718 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 74.7 



(v) The possible effect of shallow or restricted 

 water, if operation in confined areas is involved. 



The process of deriving the swinging moment 

 may be largely empirical untU the method is 

 further developed. Eventually it should be 

 determined by a relation analytically derived. 



On the basis that the sheering maneuver de- 

 scribed previously in this section calls for the 

 greatest swmgmg moment and rudder effect, 

 the analytic method appears to involve: 



1. Laying out a series of successive positions, at 

 equidifferent time intervals, with respect to the 

 point where the emergency turn order is given, 

 known as the "execute" point, and the approach 

 path extended. There is a considerable backlog 

 of this information, pubhshed and unpublished, 

 with which to approximate or to bracket the 

 required data for a number of ship types. 



2. Finding the initial angular acceleration 

 a(alpha) required to make the ship occupy these 

 positions while moving forward in the initial 

 portion of a turn. In fact, it is possible that the 

 necessary data may be obtained on board ship 

 from simultaneous course and rudder-angle meas- 

 urements, made by recorders now available. 



By calculating or estimating the polar moment 

 of inertia Js of the ship for swuiging motion, 

 including the added inertia of the water, the 

 required swinging moment N is given by 



N = Jscc (74.i) 



The value of N may well be found to vary with 

 approach speed so that the designer is called 

 upon to work out a series of solutions if the speed 

 range is large. 



On the basis that the total lateral force Fl of 

 Fig. 74. E is determined, and that the sheering 

 maneuver occupies the predominant role, the 

 next step is to determine, in terms of numbers, 

 the fractional part of this force that is exerted on 

 the hull. In the present state of the art the fraction 

 Fh/Fl , alluded to previously and called here the 

 hull-force fraction, can at best only be estimated. 

 A correct estimate must be based upon knowledge 

 of the pressure field exerted by the angled rudder 

 in its vicinity. Available data on this feature are 

 rare; they are neither analyzed nor published. 

 It might be more realistic, therefore, to say that 

 for the present the hull-force fraction is only 

 guessed. It may be of the order of 1/4, 1/3, or 1/2, 

 leaving 3/4, 2/3, or 1/2 of the total lateral force 

 Fl to be developed by the rudder blade. 



If a dynamometer is available to carry a model 

 rudder and to measure the lateral force on its 

 stock, the rudder-force fraction F r/F ^ may be 

 determined during the test of a constrained ship 

 model, run straight ahead with angled rudder 

 under a towing carriage in a model basin. The 

 model can and should be self-propelled during 

 this test. 



Following a determination or an estimate of 

 the transverse force component F g, on the rudder, 

 the designer proceeds to apply the laws of the 

 hydrofoil and to calculate how much area 4i/ is 

 required to produce a lift equal to this force. As 

 previously mentioned, the problem is simplified 

 for the case being described by assuming that 

 the effective angle of attack «/ of the rudder 

 as a hydrofoil is equal to the mechanical rudder 

 angle 5. However, it is still necessary to know 

 the relative water speed past the rudder, cor- 

 responding to the rudder's speed of advance, 

 especially as this speed enters the lift-force 

 formula to the second power. The potential-, 

 friction-, and wave-wake velocities must all be 

 taken into account, -plus the negative-wake 

 velocity due to the augmented velocity in the 

 outflow jet of any propulsion device lying ahead 

 of the rudder. 



A two-part rudder composed of a tail and an 

 underhung foil is illustrated for the general case 

 in diagram 5 of Fig. 37. D and for the transom 

 stern of the ABC ship in Fig. 74.K of Sec. 74.15. 

 For such a rudder it is undoubtedly not valid to 

 assume that each part (tail and foil) generates its 

 own lift independently, by its own set of rules or 

 by its physical action alone. Nevertheless, this 

 approximate procedure must be used until 

 something better is developed. 



In addition to the assumed kinds and nominal 

 aspect ratios of the various hydrofoil elements of 

 the rudder blade, the effective angle of attack, 

 and the speed of advance, mentioned earlier in 

 the section, the designer now knows or has esti- 

 mated the total lift force F r required of the rudder. 

 Assuming a sort of standard type of hydrofoil or 

 flap section for each part, it is possible for him to 

 estimate the lift coefficients and to determine with 

 reasonable accuracy the area necessary to exert 

 the required hft force on each part. Graphs giving 

 some of the necessary data are found in Figs. 

 44.A through 44.D. Other data are to be found 

 in the references listed in Sees. 44.3, 44.4, and 

 44.5. 



The sum of the areas thus derived may be equal 



