Panel Discussion 



Recent Developments on Bulbous Bows at Hydronautics, Inc. 



M. Martin 

 Hydronautics, Inc. 

 Laurel, Maryland 



It has been well known that a bulb at the bow reduces the bow wave height, 

 and thus the wave resistance is decreased. (Inui, 1962; Yim, 1963). A simple 

 analytical representation of a bulb is the flow due to a point doublet located at 

 the stem of a ship bow. For a given polynomial representation of a Michell's 

 ship source distribution, the optimum strength of the doublet or the approxi- 

 mate size of bulb at a given position located on the stem was given for low 

 Froude numbers Fr < 0.3 by Yim (1965). 



An approximate simple image system for a bulbous ship was also given 

 (Yim, 1966c), and plotting streamlines of a bulbous ship can easily be done. 

 However, when we plot the streamlines of a ship with a point-doublet bulb, the 

 bulb is seen to have a narrow neck and is therefore susceptible to separation. 

 Therefore, it has been customary to fair the waterlines so that separation can 

 be avoided even though the fairing was not very scientific. 



Yim (1964) has found an optimum source type of bulb for appropriate water- 

 lines. These do not have any neck to induce flow separation. This type of bulb 

 has been investigated by Maruo (1964) both theoretically and experimentally with 

 good results. Pien (1964) also made use of the source type of bulb whenever his 

 optimum ship waterline had negative-cosine bow waves. However, the source- 

 type bulb needs the consideration of sinks in order to close the body and the ship 

 shape which needs a purely source-type bulb is not too practical. Thus, this 

 idea is useful only when we consider a total ship with proper attention to both 

 the bow, the stern, and the shoulder. 



At Hydronautics, Inc., a simple cylindrical bulb with a spherical head hori- 

 zontally oriented at the bow was designed for a given ship and tested at the Naval 

 Ship Research and Development Center (formerly David Taylor Model Basin) 

 (Yim et al., 1966). Although the ship waterlines had been analyzed and it was 

 found to need a strong source-type bulb in addition to a doublet-type bulb, a 

 further important reason for taking the bulb to be a cylinder was its easy 

 fabrication. 



In this report, an optimum ship form for a given cylindrical bulb horizon- 

 tally oriented at a ship bow is analyzed. A basic mathematical form for the ship 

 is assumed based on the concept of a double model ship (Inui, 1957) and Michell's 

 ship. Considering a point-doublet bulb and the optimum ship form from the 

 theory already developed (Yim, 1965), many such bulbous ships were superposed, 

 so that the bulb would fill in the given cylinder. A typical model was selected 

 and tested in the Netherlands Ship Model Basin with good results. 



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