168 



iiM)K()n\ \ wjif.s IN siiii> nrsir.N' 



L'AHLIJ 4i>.d— (Continued) 



Sec. -Ift.? 



ratio. Also, since the surfaro partidi^ travels in 

 an orbit of radius Rs , 



Uorb = RsO} 



whence, by substitution, 



Uo.. 



7.111 





Assuming a steepness ratio of 1/12 = 0.083 

 and a wave velocity f of 36 kt, or 60.8 ft per sec, 

 corresponding tn a wave 01.5 ft high and 738 ft 

 long, the orbital velocity f/orb of a surface par- 

 ticle is T(f)/i,r/LH. = 3.14(60.8)(0.083) = 15.85 

 ft per sec, = about 9.4 kt. This means that a 

 small, shallow-draft boat traveling along the 

 surface at a constant speed of 20 kt over the 



ground, in a direction normal to the crest lines, 

 would have a relative speed through the water of 

 29.4 kt on the crest and 20 - 9.4 = 1 1 .0 kt in 

 the trough. 



For a maximum steepness ratio of 1/7, 

 f^orb = ir(/iH-/L„-)c = about 0.45c, also for a 

 surface particle. 



Table 48. e lists the orbital velocities of the 

 surface particles in a series of trochoidal waves 

 having lengths and steepness ratios covering those 

 normally encountered in service. 



Fig. 48. D gives plots of orbital velocities for a 

 range of wave lengths, wave velocities, and steep- 

 ness ratios likely to be encountered during 

 heavy-weather and emergency conditions at sea. 

 These velocities are important when pounding 



TABLE 48.e — Orbital VEiocrriEs of Surface Particlbs in a Deep- Water Trochoioal Wave 

 The values of velocity listed are in ft per sec. 



