768 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 76.9 



may then shift the various apex positions and 

 go through the dehneation process all over again. 

 Even the most experienced designers of small 

 craft with developable surfaces find this necessary, 

 but with practice it is possible to perceive when 

 the developed shape is departing from that 

 visuaUzed, and to correct it before too much work 

 is put into an undesired delineation. 



In the example described, the chine is used as a 

 directrix for both the bottom and the side. Only 

 two cones were used for the side but three, four, 

 or more could have been used to give the side a 

 greater tumble home aft or for other reasons. 

 Five cones, four above the side and one below it, 

 are employed for the 23-ft high-speed boat drawn 

 in Fig. I on page 30 of the Werback reference 

 cited. In fact, the apex can continue to shift from 

 one generatrix to the next, following a continuous 

 curve in space, provided that the apex always 

 remains clear of (outside of) the portion of devel- 

 oped surface that is to be worked into the boat. 



Reduced to their utmost simplicity, portions 

 of developable surfaces can be flat or cyUndrical. 

 In these, cases, the traces of given generatrixes 

 are parallel to each other in all three views of an 

 orthogonal projection. 



Considering the importance of the bottom 

 shape in a V-section craft with chines, both the 

 keel line and the chine may be established at 

 the outset and used as a pair of directrixes. The 

 procedure in this case, somewhat more involved 

 than that described, is covered in an unpublished 

 paper by L. K. Losee, reference (e) listed at the 

 beginning of this section. Mr. Losee is, at the 

 time of writing (1955), on the staff of the Bureau 

 of Ships of the U. S. Navy Department. 



76.9 Design of Discontinuous-Section Forms ; 

 Blisters and Bulges. Chap. 28 explains that it 

 is frequently convenient to incorporate discon- 

 tinuities in the transverse sections of an vmder- 

 water hull, either to simplify construction or to 



Re-entrant />nqle 100 deq 



Fig. 76.E Midsection of World War II German 

 Cruiser Prinz Eugen with Busters 



take care of some special situation which arises 

 after the vessel is built. The ship which has a 

 blister added to the outside of its hull, as in 

 Fig. 76. E, whether it is a vessel M'hich needs 

 torpedo protection or more beam and displace- 

 ment, or a submarine which needs external 

 ballast tanks attached to its pressure hull [USNI, 

 Feb 1955, p. 159], calls for the use of design 

 principles that are essentially the same. 



Actually, if certain basic principles are fol- 

 lowed, rather amazing discontinuities of this type, 

 in the way of saddle tanks, thick fender strakes, 

 and the like, can be worked into underwater 

 sections without incurring too much friction or 

 pressure resistance. These principles may be 

 stated as follows: 



(a) The chine lines are to be so placed that the 

 water, when flowing around the ship at the speed 

 and under the conditions considered most im- 

 portant, follows but does not have to cross them 



(b) When there are "offset" surfaces between 

 chines and coves, illustrated in diagram 3 of 

 Fig. 76. F, which are of appreciable area when 

 projected on a vertical transverse plane, it appears 

 wise to make the projected areas facing aft about 

 equal to those facing forward, even though the 

 actual offset surfaces do parallel the lines of flow. 

 For example, in the body plans of the German 

 submarine U-111 in Figs. 28.B and 28.C, the 

 projected area of the offset surfaces between the 

 chines and the coves in the forebody is of the 

 same order of magnitude as the area of those in 

 the afterbody. There is no known hydrodynamic 

 justification for this rule; only the engineering 

 intuition of the author. 



(c) The lower offset surfaces of discontinuous sec- 

 tions, if near the water surface, are shaped to 

 parallel the general surface-wave profile at the 

 selected speed. Otherwise they will lie at angles 

 to the streamlines and may produce areas of 

 separation. 



(d) It is desirable to limit the sides or offset 

 surfaces of a cove, at least those lying perpen- 

 dicular or nearly so to each other, to the minimum 

 practicable widths. This can frequently be ac- 

 complished by sloping or cutting away the edge 

 of the projecting portion beyond the region 

 where a right-angled connection is required for 

 structural reasons, indicated in diagrams 1 and 2 

 of Fig. 76.F. 



(e) The reentrant angle at the bottom of a cove 

 should be as large as practicable; in no case 



