Testing Ship Models in Transient Waves 



Brownell, W. F., "Two New Hydromechanics Research Facilities at the 

 David Taylor Model Basin," Presented before Chesapeake Section, The So- 

 ciety of Naval Architects and Marine Engineers (Dec 1962). Also David 

 Taylor Model Basin Report 1690 (Dec 1962). 



Davis, M. C, "Simulation of a Long Crested Gaussian Seaway," David 

 Taylor Model Basin Report 1755 (Mar 1963). 



Huskey, H. D., et al., "Computation of Fourier Integrals without Analog 

 Multipliers," Computer Handbook, McGraw Hill Book Co., Inc., New York 

 (1962). 



Newman, J. N., "A Slender Body Theory for Ship Oscillations in Waves," In 

 Preparation for Journal of Fluid Mechanics. 



Lamb, H., "Hydrodynamics," Sixth Edition, Dover Publications (1945). 



* * * 



DISCUSSION 



E. V. Laitone 



University of California 



Berkeley, California 



Since the linearized equations of motion for either the pitch or the roll of a 

 ship in regular waves can be written as 



e^'^*; (1) 



therefore there is a distinct advantage in running a series of model tests in 

 regular waves. This advantage over the pulse or transient- type wave test oc- 

 curs because Eq. (1) represents a circle in the velocity amplitude and phase 

 plane as shown in Fig. 1 



|0| = -^ cos 0. . (2) 



b e 



Consequently the departure of the experimental points from a perfect circle 

 for varying values of the regular wave frequency (w) directly indicates either 

 the nonlinear effects, or the dependence of b or k upon co, for constant values 

 of Aq . Similarly varying Ag and repeating the tests for different values of a 

 illustrates the nonlinear dependence of b or k upon the amplitude (A^) of the 

 regular wave. A transient wave test could not so easily pin-point the wave fre- 

 quencies or amplitudes that correspond to a breakdown of the assumed linearity 

 which results in Eq. (1). 



541 



