J 72 



ll^nR()I)^ \ wtK.s in ship dksign 



Sec. IS. 11 



jKJSotl of the WluvKick ^vll\t^•< of Kin. 48.10, 

 having a height /iir = 0.")5 V/..H- . 



A set of tPiilativp standard wave conditions 

 for the dotorniination of the wavegoing perform- 

 anee of ships in I lie design stage, adapted from 

 an initial proposal by the author in November 

 1950. is given in Table IS.i. 



TABLK IS.i — Tentativk Sta.nti.^rd W.wk Conditions 



KOR DtrrKIUUNATION OK TIIK WaVKOOING PKnf-OR.\l- 

 ANPE OF iSniPS IN TUB DkSION StAOB 



(1) Wind and wind effects on the ship are not considered 

 here. The waves describc<l are assumed to be produced 

 by some wind of undefined nature. 



"In .short, the old rule still holds, and always will, 

 that it is the waves of a storm, not its winds, that 

 the mariner has to fear: . . ." IBiRclow, 11. B., and 

 Edmon.«on. W. T., "Wind Waves at Sea; Breakers 

 and .Surf," l'. S. Navy llydroKraphic Ollice publi- 

 cation H. O. (>02, Washington, 1947, p. 401. 



(2) Unless othenvise stated, the sizes and i)roportions of 

 the swells and waves are averages or signilicunt values for 

 the water areas of the world, rather than uncommon 

 ma.\ima of one kind or another. They mux be local averages 

 if the principal conditions are such that the ship can 

 travel only in that area. 



(3) The lengths of regular or uniform swells .'ind wmvcs in 

 deep water may in general be taken as a function of their 

 velocities and \'ice versa. 



C.\SE I. This is intended to represent the conditions 

 obtaining in the general but not immediate vicinitj- of an 

 area where a wind hiis been blowing for some time in a 

 nearly constant direction. The result is a simjjli', regular 

 train of swells, in which the wave velocities may vary 

 from 0.4 to 1.2 or more times the ma.ximum speed of the 

 ship under consideration. This range is intended to be 

 large enough to cover the region of resonant pitching. 

 The steepness ratios of these swells, expressed as wave 

 height All- to wave length I^w , may vary from 0.083(1/12) 

 to 0.04(1/25) or less. The angle of encounter a of the ship 

 with the direction of travel of the wavt; train may vary 

 from (following sea) to 180 deg (head sea). The water 

 depth is (JOO ft (1(X) fathoms) or more. 



CASE II. This is intended to represent the conditions 

 obtaining in the general vicinity of one strong wind or 

 storm area and in the immediate vicinity of another. 

 Due to a shift in storm center or other cau.ses, the wind in 

 the latter an-a is blowing in a direction difTcrent from that 

 in which it bli.'W in the former area. The result is one or 

 possibly two S4-condary wave trains impo.sed upon a 

 itclceted primary train of swells of C.\SE I. When the 

 ■wells arc of simple geometric form, this is known as a 

 complex synthelii' two-comi>onent (or tliree-c(mipone.nt) 

 »ea. The secondary wave veliM-itics may vary from 0. 1 

 to 0.8 nf the maximum H{M-ed of the ship under considera- 

 tion. In othiT words, they may exceed the primary swell 

 velority. Tin- flireclion of thi- wcondary (rain (or trains) 

 nmy lie within (SO deg of tin? direction of the primary 



train. This means that l>oth trains are moving in the same 

 general direction. The water depth is (WK) ft (KM) fathoms) 

 or more. 



C.\SK III. This is intended to represent the conditionB 

 obtaining in shallow water within a strong wind or storm 

 region, where relatively' large and steep waves are produced 

 by winds of short iluralion. The result is a single, regular 

 train of waves, in wlii<-li the wave velcx-ities may vary 

 from 0.4 to 1.2 or more times the maximum spec<l of the 

 ship under consideration. The stet'pne.'w ratio may vary 

 from 0.12.5(I/S) to 0.0025(1/11)) or less. The angle of 

 encounter of the wave Iniin may vary from to ISO <|eg. 

 The depth of water may diminish to 2.5 times (he maxi- 

 mum draft, possibly to 2.0 times that draft. 



Willi the lliicc v;Mi;il)lcs listed in ( '.V.^E 1 of 

 Table 48. i, namely the ratio Lw'L, the steepne.ss 

 ratio /(»■ />i,- , and the angle of eneomiter a, and 

 even with the intervals deliberately made large, 

 the inimber of possible combinations is almost 

 prohibitive, rndoubtedly certain combinations of 

 variables, especially those producing resonant 

 motion, are critical. Study of those combinations 

 only may ultimately be found sufficient. The wave 

 velocities are extended to a low range beeau.se it 

 is possible for a ship with its forefoot nearly out 

 of the water, as in the ballast condition, to en- 

 counter short, steep waves who.sc impact coincides 

 with the natiii:il l2-n()(l('il \-iiiration of the ship 

 sfriiclurc. 



48.11 Delineation of a Synthetic Three-Com- 

 ponent Complex Sea. As an inilicatiun of the 

 appearance and the characteristics of a synthetic 

 complex sea, a graphic example is workefl out in 

 which three components or trains of regular 

 sinusoidal waves are superpo.sed. The primary 

 train is a.ssumed to travel in the direction of 90 

 (\v^ true (east), while the secondary trains travel 



T-VBLI;; 48. j — Characteristics ok Tiiukk Com- 

 ro.VKNTs OK a Complex Synthetic Sea 



The data listed here apply to the superpositions of 

 Figs. 4S.Ci anil 48.11. .\l| the wave components are sinu- 

 soidal ill form but their velocities of translation and periods 

 arc ealculateil from the fornuilius for trochoidal waves. 

 For a wave length L\y in ft, these are c " 2.201? v^Z/ic in 

 ft per .sec; 'l\y ■• 0.4419\//.,ir in sec. 



Direction of tran.slatioii, true 00 deg 75 dru i:i5drg 



Wove length, ft 4(1(1 240 120 



Wave height, ft s I 



Steepness ratio 1 /.W l/IO !/:«) 



Wave celerity, ft |M>r sec 45.20 :i5.()0 2l.7i) 



kt 20.70 20.75 14.(i7 



Wave iwriod, sec S.840 0.SI7 4.S12 

 Distance traveletl by wave in 



3 sec, ft 135.7S 105.17 74.373 



