SHIP MOTIONS 



171 



k/r AaWv^^^VV 



(a) Zero Speed 

 ' Al ' V ; \ I \ 1 . \ / ' / , 1 



/\ 



A 



/I I . / \ ; \ I 1 I 1 



/ \ 

 ,1 / \ 



(b) 2,0 Fi/Sec-12 Knots (Ship) 



Fig. 12(a) Samples of ship pitching and wave records in ir- 

 regular head seas (from Lewis and Numata, 1956) 



+ f AXco,,x.).7'*'a)„X.)'/Xe 



/yi(w,,x,) j'*('^,.x,)</x. 

 Ill 



+ 



(•28) 



where the .subscript on the integral .sign indicates the 

 transformed region where the operation is performed. 

 Eciuation (28) is the realization of the hypothesis given 

 in ecjuation (23) for short-crested irregular waves. 



The transfer function for certain ship motions may be 

 estimated analytically or measured in a towing tank 

 which permits oblique seas testing. A formal descrip- 

 tion of the foregoing procedure directly applic;it)le to tow- 

 ing tanks was given by Marks (1U.")7). In this case, 

 Tif (tOe, x«) is obtained directly from model tests and the 

 frequency mapping is performed on E{b.\ x) alone, before 

 the product in e(|uation (27) is taken. 



E(luation (21)) assumes es.sentially that an irregular sea 

 is a stationary random process which can be represented 

 as a summation of a very large number (or as an integral 

 of an infinite number) of sinusoidal waves of different 

 periods and directions superimposed in random phase. 

 A ship's respon.se is likewise represented as a steady-state 

 response to these regular waves; i.e., it is assumed that 

 no transient responses exist. Finally, the relationships 

 are assumed to be linear so that the end result can be ob- 

 tained by su]3erposition. 



The practical applicability of these a.ssumptions. for ir- 

 regular long-crested wa\'es only, was verified by Lewis 

 (1954a and 19546, 1955), Lewis and Numata (1956) and 

 Lewis and Dalzell (1957) by towing tank tests. Typical 

 results are shown in Fig. 11 and in Table 1. It will be 

 observed that good agi'eement was secured lietwecn ship 



Wave Height 



\/\AAaAA/ 



Roll 



Pitch 



Heave Acceleration 



Fig. 1 2 (b) Samples of ship motions recorded aboard an aircraft 

 carrier in a state 5 quartering sea at a ship speed of 16 knots 

 (courtesy Taylor Model Basin) 



Table 1 Comparison of Near-Maximum" Destroyer Model 



Motions in Towing Tank Irregular Head Seas, as Obtained by 



Three Different Methods 



Heave, in. Pitch, dcg 

 2 53 2.53 

 .speed fps speed fps 

 By direct analysis of model motions 



in irregular waves 1.1 1.3 52 ti 7 



By calculation from wave spectra 

 and experimentally measured re- 

 sponses to regular waves 1.1 12 43 (j.l 



By calculation from wave sjjectra 

 and analytically computed re- 

 sponses to regular waves 1.1 13 5.0 5 8 



" Mean of Vio highest amplitudes. 



motions measured directly in irregular waves, and those 

 computed by equation (23) from two alternate fre- 

 quency-response functions. One of these alternates was 

 based on towing-tank tests in regular waves and the other 

 on computations formulated by K()l■^'in-Krouko^■sky and 

 Jacobs (1957). 



Expression (23) can also be used in its transposed form 



[^(c.,)]--' = *(co.)/iiXa)J (29) 



which permits evaluation of the square of the absolute 

 value of the frequency-response function from the 

 recorded motions of a ship in irregular model-tank wa\-es. 

 This procedure can be considered as a possible alternate 

 to series of tests in regular waves, and promises a cer- 

 tain saving of experimental effort. It was tried by Lewis, 

 Numata, and Dalzell in long-crested irregular waves, with 

 reasonable success, in this application a ship's responses 

 are not completely described, as only the real part of the 



