NAVAL ARCHITECTURE TO AERONAUTICS. 293 
2 
d ; 
Next, substituting - for A and the numerical values for g and W* and 
reducing Vi in foot-seconds to V miles oe hour. 
3+ “eet ik (6) 
Vids 
This formula expresses the theoretical relation which exists between the 
efficiency, thrust, speed of advance, and diameter in feet. 
For a given speed of advance and given diameter, e may be computed 
for varying values of T and the results plotted as ordinates on thrusts as 
abscissee. ‘This curve will show how the efficiency falls off as the thrust is 
increased. 
In Fig. 4, Plate 142, the full line is the theoretical limit of efficiency for 
a propeller 25 inches in diameter moving with different thrusts at a speed 
of 2000 feet per minute or 22.7 miles per hour. This particular size and 
speed is selected because there are available accurate data for such a 
propeller. 
On the same figure the lowest line shows the actual efficiencies obtained 
with a 25-inch two-bladed wooden propeller at the same speed, the data 
being taken from a recent report of the “British Advisory Committee on 
Aeronautics.” ‘The dimensions of the propeller are shown in Fig. 5, Plate 142. 
In Fig. 4, Plate 142, it will be noted that though the actual efficiency is — 
much less than that indicated as the limit by theory, the curves are, except 
at low thrust, sensibly parallel and seem to bear some relation one to the 
other. 
It was to be expected of course that the curve of actual efficiency would 
be below that obtained by theory as in the deduction of the latter but one 
cause of loss of energy is allowed for, that is the kinetic energy lost in the 
propeller race. With a perfect and frictionless propeller this would be the 
only loss. With actual propellers, however, there are additional losses due 
to the following causes: 
(1) Surface friction, (2) resistance due to shape of Hanne section, (3) rota- 
tion velocity of race, (4) lack of uniformity of sternward velocity of race, 
(5) resistance of hub, (6) reduction of effective cross-section of race on 
account of hub. 
For this particular propeller the pitch ratio is only 0.54 and the high 
number of revolutions compared with the speed of advance naturally results 
in high friction and head resistance losses. A marine propeller of the best 
*The weight of air is taken as at 70° F. and a humidity of 70% under which conditions a cubic foot 
weighs .0746 lbs. 
