I^OGARITHMIC SPEED-POWER DIAGRAM. 



343 



Calculations at other speeds give the same results with slight variation 

 for the smaller sizes, below 50 feet. 



From such data as above, the conclusion was reached that at corre- 

 sponding speeds for similar vessels the ratio of friction power is as the 6.735 

 power of the speed ratio (or 3.367 power of the length ratio, or the 1.1225 

 power of displacement ratio) for vessels of 50 feet or over, and that it is 

 fairly approximate for lengths of 25 or even 10 feet. 



Regarding errors due to the assumptions made in the paper the follow- 

 ing calculation will give some indication. 



The error will depend upon the ratio of reduction (ratio of lengths) and 

 on the error in the exponent. The highest actual exponent found by the 

 author for a very high-speed motor boat was 6.94. By going to extremely 

 low speeds, cases are found where practically all resistance is friction, so 

 that the exponent is near 6.735, but for cases where it would be important 

 to know the power, the author has found no instance where the true ex- 

 ponent is below 6.79. 



Regarding these as the extreme departures from the average value, 

 6.866, the following table gives extreme errors due to the assumption of 

 the latter. A column is also given for the per cent within which the large 

 majority of boats are found, at speeds between .8 and 1.5 X square root 

 of length. 



It may be noted here that such errors as are given above are not negligible 

 for large ratios of length. For a 500-foot boat, the results from a 12 -foot 

 model should not be reduced by the single shifting line, but be treated as 

 previously suggested. If a curve is made correct for a length of 250 feet and 

 is used for boats from 125 to 500 feet in length, it need not be expected that 

 the error will reach one per cent at important speeds, and can scarcely be 

 as large as 2J per cent in extreme cases. 



