Sec. 49.15 



MATHEMATICAL LINES FOR SHIPS 



203 



CALCULATION OF MOLD" LOFT OFFSETS 

 For Two Frame Positions Alono Desiqned 26.163-ft Wbterline of Entrance of ABC Ship 

 Baseline Intercept ot Station Maximum- Ordi note Tanqeno^ at Station II. 



Maximum Ordinate 36.175 ft Half-Sidinq 0.475 ft Length of Curve, X^ , 1 1.0 Stations 



* Cumulotive Product = a{^ ^^[^^"^ -^{^)^ ^d(^)'+ K-^/^K^lf 



Fig. 49. J Calculation of Mold-Loft Offsets for Designed Watbbline of ABC Ship at Two Frames 



at those stations, and finally the designed water- 

 line offsets B. 



49. 1 5 Practical Use of Mathematical Formulas 

 for Faired Principal Lines. There is no reason 

 why, if the lines of a vessel can be laid down on a 

 drafting table from offsets produced by working 

 out mathematical formulas, the full-scale lines 

 can not similarly be laid down in a mold loft in 

 such manner that much of the loft fairing now 

 found necessary will be eliminated. 



The mathematical procedure which determines 

 the offsets of a faired ship line, described in Sec. 

 49.13 and illustrated in Sec. 49.14, is extended by 

 R. Taggart to calculate the offsets of that fair 

 hne at any or all frame stations along the length 

 for the actual ship. This means, for example, 

 that the mold loft can be supplied with calculated 

 offsets for a faired designed waterline, accurate to 

 as many significant figures as desired. Further- 

 more, if five shipyards are to build five sets of 

 sister vessels, each of the five is furnished with 

 exactly the same faired WL offsets, accurate to 

 say a thousandth of a foot, or 0.012 inch. 



An example of this procedure is worked out in 

 Fig. 49. J for the designed waterline entrance of 

 the ABC ship, using the waterline portion already 

 faired mathematically. The offsets are calculated 

 for two selected frames at 128 ft and 178 ft, 

 respectively, from the FP. These correspond to 

 Stas. 5.0196 and 6.9804 in the ship series, where 

 the station length is 25.5 ft. In this case the 

 0-diml diagram is exactly 1 1 ship-station intervals 

 long; Taggart has worked out other examples 

 [ASNE, May 1955, p. 354] where the "prime" 

 stations and the ship stations do not coincide, 

 and where the 0-diml curve is from 7.00 to 9.33 

 ship-station intervals in length. 



For the ABC ship the ordinates of the faired 

 designed waterline curve at the selected frame 



locations are found to be 24.900 and 32.199 ft, 

 respectively. 



The examples given by Taggart on page 350 

 and follo\ving of his paper for calculating frame 

 offsets (not station offsets) [ASNE, May 1955], 

 cover only three principal fore-and-aft ship lines: 



(1) The designed waterline 



(2) A higher waterline in the abovewater body, 

 at about 1.47i? 



(3) The bilge diagonal. 



A fourth set is established, without benefit of 



t jfli5eof Floor 1.0 ft 

 I _. Maximum Ho l f-Beom of D e signed WoteHine at Stall = 37_54ftj 



Fig. 49. K Schematic Body Plan Showing Four 



Sets of Proposed Points to be Determined by 



Mathematical Methods 



