Sec. 4S.S 



WIND-WAVE AND SHIP-WAVE DATA 



169 



^o 



200 400 600 800 1000 IZOO \400 1600 1800 2000 

 Wove Length Lvy in feet 



10 ZO 30 -^0 50 60 70 60 90 100 

 Wave celerity C in feet per second 



Fig. 4S.D Graphs Indicating Orbital Velocities 

 IN Trochoidal Waves of Varied Steepness Ratio 



and slamming, accompanied by high water- 

 impact velocities, become factors in the design or 

 performance problem. 



For the 612-ft Wheelock wave of Sec. 48.4, in 

 which the ABC ship of Part 4 is to travel, the 

 wave height h^ is ISii^l ft. The orbital velocity 

 C/orb is 7.111/ih./vL,^ . Substituting the fore- 

 going values for the given wave, C/orb = 

 7.111(13.61)724.75 = 3.91 ft per sec, for a surface 

 particle. Since the steepness ratio of the wave is 

 only 13.61/612 or 1/45, the orbital-velocity value 

 is beyond the ranges of Table 48.e and Fig. 48. D. 



Table 48. f lists values of the ratio of the orbit 

 radius R, at any depth In, to the orbit radius Rs 

 at the surface. Beyond a value of h/L^ greater 

 than 1.0, the ratio R/Ra is practically zero. 



48.8 Data on Steepness Ratios and Wave 

 Heights for Design Purposes. The steepness 

 ratios of the highest sea waves of different lengths, 

 as observed, estimated, and reported by various 

 investigators, are found to vary rather widely. 

 This is partly because of recognized difficulties in 

 making wave observations from a ship and partly 



because the average steepness ratios actually vary. 

 They are reported, for example, to be of the 

 order of 1/22 to 1/30 for storm waves in the 

 Atlantic and 1/16 to 1/18 for similar waves in 

 the Indian Ocean. 



Maximum steepness ratios on a base of wave 

 length, from a great number of records, have been 

 analyzed by J. Turnbull in connection with a 

 recent study of the longitudinal strength of ships 

 [Engineering (London), 3 Oct 1952, p. 449; 

 SBSR, 2 Oct 1952, p. 441]. Turnbull gives a 

 graph envelope covering the heights of some 

 unusually steep waves which had been encoun- 

 tered and rehably reported over a period of 50 or 

 60 years. The data exhibit a rather wide range for 

 the highest waves of the size commonly encoun- 

 tered, in some cases about 2 to 1. Further data 

 along the same line are to be found in The 

 Admiralty Ship Welding Committee Report Pi,.8, 

 describing the "S. S. Ocean Vulcan Sea Trials: 

 The Forces Acting on the Ship at Sea" [ACSIL/ 

 ADM/53/387 of 1953, pp. 8-11, esp. Fig. 9]. 



TABLE 48. f — Decrease op Orbit Radii with 

 Depth in a Trochoidal Deep-Water Wave 

 The orbit radius is assumed to vary with depth h in 

 accordance with the relationship R = Kse~^'"''^»') where 

 Rs is the orbit radius of a surface particle. The data listed 

 here are taken from W. F. Durand, RPS, 1903, p. 75, and 

 C. H. Peabody, NA, 1904, p. 262. 



