After more than 130 experiments using 14 different materials and 22 

 different grain sizes, Noda found five model profiles with beach discon- 

 tinuity distances which matched those on five profiles of Watts (1959) . 

 The five prototypes were all step-type profiles with sediment sizes of 

 D50 ^ 0.46 millimeter. 



Noda derived the following relationships based on the five matching 

 profiles : 



^ ^ 1.85 0.55 ,,7. 



and 



1.32 -0.386 ,,_,, 



X = p n^i , (18) 



which comprise the basic modeling law to be evaluated by further testing. 

 A nomograph for use of equations (17) and (18) is presented in Figure 5. 



5 . Comparison of Model Laws . 



The theoretical and practical approaches to the development of model 

 laws are considered as coming from two different philosophies. The first 

 is from a desire to reproduce the dominant physical phenomena; the second 

 is from a need to reproduce observed occurrences. Some of the theoretical 

 conditions (eqs. 2 to 13) are satisfied even when practical laws such as 

 given by equations (17) and (18) are used. A summary of the derived model 

 laws based on the various theoretical similitude conditions and a compari- 

 son with the empirical practical similitude condition of Noda (1972) are 

 given in Table 1. 



III. EXPERIMENTAL DATA 



1. Experimental Apparatus and Procedures . 



Experimental tests were performed in the wave flume shown in 

 Figure 6. The flume is 105 feet long with a square cross section 

 measuring approximately 4 by 4 feet. The wave generator is a plunger 

 type and the prime power supply is through a silicon-controlled rectifier 

 (SCR) to a 15-horsepower direct-current motor. The control system permits 

 extremely accurate speed control over a wide range of load conditions. 

 The motor is coupled through a 21:1 speed reducer. A range of wave 

 periods from about 0.5 to 6 seconds can be generated. Longer periods 

 are possible with a reduced duty cycle or by a change of speed reducer; 

 however, the extended range was not needed for this study. 



To reduce the amount of test material and to obtain larger ampli- 

 tude waves, a convergence was built to reduce the tank width by half. 

 To further increase the rate of testing, a Plexiglas partition was also 

 introduced parallel to the wave tank to test two materials simultaneously. 

 This latter partition permitted comparisons of different materials under 



22 



