116 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 45.18 



roiighiipss configurations, as yet unknown in 

 character, appear to limit the shij) roughness 

 effects to subnormal values. The nominal rough- 

 ness heights in this regime definitely exceed the 

 limiting values for hydro<^lynamic smoothness. 



IV. Large ACV , relatively uniform with speed in 

 the case of any one ship, in the larger ranges of 

 R, . This situation results largely from the use 

 of rougli plastic paints and from fouling. The 

 roughness heights in this regime far exceed those 

 for hydrotlynamic smoothness, perhaps hj' several 

 hundred times, yet the total Cp for the ship 

 continues to vary with A', in a generally normal 

 manner. 



V. Very large AC,. , with practically constant 

 total C, throughout the speed range. For ships 

 and other large floating craft, this condition 

 probably applies only when the fouling coat is 

 complete and it exceeds 0.4 to 0.5 ft in thickness. 

 In this ca.sc the friction resistance is in effect 

 entirely a pressure resistance. 



VI. Normal IC r , in which the various rough- 

 nesses are normal and the hull of the ship is kept 

 reasonabl}' clean. The AC,, values, exclusive of 

 fouling, conform to those represented by the 

 lines C-C or D-D in Fig. 45. E, or to some com- 

 bination of the two. 



To take care of the effects of normal roughness 

 on a clean, new vessel, involving manj' unknowns, 

 the Froude formulation, listed under item (7) in 

 Sec. 45.8, is still used in many parts of the world. 

 This formulation gives a so-called "Froude Fric- 

 tion Grid," indicated graphically by J. M. 

 Ferguson and others [6th ICSTS, 1951, Fig. 1.5, 

 p. 68], according to the length of the ship and 

 the speed-length constant (L). The latter is eciual 

 to 3. .545 times F, , as listed at the end of Appx. 1. 

 The lines of this grid lie sufficiently above the 

 ATTC 1947 (Schoenherr) meaniine to provide an 

 acceptable roughness allowance for a ship in the 

 "clean, new" category. 



A dimensional and carefully systematized attack 

 on the problem of predicting the friction resistance 

 of a full-scale ship, including the effects of rough- 

 ness, is given by W. W. Smith in his discussion of 

 K. E. SchcKMjhcrr's cla.ssic SXAME 193'2 paper on 

 "Uesi.slance of Flat Surfaces Moving Through a 

 Fluid," pages .305 through 308. Smith's proposed 

 methcxJ is too long to be given here, and is likewi.sc 

 wjmewhal ob.solete, but his line of attack is logical 

 and juHtilies a study of his jiroposal bj' anyone 

 working on the pr<jblcm of roughness fridioti. 



For ship-design purposes in America the Ameri- 

 can Towing Tank Conference in 1947 adopted an 

 overall tentative roughness allowance ACV of 

 0.4(10"'). This is a constant addition (not a plus 

 percentage) above the ATTC 1947 meaniine for 

 turbulent flow on a flat, smooth plate, regardless 

 of the size or speed of the vessel concerned. As 

 pictured in Fig. 1 on page 2 of SNAME Technical 

 and Research Bulletin 1-2 of March 1952, en- 

 titled "Uniform Procedure for the Calculation of 

 Frictional Resistance and the Expansion of Model 

 Test Data to Full Size," it is a compromise 

 between the equivalent plus roughness allowances 

 of the Froude formulation and the tentative 

 ATTC roughness allowances adopted in 1942. The 

 latter increase progressively as the ship length 

 diminishes from 1,000 to 100 ft whereas the 

 former decrease slowly as the ship length dimin- 

 ishes from 1,000 to about 300 ft. Below this 

 length the Froude allowances dcircaso rather 

 rapidly. 



There are definite iiuiications, described in Sec. 

 22.15, that this roughness allowance should 

 diminish with /?„ , at least for low values of speed 

 V or relative velocity U. For the lower speeds it 

 appears to diminish toward zero in the region of 

 R„ = 3.5 to 5 million, as does the allowance 

 inherent in the Froude formulation. Fig. 45. E of 

 Sec. 45.7 embodies, in addition to the ATTC 1947 

 or Schoenherr meaniine and the ATTC constant 

 ACp = 0.0004 line, a proposed roughness allow- 

 ance line C-C proposed by J. M. Fergu-son [6th 

 ICSTS, 1951, pp. 67-69], and a line D-D proposed 

 and used by L. A. Baier for some years past. 

 Baler's line leaves the ATTC line at an R„ of 

 about 3 million and reaches the (ATTC + 0.0004) 

 line at an R„ of about 600 million [SNAME, 1951, 

 Fig. 19, p. 365]. Ferguson's line reaches Baier's line 

 at an y^„ of about 7,380 million, corresponding to 

 a I,400-ft ship running at 40 kt in salt water. 



Whatever the line or table used to estimate 

 roughness effects in the early stage of a ship 

 design, as soon as more is known about the 

 roughness — or smoothness — to be expected on 

 the hull the tentative value is modified, and the 

 friction resistance is re-calculated. 



As.suming that the necessary data are available, 

 the logical method of determining a roughness 

 allowance in the pre-construction stage of a ship 

 design is to select and add together four separate 

 values for the plating, structural, coating, and 

 fouling roughnes-ses, respectively, as describeil in 

 Sees. 22.15 and 45.7 ami as lislcd in !']((. (22. iv) 



