206 



THEORY OF SEAKEEPING 



Fig. 52 



HI cr=l.9 

 17.1% 



13 4 5 6 7 



Periods- Sek 



Distribution of wave periods in a sea composed of three 

 wave systems (from Langmaack, 1-1941) 



stresses follow the same general distribution pattern as 

 do the heights of ocean waves." 



In a discussion of Jasper's paper, E. V. Lewis showed 

 that the same conclusion was reached in tests in ir- 

 regular waves in a towing tank. This is shown in Fig. 

 14. 



The usefulness of this information was described by 

 Jasper (1956) in the following two passages. The first 

 one is taken from the introduction : 



"There are many applications in which a knowledge 

 of the freciuency distribution of hull motions, stresses 

 and the heights of ocean waves can be u.sed to advantage, 

 for example: 



1 Prediction of the most probable amplitudes of roll 

 and pitch motion of ships under gi\-en en\'ironmental 

 conditions. 



2 Estimation of the extreme values of ship responses 

 or of wave heights encountered over a given period of 

 time. 



3 Statistical estimation of the capacity for which 

 shipboard stabilization eciuipment must be designed. 



4 Estimation of the endurance strength of the ship 

 structure." 



The second passage is taken from the summary: 

 "There are many practical apphcations of the fre- 

 cjuene}' distribution patterns. In the determination of 

 the capacity of .ship and shipboard stabilization ecjuip- 

 ment, it is nece.s.sary to have a reliable estimate of the 

 proljability of exceeding given angles of roll and pitch. 

 The design of aircraft landing gear, rocket launchers and 

 fire-control apparatus requires a knowledge of the ship 

 motions expected in service. The ability to land 

 planes on a carrier in a given sea can be predicted on the 

 basis of frecjuency distributions such as given herein." 

 Jasper (1956) stressed the similarities in the observa- 

 tions as shown by the Rayleigh distribution curves. 

 Langmaack (1941), on the other hand, made ingenious 

 use of file fact that normal distribution (•ur\'es have 

 their peaks at different periods for different wave systems. 

 Fig. 52 shows how an apparently complex distribution 



of wa\'e periods at sea can be considered as the super- 

 position (tf three distinct wa\'e systems. 



Representation r)f the .sea statistically by a single 

 parameter, as is done in Rayleigh 's distribution, appears 

 to be undesirable. North Atlantic waves for instance, 

 are almost always composed of a wind sea and one or 

 more swells. Distinctions between the.se are reported 

 rather imperfectl.v in ship logs. Yet pitching, rolling 

 and yawing are affected differently by these different 

 wave .systems. While it becomes practically impos- 

 sible to .see swells in a heavy wind sea they are often dis- 

 tinguishable in the records obtained by a ship-borne 

 wa\'e recorder and also can be identified by photograph- 

 ing a radar screen (Roll, 1952). 



5.3 Concluding Remarks on Ship Observations ot 

 Sea. Only sea contlition and ship-motion data were 

 considered in this section. Questions on powering are 

 deferred to Chapter 4, and those on stresses to Chapter 5. 



Reports of the early sea voyages of Kent and Kempf 

 gave a picture of the irregularity of seas and ship motions 

 in them. They also gave an idea of the magnitude of 

 ship motion to be expected. Subsequent observations 

 enlarged this picture without making it clear, however. 

 Each ^'oyage on a different ship in different weather 

 conditions produced different data. There was no way 

 to correlate the results of the different observations. 

 Practically the only definite conclusion was that a cer- 

 tain low metacentric height and a long natural period 

 of rolling are desirable for seakindliness. In this re- 

 spect sea observations have confirmed Fronde's (I86I) 

 theoretical conclusions. The best summary of informa- 

 tion on sea kindliness of ships was given bv Kent (1950, 

 19.58). 



The primaiy reason for the failure to provide tangible, 

 practical and usable information was the lack of a means 

 for measuring sea waves. The second reason has been 

 the lack of means for quantitative treatment of sea ir- 

 regularity. Although the irregularity of sea waves was 

 acknowleged, attempts to correlate ship behavior with 

 obser\-ed waves invariably were based on an assumed 

 regular average wave. Furthermore, observations were 

 usually made on isolated \'oyages. It was uncertain 

 what sort of weather would be met on these voyages. 

 The only exception was in the case of the SS Oceati 

 Vulcan on which obser\-ations were made over an ex- 

 tended period. 



The situation has Ijceii changed recently by two simul- 

 taneous de\elopments : Introduction of a ship-borne wave 

 recorder and development of the irregular sea theory. 

 The .ship-borne wave recorder (Tucker, 1-19.52, 1956) 

 now makes it possible to obtain a continuous record of 

 wa\e height from a ship.-'' The theory permits the 

 correlation of ship motions with the waves causing the 



2' Tucker's wave recorder gives the l)est results on a small ship 

 in hove-to condition. The recording high-frequency wave com- 

 ponents is inicertain when the recorder is used on a large ship. 

 The nature of the errors introduced by the speed of ship is not 

 yet established. It appears to consist of an introduction of spuri- 

 ous high-fre(|uency wave components. Certain suggestions for the 

 imiirovement of the recorder were given in Chapter 2. 



