214 THE PROBLEM OF THE HULL AND ITS SCREW PROPELLER. , 
dealing with the propeller: (1) The theoretical method, which is based entirely on 
equations or formulae deduced by applying accepted laws of physics and using the funda- 
mental units of length, mass and time. (2) The empirical method, in which the rela- 
tion between the many variables upon which the functioning of the propeller depends 
is derived from actual experience with real propellers on real ships. 
Admiral Dyson has used the second method and obtains results which are entirely 
satisfactory so long as used within the range of variables or data on which the method 
is based, though it requires skill and experience to pick out the proper coefficients to use 
in a particular case. That the method is not of universal application is readily shown 
by applying it to a ship and its model. I have done this in the case of the vessel L, the 
data for which are given on page 206 of the paper. The results for the ship agree very well 
with the design curves given in Plate 75. Thus on the ship for projected area ratio of 
.4247 at 223 revolutions per minute the tip speed is 9,000 feet per minute, the indicated 
thrust is 6.62 pounds per square inch of the projected area, and the propulsive coefficient 
is .603. I applied the same curves to the model of this ship which we tested in the model 
basin. Of course the model tip speed will be much less, also the pressure per square 
inch in the projected area is much less, so that if these curves are truly universal, they 
should fit the model as well as the ship. They go away off the curves, bringing the 
projected area ratio below anything which was possible to use in the propeller, that is 
to say, as far down as .o5, which would make a very narrow and blunt blade. 
On the model of this ship at corresponding speeds with the same projected area 
ratio the model propellers make 1,230 revolutions per minute with a tip speed of 1,640 
feet per minute and an indicated thrust of 1.2 pounds with a propulsive coefficient slightly 
less than for the ship. 
By referring to Plate 75, it will be seen that this tip speed corresponds to a P.A. + 
D.A. = .o25 and P.C. = .525, while indicated thrust per square inch of projected area 
corresponds to a P.A. + D.A. = .157 — and P.C. = .71. 
As the model, propeller and appendages are exactly similar in form to the ship, 
the factors which depend upon the interaction between the ship and propeller must be 
the same for model and ship. I thinkit is a fair conclusion that the fundamental design 
data given in Plate-75 which is found to agree with the ship data and to disagree decidedly 
with the model data must therefore be considered to be applicable to a limited field only. 
It is practically universally admitted now among naval architects that the laws con- 
necting the resistance of a ship and its model are known with sufficient accuracy to per- 
mit the prediction of the effective horse-power of the ship from model tests. It is only 
one step further to find the laws connecting the shaft horse-power and the revolutions 
per minute for the model and the shaft horse-power and revolutions per minute for the 
ship. This step has, I believe, already been taken. In tests made under my direction 
at the Washington Model Basin on a 20-foot model of the battleship New Mexico, it 
was found that when the revolutions per minute and shaft horse-power as obtained by 
tests of the model were extended to the ship they agreed with the ship trial data within 
less than 1 per cent over a range of ship speeds from 10 to 21 knots. 
The extensions from the model to the ship were made by using the principle of 
mechanical similitude or law of comparison and by assuming the thrust deduction and 
wake coefficients to be the same for both ship and model. 
When it is considered that the ship is thirty times as long as the model and that 
30,000 shaft horse-power on the ship was derived from about two-tenths of a shaft horse- 
