80 



innRoinx \Mi(.s i\ siin" disk.x 



Srr. 11.7 



Tlio roador is riuitiniicd ii> ninfmlxT that How 

 pnttoms inailo on a plate lieKl lirmly anainst tlio 

 pad of n hydrofoil, iioriual to its axis, are liahle 

 to Im? niisleadiiig. Tliere is n hoiiiulary layer of 

 indennite thickness over tliis plate, and the pattern 

 tlepiite*! on it is jilTettcHl to some extent by (low 

 ut the l)otton» of this layer ["Photographs of the 

 Flow Almut an NAt'A 2:«)1") Airfoil at an lllTec- 

 tive Reynolds Nnniher of ISO.IMMI," 'IMH Hep. 

 ■..'i7, Apr I'.MC.]. 



!•'. Ciutsehe has published a series of jjlioto- 

 graphs which show the flow traces over hydrofoils 

 which comprise the blades of experimental model 

 screw propellers. These show the i)aths taken bj' 

 the surrounding liquid when passing over and 

 between the blades, as viewed generally normal 

 to the projectttl area of the blade ("Versuche an 

 umlaufenden riiigelschnitten mit abgerisscner 

 Striinuing (Kxperiments on Rotating lilade Sec- 

 tions with Hrcakawaj' Flow)," Report, of the 

 Berlin Ahnlel liasin, published in S'R!, HMO, 

 Vol. 41. pp. 1S8-22G]. 



44.7 Pitching Moment; Center-of -Pressure 

 Location. .Vs a rule, information a.s to the ])itch- 

 ing-nioment coenicient and location of the center 

 of pressure on a hydrofoil to be used on a ship is 

 as important as that relating to the lift and drag 

 eoenicienl.s them.solves. Indeed, if the hydrofoil 



Direction of Flow for 

 &oth Oiograms 



Smoll Circles Indicate Center-of -Pressure 

 Poftitions for Nominol Anolee of AttocU 



Airfoil Section U5A5 

 Aspect Rotio 6 



1.0 0.0 06 0.4 0I~" '-2 



Chord Length from Leadmo Edqe '" 



Kio. 44. K D1AORAM8 Ii.i.i/HTiiATi.Nii Hmrr or Cf.ntkk- 

 or-l'iiKjuii'iiK Position With Anoi.k ok Attack, 



ion A l''l.AT P1.ATK ASI> A HyDKOPOM. 



can not be rotated in s«'rvice to change its angle 

 of attack it may be well-nigh useless. The torque 

 applied liy hydrmlynamic action on the blades of 

 controllable jiropellers and on rudders is necessary 

 knowledge for their design. The location of the 

 efTectivc center of pressure on the entire under- 

 water bixly of a turning ship, considered as a 

 hydrofoil, is a major factor in its maneuvering 

 characteristics and in the heel while turning. 



Most of the moment (and other) data relating 

 to foils and available for engineering use apply to 

 airfoils. For these a fore-and-aft aerodynamic 

 center is usually assumed, about which the 

 (pitching) moment coefTicient for various con- 

 ditions is relatively constant. This center is 

 sometimes taken on the chord of the meanline, 

 at a distance of c/4 from the nose, but usually it 

 lies on the ba.se chord, at the same distance from 

 the nose. 



As an indication of what may normally be 

 expected in the way of chord wi.se shift of the 

 center of pressure CP with varying angle of 

 attack, Fig. 44. F illustrates this feature graphi- 

 cally for a flat, rectangular plate (diagram 1) and 

 for an airfoil section of not-unusual .shape (dia- 

 gram 2). 



Sonie (luanlitative didii on this item, for simple 

 hydrofoils and others suitable for ship rudders, 

 arc given in items I. tlinnigh I\'. of Sec. -1 \.'.\. 



44.8 Distribution of Velocity and Pressure on 

 a Hydrofoil, 'i'lie distribution of velocity and 

 l)rc.>isure on an airfoil or hyilrofoil, discussed in 

 the jHcsent section, is that occurring on and meas- 

 ured <Iirectly at its external surface. This is to be 

 distinguished from the velocity and pressure fields 

 around it, described in Sec. 44.9 following, which 

 are tho.sc existing outside of and beyond the 

 external foil surface. In general, the pressures 

 occurring on the foil surface determine the lift, 

 drag, and other forces exert<^d on or by it. The 

 pres.sures occurring in the adjacent field determine 

 the forces on adjacent objects. 



Hydrofoils of symmetric section arc widely 

 used in ship tlesign and construction. Figs. 44.G, 

 44.11, and 44.1, adapted from Volume II of the 

 book "Modern Developments in Fluid Dynam- 

 ics," eiliteil by S. CJoldstein, Oxford Press, 1938 

 (Fig. 179 on page 455, Fig. 180 on page 4tV2, and 

 Fig. 139 on page 404, respectively), give the 

 chorilwi.se distribution of pressure coi'fTicient on 

 eight typical .symmetric .s<'ction8, covering a wide 

 range of thickness ratios tx/c. The angle of attack 

 is zero, so the pressures on both sides are the same. 



