Sec. 42.10 



POTENTIAL-FLOW PATTERNS 



47 



Experimental Towing Tank at the Stevens 

 Institute of Technology. The following references 

 pertain to this work: 



(1) Ward, K. E., "A New Method of Studying the Flow 



of the Water Along the Bottom of a Flying-Boat 

 Hull," NACA Tech. Note 749, Feb 1940 



(2) Sutherland, W. H., "Underwater Photographs of 



Flow Patterns," ETT Tech. Memo 86, May 1948. 



42.10 Velocity and Pressure Distribution 

 Around Schematic Ship Forms. For the deter- 

 mination of velocity and pressure around ship 

 forms whose shapes do not lend themselves to 

 expression in convenient mathematical terms, 

 Uke those of bodies of revolution or thin, deep 

 planks, theoretical hydrodynamics in its present 

 stage of development offers little that is of practical 

 value to the ship designer or even to the flow 

 analyst. There are definite indications, however, 

 that the theoretical work on wavemaking resist- 

 ance and on analytic ship-wave relations, de- 

 scribed in Chap. 50, may in time lead to reasonable 

 predictions of the characteristics of the flow sur- 

 rounding a ship, other than its surface configura- 

 tion and its local direction below the surface. 

 Until that time comes the marine architect has 

 recourse only to non-classified data available at 

 testing establishments and in the technical 

 literature. 



Diagrams illustrating, for simple ship forms, 

 the changes in and distribution of velocity or 

 pressure, or both, are to be found in the papers 

 listed hereunder. References which illustrate flow 

 patterns as well as velocity and pressure distri- 

 bution are duplicated from earlier sections of the 

 present chapter: 



(a) Two-dimensional ships having lenticular forms of 



waterhne [Taylor, D. W., INA, 1894, Vol. 35, 

 Figs. 24 and 25 on PI. LXXV]. Adaptations of these 

 original diagrams are to be found in S and P, 1933, 

 p. 4 and in S and P, 1943, p. 6. In the original 

 diagrams the plots are in terms of pressure heads 

 for fixed speeds, on a basis of distance along and 

 beyond the ship axis. 



(b) Five 2-diml forebodies of ship-shaped stream forms, 



with waterlines delineated by the use of line sources 

 and sinks in a uniform stream, are given by W. 

 McEntee [SNAME, 1909, Vol. 17, pp. 185-187 

 and Figs. 5 and 6, Pis. 114, 115]. These figures 

 embody curves of velocity ratio (f/co+ AC/)/C/„, 

 and of pressure head. 



(c) A flow diagram for a 2-diml ship-shaped form midway 



between two walls, with an ideal liquid streaming 

 by, is given by G. S. Baker and J. L. Kent [INA, 

 1913, Vol. 55, Part II, Fig. 5, PI. IV]. It is supple- 

 mented by curves of pressure coefficients with 



x-distance from the bow for the streamlines at 

 increasing lateral distance from the form. 



(d) Bows and forward shoulders of 2-diml ships generated 



by line sources (and sinks) in a uniform stream. 

 Curves of velocity and velocity head on a basis of 

 distance along the ship axis are published by H. 

 Fottinger [STG, 1924, Vol. 25, pp. 306-307; TMB 

 Transl. 48, May 1952, pp. 14-15]. 



(e) Complete 2-diml ship with waterlines generated by 



bow and stern line sources in a uniform stream. 

 Curves of, Ap and At/ along the ship axis are pub- 

 lished by F. Horn ["Theorie des Schiffes," Handbuch 

 der Physikalischen und Technischen Mechanik, 

 Leipzig, 1930, Vol. V; reproduced in RPSS, 1948, 

 p. 15]. 



(f) Three-dimensional ship having a lenticular form of 



waterplane, developed by D. W. Taylor [INA, 

 1895, Vol. 36, Fig. 7, PI. XVI]. Reproduced later 

 in S and P, 1933, Fig. 7 on p. 4, and S and P, 1943, 

 Fig. 7 on p. 6. 



(g) Three-dimensional model of a merchant ship of normal 



form, on which local pressure measurements were 

 made by W. Laute ["Untersuchungen iiber Druck- 

 und Stromungsverlauf an einem Schiffsmodell 

 (Investigations of Flow and Pressure on a Ship 

 Model)," STG, 1933, Vol. 34, pp. 402-460; TMB 

 Transl. 53, Mar 1939]. There is a bibliography of 

 19 items at the end of this paper; some of them are 

 quoted here. 



(h) Eggert, E. F., "Form Resistance Experiments," 

 SNAME, 1935, pp. 139-150 



(1) Eggert, E. F., "Further Form Resistance Experi- 

 ments," SNAME, 1939, pp. 303-330; abstracted in 

 SBMEB, Apr 1940, pp. 162-164. Simultaneous 

 pressure measurements were made with a multitude 

 of orifices in the hull of a battleship model having a 

 very large bulb bow. 



Methods for determining the velocity at any 

 point in the potential field around a schematic 

 ship form are described by: 



(1) Taylor, D. W., INA, 1894, Vol. 35, pp. 396-399 



(2) Lerbs, H. W. E., "Die Verteilung der Verdrangungs 



Stromung neben der Schiffswand (The Distribution 

 of the Displacement (potential) Flow Around the 

 Hull of a Ship)," WRH, 7 Jul 1928, p. 263; TMB 

 Transl. 85, Feb 1944. 



Both these methods require rather drastic simplifi- 

 cations of the actual conditions for a ship. 

 Method (1) calls for 2-diml flow throughout. 

 Method (2) requires that the ship form be con- 

 sidered as a body of revolution generated by 

 multiple sources and sinks, having a lateral plane 

 corresponding to the ship waterplane. Neither 

 method takes account of wave formation at the 

 surface, displacement thickness of the boundary 

 layer, possible separation zones, and other factors. 

 S. Yokota, T. Yamamoto, A. Shigemitsu, and 

 S. Togino describe the "Pressure Distribution over 



