THEORY OF SEAKEEPING 



Fig. 6 Same as Fig. 4 but for fourth model 



Table 



Values of Coefficients 



Model 

 No. 



1 

 2 

 3 

 4 



Ci Cr* 



0.00085 0,00375 



0.0024 0.0038 



0.0028 0.0035 



0.0195 0.0028 



(frictional drag)/}^ pMm"^- 



0046 

 0.0002 

 0.0063 

 0.0222 



TF. = 



f 



Jo 



p sin (Is 



(16) 



where S is the de\'elopecl length of the surface of the 

 wave of length X, and ds an element of the length. The 

 integration is most con\'eniently performed b.y noting 

 that sin Q ds = drj, and by plotting pressure p versus sur- 

 face elevation r;. These plots are shown in Fig. 7, and 

 the dynamic drag is represented by the area enclosed by 

 each curve. The nondimensional drag coefficient was de- 

 fined as 



C' = 



w. 



'/2 P' Uj\ 



(17) 



where u„ is the maximum wind speed in the section of the 

 wind tunnel above the wave nodal point. The values of 

 the coefficients obtained in this way are given in Table 1 . 

 The frictional-drag coefficient is listed for the discussion 

 in the following section. 



Thijsse (1952) photographed the waves generated in a 

 wind flume, made a model of one of these waves, inserted 

 it at the bottom of a flume and measured the pressure 

 distribution in smooth water flow. The wave profile, 

 air-pressure distribution, and water- velocity distribution 

 are shown in Fig. 8. The dynamic drag coefficient C\ 

 resulting from these measurements is 0.0052, or about 

 twice Motzfeld's drag for the trochoidal model No. 3. 

 Although in this case the wave is slightly lower in height, 

 \/H = 12 instead of 10, it is unsymmetric with a steeper 



front (i.e., lee side). Wind-dri\-en waves usually have 

 this unsymmetrical form, so that an increase of resist- 

 ance over the symmetrical Mot zf eld models can be 

 e.xpected. 



Lack of a precise and significant definition of air 

 velocity is the outstanding draw})ack of these experi- 

 ments. This appears to be a weak point in all experi- 

 ments on wind-wa\'e energy transmission. A theoretical 

 formulation of a similarity law and its observance in 

 planning observations and tests are sorely needed at 

 this time. 



2.4 DeterminaHon of C; from Mean Inclination of 

 Water Surface. As examples of determination of the drag 

 coefficient by measuring the mean slope of the water sur- 

 face in a wind flume, the w'ork of Francis (1951) and 

 .Johnson and Rice (1952) can be cited. Francis used a 

 wind flume about fi m (19.6 ft) long in which wind 

 velocity up to 12 meters per sec (mps) (39 fps) could be 

 produced. Two alternate forms of experiment were 

 used. In one the wa\-es were generated by the wind and 

 increased in height from zero at the windward end to 

 maximum at the lee end. In another, the waves were 

 artificially generated at the windward end, and dimin- 

 ished or increased towards the lee end depending on the 

 wind strength. The mean ele^'ation of the water surface 

 was measured at se\-eral points along the flume, and 



Table 2 Results of Measurements 



