IIM)R()l)V.\AMI(;s l\ Mill' DlSU.N 



Sfc. -fO.H 



If nrv Ixjtli plai'oti e<|nal tti 1.0. This pliut-.s tlu; 

 data in O^liml fomi. 



Taggart's intrgnitiHl relationsliips are: 



f, = I' ;/ th 

 r ', - j xy ilx 



(l'.).xxv) 



( I'.l.wvi) 



r, -= / T-yiLr (ID.xxvii) 



Jo 



(\ = I .r'//f/j (lO.xxviii) 



These may be detennincd fiDin iiiiy curve l)y the 

 application of Simpson's rule. Tlie relationship 

 between the constants and the eocfficients a, b, 

 c, d, c, and / are given in Taggart's Fig. 3, cor- 

 responding to Fig. 49.11 of See. 49.14. His explana- 

 tion of the mathematical procedure Ls detuilwl 

 and complete, hence it is not repeatetl here. His 

 worked-out example is supplemented by a second 

 example in Sec. 49.14, covering the fairing of the 

 designwl entrance waterline of the transom-stern 

 ABC ship, described in Part 4 of this volume. 



49.14 Illustrative Example for Fairing the De- 

 signed Waterline of the ABC Ship. To illu.-trate 

 Taggart's method, a sample calculation for fairing 

 the designetl (2fi.l(l.]-ft) waterline abreast tlie 

 entrance of the ABC ship is carried out according 

 to the steps listed hereunder. Actually, the fairing 

 is accomplished on that portion of the DWL from 

 the FP back to the position of maxinunn waterline 

 beam B^x ■ From Fig. 07. A in Part 4 this is at 

 Sta. 11. It is not to be confused with the fore- 

 and-aft position of the .section of maximum area, 

 which is at Sta. 10.0. The successive steps are 

 described in .some detail: 



I. Draw the designed waterline from the I'P to 

 Sta. 1 1 as accuratel}' as po.ssible, considering the 

 stage of the hull design, or use a waterline drawing 

 already made. It is helpful to continue the 

 waterline for at least two stations abaft (he 

 po.sitiiMi of li„x , as is done in Fig. 49.(1. Actually, 

 the \)\\'\j in this figure is drawn with a vertical 

 Kcule much larger than the honzontal .scale, lo 

 show the various features to better advantage. 

 Drawing thin or any other .ship line to a fairly 

 largo Hculo will i)r(Kluc(! the accurate olTsets 

 necdc-d to take full advantage of the mathematical 

 mctluKi. It is preferable to make the scale largo 

 enough Ht) that the derive<l 0-<lind values of 

 li/Hx (or actual ofT.si-ls diviiled bv the half-beam) 



are accurate to 4 significant ligures following tlie 

 decimal point. In the SXAME HD shwts the 

 0-<iind values are given to only three significant 

 de<inud places. For the .VBC ship example 

 worke<l out here, tlie 0-<lind li lix coordinates 

 are tho.se listcxl in (he SX.VMIO |{D sheet for the 

 (ransom-s(ern design, T.MB miMlel l.jO"), repro- 

 iluced as I'"ig. 7.S.,la in Pari I. They are lisle<l in 

 Col. B of Table I9.a. 



T.\HI,E W.-.i .MoinKicATioNs OF OrrsFn^ •■•on 



l)K.SI(i.Sl-;i> \V.\TKKI.INK OK .\UC SlUP TO Sl'TP LiMITINf! 



CoNDrno.ss kor Mathematical I'aiiu.vg Pbocess 

 Col. F lists the 0-diml offsets used in this calculation. 



Col. .\ Col. B Col. C Col. D Col. E Col. F 



Original Ti/By li/Bx - New Offsets Col. E 



ship from (fi/Bx)o "prime" from Fig. times 



stations RD sheet stations ■Hi.G 1/0.990 



0.013 

 0.121 

 ().2o2 



. :m> 



0.512 

 0.079 

 0.794 

 0.S82 

 0.943 

 9S0 

 9 . 997 

 l.OOS 

 999 

 0.983 







O.IOS 

 . 239 

 0.3S3 

 l)..V29 

 O.GGO 

 0.7S1 

 0.SG9 

 0.930 

 n 9(i7 

 0.9S4 

 0.990 



S' 

 9' 

 10' 





 0.120.'> 

 0.20(i5 

 0.-l2Gri 

 0.5850 

 0.72.S0 

 0,8370 

 0.9153 

 0.9f.lO 

 9S35 

 (I 9U(K) 







1217 



2092 



430S 



5909 



7354 



8455 



9245 



9707 



9931 



(K)00 



II. Locate on Ihe waterline ilrawing the origin 

 O of the O-diml waterline which is to be used in 

 the mathematical analysis. This waterline Is to 

 have a lenglli C()rrcs|)onding to 1 1 station intervals 

 on the ship, from the FP back to the position of 

 ^ii-.v , and it is to jiass through the point where 

 2/ = when x = 0. Fig. 07.10 of Part 4 shows that 

 the DVVIi offset at the FP is 0.5 ft, wlu'ii con- 

 tinued forward as indicated by the diagonal 

 broken liiu" in the upper right-hand corner of 

 Fig. 19. Ci. However, it is a.ssumed here, t<i keep 

 the numerical figures coiisisttMit, that the inuldeil 

 ofT.set a( (he FP on the shi)) corresponds exactly 

 (o 0.0i:{ times the half-beam, tabulated on Fig. 

 78. .la. In ab.solute dimensions on the ship this is 

 0.0i:{(7:i.08/2) = 0.47') ft. A stem of .semi- 

 circular .section, lying inside the cutwater shown 

 in I'ig. 7.{.B, would then have a molded radius of 

 0..'i|.") ft, from the large-.scale diagram <>f l'"ig. 



