Current Progress in the Slender Body Theory 



and moment. The experimental points were obtained both from regular wave 

 tests and from transient or "pulse" type tests, as described in the paper by 

 Davis and Zarnick at the present Symposium; these experiments were made in 

 the Maneuvering and Seakeeping Facility, so that wall effects are minimized. It 

 is clear that under these conditions the seemingly crude first order slender 

 body theory gives a very good prediction of pitch and heave, in fact much better 

 than is usual in this field. 



The above results are less surprising if we recall that they are for zero 

 forward speed, and in this condition the resonant frequencies of conventional 

 ships in pitch and heave correspond to very short wavelengths, on the order of 

 50-75% of the ship length, or much shorter than the range of practical signifi- 

 cance. In other words, at zero speed with conventional ship forms the practical 

 frequency range for heave and pitch is substantially below resonance. Clearly, 

 however, the situation will change when forward speed is involved, at least in 

 ahead waves, since the frequency of encounter will be increased. This is illus- 

 trated in Figs. 3 and 4, showing the same theoretical curves compared to ex- 

 perimental data with forward speed (at a Froude number 0.14). There is now a 

 resonant peak within the domain of interest, although the data are essentially 

 unchanged away from resonance. This suggests that a second order slender 

 body theory, including the mass of the ship and all other effects of equal order, 

 might be sufficient to give predictions with forward speed of the same accuracy 

 as those shown for zero speed. It is for this reason that we have been examining 

 the second order slender body theory for ship motions in waves, which includes 



.2 .4 .6 .8 1.0 1.2 



FREQUENCY IN CYCLES PER SECOND 



Fig. 3 - Pitch response calcu- 

 lated from first order theory and 

 compared with experimental data 

 at 0.14 Froude number 



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