50 A SUBSTITUTE FOR THE ADMIRALTY FORMULA. 



Now substituting the above value of D^ and taking C out of the radical we 

 get 



F=C^ 



As it is a known fact that at the higher speeds the power required to drive a 

 ship of a given length at a given speed increases at a greater rate than the displace- 

 ment, and in order to encourage heavier and more substantial construction in rac- 

 ing motor boats, and also to simplify the formula, D'^ was replaced by D, thus 

 favoring the heavier boat on a given water-line length. This formula, with the 

 exception that D was taken in pounds instead of cubic feet, was applied to several 

 motor boats as shown in Table i, Plate 35. The average constant here works out to 

 be 42.9. In taking D in cubic feet instead of pounds C would therefore be slightly 

 under 11. Several other boats were tried under this formula, but the results ob- 

 tained were not used on account of the uncertainty of the data at hand. In fact the 

 data on the boats given in Table i, Plate 35, cannot be said to be absolutely accu- 

 rate but the committee considered it sufficiently close to work on. 



APPLICATION OF THE FORMULA TO STEAMSHIPS. 



About a year ago it occurred to the writer that this formula might be used in 

 place of the Admiralty formula with more accurate results, as length is taken as 

 a factor in this new formula. It was applied to several vessels as shown in Tables 

 2, 3, 4 and 5, Plates 36, 37, 38 and 39. I. H. P. was used in place of P, and tons 

 were used in place of cubic feet for displacement. 



Table 6, Plate 40, shows the constants at different speeds as worked out for 

 five torpedo-boat destroyers all of the same length and similar model but varying 

 in displacement. From this table the curves of C in Plate 30 were drawn. The aver- 

 age value of C for these five ships was worked out, the curve of which is shown in 

 the same plate, above those of the individual ships. 



Table 7, Plate 41, shows the values of C at different speeds, of the Delaware, 

 North Dakota and Utah ; and Table 8, Plate 42, shows the value of C for the Mar- 

 ietta, Wheeling, Dubuque and Bancroft, from which data the curves on Plate 31 

 were drawn. Both Table 7, Plate 41, and Plate 31 show the difference between a 

 turbine-driven ship and one driven by reciprocating engines. 



THE NEW FORMULA COMPARED WITH THE ADMIRALTY FORMULA. 



In using the Admiralty formula there are two things to be taken into consid- 

 eration, namely, the displacement ratio and the speed ratio, both of which affect 

 the value of the constant considerably, and to use this formula with any degree of 

 accuracy great care has to be taken in choosing the proper value for the constant. 

 If in calculating the speed of a new ship this formula is used, quite accurate results 

 can be obtained by using the same value for the constant as that of a given ship 

 of about the same size, providing the displacement and speed ratios of the two are 



