ANALYSES ON BOW WAVES AND 



STERN WAVES AND SOME SMALL-WAVE 



SHIP SINGULARITY SYSTEMS 



B. Yim 



Hydronautics, Incorporated 



Laurel, Maryland 



ABSTRACT 



The qualities of the bow and stern waves of a ship are discussed. The 

 local disturbance of ships with zero wave resistance is formulated. 

 Thus the innage systems of sinnple no-wave singularities are obtained. 

 The force distribution of the zero wave ship is analyzed. The applica- 

 tion of these theories to the case of practical ships is discussed. 



INTRODUCTION 



The mechanism of the reduction in wave resistance due to a bulb appendage 

 at a ship bow has been explained by the reduction in the wave height of each ele- 

 mentary wave starting from the bow (1). This explanation has been further veri- 

 fied through the existence of an ideal bulb which cancels all the elementary bow 

 waves (2), However, complete understanding of ship wave phenomenon even just 

 in connection with bulbs is yet far from complete. For the time being, we may 

 ask ourselves two questions: First, what happens to the local disturbance when 

 we cancel all the regular bow waves? This is directly concerned with higher 

 order effects, and, in addition, this question leads us to find the exact and sim- 

 ple image system which satisfies the linearized free surface boundary condition. 

 Second, what is the relation between the wave height on the ship hull and the total 

 wave resistance, especially when the regular bow waves are canceled? The an- 

 swer to this question may explain the sizable wave resistance for a ship which 

 appears to have small wave heights on the hull. These questions are of funda- 

 mental importance not only in connection with the design of a bulb through the 

 observation of wave heights on the ship's hull but also for a more profound un- 

 derstanding of the mechanism of ship waves. 



Before investigating these questions we will re-examine the physical and 

 mathematical meanings of bow waves and stern waves, and their relation to the 

 waves due to a bulb. 



It turns out that the local disturbance due to the small-wave ship treated by 

 bulbs is in low Froude numbers, approximately the same as the local disturbance 



681 



