greatest importance at low speeds and prac- 
tically insignificant in flight at high dynamic 
pressures. For example, a typical single en- 
gine jet airplane at low altitude and maximum 
level flight airspeed has an induced drag which 
is less than 1 pcrccont of the total drag. How- 
ever, this same airplane in steady flight just 
above the stall speed could have an induced 
drag which is approximately 75 pnrcnt of the 
total drag. 
EFFECT OF ASPECT RATIO. The effect 
of aspect ratio on the induced drag 
is the principal effect of the wing planform. 
The relationship for induced drag coefIicient 
emphasizes the need of a high aspect ratio 
for the airplane which is continually 
operated at high lift coefficients. In other 
words, airplane configurations designed to 
operate at high lift coefficients during the 
major portion of their flight (sailplanes, cargo, 
transport; patrol, and antisubmarine types) 
demand a high aspect ratio wing to minimize 
the induced drag. While the high aspect 
ratio wing will minimize induced drag, long, 
thin wings increase structural weight and have 
relatively poor stiffness characteristics. This 
fact will temper the preference for a very high 
aspect ratio. Airplane configurations which 
are developed for very high speed flight (es- 
specially supersonic flight) operate at relatively 
low lift coefficients and demand great aero- 
dynamic cleanness. These configurations of 
airplanes do not have the same preference for 
high aspect ratio as the airplanes which op- 
erate continually at high lift coefficients. 
This usually results in the development of low 
aspect ratio planforms for these airplane con- 
figurations. 
The effect of aspect ratio on the lift and drag 
characteristics is shown in figure 1.31 for 
wings of a basic 9 percent symmetrical section. 
The basic airfoil section properties are shown 
on these curves and these properties would be 
NAVWEPS OD-SOT-BO 
BASIC AERODYNAMICS 
typical only of a wing planform of extremely 
high (infinite) aspect ratio. When a wing of 
some finite aspect ratio is constructed of this 
basic section, the principal differences will be 
in the lift and drag characteristics-the mo- 
ment characteristics remain essentially the 
same. The effect of decreasing aspect ratio on 
the lift curve is to increase the wing angle of 
attack necessary to produce a given lift co- 
efficient. The difference between the wing 
angle of attack and the section angle of attack 
is the induced angle of attack, orit18.24 L AR’ 
which increases with decreasing aspect ratio. 
The wing with the lower aspect ratio is less 
sensitive to changes in angle of attack and re- 
quires higher angles of attack for maximum 
lift. When the aspect ratio is very low (below 
3 or 6) the induced angles of attack are not 
accurately predicted by the elementary equa- 
tion for 01~ and the graph of C, versus 01 develops 
distinct curvature. This effect is especially 
true at high lift coefhcients where the lift 
curve for the very low aspect ratio wing is 
very shallow and CL- and stall angle of attack 
are less sharply defined. 
The effect of aspect ratio on wing drag char-. 
acteristics may be appreciated from inspection of 
figure 1.31. The basic section properties are 
shown as the drag characteristics of an infinite 
aspect ratio wing. When a planform of some 
finite aspect ratio is constructed, the wing drag 
coefficient is the rtlm of the induced drag coe&- 
c,” cient, C,,=O.318 AR, and the section drag co- 
efhcient. Decreasing aspect ratio increases the 
wing drag coefficient at any lift coefficient since 
the induced drag coefficient varies inversely 
with aspect ratio. When the aspect ratio is 
very low, the induced drag varies greatly with 
lift and at high lift coefficients, the induced 
drag is very high and increases very rapidly 
with lift coefficient. 
While the effect of aspect ratio on lift curve 
slope and drag due to lift is an important re-