NAVWEPS OO-SOT-~O 
BASIC AERODYNAMICS 
quence of developing lift with a finite wing 
and is termed INDUCED DRAG, D+ In- 
duced drag is separate from the drag due to 
form and friction and is due simply to the de- 
velopment of lift. 
By inspection of the force diagram of figure 
1.30, a relationship between induced drag, lift, 
and induced angle of attack is apparent. The 
induced drag coeficient, CDi, will vary directly 
with the wing lift coefficient, C,, and the in- 
duced angle of attack, as. The effective lift 
is the vertical component of the actual lift and, 
if the induced angle of attack is small, will be 
essentially the same as the actual lift. The 
J horizontal and vertical component of drag is 
insignificant under the same conditions. By a 
detailed study of the factors involved, the fol- 
lowing relationships can be derived for a wing 
with an elliptical lift distribution: 
(1) The induced drag equation follows the 
same form as applied to any other aerody- 
namic force. 
Di=CDigS 
where 
Di=induced drag, lbs. 
4= :Vymic pressures; psf 
=295 
Cni= induced drag coefficient 
S=wing area, sq. ft. 
(2) The induced drag coefficient can be 
derived as : 
or 
CD,-C, sin ai 
CD& 
c,P =0.318 -Jjj ( ) 
where 
C,= lift coefficient 
sin ai=natural sine of the induced angle 
of attack, Eli, degrees 
r=3.1416, constant 
AR= wing aspect ratio 
(3) The induced angle of attack can be 
derived as: 
a~= 18.24 & (degrees) ( ) 
(NOTE: the derivation of these relationships 
may be found in any of the standard engi- 
neering aerodynamics textbooks.) 
These relationships facilitate an understanding 
and appreciation of induced drag. 
The induced angle of attack Eli= 18.~4$~ ( > 
depends on the lift coefficient and aspect ratio. 
Flight at high lift conditions such as low speed 
or maneuvering flight will create high induced 
angles of attack while high speed, low lift 
flight will create very small induced angles .of 
attack. The inference is that high lift coefli- 
cients require large downwash and result in 
large ,induced angles of attack. The effect of 
aspect ratio is significant since a very high 
aspect ratio would produce a negligible induced 
angle of attack. If the aspect ratio were in- 
finite, the induced angle of attack would be 
zero and the aerodynamic characteristics of the 
wing would be identical with the airfoil sec- 
tion properties. On the other hand, if the 
wing aspect ratio is low, the induced angle of 
attack will be large and the low aspect ratio 
airplane must operate at high angles of attack 
at maximum lift. Essentially, the low aspect 
ratio wing affects a relatively small mass of 
air and consequently must provide a large de- 
flection (downwash) to produce lift. 
EFFECT OF LIFT. The induced drag co- 
e&cient ( 
C&l CDi=0.31E - shows somewhat sim- ,I AR 
ilar effects of lift coefficient and aspect ratio. 
Because of the power of variation of induced drag 
coefficient with lift coefficient, high lift coefli- 
cients provide very high induced drag and low 
lift coefficients very low induced drag. The di- 
rect effect of C, can be best appreciated by assum- 
ing an airplane is flying at a givenweight, alti- 
tude, and airspeed. If the airplane is maneuvered 
from steady level flight to a load factor of two, 
hWd Jonua~ 1965 
68