314 THE INFLUENCE OF SHAPE OF 



The wave horse-power goes up as l.P° = 1.395, while the friction horse-power goes 

 up as \.V"^ = 1.388, with a sHght modification for difference in frictional coefficient. If 

 the form is good and the speed not excessive, the friction horse-power will constitute from 

 70 to 75 per cent of the total. If a multiplier nearer to 1.388, say 1.39, should be used, the 

 approximation is very close. 



The use of the approximate formula is well illustrated by the table in Mr. Rigg's paper, 

 on page 282. He starts out with a vessel of 585 feet length and goes up to one of 930 feet 

 length. I do not know how he obtained those powers, but you can see how simple a matter 

 it is if you make use of the approximate expression. 



Length (feet) 



Length ratio to preceding 



Length ratio raised to 3.5 power 



Power given by approximate formula 



Power given by Mr. Rigg 



Occasionally it is desirable to be able to determine approximately the horse-power nec- 

 essary to drive a ship at a certain fixed speed as the length is increased or decreased. If 

 we have the horse-power for a ship at a certain speed, the horse-power at the same speed for 

 a longer or shorter similar ship can be obtained from this by multiplying by the length ratio 

 raised to the 1.7 power. This approximate formula should be used only when the speed of 

 the derived ship is not in excess of a speed-length ratio of 0.6. When working from a model 

 ship to a derived ship of greater length the power curve will be slightly under the true 

 curve, crossing it at a speed-length ratio of about 0.6 and at high speeds will lie above the 

 true curve. The reverse will be true when working from the model ship to a shorter de- 

 rived ship. 



The data here given can be carried to any length of vessel desired by the formulae 

 given in the appendix. If the displacements of various 425-foot ships are desired, they can 

 be obtained from the prismatic coefficients given in Plate 54 and the midship-section coeffi- 

 cients of .979, .981, .983 and .985 for the four draughts tested. The wetted surface can be 

 found with all the accuracy needed for these formulae by means of the expression : 



Wetted surface = 16 V length X displacement. 



Mr. Robertson is quite right in calling attention to the fact that the parallel middle body 

 percentage is of minor importance and the ratio of ends is the important factor. Plate 2 

 gives the ratio of ends in terms of parallel middle body for the various models tested. 



The reduction of results to a standard temperature of 65° has been criticised. The tem- 

 perature correction is uncertain at best, and it seemed wise to use 65° since the water varies 

 from about 60° to 70° in our tank. The data were corrected at the rate of 1 per cent for 

 every 3° of temperature variation. 



Various criticisms have been made regarding the form in which the results are given. 

 Some would like to have the [c] values used, some would like to have the residuary horse- 

 power given in term of (displacement)'/^, some would like to have all results reduced to 

 a length of 400 feet. 



The authors would like to call attention to the fact that the paper was written primarily 

 to call attention to the influence of shape of transverse sections upon resistance. No one has 



