Applying Results of Seakeeping Research 



Also shown in this plot are the head sea response operators expanded to 

 ship lengths of 900 and 1,200 feet, and reduced to 300 feet. The other angular 

 components for these lengths have been omitted from the figure for clarity. A 

 comparison of the operator curves for different ship lengths demonstrates the 

 advantage of the form of presentation used in these calculations — the response 

 operators for any series of geometrically similar ships plot as a set of identi- 

 cally shaped curves, shifted on the i-og^co axis according to the absolute sizes 

 of the ships. Portions of the curves shown by broken lines are extrapolated be- 

 yond the measured data. 



The product of a sea spectrum component for a certain angle m^, and the 

 response amplitude operator component associated with that wave direction 

 gives a response spectrum component curve. The family of curves obtained in 

 this way (one curve for each wave component) is then integrated over direction 

 (angle) to obtain a single response curve. Four such integrated response curves 

 for the four ship lengths are shown in the lower plot of Fig. 3. The angular 

 components of the response spectra have not been plotted. 



Finally, the integration of a response spectrum curve over wave frequency 

 gives the cumulative energy density, R, for the bending moment coefficient. 

 From values of R for each ship size statistical parameters, such as the average 

 value of the highest expected wave bending moment coefficient out of a total of N 

 oscillations, may be calculated from the expression, h^/L = Cv^ where the mul- 

 tiplier c takes different values depending on the number of oscillations consid- 

 ered. For example, assuming a Rayleigh distribution. 



Average h^/L = 0.866 v'R" 



Average of 1/10 highest h/L = 1.800 ^/R 



Highest expected h^/L in 100 oscillations = 2.280 v^ 

 Highest expected h^/L in 1,000 oscillations = 2.730 v^ 

 Highest expected h^/L in 10,000 oscillations = 3.145 Vr". 



The variation of wave bending moment with ship speed is shown in Fig. 4 

 for a ship headir^ directly into a severe 62-knot spectrum [12]. It is evident 

 that increasing the speed of a ship does not in general increase the wave bending 

 moments. Decreasing speed can, in fact, increase the wave bending moments 

 slightly. No consideration is given here to two other effects of speed, namely 

 the increase in the bendii^ moment caused by ship-produced waves as speed in- 

 creases and the effect of speed on slamming which may increase midship hull 

 stresses. The former causes a shift of the mean value; the magnitude of the 

 effect of slamming requires further detailed study. 



The vertical wave bending moment is also influenced by the direction of the 

 ship's travel relative to the waves. In a short-crested sea the wave components 

 come from various directions simultaneously, so that regardless of its heading 

 the ship reacts to waves coming from many angles. The heading of a ship is 

 defined here as the angle between the direction of ship's motion and that of the 



197 



