Sec. 49.11 



MATHEMATICAL LINES FOR SHIPS 



201 



13 I 



^"1,000 



Half-Sid nq~O.OI3 Byf ~^ 



5hip Centerlme-' -D 



Fig. 49.G Definition Sketch foe Mathematical Faieing op Designed Watehline Entrance of ABC Ship 



49.G. The origin O is accordingly fixed at the 

 FP at a distance of 0.013(B„,x/2) from the ship 

 centerhne. A line OC, drawn through O parallel 

 to the ship centerline, then forms the basis for 

 measuring the ^/-coordinates of the 0-diml DWL 

 which are to be introduced into the mathematical 

 formulas. 



III. The length of the 0-diml waterline diagram 

 to be analyzed is the distance OC in Fig. 49. G, 

 corresponding to the length of 11 station intervals 

 on the ship. This distance is divided into 10 equal 

 lengths and new ordinates are erected, marked on 

 Fig. 49. G as 1' through 9'. The ship station 11 is 

 at the "prime" station 10'. The distance OC is 

 then the 0-diml a;-distance of 1.000. 



IV. The 0-diml value of B/B^ from D to E is, 

 from the referenced RD sheet, equal to 1.003. 

 The 0-diml value of CE, equal to DE - DC, is 

 1.003 - 0.013 = 0.990. The values of the 0-diml 

 ordinates FG, HJ, and so on, at the ship stations, 

 are then found by subtracting the constant value 

 0.013 from the RD sheet values. They are hsted 

 in Col. C of Table 49.a. 



V. The offsets of the DWL curve at the 10 

 "prime" stations are then taken off the diagram 

 of Fig. 49.G for the distances marked KL, MN, 

 PQ, and so forth. They are converted into 0-diml 

 values by dividing the half- value of B^x into 

 them, following which they are hsted in Col. E 

 of the table. Since the 0-diml ^/-ordinate at Sta. 11 

 must equal 1.000 for the mathematical computa- 

 tion, when the 0-diml .T-abscissa also equals 1.000, 

 it is made so by dividing the 0-diml ordinate at 

 station 10' by itself. For this station, 0.9900/0.9900 

 = 1.000. All other 0-diml ordinates at the prime 

 stations are divided by the same factor 0.9900, 

 producing the final 0-diml computation ordinates 

 in Col. F of Table 49.a. 



VI. If the 0-diml B/Bx values are already 

 available for a given designed waterline, as they 

 were for the ABC ship, it is somewhat simpler 

 to plot a diagram like Fig. 49. G, embodying 

 0-diml B/Bx ordinates on a base of ship length, 

 rather than ordinates of ship beam to some 

 selected scale. The diagram then becomes simply 

 a graphic means of picking off the 0-diml ordinates 



C| = 2M|-(0rdinat6)-^ \5 



= 9.5679 -^ 15 = 0.639193 



C2 = 2M2-(0rdlnQte) -^ 75 



= 30.87354-75= 0.411647 



C3= 2M3-(0rdinQte)-;- 750 



= 224.697^750=0.299696 



C4= 2 M4.(0rdi note) -^ 750O 



= 1754.769 -^ 7500 = 0.233969 



Fig. 49.H Calculation of Curve Coefficients for ABC Ship 



