Hydrofoil Motions in a Random Seaway 



Random Seas 



At the beginning of the hydrofoil stability study, it was recognized that ex- 

 clusive use of regular sinusoidal seas as forcing functions might be misleading, 

 since they are hardly representative of actual seaway conditions. It was de- 

 cided, therefore, to simulate a random seaway based on a mathematical model 

 which is used successfully for wave forecasting purposes. 



The following subsections are contributed by E. R. Case (De Havilland Staff 

 Engineer) who was responsible for the original analysis and simulation of the 

 random seaway for the hydrofoil study, and the subsequent spectral and statis- 

 tical analysis of the computer and trials results. 



The random seaway 



The most obvious feature of a seaway is the almost complete lack of any 

 consistent order or pattern to the wave motion, an observation which led to con- 

 sideration of the seaway as a random process. By assuming further that the 

 process was Gaussian, Pierson [23,24] derived a mathematical model based on 

 a Fourier representation of random noise due to Rice [26], and the propagation 

 properties of deep-water gravity waves. About the same time, Longuet-Higgins 

 [22], using the Gaussian assumption, and the results of Rice's paper, derived 

 the statistical distribution of wave heights for wave forecasting purposes. The 

 remaining quantity required to complete the description of the seaway as a ran- 

 dom process was the power spectrum, which was supplied by Neumann [27] on 

 the assumption that the wave energy varied as the fifth power of the generating 

 wind velocity. These results were successfully incorporated in a book published 

 by the United States Navy [23] on practical methods of wave forecasting. 



On the basis of the above, the Pierson representation and the Neumann 

 spectrum were assumed to characterize a seaway with sufficient accuracy for 

 the purposes of the stability study. It was assumed further that a Neumann wind 

 speed of 22 knots corresponds to a Sea State Five. 



A typical estimate of a seaway surface elevation probability distribution 

 function is shown in Fig. 8. The linearity indicates normality out to over four 

 standard deviations, which validates the Gaussian assumption for engineering 

 purposes. 



Attention was restricted to the consideration of "sea" waves, which, as dis- 

 tinct from "swell" waves, exist within a storm generating area due to the action 

 of the local winds. Attention was further restricted to a seaway which had 

 reached the fully- developed state, where a state of equilibrium exists in the in- 

 terchange of energy between the waves and the wind. The fully-developed sea 

 state is reached only when the generating wind has blown over a svifficient fetch 

 and time duration [23], and can be considered a stationary, ergodic random 

 process. 



The Neumann spectrum applies only to the fully-developed seaway [28], and 

 takes the form in the one-dimensional case, for f > 



633 



