RESISTANCE, PROPULSION AND SPEED OF SHIPS 



249 



ciit'fc'ii'd more than 2 points on the wind and sea scales 

 for the data used.) 



"The direction of wind and sea with respect to the 

 ship's heading w^as determined approximately from : 



(1) log data on wind and sea compass directions, 



(2) estimated heading of ship on the basis of track 

 normally followed. . . 



"A plot was made of average daily s])eed \'ersus sea 

 condition, as showai in the accompanying graph. Fig. 

 10. '* A different symbol was used tor each sea direction, 

 and lines drawn to show the trend of speed for each case. 

 The tlefinition of sea condition used is as follows (U. S. 

 Hydrographic Ofhce modified Douglas Sea Scale) : 



"It may be seen that .some verj^ clear trends of speed 

 in relation to sea condition emerge from this plot. The 

 records show full power to have been used on only a few 

 of the high-speed runs. In all other cases, power (as 

 estimated from fuel consumption) was reduced by \'ary- 

 ing amounts, in some cases the power being as low as 30% 

 of normal. This indicated the predominant importance 

 of ship motions in a rough weather service such as this. 

 Apparently the principal reason for loss of speed was the 

 voluntary reduction of power to ease the motions of the 

 vessel." 



3.1 Speed Loss Versus Ship Form. Considerable 



clarification of the relation.ship between a ship's propor- 

 tions and its beha\'ior in head irregular seas was fur- 

 nished by semi-theoretical investigation of E, V. Lewis 

 (19556) . This is based on three postulates : 



(a) Only waves equal or longer than a .•^hip pro^'ide 

 sufficient excitation for large motions. 



(b) Prohibitively large ship motions occur only 

 when the ship's natural period of pitching and the period 

 of wa\'e encounter are nearly equal. 



(c) In a stormy irregular sea the wave components of 

 all lengths are present and a ship, therefore, can always 

 find a component with which it can fall into synchronism. 



It follows from the foregoing that violent ship motions 

 can be expected if the synchronous wave component has 

 the wave length equal to or longer than ship's length. 

 The periods of encounter depend on the wave celerity 

 (in turn dependent on wave length) and on a ship's 

 speed. The natural pitching period is approximately 

 proportional to the square root of a ship's length. Fig. 

 11 was drawn on this basis with speed-length ratios as 



'5 Figure number of quotation was changed to refer to the present 

 monograph. 



0.8 1.0 1.2 1,4 1.6 1.8 2.0 2.2 24 

 T/VI/g 



1 J I I I 1 1 1 



0.1 0.2 0.3 0.4 



Period -Length Ra+io,T/VU 



Fig. 1 1 Theoretical ship speed-length ratios for synchronous 



oscillation in regular head seas of different lengths — defining 



typical zones of severe and moderate motions in irregular seas 



(from Lewis, 1955^) 



ordinates and T/\/L ratios as abscis.sae, where T is the 

 natural pitching period and L is the ship's length. The 

 parametric lines are the X/L ratios for the wave compo- 

 nents of synchronous frecjuencj' of encounter. The 

 heavy line, ^/L = 1.0 has been interpreted as the de- 

 marcation between the zones of moderate and severe 

 ship motions. A ship can always be placed in a moderate 

 region by sufficient reduction of its speed. 



Lewis next established an empirical relationship be- 

 tween the period ratio, T/\/L, and the displacement/ 

 length ratio, A/(L/1G0)'' for typical ships. By means of 

 this relationship he converted Fig. 11 into the form 

 shown in Fig. 12. The solid curve in this figure corre- 

 sponds to >/L = 1.00. This curve is now assumed to be 

 the demarcation line between regions of a satisfactory 

 and unsatisfactory behavi(jr of ships under st(n-m condi- 

 tions. A number of points above this line were plotted 

 on the basis of available data on smooth-water speeds of 

 ships. A few points (mostly towing-tank models) below 

 the ciu've represent the speeds at which ship's motions 

 under storm conditions were mild. F(jur hea\-y \'ertical 

 arrow's indicate the reliably reported reductions of speed 

 on ships at sea. These observed data agree well with 

 Lewis' curve. 



