722 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 74.9 



the blade working in the boundary layer and the 

 short portion in a propeller outflow jet, the 

 balance ratios mthin the jet largely determine the 

 actual rudder balance and are the ones to be 

 given primary consideration in the design. 



If a partly underhung rudder is laid out with 

 a balance portion so long that, at or near the 

 hard-over position, the forward end of this 

 portion swings into a propeller-outflow jet, the 

 negative torque thus created appreciably affects 

 the balance situation as determined on a uniform- 

 flow basis. 



In some cases a balance portion hes only in 

 one-half of a scrcAV-propeller outflow jet, or 

 mostly in that jet. It is then acted upon by water 

 having a tangential component of velocity due 

 to rotation imparted by the propeller, primarily 

 in one direction. A balance performance predicted 

 for uniform or for axial flow may require appre- 

 ciable modification because of this tangential or 

 rotary flow, quite apart from any consideration 

 of the neutral angle of the rudder. Special studies 

 or model tests are required to insure proper 

 design. The same may apply to the design of 

 offset rudders encountering inward-and-aft flow 

 at the stern. 



Numerical balance ratios, either of area or of 

 length, have meaning only when apphed to control 

 surfaces of given section and shape in a given 

 type of flow. They can be distinctly misleading 

 when comparisons are made between dissimilar 

 rudders. It is the position of the CP with respect 

 to the axis for each condition which counts. 

 In other words, the degree of balance is deter- 

 mined by the actual rudder torque and not by the 

 balance ratio. The CP position requires careful 

 determination when the torques are large or when 

 definite over- or underbalance is being sought. 



The foregoing general design procedure apphes 

 also to the positioning of the stock axes for diving 

 planes, active fins, and other control surfaces. 



Data for estimating control-surface torques for 

 a degree of balance and for a blade shape tenta- 

 tively selected are given by: 



(a) Darnell, R. C, "Hydrodynamic Characteristics of 



Twelve Symmetrical Hydrofoils," EMB Rep. 341, 

 Nov 1932 



(b) Schoenherr, K. E., PNA, 1939, Vol. II, pp. 204-210. 



Chap. 44 of the present volume gives adaptations 

 of some of Schoenherr's diagrams. 



(c) Van Lammeren, W. P. A., RPSS, 1948, pp. 319-332 



(d) Hagen, G. R., "Rudder Design Data . . . Obtained 



from Tests on Five Model Rudders," TMB^Rep. 

 C-125, Jun 1948 



(e) Hagen, G. R., "Effects of Variations in Thickness- 

 Chord Ratio of Rudders in a Slipstream," TMB 

 Rep. C-487, Jan 1952. 



Additional design data are given in Part 5 of 

 Volume III. 



74.9 Selection and Proportion of Chordwise 

 Sections. Considering solely the development 

 of lift or lateral force, there are situations — un- 

 fortunately not yet fully predictable — for which 

 a thick, flat-plate blade attached at the ship or 

 hull end to a cylindrical stock is the best rudder 

 section to use. Certainly nothing much more 

 elaborate than such a plate, rounded at the leading 

 edge and fined at the trailing edge, is justified for 

 many small boats. 



A rudder on a large ship, however, gets a free 

 ride, as it were, for a good part of the time that 

 the ship is in operation, since steering rarely in- 

 volves a contmuous rudder motion. In this case 

 high lift is only one of several factors; easy flow 

 and low resistance carry considerable weight 

 when a rudder-blade section is chosen. As a 

 consequence, the overall advantages of fitting 

 streamlined rudders are so outstanding that 

 then- use is taken for granted wherever this type 

 of construction is at all feasible. The exact section 

 shape is not too important provided certain basic 

 principles are borne in mind: 



(a) The leading edge is to be neither too sharp, 

 so that it produces discontinuous flow when the 

 angle of attack is large, nor too blunt, so as to 

 develop excessively high dynamic pressures at 

 the nose 



(b) The section at the leading edge is made 

 elliptical in shape, not semicircular, for the 

 reasons given in Sees. 36.3 and 67.5. If cavitation 

 is not expected at zero or neutral angle, it should 

 be deferred, at least for the small angles en- 

 countered when steering. 



(c) The curvature in the entrance or leading 

 portion is easy, diminishing gradually from the 

 nose to the region of maximum thickness, comply- 

 ing with instructions in the last paragraph of Sec. 

 49.8 



(d) The section outhne or contour along any 

 streamline is fair, without jogs, buckles, welding 

 creases and upset Unes, or other discontinuities 

 across the streamlines 



(e) The extreme trailing portion is no thicker 

 than it need be for structural purposes. It is well 

 tapered, terminating in an edge that is only 

 thick enough to withstand nicking and corrosion. 



