 \'ersus model speed with wave .size as the parameter. 

 An example of such a plot is shown in Fig. 3, taken from 

 Oerrit.sma (3-1957, NSMB Symp.). 



The .second method is employed in the towing tanks not 

 equipped with a towing carriage. It is used by Newport 

 News Shipbuilding and Dry Dock Company (Hancock, 

 3-1948()), Massachusetts In.stitute of Technology 

 (Al)kowitz and PauUing, 3-1953) and at the UO-ft tank 

 of the David Taylcjr Model Basin (V. H. Todd, 3-1954). 

 In this method the model is towed by a long cord and a 

 falling weight at the end of a tank. The test results are 

 given in a plot of model speed versus wave length. 



Listed in the bibliography at the end of Chapter 3. 



