178 FEATHERING PADDLE-WHEELS. 
ing. The true slip of the wheel will differ from the apparent slip because of the ve- 
locity of approach, wake, stream-line flow, and orbital motion of the water in wave 
formation. If the wheel is working in the hollow of the wave all of these except the 
wake make the true slip less than the apparent slip. If the wheel is working in the 
crest of the wave the wake and orbital motion are opposed to the stream-line flow 
and velocity of approach, and the true slip is probably greater than the apparent 
slip. It would appear, however, that the change in slip is much less in degree than 
the change in dip. 
In addition to this uncertainty regarding the true slip and true dip of the full- 
sized wheels, there is further uncertainty regarding the variation of thrust with 
speed of advance. The usual assumption is that the thrust varies as the square of the 
speed of advance. The models were all tested at a speed of advance of 100 feet per 
minute while the full-sized wheels were moving at a velocity of about 2,000 feet per 
minute (see line 20, Table 1). The model wheels were practically 1 foot in diameter, 
while the full-sized wheels were from 25 feet to 30 feet in diameter. According to 
the law of comparison the corresponding speed for the full-sized wheels would be 
about 1007/30, or about 550 feet per minute. The full-sized wheels are advanc- 
ing at speeds which were three to four times the corresponding speed (see line 28, 
Table I). 
With these three unknown conditions—namely, the variation of thrust with 
speed of advance, the variation of true dip from the observed dip at rest, and the 
variation of true slip from the apparent slip—it can be readily seen that there are a 
large number of relation factors which might be derived, depending upon the as- 
sumptions made regarding one or all of the unknowns. I have given here only two 
relation factors, one which I have called the virtual slip and one which I have called 
the virtual dip. 
In Fig. 10, Plate 96, the relation factor is worked up on the assumption that the 
thrust varied as the square of the speed of advance, that the engine efficiency was 
0.85, and that the wheel efficiency could be obtained from Fig. 5, Plate 93, by using 
the apparent slip and the apparent dip. 
The unit pressure on a wheel advancing at the rate of 100 feet per minute was 
worked out (see line 36, Table 1) and from Figs. 2 and 3, Plates 91 and 92, the 
slip that would give this unit pressure at the apparent dip was determined. This was 
called the virtual slip and the ratio of this to the apparent slip is given in Fig. ro. 
The virtual slip was obtained by entering Figs. 2 and 3 with the thrust ¢ (line 36, 
Table I) at the proper value of pitch ratio (line 14, Table 1). Rising from this 
point to the apparent dip ratio (line 13, Table I), and then moving horizontally to 
the proper value of eccentricity ratio (line 17, Table I) a slip value was obtained 
which I have called the virtual slip (line 39, Table I). 
It is obvious that the variation in dip is affected by the size of wave formed by 
the boat, and the size of the wave will vary with the speed-length ratio and the dis- 
placement-length ratio. The quantities used in Fig. 10 have been modified by using 
a wave factor equal to— 
