generator were about 10 percent less than indicated by small-amplitude 

 theory for wave steepnesses between 0.045 and 0.048; for steepnesses 

 between 0.002 and 0.03 the experimental values were only 3.4 percent less 

 than the theoretical). The wave height that a generator produces can 

 also be estimated with sufficient accuracy, for the purposes mentioned 

 above, by using an equation based on a simple wave generator theory. 

 This equation, derived by equating the volume displaced by the wave gen- 

 erator in one-half of a wave period to the elevated volume in one-half a 

 wavelength of a sinusoidal wave, is 



H = ^V (6-22) 



X w 



where X is wavelength and V^^ is the volume of water, displaced per 

 foot length of generator in one-half the wave period, that is lised in the 

 generating of that part of the wave train that travels toward the test 

 section (some generators displace water in both directions depending on 

 the type and shape of the generator,' and all have some_leakage between^ 

 the generator and the flume walls and bottom). Since V^^ = S(Aj,)(3 - AV^^, 

 where S is the generator stroke, (^^^G ^^ ^ characteristic linear 

 dimension of the generator, and AV^^ is the leakage volume. 



With proper care AV„ can be reduced to such an extent that, for the pur- 

 poses discussed above, it can be ignored. For the shapes of generators 

 shown in Figure 6-9, Galvin (1964) gives the following values for ia^^Q: 



Generator t'^c-^G 



(ft) 



Piston d 



Flap d 



Cylindrical plunger r 

 Prismatic plunger b + h tan a 



The terms S, d, r, b, h, and a are as shown in Figure 6-9. Galvin's 

 experiment showed that observed values of wave height were in good agree- 

 ment with those calculated from equation (6-23), except for the flap-type 

 generator. Ursell, Dean, and Yu (1958), state that the equation for the 

 flap generator (derived on the basis of the complete linear wave generator 

 theory and which agrees with the equation derived on the basis of the sim- 

 ple theory for values of 2ird/A < 1) should be as applicable as the equa- 

 tion derived for the piston-type generator. The lack of verification of 

 the theory for the flap generator was considered the result of effects 

 not accounted for in the theory, such as leakage around the edges of the 

 generator, motion of the generator which was not simple harmonic, or other 

 effects. Additional research is needed to determine whether the flap gen- 

 erator theory is as accurate as the theories for the other generators and 

 to determine the effects of leakage and other factors on the generated 

 wave heights. 



348 



