Sec. 44.12 



FORCE AND FLOW DATA FOR HYDROFOILS 



83 



44.10 Spanwise Distribution of Circulation 

 and Lift. Sees. 14.8 and 14.9 and Fig.s. 14.1 and 

 14.J illustrate the variations that may occur, or 

 that may be planned in the spanwise distribution 

 of circulation and lift across a hydrofoil. These 

 diagrams, plus Figs. 14. L and 14.0, show about 

 where the principal trailing vortexes may be 

 expected for certain circulation distributions. In 

 practice, particular spanwise distributions of 

 circulation and lift are desired for the purpose of: 



(a) Reducing the tip-vortex strength and severity, 

 in an effort to reduce the force and energy losses 

 there, as well as the induced drag 



(b) Eliminating almost entirely the root vortexes 

 in a cantilevered hydrofoil. This may be done at 

 the roots of screw-propeller blades to reduce the 

 strength and harmful effects of the swirl core. 



(c) Applying the greater part of the lift load at a 

 given point or in a given region across the span, 

 because of strength, rigidity, or other require- 

 ments 



(d) Reducing the magnitude of the — Ap values 

 in a region where air is liable to be sucked down 

 from the surface. An example is the top of a 

 rudder which has only a thin layer of water above 

 it. 



(e) Distributing the lift load to achieve the 

 greatest efficiency for the hydrofoil as a whole. 



The desired circulation distribution is generally 

 obtained by changing the nominal angle of attack 

 across the span, with respect to the probable 

 direction of the inflow velocity. In this connection, 

 it is to be remembered that, as the angle of attack 

 is reduced, the circulation, the lift, and the 

 induced velocity diminish with it. A large induced 

 velocity results in a large actual angle of attack, 

 for which compensation must be made when 

 shaping the hydrofoil. 



Another method of reducing the circulation and 

 the lift is to diminish the camber of the sections 

 in question. This must usually be done without 

 changing the section thickness, since the latter is 

 required for strength, rigidity, and other con- 

 siderations. 



44.11 Effective Aspect Ratio for Equivalent 

 Ship Hydrofoils. No general procedure is known 

 for determining the effective aspect ratio of a 

 hydrofoil when either or both ends lie close to 

 surfaces which may act as the end plates described 

 in Sees. 14.7 and 14.8 and illustrated in Figs. 

 14.H, 14.1, and 14.M. Indeed, the effective aspect 

 ratio depends largely on the spanwise distribution 



of circulation and lift that actually obtains, and is 

 by no means an independent function of the 

 geometric planform shape and proportions. This 

 is because the effectiveness of the end plate 

 depends upon the magnitude of the overall 

 pressure differential between the +Ap and the 

 — Ap surfaces. If the pressure differential at the 

 tip is zero, and if this differential increases at 

 only a slow rate inboard from the tip, there is no 

 need for an end plate. With a large pressure differ- 

 ential at the tip, an end plate of adequate area 

 (if it were practical) would create an effective 

 aspect ratio roughly twice that of the actual 

 geometric ratio. 



At one limit it is probably sufficiently accurate 

 for engineering purposes to say that a gap parallel 

 to the span, equal to the adjacent chord length, 

 has the same effect as one of great width. A tip 

 or an end next to such a gap may be considered 

 free, beyond the influence of the adjacent structure 

 acting as an end plate. 



At the other limit the customary working or 

 construction tip clearance used in mechanical 

 design is large enough to prevent the adjacent 

 structure from serving as an end plate, and the 

 hydrofoil from behaving as one of infinite length 

 and aspect ratio. Furthermore, an end plate 

 attached to a tip with zero gap is probably not 

 effective as such unless it extends for at least one 

 chord length all around the section. The hub 

 surface of a screw propeller, as one example, is 

 almost never adequate for this purpose, when 

 considered as a combined inner end plate for all 

 the blades. 



44.12 Design Notes and Drag Data on Hydro- 

 foil Planforms and Sections. This section is in- 

 tended to cover hydrofoils designed and fitted for 

 general and special purposes. The design of 

 control-surface hydrofoils is discussed in Chap. 74 

 and of screw-propeller blades in Chap. 70. 



Aside from the influence of planform on the 

 aspect ratio, the principal features in the selection 

 of hydrofoil planforms and section shapes involve: 



(a) Increasing the chord length and thickness at 

 points where the foil attaches to some fixed 

 member or structure and where the end-plate 

 effect is sufficient to prevent loss of overall Ap 



(b) Diminishing the chord length at the tip 

 because of the low strength needed there and the 

 reduction in tip-vortex loss which normally ac- 

 companies the use of a short tip. Values of the 

 taper ratio Ct/cr may range from 0.3 or less for 

 fixed fins to 1.0 or more for screw-propeller blades. 



