Sec. 49.10 



MATHEMATICAL LINES FOR SHIPS 



197 



Fig. 49. E Aerial View of a Ship, Showing Relatively Shabp Transition between Hollow Entrance 

 Waterline and Parallel Waterline Amidships 



the same units as are to be used for measuring the 

 beam on the dramng, the length of a 1-deg arc 

 on the transparency, calculated from the relation- 

 ship: Length = 0.017453i?c • 



Three such series of arcs, on two separate 

 sheets of film, have been prepared by the Society 

 of Naval Architects and Marine Engineers, which 

 can furnish film positives for the use of naval 

 architects. The radii of the circles of curvature 

 vary from 0.2865 to 28.65 inches on one sheet 

 and from 25 inches to 500 inches on the other 

 sheet. A small section of the first sheet is repro- 

 duced, but 7iot to full size, in the upper LH corner 

 of Fig. 49. F. The lengths of the 1-deg arcs on 

 these sheets are given in inches. The waterline 

 beams on the drawings to be analyzed are there- 

 fore also measured in inches. 



The transparent sheet is placed over the ship 

 line and moved aroimd until some circle of curva- 

 ture on it fits the waterline at a selected station, 

 indicated in the lower diagram of Fig. 49. F. The 



number or location of the station is then tabulated 

 and wdth it the dimension found opposite that 

 circle of curvature. The process is repeated along 

 the length until all stations or selected points are 

 covered. When working from large-scale ship 

 lines it is often difficult to determine just which 

 circle of curvature makes the best fit. The solution 

 is to determine which circle is obviously too 

 slack, then which is definitely too sharp, and 

 select the mean between the two. 



The 1-deg arc length found for each station or 

 point is then divided into Bx and the ciuotient is 

 tabulated. The 0-diml curvatures are plotted on 

 length, follomng the method of Figs. 4.H, 24. F, 

 and 67. C. They are reckoned as positive and laid 

 off above the axis for lines convex to the water; 

 negative and below the axis for lines concave to it. 

 The method falls down for sharp corners and 

 discontinuities, as where an entrance (or a run) 

 waterline with finite slope meets the imaginary 

 prolongations of the ship along the centerplane, 



