Snc. 67.22 



UNDERWATER-HULL DESIGN 



533 



for the entire radial extent of the deflectors. 

 This means roughly that the natural sine of the 

 deflection angle ds imparted to the water abaft 

 the skeg termination at any selected point, times 

 the propeller radius R at that point, is constant, 

 or that the natural sine of the deflection angle 

 varies inversely as the radius. 



A. Betz of Gottingen in his paper "Zur Theorie 

 der Leitapparate fiir Propeller" ["The Theory of 

 Guide Vanes Apphed to the Propeller," NACA 

 Tech. Memo 909, Sep 1939], makes the basic 

 assumption that the tangential velocity com- 

 ponent in the outflow jet, due to induced velocity, 

 varies inversely as the radius from the propeller 

 axis. This corresponds to the variation mentioned 

 in the Haas patent. Unfortunately, the Betz 

 paper does not tell how to design the vanes. The 

 outline of a proposed method follows. 



Consider first the determination of the correct 

 or effective deflection angle for any given un- 

 symmetrical skeg ending. Obviously, from refer- 

 ence to Fig. 67.S, there is no single flow in the 



Direction of Motu 

 Streomlines 



Maximum Waterline 5lope^^ 



Fig. 67. S Method of Laying Out Skeg Waterline 

 FROM Median Line 



region abaft the ending where the propeller 

 works but a confluence of two flows. There is 

 httle reason to believe that the flow over the 

 convex side, having the greatest slope to the 

 longitudinal axis, is the predominant one. There 

 is ample evidence that the effective flow abaft 

 the traihng edge of a hydrofoil surrounded by 

 circulation moves more nearly in the direction 

 of the concave or straight side. However, the 

 circulation around the whole ship hull in a hori- 

 zontal plane, due to the sUght asymmetry in 

 question, is surely very small. Whereas the flow 

 abaft a thick airfoil or hydrofoil producing hft is 

 predominantly in the direction of that passing 

 along the face or +Ap side of the foil, as is 

 indicated by many published flow photographs, 

 this is unhkely to be the case here. If it were, 

 the prerotation which could be given to a screw- 



propeller inflow jet would be rather moderate. 

 If, on the other hand, what is desired is to lessen 

 the angle of flow by which water in the inflow 

 jet follows the blades, described in Sec. 33.12, 

 then even small slopes on the concave or pressure 

 side of a skeg ending or bossing termination can 

 be most effective. 



For design purposes it is sufficiently precise to 

 assume that, as indicated in Fig. 67.S, the direc- 

 tion of flow at a small distance abaft the traihng 

 edge of a skeg corresponds to the direction of a 

 tangent to or extension of the median line of the 

 skeg ending at that edge. A "small" distance is 

 assumed to be from 0.5 to 0.9 times the width 

 of a blade on the propeller. If the aperture 

 clearance is greater than 0.9 times a blade width, 

 the direction of flow expressed by the speed-of- 

 advance vector Ua is assumed to be more nearly 

 a prolongation of the +Ap or concave side of the 

 unsymmetrical skeg ending. 



Actually, the amount of prerotation to be 

 imparted ahead of the disc by the design being 

 worked out depends upon: 



(1) The tangential component of induced velocity 

 which is to be imparted by the blade element at 

 any radius. This in turn is a function of the 

 effective or hydrodynamic angle of attack aj of 

 that element, the strength of the circulation there, 

 and the magnitude of the induced velocity Ur 

 far astern. 



(2) Whether enough rotation is to be put in 

 ahead of the disc to give zero resultant rotation 

 abaft the disc, or whether some contra-guide 

 feature, such as a contra-rudder, is to be fitted 

 abaft the propeller, to take out the remainder of 

 the rotation in that region. 



It is often necessary to design the appendages, 

 at least for a model test, before the propeller 

 design is worked out, so that the values in item 

 (1) may have to be estimated or taken from data 

 on some other design. It is a difficult design 

 problem to achieve the first step listed in item (2). 

 It may be said, therefore, that in the present 

 state of the art a skeg ending should not be 

 called upon to compensate for lack of a contra- 

 guide device abaft the propeller. 



It is not possible without more extended 

 knowledge of the intricate flow which takes place 

 between a skeg ending and a screw propeher to 

 state definitely the parameters and the relation- 

 ships which should govern the variation of median- 

 line slope ds with radial distance from the pro- 



