64 DISCUSSION ON TWO PRECEDING PAPERS. 



valuable information than from a series of experiments on the ordinary ship shape form, be- 

 cause they do indicate in a very clear manner the way in which the water seeks to flow 

 around a ship's hull. 



The Chairman: — Is there any further discussion? 



Professor William Hovgaard, Member: — The influence upon resistance of expansion 

 or contraction along the principal dimensions has been studied experimentally by R. E. Froude, 

 by Naval Constructor D. W. Taylor, and by Col. G. Rota. These experiments I have ana- 

 lyzed, and the result was published in the Transactions of the Institution of Naval Architects 

 in London in 1908. I found that the residuary resistance for ships of the cruiser type varied 

 as the square of the beam and as the draught to the first power for speed-length ratios not 

 greater than 1.35. I had not then at my disposal any serial experiments on the expansion of 

 the transverse dimensions in ships of full form such as those experimented on by Professor 

 Sadler. 



For changes in length-scale of cruiser models, I found that the residuary resistance was 

 constant at corresponding speeds for speed-length ratios up to unity, but for models of the 

 Connecticut type a discrepancy in this law appeared at speed-length ratios exceeding about 

 .75. 



I arrived at the following empirical expression for the residuary resistance: 



L 



where & is a coefficient that varies with the cylindrical coefficient of fineness. This may be 

 written : 



, V 



which appears to hold good for vessels of the warship type up to the point where interfer- 

 ence between the bow and stern waves begins to be sensibly felt. 



I am much interested in the results obtained by Professor Sadler, according to which the 

 resistance for ships of ordinary mercantile form at corresponding speeds varies as B^'^ D^ L'^ 

 as against E^D^V for warships. The discrepancy between these results and those of earlier 

 experimenters must be due to the great difference in the type of the models. Possibly the 

 wave interference is felt earlier in Professor Sadler's model, and may have obscured the true 

 law of variation, which might still be that obtained for finer vessels. The analysis of the 

 results obtained with the Connecticut model points in that direction. It would be interesting 

 to have Professor Sadler's opinion on this point. 



Professor Sadler : — In reply to Professor Hovgaard, I would state that, being aware 

 of his deductions from former experiments, I was a little surprised to find the factors for 

 variations of dimensions come out in the manner given in the paper. The difference is prob- 

 ably due to the difference in type of vessel; in the one case you have a somewhat high rise 

 of flow, easy bilge, fine lines and cruiser stern, and in the other a flat bottom, sharp bilge, 

 flat sides and counter stern. In no case, however, in the above experiments, did the resid- 

 uary resistance appear to vary as so high a power as the square of the breadth. 



