RESISTANCE OF BILGE KEELS. 19 



discussion on that point, based on his results. I have a diagram prepared. In Fig. A, this 

 cun^e 1 (indicating on diagram) — these diagrams are, of course, a little rough — this curve 

 1 reproduces the curve of thrust upon revolutions in Plate 15 of the paper. The curve 2 is 

 the estimated curve of resistance, not of thrust, of the Fulton, based on model basin experi- 

 ments, at almost the same displacement, 9.3 tons against 9.6. Of course the slight differ- 

 ences of frictional resistance, etc., make it impossible to say that curve 2 is in every detail 

 comparable with curve 1, but for an approximate comparison the difference between the two 

 curves indicates the thrust deduction under the conditions of the experiment. This, as you 

 see, is quite large, but we expect a large thrust reduction for a vessel of this type and of 

 the single-screw type. 



Fig. B I have reproduced in curve 1 — this full curve here (indicating) — the observed 

 curve of speed and revolutions in Plate 14 of the paper. The dash curs'e is a theoretical 

 curve of speed and revolutions for a phantom ship, to adopt Mr. Froude's supposition ; in 

 other words, if we had a ship with the resistance shown in this curve and driven by the pro- 

 peller, no disturbance being caused in the water by the ship, we would get curve 2 for the 

 curve of speed and revolutions. As you will see, curve 2 coincides with curve 1 very closely, 

 throughout a certain range, and then a little above 5 knots it breaks away from it. 



Curve 3, on the other hand, is a curve such as is used in model work to obtain the wake 

 fraction or the velocity with which the ship drags the water behind it. That is obtained by 

 assuming that the propeller at the revolutions shown was advancing, not at the actual speed 

 of the boat but at sufficient speed to produce the actual thrust shown here. The only natu- 

 ral and proper assumption is that the propeller advances through the water at this speed 

 (indicating on diagram) and not the speed of the boat; in other words, there is a following 

 current which makes the speed of the propeller through the water less than the speed of the 

 boat through the water. 



This curve of wake fraction shows the wake fraction or the speed with which the water 

 follows the boat, expressed as a percentage of the speed of the boat. As you will observe, 

 there is a moderate increase from 0.08 per cent to something over 0.12 per cent, and then a 

 rapid falling off at the speed at which these two curves diverge. There is a reason for that, 

 and I would surmise (perhaps Professor Peabody or Professor Everett could say whether it 

 is the case or not) that it is due to the change in the wave just over the propeller. Some- 

 where in the neighborhood of 5 knots for this boat 30 feet long there would be a wave crest 

 over the propeller, and as we increase speed we reach a condition where there is a wave hol- 

 low, and a natural result is a rapid falling off in the wake fraction and a corresponding re- 

 duction here. 



Professor Peabody calls attention to the fact, and it is a fact, that in most of our experi- 

 ments with models at the Model Basin we found the increase due to the installation of 

 bilge keels not much, if any, more than that due to the friction of the added surfaces. That 

 is generally the case ; in fact, there have been cases where it has been hard to get a difference 

 equal to the computed frictional difference. You may remember that in the classical experi- 

 ments of Mr. Froude on the Greyhound, when he towed an 800-ton vessel, he found the 

 same condition — that the resistance of the bilge keels was scarcely up to that of the friction. 

 The probability in this case is that the bilge keels have some influence upon the propulsive 

 efficiency. These very deep bilge keels have probably changed the flow of the water, so that 

 there is some effect different from the natural resistance. We measure in the Model Basin 

 simply the resistance of the model — this is a case where the thrust is measured. 



