730 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 74.16 



AUi-»^h- 



1<2U[ 0060 



^ t Q n"' r'<2UiSini;(-UASin9s1 



Ec^.(74.l) 



Fig. 74. M Vector Diagram for Design of Contra-Rudder 



which separate velocity diagrams and rudder 

 sections are to be drawn 



(b) Estimating the magnitude of the mduced 

 velocity Uj at each propeller radius, as well as 

 the factors fci , k^ , and fcj in Fig. 74.M. These 

 data are required to determine the resultant 

 velocity vector Urs for the given radius at the 

 fore-and-aft location selected for the leading 

 edge of the contra-rudder. The latter position is 

 usually determined by the aperture clearance 

 provided abaft the wheel. 



(c) Drawing velocity diagrams smiUar to those 

 in Fig. 74.M, assuming that a contra-guide skeg 

 ending, if one is to be used, is already designed 



(d) Estimating the magnitude of the induced 

 velocity to be set up by the contra-rudder hydro- 

 foil section itself, of which half may be expected 

 to develop ahead of the leading edge of the contra- 

 rudder. It is of interest to note that the flow due to 

 cii'culation through the aperture between a 

 propeller blade and a contra-rudder blade is in 

 the same direction for both, namely forward in 

 the direction of motion of the propeller blade. In 

 many cases the velocities induced by the rudder 

 are small and may be neglected in the design. 



(e) Selecting a curve for the leading edges of the 

 hydrofoil sections of the rudder blade at the 

 various levels or propeller radii, as projected on a 



transverse plane. The offsets of these edges are 

 then laid off at each level. This matter is discussed 

 in detail in a paragraph following. 



(f) Calculating (or estimating) a minimum 

 thickness for the contra-rudder. This involves the 

 calculated diameter of the stock or main vertical 

 structural member necessary to carry the side 

 loads expected. These in turn have to be estimated 

 rather roughly until more of the rudder is laid out. 

 If the contra-rudder is to be of the compound 

 type, with a fixed forward portion, a certain 

 stiffness is required for this latter member. 



(g) Selecting a hydrofoil section thick enough to 

 meet the needs of (f), combmed with proper 

 fore-and-aft position of the maximum thickness tx 

 (h) Calculating the lift on the selected section 

 at the nominal angle of attack indicated by the 

 velocity diagram for the propeller radius in 

 question. From these data a second approximation 

 to the loading curve on the stock is found, by 

 which the stock scantlmgs are checked. Although 

 the lateral thrust loads are m opposite directions 

 above and below the shaft axis the bending 

 moments and shear loads are heavy in the vicinity 

 of that axis. 



(i) Adjusting the several hydrofoil shapes and 

 positions so that a S-dunl body based upon them 

 is fair with respect to its traces in a series of 



