180 THE PROBLEM OF THE HULL AND ITS SCREW PROPELLER. 
Let e. h. p. be the effective horse-power required by a given vessel for a 
speed v, then— 
C1 1 fraction of basic load and 4 = 
EILP. V fraction of basic speed. 
Taking a large number of vessels having hulls of such form and propellers so 
located that the value of the power augment K will be unity, and from the curves 
of performance of each vessel obtaining the I. H. P. required to deliver fractional 
loads, with the speeds v at which these fractional loads were required and denoting 
this Il. H. P. by 1. H. P., the equation for I. H. P., will be:— 
Li Pl (7) 
Ge! Ink 40)5 
in which the factor (2) i : 
in whic SONOS || a) as constant for any given value of EHP. 
This equation may be expressed thus:— 
Log I. H. P., = Log I. H. P. + w (Log v —Log V) 
which, by transposing, becomes— 
w (Log V — Log v) = Log I. H. P. — Log I. H. P., 
Now represent this value w (Log V — Log v), by the symbol Z, and, after 
establishing several values of it at corresponding load fractions, determine the 
equation to the curve passing through these points and the basic point where 
eyhiip: v 
BEE) OV; 
This equation will be— 
both equal unity. 
or, to simplify it, 
Z, = 1.0414 Log (=) 
e. h. p: 
E.H.P. 
for values of less than unity, and 
e. h. p. 
I. H. P. in the first case and additive in the second, so that for values of 
for values of greater than unity; these values are subtractive from Log 
ails) 50)5 
EAH Pe: 
e. h. p. 
IBgle (lek 
Should the efficiency of the combined hull and propeller be such that the value 
S21) ge iL) 18h, ey, = Ibo Il, 18L, PP %, 
Saiiiw Potty lal dew. eo Moet I Iet. IP oo) Zin. 
