This figure clearly indicates the relationship between directional stability and aft frame line shapes. As aft frame line shape is changed from Utype to Vtype, directional stability is decreased mainly according to the increase of sway damping lever.
Fig.9 shows the relationship between σa and overshoot angles for 10 degrees zmaneuver test derived from free running model tests, where clear correlations between σa and overshoot angles are shown here. Further, trial data are plotted on the same figure for a particular ship.
From this figure, full scale second overshoot angle won't be met with IMO standard in case of ship with smallest σa value (marked with × ). Because second overshoot angle derived from model test is increased by certain amount compared with a ship whose trial result is very close to limitation by IMO standard. Since run coefficient of this ship is close to that for a ship with mark ※ in Figs 5 and 6, energy saving of 5% may not be expected to keep the restriction of second overshoot angle by IMO standard.
Fig.8 Directional stability factor for different σa values
Fig.9 Overshoot angles for different σ a values
24 Restrictions for fore fullness
Fig.10 shows a response function of resistance increase in regular waves for a ship with different fore fullness.
Measured response functions corresponding to the ship length to wavelength ratio of 0.5 with different wave heights are plotted. Fore fullness is represented by bluntness factor(βf) which is a representative factor in a region where diffraction component around bow is dominant.
As is shown in this figure, resistance increase in waves is increased as fore fullness is increased. On the other hand, wavemaking resistances in still water, plotted on a same figure, are not so influenced by the fore bluntness.
Tentative calculations of required sea margin based on the above data were carried out for VLCC with different beaufort scale. Calculated sea margin in head irregular waves for each bluntness factory are shown in Fig.11.
Fig.10 
Response function of resistance increase for different bluntness factors 
Fig.11 Calculated sea Margin for different fore fullness
Fig. 12 
Wave making resistance entrance coefficients for different 
Results of calculation indicate that difference of fore fullness affect sea margin as wave condition becomes worse which suggest that fore fullness should be limited considering the weather condition of the rout for target ship.
Fig. 12 shows the relationship between fore fullness and wave making resistance coefficient derived from resistance test in still water. Although wave making resistance coefficient is not so influenced by fore fullness at low speed, it should be noted that they might be increased rapidly by increased fore fullness when Froude number exceeds over specific border line. From the above fact, fore fullness should be carefully determined as a function of Froude number, not to injure the propulsive performance excessively.
