A THEORY OF FLUID FRICTION. 83 
I refer particularly to light boats. Our lake steamers, of course, as most of you know, are 
flat-bottomed, with a spoon bow, and when they are running light their bow is entirely out 
of water. They plane up to such an extent that sometimes, when a boat is running with very 
little water ballast in her, as she is standing the propeller will be out of water as much as 18 
inches. When she is running she planes up so much forward that her propeller wheel is 
completely buried, and great volumes of air—great pockets—come under the bow and go 
backward sometimes 250 to 300 feet, some of the pockets going back farther than that. 
I was under the impression at the time that 1 spoke of that that there would be less 
friction with these air pockets under the bottom of the boat. But since that time I have 
been considering the subject, and I would like to have some of the scientific men here (as 
I am a practical man, not a scientific man) who have considered the subject, of these bodies 
of air coming under the bottom and helping to plane the boat up and lifting her still more 
out of the water so that there is less surface friction than if the air did not come under the 
bottom, state why it is we get such wonderful speeds out of these boats through this plan- 
ing. When they are standing still the turn of the fore foot will be even with the water, and 
when they are running sometimes 10 feet of the keel will stand out of water and the stern 
go down deeper in proportion. For that reason the engineers will pump them out until the 
tops of the blades are 18 inches out of water in a standing position, and when they get going 
the bow goes up and the stern down. The consequence is they get the full force of the water 
on the wheel and the boat is lifted bodily up, like an aquaplane to a certain extent. 
Mr. Cuartes H. Lees (Communicated) :—I thank you for the copy of Mr. Gatewood’s 
paper on “A Theory of Fluid Friction.” 
The problem provided by the friction of a fluid in turbulent motion is a very impor- 
tant and a very difficult one, and no one is more anxious to welcome a satisfactory solution 
than the naval architect. I am afraid Mr. Gatewood has not succeeded in finding the solu- 
tion. His theory appears to me to be a revival of the theory published in the Memoires of 
the Academie des Sciences in 1877, and known to be unsatisfactory even for the simple 
case of turbulent flow through a pipe. 
It is only necessary to quote Mr. Gatewood’s result on page 80 of his paper, that the 
resistance R varies as the velocity Vy, to show how far his theory is from explaining the 
skin friction of ships, which is known to vary as the 1.8th power of the speed. 
Mr. GaTEwoop (Communicated) :—In connection with the communication of Mr. Lees 
I would merely state that he seems to have misunderstood the reference in the paper that 
the resistance varies directly as the speed. This statement in the paper is accompanied by 
the further statement that the length over which the resistance is measured varies inversely 
as the speed. The result of these two statements is that the resistance for a given length 
varies as some power of the speed less than the square, but this power of the speed may not 
be constant. This is shown by an examination of Fig. 9, Plate 61. 
THE PRESIDENT :—Is there any further discussion on this subject? As there is no 
further discussion, we will give Mr. Gatewood a vote of thanks of the Society for his 
interesting paper, and proceed to the next paper, No. 10, which is entitled “Notes from 
the Model Basin,” by Naval Constructor Wm. McEntee. In the absence of Naval Con- 
structor McEntee, this paper will be presented by Professor Sadler. 
