PART 3 



Prediction Procedures and Reference Data 



CHAPTER 40 



Basic Concepts Underlying All Calculations 

 and Predictions 



40 . 1 The Calculation of Ship-Design and Perform- 



ance Data 



40.2 Useful Formulas Embodied in Theoretical 



Hydrodynamics 



40 . 3 Present Limitations of Mathematical Methods 



40.4 The Principles of Similitude 3 



40.5 Dimensions of Physical Quantities 4 



40.6 The Derivation and Use of "Specific" Terms 5 



40 . 7 Double or Multiple Solutions to the Equations 



of Motion 6 



40.1 The Calculation of Ship-Design and 

 Performance Data. The reader who progresses 

 this far in a consecutive perusal of the book has 

 found a word and a graphic picture of the flow 

 phenomena associated with the motion of a ship. 

 The first part is in general form, considering a 

 simple or schematic ship. The second part is in 

 successively more detailed form, having to do 

 with the behavior and effect of an actual ship 

 and its many components. 



To avoid breaking up the story, mathematical 

 derivations, processes, and formulas are purposely 

 omitted from the first two parts, except in a few 

 special cases. The reader has been asked to take 

 the story largely on faith, with copious references 

 if his faith appears to waver at any point. 



There is another reason for this procedure, well 

 expressed by R. E. Froude when discussing the 

 second of D. W. Taylor's papers on stream forms 

 m 1895 [INA, Vol. 36, p. 246]: 



"... The problems of stream-line motion have hitherto 

 been almost out of the reach of everybody except practical 

 mathematicians; not because all such problems are too 

 abstruse for anyone but a practical mathematician to 

 understand, but rather, because all treatises dealing with 

 those subjects have been condensed and written, so to 

 say, in a language which no one but practised technical 

 mathematicians can understand." 



Manifestly, a story alone can not design a 

 ship, nor meet those modern needs which demand 



answers of how much and how many. Nor will a 

 story alone, no matter how explicit, point the 

 way out of the hydrodynamic tangles that may 

 be expected to confront the naval architect and 

 marine engineer of tomorrow. He must have better 

 and sharper tools with which to face newer and 

 more puzzhng problems. 



This third part of the book, therefore, is de- 

 voted to an exposition of the methods whereby 

 flow and its phenomena may be deflned in 

 graphical, mathematical, and numerical terms. It 

 gives a description of the methods, formulas, 

 procedures, and other aids whereby the influences 

 and effects described in Parts 1 and 2 may be 

 predicted or calculated in quantities useful to 

 the ship designer. 



Indeed, it is the ultimate aim of all those who 

 take a deep interest in these phases of naval 

 architecture, to develop and to refine methods of 

 computation and calculation by which any aspect 

 of the performance of a ship or any of its parts 

 may be predicted on paper and in the design 

 stage. The modern hydrographer can not afford 

 to wait on the spot to see what the height of the 

 tide and the strength of the tidal current will be 

 at Point X ten years hence; he has designed and 

 built a machine that predicts it for him. The 

 modern owner, operator, and naval architect, by 

 the same token, can not wait, with a ten-million 

 dollar ship at stake, until it runs sea trials to 



1 



