Sec. 44.5 



FORCE AND FLOW DATA FOR HYDROFOILS 



75 



hydrofoils of symmetric section, having varied 

 aspect ratios and blade outlines. The results of 

 these tests were reported by R. C. Darnell 

 ["Hydrodynamic Characteristics of Twelve Sym- 

 metrical Hydrofoils," EMB Rep. 341, Nov 1932]. 

 The hydrofoils were towed beneath a special flat- 

 bottomed float which carried a dynamometer to 

 measure the lift, the drag, and the torque. The 

 angle of attack was varied from to 45 deg and 

 the gap between the top of the hydrofoil and the 

 bottom of the float was varied from to 2 inches. 

 The report gives the 0-diml lift, drag, and moment 

 coefficients for each hydrofoil in each test condi- 

 tion, together with the positions of the center of 

 pressure with respect to the leading edge. The 

 effect of running the hydrofoils with their trailing 

 edges foremost was also studied. 



For hydrofoils having raked or swept-back 

 leading (and trailing) edges and some taper, it is 

 customary to assume a nominal chord length 

 equal to the mean chord length, neglecting local 

 rounding of the outlines at the corners. Although 

 not clearly stated in EMB Report 341, this 

 scheme was followed for the 12 hydrofoils reported 

 upon in that publication. 



For fixing the fore-and-aft position of the 

 center of pressure CP or of the point of zero 

 pitching moment, this distance is reckoned along 

 the direction-of-motion chord at midspan. For a 

 blade outline with rake and taper but with 

 straight leading and trailing edges, the chord at 

 midspan is also the mean chord. 



In PNA, 1939, Vol. II, Fig. 9 and pages 206-207, 

 K. E. Schoenherr summarized the results of 

 selected tests on five of the twelve symmetrical 

 hydrofoils tested by Darnell, involving those with 

 varied rudder outlines but with the aspect ratio 

 limited to 1.0. In the figure cited he gave graphs 

 of lift coefficient C^ and of the ratio of CP position 

 from the leading edge to the mean chord length 

 of the hydrofoil for the five blade outlines dia- 

 grammed in the figure. 



IV. Data on Tests of Wageningen Rudders A and 

 B, with Symmetric Sections and Different 

 Outlines. The results of open-water tests on two 

 model spade-type rudders of orthodox shape, 

 outline, and proportions are described by W. P. A. 

 van Lammeren, L. Troost, and J. G. Koning 

 [RPSS, 1948, Figs. 210-214 and pp. 319-322]. 



44.4 Polar Diagrams for Simple Hydrofoils. 



A Hft-coefficient, drag-coefficient graph such as 



one of the four in Figs. 44. A and 44.B serves also 

 as a so-called -polar diagram, which is useful in 

 determining the Cl/Cd ratio at one aspect ratio 

 when the Cl/Cd ratio at another aspect ratio is 

 known [Rouse, H., EMF, 1946, pp. 285-286]. 

 When the ordinate scale of C^ is the same as the 

 abscissa scale of Co , the slope of a line (with 

 respect to the horizontal) drawn from the origin 

 to any selected value of a along the graph is the 

 value of the hft-drag ratio CJCd ■ A line from the 

 origin of coordinates, tangent to the graph, 

 represents the maximum lift-drag ratio of the 

 foil; the corresponding angle of attack is indicated 

 at the point of tangency. 



Table 44. a lists a number of references to pub- 

 lished polar diagrams for representative airfoils. 

 Diagrams of this type are of little use for practical 

 and design purposes, however, unless the section 

 contours of the hydrofoils or airfoils are defined 

 by a rather complete set of coordinates. 



44.5 Test Data from Compound Hydrofoils. 

 Figs. 37.A, 37.B, 37.C, and 37.D of Sees. 37.2 

 and 37.3 indicate that for boats and ships the 

 compound hydrofoil is used as extensively as the 

 simple hydrofoil for movable appendages and 

 control surfaces. Included in this category are 

 hydrofoils with flaps and tabs as well as hydrofoils 

 placed abaft fixed leading-edge portions and abaft 

 fixed horns, fins, and skegs. For steering rudders, 

 diving planes, active roll-resisting fins, and other 

 movable appendages the hydrofoils and hydrofoil 



Fig. 44.C Graphs of Lift Coefficient for Com- 

 pound Hydrofoils Having Varied Proportions 

 AND Varied Angles of Attack of the Movabm; 

 Blade 



