290 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 55.4 



Lammeren, L. Troost, and J. G. Koning [RPSS, 

 1948, p. 69]. They are reproduced in Table 55.a. 

 The graphs of Fig. 55. A show the increases in 

 effective power Pe for a large destroyer when 

 four types of appendage are added, one by one. 

 The individual percentages may be obtained by 

 the proper subtraction, on the basis that the 

 resistance effects of the four appendage types are 

 independent of each other. 



26 28 30 32 34 36 38 40 

 Ship Speed, kt 



Tq = I46 



To = 1.98 



Fig. 55.A Graphs Indicating Percentage Incre- 

 ments OF Babe-Hull Resistance for Four Series 

 OF Appendages on a Destroyer 



The graphs of Fig. 55.A indicate, for this model 

 at least, that the percentage additions vary 

 somewhat with the ship speed. 



Table 55.b lists the percentage differences of 

 total bare-hull resistance when a quadruple-screw 

 cruisei^ model is run at three values of T, = 

 V/ V L, with all appendages, and when six series 

 of appendages are removed, one by one. Again the 

 percentage differences are found to vary some- 

 what with the speed. 



P. Mandel gives data on appendage resistance 

 as a percentage of bare-hull resistance for five 

 types of ship, at three speed-length quotients 

 [SNAME, 1953, Table 8 on p. 494]. Table 55.c 

 is adapted from the reference. 



55.4 Classification of Appendages by Pre- 

 dominant Type of Drag. It is customary to 

 treat the resistance of each ship appendage as 

 predominantly friction or pressure drag. This 

 avoids the complicated extrapolation method 

 customarily used for the ship prediction. 



An appendage is considered to add wetted 

 surface and friction drag only if: 



(a) Its greatest dimension lies in the direction of 

 motion; in other words, it has a low aspect ratio 



(b) Its surfaces lie in the general direction of flow 

 when the ship motion is steady 



(c) Its thickness, as a fraction of its length in the 

 direction of flow, is small or neghgible. 



A roll-quenching keel is an excellent example 

 for all the foregoing. Both long and short bossings 

 for propeller shafts and large skegs are considered 

 essentially as parts of the hull in that their wetted 

 surfaces are added to that of the hull. Docking 

 and resting keels are in the same category if their 

 edges and endings are fair and they lie in the lines 

 of flow. The friction drag R,, added by each is 

 then proportional to its wetted area <S. The 

 discussion of Sec. 22.9 of Volume I indicates that 

 there is as yet no definite rule for assessing the 

 proper 72^ for these appendages, and for deter- 

 mining the Cf value for each. 



The appendage is presumed to add pressure 

 drag only when one or more of the following 

 conditions obtain: 



(1) Its greatest dimension lies across the flow, 

 and it has an appreciable or a high aspect ratio 



(2) Its thickness, as a fraction of its length in the 

 direction of flow, is about 0.1 or more 



(3) Its fore-and-aft length is short, say not 

 exceeding 0.02 the length of the ship. If wake 

 velocities are neglected, V and ;'(nu) are always 

 the same, for both the appendages and the ship as 

 a whole. This is equivalent to saying that R,, for 

 the appendage is less than about 0.02i2„ for the 

 ship. The arm of the strut for an exposed shaft 

 is an example falUng within the limits of (1), (2), 

 and (3). 



Diving planes, short skegs, rudder support 

 horns, strut hubs, exposed shafts, guards, fixed 

 screw-propeller shrouding, and sound domes are 

 among the appendages causing pressure drag only. 

 A rudder, if forming a continuation of the ship 

 hull or of a large skeg, may have its wetted area 

 included in that of the main hull, with its drag 

 assumed as entirely frictional. If separate from 

 the hull, like an underhung spade rudder, its 

 resistance is usually reckoned as a pressure drag 

 only. W. P. A. van Lammeren, L. Troost, and 

 J. G. Koning give 0-diml drag coefficients for 

 seven types of rudders of varied section, all 



