High Performance Ships—Promises and Problems 17 
\ a ay INTERMEDIATE 
abc 
Wy a 
TS 
FINAL DESIGN Be 
PITCH AMPLITUDE 
ORIGINAL DESIGN min cee ce eee 
FOLLOWING SEA O HEAD SEA 
SPEED 
Fig. 17. Pitch behavior of various designs of the escort research ship 
When firm requirements were established for the design and the design adjusted to 
accommodate them it was found that by designing in the new features we had also designed 
out the favorable pitch characteristics of the original design. The long-dashed line in Fig. 
17 shows the disappointing results. The pitch period had been shortened so that resonant 
pitching occurred near operating speeds. 
It was found that we could calculate the period of pitch, using simple single degree 
of freedom relationships, to agree quite well with model tests by using F’. M. Lewis’ data 
for added mass plus allowances based on simplified shapes for the end nacelles. This 
proved to be a useful design tool and we set about to make changes to lengthen the natural 
period to approach that of the original design. A period length 7/VL was chosen in 
accordance with Mandel’s analysis which would place the design in the supercritical range 
for all but very low speeds. 
This was accomplished by shortening and deepening the hull, shaving away the ends 
of the water plane to reduce longitudinal moment of inertia, and increasing the nacelle 
sizes. For a single degree of freedom system the natural frequency is given by 
a Kies 
Ld | Cerra) 
where f is the natural frequency in pitch, Twp is the moment of inertia of water plane, 
I, is the mass moment of inertia of ship, and I, is the mass moment of inertia of 
entrained water. The changes enumerated above obviously tend to lower the natural 
frequency. 
It is not easy to alter the natural frequency of a ship while still keeping other charac- 
teristics unimpaired. For one thing the longitudinal radius of gyration in ordinary ships is 
about 0.22L or 0.25, not counting entrained water. In this design a value of close to 
