55 



procedure, although we cannot expect that Michell's theory will give a com- 

 plete answer for forms with a steep inclination of the sections at the bow. 



Still more serious objections can be made when applying the theory 

 to hulls with bulbous bows; but nevertheless the resistance properties of 

 bulbs have been studied with success. 



The "bulb effect" is a wave-making phenomenon. In principle the 

 pearlike shape of the bow sections is not a necessary attribute of a bulb form; 

 the latter is defined by the shape of the water lines or of the sectional-area 

 curve, for instance by the ratio / proposed by Taylor (Figure 30a). 



However, the pearlike form has resulted from the necessity of avoid- 

 ing spray formations, which arise when the load water line is rounded off by 

 a large radius . 



Replacing the bulb by a sphere (doublet) located at the bow (and 

 later at different distances from the bow) Wigley explained very clearly how 

 the wave trough which generally starts just abaft the sphere diminishes the 

 bow wave of the normal ship and thus also the resistance. He further succeed- 

 ed in demonstrating that the most advantageous position for the bulb was, gen- 

 erally speaking. Just at the bow over the whole useful range of speeds.*^ 



For practical work it is preferable to express the bulb by a high- 

 power polynomial ;-'-°^ the resistance effects of this bulb and of any normal 

 form can be easily combined using the appropriate S(y) functions. Figure 25 

 indicates how the S(y) function corresponding to a normal form is favorably 

 influenced by a bulb of definite shape and strength. The bulb shape is fixed 

 by the equation of the polynomial used; the strength of the bulb is denoted by 

 a constant factor "a" by which the polynomial is multiplied. Obviously for a 

 given hull, bulb shape and Froude number, the strength "a" will have an opti- 

 mum value, which theory seems to overestimate. 



By the method proposed, we get a much closer description of the bulb 

 form than by Taylor's rather summary procedure: 



a. It is easy to show that the efficiency of a bulb depends both on its 

 own shape and upon the character of the ship lines. Generally speaking, the 

 bulb is more advantageous for hollow than for straight lines. 



b. The advantage of the bulb disappears at low speed-lengtn ratios; 

 its lower limit of effectiveness depends on the shape of the normal ship form. 

 For hollow lines it- is about F ~ 0.2 or even less, while for straight lines 



it may be as high as F ~ 0.24 or 0.26. Theory indicates as upper limit for 

 the application of a bulb a Froude number of approximately 0.6, the exact val- 

 ue depending somewhat upon the form of the bulb and the ship; in fact the lim- 

 it is somewhat lower. 



