\ 
EOE eS BREE RE RE IS 
FEATHERING PADDLE-WHEELS. 179 
Re eeaiene ratio X 
Displacement-length ratio 
100 
and the results are plotted in Fig. 11, Plate 96 (line 41, Table 1). The dotted por- 
tions of the curves are simply suggestions as to the shape the curve might have; 
there are not enough points to determine it with any degree of accuracy. 
The virtual slip factor is given because the quantities used in entering Figs. 2 
and 3 fall within the range of the tests upon the models. The efficiency obtained 
by using the apparent dip may differ quite widely from the actual efficiency. 
The extension of the curves for thrust and efficiency beyond dip ratios of 1.5 
enables us to determine the other relation factor given in Figs. 12 and 13, Plate 97. 
This factor was determined by assuming that the thrust varied as the 1.75 power 
of the speed of advance, that the engine efficiency was 0.85 and that the wheel effi- 
ciency could be obtained from Fig. 5 by using the apparent slip and the virtual dip. 
The thrust of the full-sized wheels at a speed of advance of 100 feet per minute was 
determined from these assumptions. Figs. 2 and 3 were used to determine the dip 
ratio which would give this thrust at the apparent slip. This dip ratio divided by the 
apparent dip ratio gave the relation factor shown in Fig. 12, Plate 97. 
The virtual dip ratio was determined by entering Figs. 2 and 3 with the thrust 
t (line 46, Table I) at the proper pitch ratio. A vertical line was drawn through 
this point. This vertical line was intersected by a horizontal line drawn through 
the point where the apparent slip intersects the proper eccentricity ratio. The in- 
tersection of these lines determined the virtual dip ratio. 
The quantities used in Fig. 12 when divided by the wave factor gave the quan- 
tities shown in Fig. 13, Plate 97 (line 51, Table I). 
It will be noticed in Fig. 12 that in the hollow of the wave there is a loss of dip 
of about 35 per cent, while in the crest there is a gain of about 60 per cent. A small 
portion of this loss and gain makes allowance for the fact that we have assumed the 
true slip to be equal to the apparent slip, whereas actually it is less in the hollow 
and more in the crest. 
A study of the trochoidal wave shows us that the loss of dip in the hollow will 
be considerably less than the gain of dip in the crest. Fig. 14, Plate 98, shows half 
of a trochoidal wave. The center of the describing circle moves along the line 4A. 
The line WL cuts the wave profile in such a manner that the area above WL is equal 
to the area below. Ifa ship of uniform cross-section were placed upon this wave, 
the line WYWL would represent its water-line in still water. If the ends of the vessel 
are fined away the ship will sink further into the wave to some such line as W’L’. It 
can be seen from the figure that the loss of dip in the hollow would be about half of 
the gain in the crest. 
The assumption that the thrust varies as the 1.75 power of the speed of advance 
seems to give a reasonable variation of the dip along the wave. 
For purposes of design either the slip factor curve or the dip factor curve could 
be used. The different points which determine the curves lie as nearly in a fair 
