it is more appropriate to define propeller effi- 
ciency in the following manner: 
‘)~= output propulsive power 
mput shaft horsepower 
where 
vP= propeller efficiency 
T= propeller thrust 
V= flight velocity, knots 
BHP= brake horsepower applied to the 
propeller 
Many di,fferent factors govern the efficiency of 
a propeller. Generally, a large diameter pro- 
peller favors a high propeller efficiency from 
the standpoint of large mass flow. However, 
a powerful adverse effect on propeller efficiency 
is produced by high tip speeds and conipressi- 
bility effects. Of course, small diameter pro- 
pellers favor low tip speeds. In addition, the 
propeller and powerplant must be matched for 
compatibility of output and efficiency. 
In order to appreciate some of the principal 
factors controlling the efficiency of a given 
propeller, figure 2.18 Uustrates the distribu- 
tion of rotative velocity along the rotating 
propeller blade. These rotative velocities add 
to the local inflow velocities to produce a 
variation of resultant velocity and direction 
along the blade. The typical distribution of 
thrust along the propeller blade is shown with 
the predominating thrust being located on the 
outer portions of the blade. Note that the 
propeller producing thrust develops a tip 
vortex similar to the wing producing lift. 
Evidence of this vortex can be seen by the con- 
densation phenomenon occurring at this Ioca- 
tion under certain atmospheric conditions. 
The component velocities at a given propeller 
blade section are shown by the diagram of 
figure 2.18. The inflow velocity adds vec- 
torially to the velocity due to rotation to pro- 
duce an inclination of the resultant wind with 
respect to the planes of rotation. This incli- 
nation is termed + (phi), the effective pitch 
NAVWEPS 00-8OL80 
AiRPlANE PERFORMANCE 
angle, and is a function of some proportion of 
the flight velocity, V, and the velocity due to 
rotation which is mD at the tip. The pro- 
portions of these terms describe the propeller 
“advance ratio”, J. 
where 
J=propeller advance ratio 
V=flight velocity, ft. per sec. 
n=propeller rotative speed, revolutions 
per sec. 
D = propeller diameter, ft. 
The propeller blade angle, fi (beta), varies 
throughout the length of the blade but a 
representative value is measured at 75 percent 
of the blade length from the hub. 
Note that the difference between the effec- 
tive pitch angle, 4, and the blade angle, 8, 
determines an effective angle of attack for the 
propeller blade section. Since the angle of 
attack is the principal factor affecting the 
efficiency of an airfoil section, it is reasonable 
to make the analogy that the advance ratio, J, 
and blade angle, 8, are the principal factors 
affecting .propeller efficiency. The perform- 
ance of a propelleris typified by the chart of 
figure 2.19 which- illustrates the variation of 
propeller efficiency, ~a, with advance ratio, J, 
for various values of blade angle, 8. The 
value of vP for each fl increases with J 
until a peak is reached, then decreases. It is 
apparent that a fixed pitch propeller may be 
selected to provide suitable performance in a 
narrow range of advance ratio but efficiency 
would suffer considerably outside this range. 
In order to provide high propeller efficiency 
through a wide range of operation, the pro- 
peller blade angle must be controllable. The 
most convenient means of controlling the 
propeller is the provision of a constant speed 
governing apparatus. The constant speed gov- 
erning feature is favorable from the standpoint 
of engine operation in that engine output and 
efficiency is positively controlled and governed. 
147