If the relationship between waves measured in the water and voltage applied to the 

 wavemaking servos is approximately linear, then the waves will represent a Gaussian random 

 process since it is well known that a Gaussian signal passing through one or more linear 

 systems remains Gaussian, 



OUTLINE OF RESULTS 



Initial programming for the wave spectra was completed in June 1962. After several 

 programming corrections and retaping, successful spectra suitable for ship-model testing 

 were created and measured in MASK in September 1962. Figure 3 shows a typical wave 

 pattern in the basin. Figure 4 is a typical recording of the wave heights observed in the 

 water. Figures 5 and 6 depict the result of a spectral analysis of two of the most successful 

 wave programs plotted for comparison with the desired Neumann weighting of power. 



It is obvious from these results that the basic goals of this exploratory wave- 

 programming effort have been satisfied— the waves appear to the eye to be similar to those 

 observed at sea, they are as close to a Gaussian random process as can be generated, and 

 they have a controlled distribution of average energy in each band of wave lengths. As of 

 January 1963, they had been successfully used in over 60 hours of model testing. 



The remainder of this report discusses in some detail the programming techniques 

 used and the difficulties encountered; it presents a plan for the development of a series of 

 wave-generation programs which will meet the simulation needs for ship models in sea 

 conditions up to State 7 severity as well as extending to the directional case. 



ANALOG PROGRAMMING TECHNIQUES 



As will be recalled, the development of the wave program required that a random 

 voltage be recorded on magnetic tape which has a power density spectrum equal to the 

 product of the Neumann spectral shape and the square of the inverse frequency-response 

 characteristics of the wavemaker. From linear statistical theory, this spectrum will result 

 from excitation of a linear system by a white noise generator if the linear system has a 

 transfer function or frequency response equal to the square root of the Neumann spectrum 

 multiplied by the reciprocal of the wavemaker frequency response. The programming or 

 synthesis of the proper frequency characteristics of a linear system on an analog computer 

 is logically divided into the following two parts which represent two linear systems in 

 tandem. 



