the lift coefficient is doubled and the induced 
drag is four times 0.1 grsat. If the flight load 
factor is changed from one to five, the induced 
drag is twenty-five times as great. If all other 
factors are held constant to single out this 
effect, it could be stated that “induced drag 
varies as the square of the lift” 
Di, ’ 
0 
L! Di,= L1 
where 
Di,= induced drag corresponding to 
some original lift, L1 
Di,= induced drag corresponding to 
some new lift, Lp 
(and q (or EAS), S, AR are constant) 
This expression defines the effect of gross 
weight, maneuvers, and steep turns on the 
induced drag, e.g., 10 percent higher gross 
weight increases induced drag 21 percent, 4G 
maneuvers cause 16 times as much induced 
drag, a turn with 4s0 bank requires a load 
factor of 1.41 and this doubles the induced 
drag. 
EFFECT OF ALTITUDE. The effect of 
altitude on induced drag can be appreciated by 
holding all other factors constant. The gen- 
eral effect of altitude is expressed by: 
where 
Dil= induced drag corresponding to some orig- 
inal altitude density ratio, 0, 
D&= induced drag corresponding to some new 
altitude density ratio, q 
(and L, S, AR, V are constant) 
This relationship implies that induced drag 
would increase with altitude, e.g., a given 
airplane flying in level flight at a given TAS 
at 40,000 ft. (u=O.25) would have four times 
as much induced drag than when at sea level 
(u= 1.00). This effect results when the lower 
NAVWEPS 0040240 
BASIC AERODYNAMICS 
air density requires a greater deflection of the 
airstream to produce the same lift. However, 
if the airplane is flown at the same EAS, the 
dynamic pressure will be the same and induced 
drag will not vary. In this case, the TAS 
would be higher at altitude to provide the 
same EAS. 
EFFECT OF SPEED. The general effect of 
speed on induced drag is unusual since low air- 
speeds are’associated with high lift coefficients 
and high lift coefficients create high induced 
drag coefficients. The immediate implication 
is that induced drag inmaw with decreasing air 
J@. If all other factors are held constant to 
single out the effect of airspeed, a rearrange- 
ment of the previous equations would predict 
that “induced drag varies inversely as ,the 
square of the airspeed.” 
where 
Dil= induced drag corresponding to some orig- 
inal speed, Vi 
Di,= induced drag corresponding to some new 
speed, Vs 
(and L, S, AR, ,J are constant) 
Such an effect would imply that a given air- 
plane in steady flight would incur one-fourth 
as great an induced drag at twice as great a 
speed or four times as great an induced drag at 
half the original speed. This variation may 
be illustrated by assuming that an airplane in 
steady level flight is slowed from 300 to 150 
knots. The dynamic pressure at 1% knots is 
one-fourth the dynamic pressure at 300 knots 
and the wing must deflect the airstream four 
times as greatly to create the same lift. The 
same lift force is then slanted aft four times 
as greatly and the induced drag is four times 
as great. 
The expressed variation of induced drag with 
speed points out that induced drag will be of