TEST PROGRAM 



It was necessary to determine the influence of forward speed and amplitude and fre- 

 quency of oscillation on the hydrodynamic forces and moments. 



Tests were run at 0, 1, 2, 3, and 4 knots, corresponding to Froude numbers of to 0.35. 

 The amplitude of oscillation was + 1/4, ■+ 1/2 or + 1 inch, and the frequency was varied from 

 about 1/8 to 3 cycles per second. It was hoped that the amplitude range was broad enough to 

 establish the linear range of the equations of motion. The practical range of frequencies for 

 ship motions at model scale would not exceed 2 cycles per second but the higher frequencies 

 are of interest in establishing the validity of several theoretical methods of determining ship 

 damping. 



METHOD OF ANALYSIS 



A surface ship model is constrained to oscillate sinusoidally, z = z^ e'*" , at frequen- 

 cy oi and with amplitude z . It will be assumed that the ship experiences forces and moments 

 proportional to the instantaneous displacement and its first and second derivatives. A bal- 

 ance, located between the ship and the oscillating support senses the lift force and pitching 

 moment on the ship, F = K. e'^'^'~^and M = ^L e'^*"' ~"\ The force and moment equations 

 are 



A'z + Bz + Cz r^/Te'Ct^'-S) 



i'z + ek + fz =WQe'(<"' " «> 



[la] 

 [lb] 



Substituting z = z e'^ into these equations yields 



{-Aco^ + C) + icoB = -^ e~'^ 

 ^0 



{- do,^ + f) + i(oe = -^ e-'" 



[2a] 



r2b] 



Equating real and imaginary parts of [2], we obtain 



-Aci^ + C = — cos S 

 oiB = — 2 sin S 



[3a] 



% 





■Ax 





Figure 4 - Schematic Diagram of 

 the Model and Balance 



