176 FEATHERING PADDLE-WHEELS. 
from A. Asa matter of fact the feathering gear causes the blade to move through 
the water approximately in a vertical position rather than a radial position, and 
the velocities of all points in the blade are approximately the same and equal to the 
velocity of the trunnion C. For this reason the slip based upon the velocity of the 
middle of the blade is more nearly the actual average slip of the entire blade and is 
the one used in this paper. 
If the slip S,, at the outside of the wheel, is desired rather than the slip S,,, at 
the middle of the blade, it can be found by means of the following formula, 
S =I- (1 = Six) Rm Sale 
R, is the radius of the outside of the wheel and F,, is the radius of the middle 
of the blade. 
The eccentricity ratio is the ratio of E to L (see Fig. 6, Plateg4). If EH =o 
the wheel becomes a radial wheel with fixed blades, and if E = L the blades would 
not function properly. The eccentricity ratio is usually between 0.55 and 0.70. The 
effect of variation of eccentricity ratio upon thrust and efficiency can be seen in 
Fig. 7, Plate 94. 
Larger values of eccentricity ratio are accompanied by a reduction of thrust 
and an increase in efficiency, dependent upon the slip. For each position of the ec- 
centric and each dip of the blade there is a certain slip at which the blade will 
enter the water without disturbance. [If the slip is less than this amount, there is 
pressure upon the back of the blade when it first enters, and if the slip is greater 
there is pressure on the driving face when the blade enters the water. 
These curves would seem to indicate the desirability of using a true slip of about 
I5 per cent and an eccentricity ratio of about 0.55. While a larger eccentricity ratio 
would give a slight increase in efficiency, the thrust would be considerably smaller 
and a larger, heavier wheel would be needed. 
The model wheels were tested with the center of the eccentric at the same level 
as the center of the wheel. Wheels are often made with the eccentric placed from 
o inch to 4 inches above the center of the wheel. It does not seem probable that this 
has any appreciable effect upon the thrust or efficiency. 
The dip ratio is the ratio of the greatest immersion of the blade to the width of 
the blade. The thrust increases with increased dip but the efficiency falls off, as 
shown in Fig. 8, Plate 95. These curves show the desirability of using a true slip 
of about 15 percent. The true dip used will depend upon what is of most importance 
in the design in hand, efficiency or power. 
The object of the model tests was to determine the best proportions for stern- 
wheels on boats of moderate speed. The dip ratios used were between 1 and 1.5. 
In applying these results to side-wheels on boats of rather high speed it was neces- 
sary to extend the curves to dip ratios of 2.5. This was done on the assumption 
that the maximum thrust would occur when the wheel was immersed to the center 
