NAVWEPS OD-8OT-80 
BASIC AERODYNAMICS 
matched with a planformwhose chord is dis- 
tributed in an elliptical fashion (the elliptical 
wing), each square foot of area along the span 
produces exactly the same lift pressure. The 
elliptical wing planform then has each section 
of the wing working at exactly the same local 
lift coefhcient and the induced downflow at 
the wing is uniform throughout the span. In 
the aerodynamic sense, the elliptical. wing is 
the most efficient planform because the uni- 
formity of lift coefficient and downwash incurs 
rbt iea$t induced drag for a given aspect ratio. 
The merit of any wing @anform is then meas- 
ured by the closeness with which the distribu- 
tion of lift coefficient and downwash approach 
that of the elliptical planform. 
The effect of the elliptical planform is illus- 
trated in figure 1.32 by the plot of local lift 
coefficient to wing lift coefficient, f! G’ versus 
scm:spnn L.“CY.ICG. ,4;..t,or, Tbac e!liptical wing p* 
duces a constant value of$=J.O throughout 
the span from root to tip.‘ Thus, the local 
section angle of attack, LYE, and local induced 
angle of attack, CY,, are constant throughout 
the span. If the planform area distribution is 
anything other than elliptical, it may be ex- 
pected that the local section and induced angles 
of attack will not be constant along the span. 
A planform previously considered is the 
simple rectangular wing which has a taper 
ratio of 1.0. A characteristic of the rectangular 
wing is a strong vortex at the tip with local 
downwash behind the wing which is high at 
the tip and low at the root. This large non- 
uniformity in downwash causes similar varia- 
tion in the local induced angles of attack along 
the span. At the tip, where high downwash 
exists, the local induced angle of attack is 
greater than the average for the wing. Since 
the wing angle of attack is composed of the 
sum of at and aor a large local (x, reduces the 
local a0 creating low local lift coefficients at 
the tip. ‘Ihe reverse is true at the root of the 
rectangular wing where low local downwash 
exists. This situation creates an induced angle 
of attack at the root which is less than the 
average for the wing and a local section angle 
of attack higher than the average for the wing. 
The result is shown by the graph of figure 1.32 
which depicts a local lift coefficient at the root 
almost 20 percent greater than the wing lift 
coefficient. 
The effect of the rectangular planform may 
be appreciated by matching a near elliptical 
lift distribution with a planform with a 
constant chord. The chords near ‘the tip 
develop less lift pressure than the root and 
consequently have lower section lift coe&- 
cients. The great nonuniformity of local lift 
coefficient along the span implies that some 
sections carry .more than their share of the 
load while others carry less than their share 
of the load. Hence, for a given aspect ratio, 
the rectangular planform will be less efficient 
-t-- -L. -11:. -!-~I LlLill UK C‘lqJLlCal wing. For exampie, a 
rectangular wing of AR=6 would have 16 
percent higher induced angle of attack for the 
wing and 5 percent higher induced drag than 
an elliptical wing of the same aspect ratio. 
At the other extreme of taper is the pointed 
wing which has a taper ratio of zero. The 
extremely small parcel of area at the pointed 
tip is not capable of holding the main tip 
vortex at the tip and a drastic change in down- 
wash distribution results. The pointed wing 
has greatest downwash at the root and this 
downwash decreases toward the tip. In the 
immediate vicinity of the pointed tip, an 
upwash is encountered which indicates that 
negative induced angles of attack exist in this 
area. The resulting variation of local lift 
coefficient shows low cr at the root and very 
high c, at the tip. This effect may be appre- 
ciated by realizing that the wide chords at 
the root produce low lift pressures while the