Nowaekt and Sharma 
hardly be asserted that the effects involved have been really clarified, 
The confusion and mystery still surrounding the relative ro- 
tative efficiency are best illustrated by the fact that values larger 
than unity are often observed on models of single screw ships while 
physical reasoning suggests that nonuniformities of flow would in ge- 
neral tend to lower propeller efficiency. The traditional explanation 
for this phenomenon used to be a favorable propulsive effect attribut- 
ed to the rudder. However, it is doubtful whether this view can be 
sustained in view of recent rational calculations of propeller-rudder 
interaction such as by Isay (1965) and Brunnstein (1968). They have 
evaluated this interaction in three parts. First, it is found that a sui- 
tably profiled rudder does experience a thrust in the slip stream, 
However, a force acting on the rudder must by definition show up in 
the thrust deduction fraction and not in the relative rotative efficiency. 
Second, the displacement flow associated with a thick rudder tends to 
increase both propeller thrust and torque. This, however, is justa 
consequence of the increased mean effective wake. Third, what then 
remains as contribution of the rudder to relative rotative efficiency 
is a guide vane effect reflected in a nonuniform flow induced by the 
rudder singularities in way of the propeller. This effect, as Isay and 
Brunnstein conclude, actually tends to decrease propeller efficiency! 
It is true that Professor Telfer in his (1951) paper had sug- 
gested a different explanation of relative rotative efficiency. His ar- 
gument was based on the notion that the simple thrust identity princi- 
ple yields a wrong value of mean effective wake since propeller per- 
formance behind the hull is affected in a peculiar way by the radial 
variation of the (circumferentially constant) axial wake. He proposed 
an alternative analysis in which the mean effective wake is determin- 
ed from the Ky vs. J curve ofa virtual propeller which is similar 
to the real propeller in all respects except pitch, such that the open- 
water Ky vs. Ko polar of the virtual propeller matches the behind- 
hull Ky vs. Koy polar of the real propeller, It is easy to deduce 
from propeller series charts that Telfer's analysis would almost al- 
ways lead to a value of relative rotative efficiency closer to unity than 
the conventional analysis. Suppose for instance that the conventional 
analysis produces np >1. Then the behind-hull Kypy, vs. Koy polar 
will lie to the left of the open-water Kr vs. polar and hence a 
virtual propeller of lower pitch will have to be chosen, This would 
indicate a lower value of J , which in turn due to the convex shape of 
the ng vs. J curve would yield a higher value of 7 o/(1-w) for the 
real propeller, But since 7, and t are independent of the choice of 
wake, so is the quantity 
Me No/(1-w) = 2)/(1-t) 
