LOGARITHMIC SPEED-POWER DIAGRAM. 

 By Thomas M. Gunn, Esq. 



[Read at the twentieth general meeting of the Society of Naval Architects and Marine Engineers, held in 



New York, November 21 and 22, 1912.] 



To logarithmic diagrams of one type or another the modern engineer is 

 indebted for the rapid and easy solution of many cumbersome formulas. The 

 calculations which yield themselves most readily to its use are those involving 

 products, quotients, or powers of numbers. It matters little what the expo- 

 nent is, the solution of a formula consisting of (a constant) X (a variable) 

 raised to any known power, requires for its repeated solution only the drawing 

 of one straight line, and thereafter, for any value of the variable within the 

 range of the diagram, the result is read off directly. For such purposes it is 

 common to use logarithmic co-ordinate paper, which is available in two or 

 three sizes. Diagrams have already been used repeatedly for the calculation 

 of frictional resistance of ships. 



It is not desired in this paper to present new information upon the power 

 of ships or propellers, but rather to submit a means of convenient application 

 of the laws of comparison for ships and propellers. The diagram used cannot 

 be shown here to such a scale as to make it sufficiently accurate for calcula- 

 tions where very close approximation is required; the principle, however, 

 will be shown so that large scale diagrams may be made to suit the individual 

 needs. 



The following table summarizes some of the commonly known relations 

 between similar ships of different size. For convenience, all of these relations 

 are stated in the last column in terms of speed. 



Function. 



Length or other linear dimension, L 



Surface, S 



Speed, V 



Displacement, D 



Wave resistance (residual) 



Wave power 



Quantity in proportion to which 

 function varies, in terms of: 



L 

 L' 



L* 

 V 



D. 



D 



D 

 D 



7 



V. 



v 



V 

 V 

 V 

 V 



