170 



IIM)R()in \ \\ll( s 1\ MIIF' nrSIGN 



Src. 4S.9 



'1'aIII.K IS.Il -OlUllNATKS VOR A SiNK-WaVK PhOKILE 



Tlio tabic gives 17 ordinut^is for the hiilf-loiigtii of a 

 aitmsoidul nave, distributed at IG equal iutcr\-alB between 

 crest and trough, as projected on a horizontal plane. 



/« 



Ti6b 



Fig. 4S.E Ratios ok Wave Height to Wave Length 

 FOR Charactemstic Waves Used in Ship Design 



It has been the practice for manj'' j^ears to base 

 ship-strength calculations on a wave having a 

 steepness ratio of 1/20. Tliis is often referred to 

 as a "static" wave but it niaj' be considered as a 

 following wa\-e that luxs exactly the same speed 

 as the ship, and is not distorted bj' the presence 

 of the ship. 



Because this wave is not as steep as tlie storm 

 waves which make trouble for small ships, and is 

 steeper than tho.se which make wavogoing 



TABLE 48.g — Niedermaib and Wueelock Wave- 

 Height Design Values 



Station 



0, Crest 



1 



2 



3 



4 



5 



6 



7 



8 



9 

 10 

 11 

 12 

 13 

 14 

 15 

 16, Trough 



Ordinate 



1.0000 

 0.9904 

 0.9019 

 0.91.57 

 0.8.5.30 

 0,7778 

 0.0913 

 0.5976 

 0.5000 

 0.4025 

 0.3087 

 0.2222 

 0.1404 

 0.0843 

 0.0:581 

 0090 

 0.00{X) 



difficult for large ones, J. C. Niedermair recom- 

 mends a "design" steepness ratio varying with 

 wave length, represented hy hw = 1.1 vLi,- 

 ["Ship Motions," INA, Int. Conf. Nav. Arcli. 

 and Mar. Engrs., 1951, pp. 137-152; A8NE, 

 Feb 1952, pp. 11-34]. A graph giving the variation 

 of wave height /iir with wave length Lw for this 

 "Niedermair" wave is shown in Fig. 48. E. For 

 tests of models in regular wave trains, a steepness 

 ratio of half this amount, namely /; „- = 0.55 vL-ir, 

 is proposed by C. D. Wheclock. It appears to 

 give waves as high as those in which ships can be 

 expected to make reasonable headway at sea. 

 All three steepness ratios are plotted in Fig. 48. E, 

 together wdth a line for waves ha\"ing a steepness 

 ratio of 1/40. 



For convenience, Tabic 48.g gives the wave 

 heights of both the Niedermair and Wheelock 

 waves fur a range of wave lengths sufficient to 

 (•()\('r most, practical needs. 



48.9 Formulas for Sinusoidal Waves. The 

 prulile of a sinusoidal wave, de.scriix'd in Sec. !).(i 

 of Volume I and illustrat^'d in Fig. 9.E, is an 

 cNlremcly .simple geonictri(! construction, pictured 

 in (liagnim 1 nf Fig. 48. F, using 10 stations along 

 the half-length of the wave. The orilinate heights 

 for each station are indicated. Table 48. h gives 

 the ordinate height.s along the haif-leiigtli fm- ICi 

 station intervals. 



l''nr the convenience of wurkiMs plot I inn cdMi- 



