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52 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
According to the conventional definition oflift, we have
Equating the two, we get
or
where
L = ~p Vo%SCr.s
Cu. = aa cos A
ay - a cos A
a, = (aac. ),.
(1.69)
(1.70)
(1.71)
(1.72)
From the consideration of delaying the adverse effects ofcompressibility to higher
Mach numbers, one can either use a swept-back or a swept-forward wing. However,
in many other ways, the two wings do not function in the same manner as discussed
in the following section.
Swept-back wings. On a finite straight-rectangular wing, the root sections
operate at relatively9higher angles of attack compared to the tip sections. As a
result, the stall on a straight-rectangular wing offinite aspect ratio originates at the
root and progresses outboard as shown in Fig. 1.53a. As angle of attack increases,
the stall spreads outward, and eventually the entire wing will stall at some angle
of attack. A :finite wing is said to stall when any of the sections stall. Thus, at stall,
the ailerons located outboard are still effective, and the aircraft has good lateral or
roll control authol:ity.
On the other hand, for the swept-back wing, the tip sections stallfirst as shownin
Fig. 1.53b. To understand why this happens,let us refer to the schematic variation
of the lift coefficient along the span as shown in Fig. 1.54. We observe that the
tip sections on a swept-back wing develop relatively higher lift coefficients, which
means that they are operating at higher angles of attack compared to the root
sections. Thus, the stall originates from the tip sections. In addition, the existence
ofspanwise pressure gradient causes the wing tips to beloaded.with thick boundary
layers, which further aggravate the tip stall tendency of swept-back wings. As a
result, an aircraft with swept-back wings willlose roll control at stall. As we shall
discuss later in the text, a loss of roll control at stall makes an aircraft susceptible
to problems of stability and control at high angles of attack.
To understand why a spanwise pressure gradient exists on a swept-back wing,
consider the pressure distribution along chordwise sections I, II, andPIII as shown
in Fig. 1.55. Now let us pick three poLnts such as Ai, Bi, Ci on section I as shown.
Because point Ci is closest to theleading edge compared to Bi and Ai, the pressure
at Ci is the lowest of all the erree points on section I. Similarly, the pressure at point
Bi is lower that that at Ai. Thus, we have a spanwise pressure gradient along the
section I. Similarly, we can show that spanwise pressure gl:adient exists along other
chordwise sections such as II and III.}9ecause of this spanwise pressure gradient,
the inboard tluid particles will drift towards the tip. As a result, the wing tips will bc
loaded with thicker boundary layers that are more susceptible to flow separation.
REVIEW OF BASIC AERODYNAMIC PRINCIPLES 53
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