166 



11M)R()1)\.\AMU.S IN Mill' DLSICN 



Sec. 48.6 



T.\HI,I'; IS.c- I'khioii, Lbnctii, and Vki/icity of Tro(-hoii>ai. Dkki'-Watkii Waves 

 This tablo is iiuluxcxi l)y iiitof^al values of tlip wave [H-ritxl 7'if in wo. The table inrludos also the angular orbital 

 velocities and the frequencies nith which various waves pass a point in space. 



generated. From Fig. 48.B and the foregoing 

 summary, Rg is half of the wave height hw or 

 13.61/2 = 6.85 ft. The value of i2„c is L„/2-k = 

 612/6.28 = 97.5 ft. The maximum wave slope 

 fM« = sin"' (Rs/Rrc) = sin"' (6.85/97.5) = 

 about 4.03 deg. 



48.6 Tabulated Data on Length, Period, Ve- 

 locity, and Frequency of Deep- Water Trochoidal 

 Waves. It i.s u.seful to know the comhiniitions of 

 wave length, wave velocity, and period for anj' 

 one of a large range of trochoidal waves, corre- 

 sponding generally to the range of natural waves 

 to be found in the oceans. Small and large tables 

 of this kind have been embodied in many stand- 

 ard works on naval architecture and shiplmilding, 

 at least since the publication of W. J. M. Han- 

 kinc's "Shipbuilding: Theoretical and Practical," 

 in 1866, with some small variations in numerical 

 values. 



Tables 48.b, 48. c, and 48. d give related numer- 

 ical value.H of length, peri(Kl, and velocity, the 

 lattiT in both fps and kt, f(ir a series of deep-water 

 trochf)idai wavi-.s varying in length from less 

 than 1 ft (o 2,iHH) ft. 'i'liey are indexed by integral 

 values of length in ft, perirnl in sec, and velocity 

 in kt, respectively. The calculated values are 



theoretical, derived from the relationships set 

 down in Sec. 48.4. All values are carried out, 

 wherever applicable, to the nearest fourth 

 significant figure. 



These tables include also the angular orbital 

 velocities and the frequencies with which the 

 various waves pass a point in space. 



For the as.sumed wave of Sec. 48.4, in which the 

 ABC ship of Part 4 is to run, the length L,r is 

 012 ft. Then by interpolation from Table 48. b, 

 the following characteristics are found: Celerity 

 c = 55.99 ft per sec, equivalent to 33.15 kt; 

 period Tn- = 10.93 sec; frequency = 0.0915 wave 

 per sec. These agree with the values calculated by 

 the formulas within 2 uiiit.'^ in the fouiili .signifi- 

 cant place. 



48.7 Orbital Velocities for Trochoidal Deep- 

 Water Waves. .\ny water ])articie makes one 

 coniplcle revolution in its orbit in one wave 

 I)eriod 7',,- . For a particle lying in the surface, the 

 orbital distance traveled dining this period is 

 irlhr and the (tangential) orbitnl velocity is 

 f^o.i, = irhw/Tw • The wave velocity c is the 

 length of a complete wave L,r divided by the 

 I)eriod 7'„- , whence 7'ir = J-iw/c- Substituting, 

 i/(>,b = ir(r)/i„-/L,r = irc times the stccimess 



