110 



11M)RI)1)V.\AM1C;S l.\ Mill' Dl.SlGN 



Src. 16.6 



Now York Sect., 'Jf. Apr 1951, p. 7, Fig. 1]. Tliia 

 lonstaiit specific r»'sistaiirc is n-rkoiuHl iibuvc ull 

 nllowniucs for i)oth transverse and longitudinal 

 iur\ature and for plating, stnictural, and coating 

 roughneSv<«\s which are applieil to tlie flat, smooth- 

 plate, turlnilent-flow friction line. 



In the usual case the +Ap's and — Ap's caused 

 by out wan! deflection of the water at the bow, 

 by speetling up between the forward and after 

 neutral point.*, and by closing in astern, are not 

 of such sign and magnitude as to balance each 

 other, when integrated over the transverse 

 maximum-area .'icction. This is especially true if 

 the vesj^el has a bulb of appreciable size at the 

 bow, or if the separation zone at the stern is large 

 enough to interfere with the closing in of the 

 potential flow along the run. Some of the low- 

 speed specific pressure resistance is probably 

 always the result of this action. The remainder, 

 and greater part, is chargeable to separation at 

 the stern, especially if the criteria of Sec. 46.2 

 indicate a sizable zone of — Ap, when projected 

 on a transverse plane. Areas of this kind are 

 illustrated by the hatched portions of diagrams 

 1 and 2 of Fig. 46. A. 



There are insuflicient data from model tests, 

 and practically none from ship trials, to afford 

 an indication of the numerical values of — Ap or 

 of the pressure coefficient — Ap/5 to be found 

 in ship separation zones. Tests in air on geometric 

 forms indicate separation-zone pressures varying 

 from —\Aq behind a 2-diml flat plate to —1.15(7 

 behind a 2-diml circular cj-linder, with its axis 

 normal to the stream, to — 0.4g or le.ss for a 

 sphere and a circular flat plate, depending upon 

 the /?. of the test. There is little doubt that these 

 values are much too high for separation zones at 

 the stern of a ship. In fact, it is not yet known 

 whether the — Ap in those zones is a function of 

 q or perhaps of the hj'drostatic pressure -p,, . 



It is pointed out in Sec. 7.3 of Volume I that 

 aeration, defined as the natural or deliberate 

 admission of air to a separation zone where the 

 — Ap's cause added drag, acts to diminish that 

 drag. \Vhen di.scussing separation drag, therefore, 

 it is most necessary to know the extent to which 

 atmaspheric air has been admitted to or has found 

 its way into a — A/j region that is under a pressure 

 le.ss than atmo.spheric. In certain regions —Ap's 

 arc wt up deliberately, for propulsion purpo.ses, 

 as on the ijacks of the blades of screw propellers. 

 It iH important to know to what extent, if any, 

 air has leaked into the.sc regions and diminished 



the u.seful —Ap's. For cxaiiiplc, air drawn down 

 to fill the .separation zones behind the arms, legs, 

 and feet of swimmers, as revealed by special 

 high-speed photography, may be helpful or 

 detrimental, depending upon whether drag or 

 propelling forces are involved. 



B. Perry reports the results of drag measure- 

 ments on surface-piercing bars of rectangular 

 and circular section, and gives excellent photo- 

 graphs of the air-filled holes alongside of and 

 abaft these bars [llydrodyn. Lab., CIT, Rep. 

 E-55.1, Dec 1954]. He reports an effect of surface 

 tension in the formation and behavior of the 

 .spray roots at the water surface. Sometimes these 

 roots form a sort of closure over the separation 

 zone which prevents the admission of air to it. 



Neglecting the free-surface and lower-end 

 efi"ects. Perry reports that tlie drag of the \-ertical 

 bars per unit depth, at a submergence h, may be 

 derived from the drag of similar bodies well 

 submerged and trailing water-vapor cavities 

 abaft them. The referenced report gives drag 

 coefficients for bars of circular section, for rec- 

 tangular bars with one flat edge leading, for 

 wedge-shaped bars with the apex leading (and 

 for various included angles), and for all three 

 kinds when placed at an angle to the flow. 



46.6 Separation Phenomena Around Geo- 

 metric and Non-Ship Forms. It is often useful, 

 in the design of bo.x-typc or non-ship-shaped water 

 craft, and in tlic design and application of append- 

 ages, to have information as to the nature of the 

 separation to be expected around them. Some of 

 these data are given in the illustrations on Chap. 7, 

 and references to other data arc furnished in 

 certain sections of Chap. 42. 



Research on this phenomenon has been under- 

 way for many years but the data have not yet 

 been collected and presented in systematic 

 fashion. Over three-quarters of a century ago 

 the following quantitative data were given by 

 W. Froude as the result of towing tests on a 

 cylindrical pitot tube 0.125 ft in diameter and 

 projecting 1.75 ft below the free-water surface. 

 The test was made at a speed of 15 ft per sec, 

 corresponding to about 9 kt. An air-filled hole, 

 called by Froude a "ga.sh," extended for about 3 

 ft abaft the tube, at which point the ga^sh closed 

 by the gradual meeting of the side streams which 

 boundeii it. 



". . . from lliis point to alxiut 7 or S feel furlliiT stcrnwarda 

 there ro.sc vcrlicnlly a rentriil wall of wat<T, the crest of 

 which, ill its niilc elevation, hail a paraliolic form (aa far 



