Hydrofoil Motions in a Random Seaway 



A 14 channel oscillograph paper recorder is used except when acquiring 

 data for spectral analysis of response in a random seaway. This work requires 

 a 7 channel FM tape recorder for craft motions and seaway characteristics, the 

 latter measured separately at a moored wave pole. 



1/12 Scale Cavitation Models 



Two dimensional models of the main foil subcavitating section and the fully 

 cavitating bow foil sections were tested at speeds up to 50 knots in the A.R.L. 

 whirling arm facility. The lift, drag, and pitching moment data was obtained 

 which verified the predicted cavitation limits for the subcavitating foil and the 

 nonlinear characteristics of the super cavitating section. 



POWER SPECTRAL ANALYSIS 



It is necessary to use statistical methods in order to compare predicted 

 and measured hydrofoil response in a random seaway. 



One suitable method is to compare the power spectral densities of the pre- 

 dicted and measured data. This approach gives R.M.S. values and a measure of 

 how closely the random motions approach a Rayleigh distribution. 



If Rayleigh statistics are assumed, then all the statistical characteristics 

 are defined as shown in Table 2. 



Table 2 

 Rayleigh Probability Distribution 



Peak amplitudes may be obtained using the following constants: 



The most frequent amplitude = 1.41 x R.M.S. value 

 The average amplitude = 1.77 x R.M.S. value 



Average of highest 1/3 = 2.83 x R.M.S. value 



Average of highest 1/10 = 3.60 x R.M.S. value 



Strictly speaking, the Rayleigh probability distribution only ap- 

 plies when the spectrum is narrow. 



Results from simulated and measured hydrofoil ship response in a random 

 seaway indicate that most of the response variables have sufficiently narrow 

 spectra so that their peak distributions are predominantly Rayleigh, For design 

 purposes, such as defining the foil system fatigue environment, the assumption 

 of Rayleigh statistics is considered adequate. 



Power spectral analysis has been used extensively in the FHE-400 design, 

 for stress and fatigue life predictions, habitability requirements and equipment 

 installation design. 



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