NAVWEPS 00-8OT-80 
BASIC AERODYNAMICS 
vortex filaments which consist of the tip or 
trailing vortices coupled with the bound or 
line vortex. The tip vortices are coupled with 
the bound vortex when circulation is induced 
with lift. The effect of this vortex system is 
to create certain vertical velocity components 
in the vicinity of the wing. The illustration 
of these vertical velocities shows that ahead 
of the wing the bound vortex induces an up- 
wash. Behind the wing, the coupled action 
of the bound vortex and the tip vortices in- 
duces a downwash. With the action of tip 
and bound vortices coupled, a final vertical 
velocity (220) is imparted to the airstream by 
the wing producing lift. This result is an 
inevitable consequence of a finite wing pro- 
ducing lift. The wing Producing lift applies 
the equal and opposite force to the airstream 
and deflects it downward. One of the impor- 
tant factors in this system is that a downward 
velocity is created at the aerodynamic center 
(w) which is one half the final downward 
velocity imparted to the airstream (2~). 
The effect of the vertical velocities in the 
vicinity of the wing is best appreciated when 
they are added vectorially to the airstream 
velocity. The remote free stream well ahead 
of the wing is unaffected and its direction is 
opposite the flight path of the airplane. ‘Aft 
of the wing, the vertical velocity (2~) adds to 
the airstream velocity to produce the down- 
wash angle e (epsilon). At the aerodynamic 
center of the wing, the vertical,velocity (w) 
adds to the airstream velocity to produce a 
downward deflection of the airstream one-half 
that of the downwash angle. In other words, 
the wing producing lift by the deflection of an 
airstream incurs a downward slant co the wind 
in the immediate vicinity of the wing. Hence, 
the JeCtionJ of the wing operate in an average rela- 
tive wind which is inclined downward one-half the 
final dowraw& angle. This is one important 
feature which distinguishes the aerodynamic 
properties of a wing from the aerodynamic 
properties of an airfoil section. 
The induced velocities existing at the aero- 
dynamic center of a finite wing create an aver- 
age relative wind which is different from the 
remote free stream wind. Since the aerody- 
namic forces created by the airfoil sections of a 
wing depend upon the immediate airstream in 
which they operate, consideration must be 
given to the effect of the inclined average rela- 
tive wind. 
To create a certain lift coefficient with the 
airfoil section, a certain angle must exist be- 
tween the airfoil chord line and the avcragc 
relative wind. This angle of attack is a,,, the 
section angle of attack. However, as this lift 
is developed on the wing, downwash is in- 
curred and the average relative wind is in- 
clined. Thus, the wing must be given some 
angle attack greater than the required section 
angle of attack to account for the inclination of 
the average relative wind. Since the wing 
must be given this additional angle of attack 
because of the induced flow, the angle between 
the average reiative wind arid tlie remote fiCC 
stream is termed the induced angle of attack, 
ai. From this influence, the wing angle of 
attack is the sum of the section and induced 
angles of attack. 
a=ul)+a; 
where a= wing angle of attack 
OLD= section angle of attack 
OI;= induced angle of attack 
INDUCED DRAG 
Another important influence of the induced 
flow is the orientation of the actual lift on a 
wing. Figure 1.30 illustrates the fact that the 
lift produced by the wing sections is perpen- 
dicular to the average relative wind. Since 
the average relative wind is inclined down- 
ward, the section lift is inclined aft, by the 
same amount-the induced angle of attack, 
ai. The lift and drag of a wing must continue 
to be referred perpendicular and parallel to the 
remote free stream ahead of the wing. In this 
respect, the lift on the wing has a component