Sec. 7-f.7 



MOVABLE APPENDAGE DESIGN 



717 



force exerted on a ship model aljreast a rudder 

 position when the rudder is angled and the model 

 is constrained to move in what amounts to a 

 straight continuation of the approach path. This 

 serves as some sort of check for a particular pre- 

 liminary design of rudder rather than as an aid 

 in the course of the design. 



The sheermg maneuver must be defined in 

 specific terms if it is to form part of the maneu- 

 vering specifications of a ship or if it is to serve 

 as the controlling factor in a rudder design. 

 These terms should include the rate of change of 

 heading followmg an order to turn and the shift 

 of position of the CG laterally from the approach 

 path, in the positive or negative direction of the 

 2/o-motion axis. All these should be on a basis 

 of time and of advance in the .ro-direction. 



The complete solution outlined in the first 

 sentence of the second paragraph of this section 

 involves too many answers to render itself work- 

 able with present techniques (1955). It is neces- 

 sary at this stage to assume reasonable, tentative 

 values or conditions for some of the answers, 

 namely: 



(1) The general dimensions, size, and shape of the 

 ship hull, as well as certain of its maneuvering 

 characteristics 



(2) The fore-and-aft position of the rudder and 

 rudder stock along the hull axis. The assumed 

 swinging axis of the vessel may be taken at its CG. 

 The distance from the CG to the rudder-stock 

 position is the moment arm of the lateral rudder 

 force, although, strictly speaking, this distance 

 should be measured to the instantaneous center of 

 pressure CP of the rudder blade. 



(3) The type (or types) of rudder to be worked 

 into the design problem. Alternative preliminary 

 designs may be required for alternative rudder 

 types (and shapes). 



(4) Some idea of the shape of the rudder blade 

 and of its position with respect to the adjacent 

 hull or the nearby fixed appendages 



(5) The maximum swinging moment A'^ to be 

 applied to the hull under the most severe man- 

 euvering requirement. This is a major feature, 

 which should be derived rather than assumed, by 

 a process to be discussed shortly. 



The situation is as sketched in Fig. 74. E. 

 Dividing the swinging moment A'^ by the moment 

 arm a of the rudder gives the transverse force 

 Fl required to be exerted on both the rudder blade 

 and the ship at and near the rudder-stock position. 



The designer then determines, by estimate from 

 empirical data and possibly ISiter by calculation, 

 the proportion of this lateral force F^ which he 

 may reasonably expect to be exerted on the hull 

 and the fixed appendages. This portion is indicated 

 as Fu in the figure. The remainder of the transverse 

 force is that to be exerted on the movable rudder 

 blade when fully angled. This is normal to the 

 ship axis, mdicated as F^ . With an assumed 

 maximum rudder angle 5 (delta), an effective angle 

 of attack of the rudder equal to it, an assumed 

 aspect ratio, and an average value of lift coefficient 

 for hydrofoils suitable as rudders, the problem is 

 worked backward and the hydrofoil or blade area 

 is approximated. The calculation is repeated for 

 as many different ship speeds, or as many different 

 initial assumptions, as may be desired. 



Of the data listed under (1) through (5) pre- 

 ceding, the determination of the maximum 

 swinging moment N poses by far the most difficult 

 problem. The method of finding it for any 

 particular design situation is not yet worked out 

 but the following factors require consideration: 



(i) The maneuvering characteristics of the hull 

 proper, without the rudder (s). Carried to the 

 limit with respect to rapid change of heading, a 

 ship in the form of a circular tub would require 

 only enough tangential force at its surface to 

 overcome the polar inertia and the friction 

 resistance. Carried to the opposite limit for rapid 

 lateral change in position, a long slender craft 

 requires rather extreme measures in the way of 

 applied forces and moments to accomplish the 

 offset from the extended approach path which 

 is required for a sheering maneuver, 

 (ii) The polar moment of inertia of the ship about 

 the vertical swinging axis for the particular 

 loading condition specified 



(iii) The added inertia of the entrained water for 

 the superposition of the swmging mode of motion, 

 when the ship starts to turn 

 (iv) The steady speed of the ship along the ap- 

 proach path 



Lever Arm for Reauired Rudder Moment on 5hip ' ] 



Fig. 74. E Diagram of Rudder and Ship Forces and 

 Moments 



