Sec. 40.4 



BASIC CONCEPTS FOR CALCULATIONS 



can not, in fact, supply any but incomplete 

 answers in cases where the physical phenomena 

 are not as yet fully understood. Friction-drag 

 formulas for ship plating are a case in point. 

 Despite an enormous amount of time and energy 

 expended on the problem of friction flow, both 

 in air and in water, the mechanism of fluid 

 friction is still incompletely understood. Formulas 

 much better than those now in use can not be 

 expected until this knowledge is achieved. 



Heretical as it may seem to mathematicians, 

 the use of mathematics, in both science and 

 engineering, must always be tempered by good 

 judgment. In fact, it is a generous gift of this 

 same good judgment that makes a good engineer 

 in any line of work. 



It must be recognized that mathematics is 

 always based on some kind of assumptions and 

 conditions, which the mathematician hopes are 

 always complete and correct. They may be 

 neither. This is Avhere judgment enters, in advance 

 as well as in the wake of the mathematics. 



It may be interesting to quote here the com- 

 ments of one well-known designer on this phase 

 of the subject [Fox, Uffa, "Sail and Power," 

 New York, 1937, p. 20]: 



"Mathematics are only of value to the person who has 

 the sense to use the right formula and start with the true 

 value. Too many mathematicians today multiply an un- 

 known quantity by an illogical factor, and arrive at pro- 

 portions that a man with discerning eyes can see are 

 wrong, even though the mathematicians believe the answer 

 to be correct if the mathematics are correctly worked." 



It must be said in defense of mathematicians 

 that they are by no means the only people who 

 "multiply an unknown quantity by an illogical 

 factor." This is the reason for inserting some 

 mathematical cautions in a design book for naval 

 architects and marine engineers. Nevertheless, it 

 becomes necessary at times to venture far afield 

 in one's need for arriving at some kind of numerical 

 answer. 



A classic example of this kind was well de- 

 scribed by William Froude in his reports of the 

 early 1870's to the British Association [Todd, 

 F. H., SNAME, 1951, p. 316], when discussing 

 the means of extrapolating his 50-ft plank friction 

 data to ship lengths of 300 ft or more. The 

 comments in parentheses are those of the present 

 author: 



"... it will make no very great difference in our estimate 

 of the total resistance of a surface 300 feet long, whether 

 we assume such decrease to continue at the same rate 



(as for the lapt foot of the 50-foot plank) throughout 

 the last 250 feet of the surface, or to cease entirely after 

 50 feet; while it is perfectly certain that the truth must lie 

 somewhere between these assumptions." 



According to E. V. Telfer and F. H. Todd, as 

 described in the reference cited: 



". . . believing the truth to lie between them, but 

 unable to decide on which was nearer to the absolute truth, 

 he (Froude) compromised by taking an exact mean curve." 



A more modern example might arise if a marine 

 architect were called upon to estimate the hydro- 

 dynamic resistance of the balsa-log raft of South 

 American design, called Kon-Tiki and used by 

 Thor Heyerdahl and his companions in their 

 voyage from Peru to the South Pacific Islands in 

 1947 [Heyerdahl, T., "Kon-Tiki," Rand-McNally, 

 1950]. Assuming that he could approximate the 

 drag of one log, moving end on, he would with 

 reasonable certainty estimate that the total drag 

 of the nine logs abreast was less than nine times 

 the drag of one log. Similarly, he would know 

 that the drag was more than that of a box-shaped 

 body having the same planform, the same 

 general dimensions, and the same volume dis- 

 placement. By a series of approximations of this 

 kind he could narrow the probable resistance to 

 within rather close limits. 



The diversion in this section is intended partly 

 as a caution, and is in no sense to be looked upon 

 as a discouragement. The fact that considerable 

 space is devoted in the chapters following to 

 means for deriving quantitative data should serve 

 as an indicator of its importance in this line of 

 work. 



For an intelUgent and proper use of the data, 

 however, a certain amount of preliminary knowl- 

 edge is necessary, and a few specific rules are to 

 be observed. These are described briefly in the 

 sections following. 



40.4 The Principles of Similitude. A knowl- 

 edge of the theory of similitude, forming the basis 

 of all model-testing procedures, is not necessary 

 for an understanding of the calculation, prediction, 

 and ship-design methods described in Parts 3 and 

 4 of this book. However, for the marine architect 

 who is interested in knowing the conditions for 

 dynamic similarity of flow and motions, and in 

 utilizing the dimensional-analysis methods ex- 

 pounded by Lord Rayleigh, the n Theorem of 

 Riabouchinsky, and elaborations upon them by 

 R. C. Tolman, E. Buckingham, P. W. Bridgman, 

 and others, a background of general knowledge of 



