given by equation (57) with Rc/R^j^*^ 1- The scale effect is accounted 

 for in the present analysis by the inclusion of the effect of the ratio 

 R(,/Rj which in a Froude model will be greater in the model than in the 

 prototype. 



An additional set of experiments is reported by Keulegan (1973). 

 These experiments were performed for rectangular breakwaters of different 

 materials and widths £ = 0.253 0.5, and 1 foot. As an example the 

 experimental data corresponding to relatively long waves, hg/L = 0.1, 

 as reported by Keulegan (1973, Table 12) are plotted in Figures 9, 10, 

 and 11 versus Hj^/L. For comparison the predictions afforded by the 

 procedure developed in Section II. 2 are also shown. The choice of 

 parameters 6q = 2.2, R,, - 70 yields a slightly better representation 

 of the experimental data as could be expected from the comparison made 

 in Figure 5. However, the predictions obtained from Sq = 2.7, R^, = 70 

 are fairly good. The discrepancy between observed and predicted 

 reflection coefficients is of the type noted in conjunction with the 

 comparison with Wilson's (1971) data and may again partially be 

 attributed to experimental errors in the determination of R. Keulegan 's 

 (1973) and Wilson's data on the reflection coefficient show the tendency 

 of decreasing slightly with increasing height of the incident waves. 

 However, it is noted that the experimental reflection coefficient (Fig. 9) 

 increases slightly with Hj^/L. Since the' reflection coefficient for this 

 set of experiments is relatively small, R - 0.3, the error in the 

 experimental determination of H^i^i "^^y ^® expected to be rather small, 

 thus essentially substantiating the previous hypothesis for the nature 

 of the discrepancy. 



As a final comparison between the experimental data presented by 

 Keulegan (1973) and the analytical procedure developed in this study. 

 Figures 12 and 13 show a comparison between observed and predicted 

 transmission and reflection coefficients for all the experiments 

 reported by Keulegan corresponding to hQ/L ==0.1 and Hj^/hQ = 0.1. With 

 the generally good agreement between the experimental and predicted 

 transmission coefficients exhibited in Figures 9,10, and 11, the 

 comparison given in Figure 12 shows the general applicability of the 

 present procedure to predict transmission coefficients. The comparison 

 of reflection coefficients given in Figure 13 is quite encouraging. 

 However, it should be recalled that the predicted trend of increasing R 

 with Hj/L was not observed in the experimental data. 



4. Discussion and Application of Results. 



A theoretical solution for the transmission and reflection 

 characteristics of a homogeneous breakwater of rectangular cross section 

 was obtained. The main assumptions were that the incident waves should 

 be normal to the breakwater and that the motion should be adequately 

 described by linear long wave theory. The general solution for the 

 transmission coefficient, T, and the reflection coefficient, R, is 

 presented in graphical form in Figures 2 and 3. For small values of 



37 



