Sharma 



disturbances (Fig. 2) and of a distributed singularity (Fig, 3) is not quite as 

 good. In any case the truncation correction itself becomes more and more ef- 

 fective with increasing length of run (see Fig. 3). The residual errors are rel- 

 atively larger at hump speeds (Fig. 3) than at hollow speeds (Fig. 2) as may be 

 expected in view of the different relative importance of the lower end of the 

 spectrum. 



On the whole, it appears that the analysis of a longitudinal cut located at a 

 realistic transverse distance (say one fundamental wavelength, y = 27t) and con- 

 tinued to a realistic extent behind the disturbance (say -x = 40Tr) in realistic 

 steps (say Ax = 7t/io) would yield, after application of suitable truncation correc- 

 tions, the free wave spectrum with fair accuracy and the wave resistance with 

 an error of less than 5 percent. 



EXPERIMENTAL VERIFICATION 



A further demonstration of the feasibility of the longitudinal-cut method of 

 wave analysis was obtained from a special test run on the mathematical model 

 Inuid S-201. This same model had been previously subjected to a series of ex- 

 tensive tests, including wave analysis, based on the transverse-cut method; 

 hence sufficient reliable data for crucial comparisons were available. Refer- 

 ences 4, 5, and 6 may be consulted for a description of the model and the details 

 of past experiments and analysis. 



For the present purpose a new resistance-wire-type wave probe which si- 

 multaneously records wave height and partial slope in any one desired orienta- 

 tion was designed and constructed by Mr. Hans Luft of the HSVA (Hamburgische 

 Schiffbau-Versuchsanstalt, Hamburg, Germany) with the expert advice of Pro- 

 fessor L. W. Ward of the Webb Institute of Naval Architecture, Long Island, N.Y. 



The test runs on Inuid S-201 were conducted in the HSVA on May 9, 1966, in 

 collaboration with Dr. Klaus Eggers of the Institut fur Schiffbau der Universitat 

 Hamburg and with the financial support of the Deutsche Forschungsgemeinschaft. 

 The wave probe was located at a fixed point in the tank at a transverse distance 

 of 1655 mm from the model center plane, and time records of wave height ^ and 

 transverse slope l^ were taken as the model passed by at six different speeds 

 between 1.4 and 2.0 m/sec. The comparative geometry of the longitudinal cuts 

 thus obtained and the transverse cuts measured in August 1962 with the same 

 model in the same tank but using a sonic wave probe is shown in Fig. 4. It may 

 be noted that actual tank dimensions allowed recording of very much longer 

 runs, but these were deliberately restricted to keep them well outside of the 

 wave system reflected from the tank walls, which is an extraneous effect not 

 accounted for in the present methods of longitudinal-cut analysis. 



Owing to an unexpected ambiguity in the calibration of the slope signal it 

 has not yet been possible to evaluate the ly records, but four height records 

 have already been analyzed. The relevant parameters of these runs are listed 

 in Table 4 and the height data as used for analysis are recorded in Tables 5 to 

 8. It should be noted that although the data are reproduced to four digits, the 

 accuracy of measurement is not claimed to be any better than about 2 percent of 



746 



