FEATHERING PADDLE-WHEELS. 177 
and that the thrust would be approximately zero when the wheel was fully im- 
mersed. The efficiency curves were extended on the assumption that when the wheel 
was fully immersed the efficiency would be approximately zero. 
The pitch ratio is the ratio of the distance between the trunnions, measured on 
the arc of the circle, to the width of the blade. Fig. 9, Plate 95, shows how thrust 
and efficiency vary with this factor. These curves indicate that as a rule it would 
be better to sacrifice a little thrust in order to gain in efficiency. If a blade-width 
ratio of 0.16 is used, a pitch ratio of 1.85 would call for 9 blades, while a pitch ratio of 
1.5 would call for 11 blades. At 15 per cent slip the unit pressure at pitch ratio 
1.85 is 1.6 pounds and the efficiency is 0.668, while at pitch ratio 1.5 the thrust is 
1.66 pounds and the efficiency is 0.64. Each of the 9 blades would have to be 4 per 
cent larger than each of the 11 blades, but the efficiency would be a little over 4 
per cent greater, and the total blade area would be about 86 per cent of the 11-blade 
wheel. Some designers use a large number of blades to reduce vibration. 
An attempt has been made to correlate the results obtained from model feath- 
ering-wheels with the trial trip results of full-sized wheels, and Figs. 10 to 13, Plates 
96 and 97, show the relation between the two sets of results. The data for the full- 
sized wheels is given in Table I, Plate go. 
It is obvious that the location of the wheel relative to the bow wave is going to 
influence the working of the wheel to a large degree, and this quantity has been 
used as the abscissz in plotting the results. In the determination of the wheel loca- 
tion relative to the crest of the bow wave it was assumed that the length of the wave 
created by the passage of the boat would be .5573V’’, and that the first crest would 
be 12 per cent of the wave length aft of the bow. V is the velocity of the boat in 
knots per hour. 
It will be noticed that the maximum quantities do not occur at the wave crest 
but a little aft of it. This seems plausible when it is considered that the blades enter 
the water some distance forward of the center of the wheel and it is the first part 
of the stroke which is most effective. Also the wheels have considerable length, 
and the wave crests are not parallel to the axis of the wheel but rake aft. Another 
possibility is that the wave crest is more than 12 per cent aft of the bow. 
The model wheels, when tested in the tank, were not adjacent to the hull of a 
boat, and by reason of this condition the dip observed when at rest would be very 
close to the dip when in motion. The apparent slip and true slip of the model wheel 
would be practically the same. The only condition tending to affect these would be 
the velocity of approach of the water to the wheel, which would be very small. 
The paddle-wheel of a side-wheel boat is working under quite different condi- 
tions as regards dip and slip. The velocity of approach would be somewhat larger, 
due to the proximity of the hull. Due to the passage of the boat through the water 
there will be stream-line flow, wake, and waves. 
The dip of the blades when the boat is in motion may differ considerably from 
the dip when at rest, depending upon the part of the wave in which the wheel is work- 
