Computing Hearing and Pitching Motions 519 
The aim of this work coincided in some respects with that of Dr. Grim in that we 
wished to obtain information for forms of shiplike section which could be used later in com- 
putations for three-dimensional bodies by a strip method or some modification. However, 
there was a further aim. Experimental evidence confirming the applicability of perfect-fluid 
theory with a linearized free-surface condition to oscillatory motion of a body in a real fluid 
with a free surface seemed to be very scarce, and we felt that more was needed. In order to 
make a comparison of theory and experiment, configurations were needed for which the the- 
oretical calculations could be made with controllable accuracy and for which the correspond- 
ing experimental measurements could be carried out with available equipment. Two- 
dimensional shapes had several advantages for the experimental work. Furthermore, it was 
known how to generate by conformal mapping of a circle families of shiplike sections, the so- 
called Lewis forms, Landweber forms, Prohaska forms, etc. In addition, Ursell* had al- 
ready carried through computations of added mass and damping coefficients for a circular 
cylinder by a method which seemed likely to lend itself to further generalization to include 
the forms mentioned above. This turned out to be the case. Further modification allowed 
the inclusion of a horizontal bottom. 
In order to have a more sensitive test of the perfect fluid theory, it was decided to com- 
pute and measure the pressure distribution around the cylinders as well as the added mass 
and damping coefficients. The computations were programmed for and carried out on an 
IBM 704. We believe them to be accurate to within 0.5 percent. 
At the time this work was carried out we did not know that Dr. Grim was also engaged 
in similar computations for infinite depth by the method which he had proposed much earlier 
in 1953. However, Tasai’s paper in J. Zosen Kyokai 105:47 had come to our attention, after 
this work was well under way, and we recognized that the two approaches were identical.t 
However, since Tasai had not included the pressure distributions, in which we were espe- 
cially interested, or finite depth, we decided to continue with the computations. Although 
Porter’s computations show some small discrepancies with Tasai’s, they confirm them gen- 
erally, as well as those of Dr. Grim. 
The experimental measurements have at this time been carried through only for a circu- 
lar cylinder (10-inch radius). However, other shapes, especially U-shaped and bulbous sec- 
tions, will be tested later. In carrying out the force and pressure measurements a retreat 
was necessary in one respect. Although, a phase resolver had been designed, constructed, 
and tested, it was not feasible during the first set of experiments to make use of it because 
of excessive noise in the signal, a difficulty we are confident of being able to overcome 
later. As a result, the experimental points shown in Figs. D1 and D2 are for the amplitudes 
of fluctuation of the total pressure and force. For these the agreement between theory and 
experiment seems to be very satisfactory. Although, extremely square U-sections may show 
greater deviations, it seems likely that perfect-fluid theory can be used to give adequately 
reliable predictions of the motion of stationary oscillating bodies. 
A detailed description of this work may be found in the report of W. H. Porter, “Pres- 
sure Distributions, Added-Mass, and Damping Coefficients for Cylinders Oscillating in a 
Free Surface,” Inst. of Engrg. Res., Univ. of Calif., Berkeley, Series No. 82, Issue No. 16 
(July 1960). 
*Quart. J. Mech. Appl. Math. 2:218 (1949). 
t An English version of Tasai’s paper (Rep. Res. Inst. Appl. Mech., Kyushu Univ., Fukuoka, Japan, 
8(No. 26):131 (1959)) was later brought to our attention, and presumably renders our translation of 
the Japanese version (Inst. of Engrg. Res., Univ. of Calif., Berkeley, Series No. 82, Issue No. 15 
(July 1960)) superfluous. 
