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curvature is regained by substantial camber of the rear portion of the supercritical
airfoil. The supercritical airfoil gives considerable increase in the critical Mach
number and the drag divergence Mach number. For example, at a lift coefficient of
0.7 for the NACA 64A-410, the drag divergence Mach number is around 0.66. For
a supercritical airfoil of the same 10% thickness ratio, the drag divergence Mach
numberis 0.80 (Refs. 6 and 7). This increase in drag divergence Mach number of
0.14 is of great significance to the airline industry.
A comparison of the pressure distribution for conventional and supercritical
airfoils is shown schematically in Fig. 1.48b.
Wing sweep. Research on swept-wing concept for high-speed flight origi-
natedin Germany in thelate 1930s or 1940s but was not known outside of Germany
because of World War II. The Allied pilots first encountered the German swept-
wing Messerschmitt Me 262 jet fighter during 1944, which had speed advantage
because of a delay in the onset ofcompressibility effect and the attendant drag rise.
The choice of18 deg ofsweep-back was fortuitous because this was done primarily
to resolve the center of gravity problem. However, at approximately the same time,
researchers in Germany demonstrated through wind-tunnel tests that Busemann's
supersonic swept-wing theory also applied to subsonic speeds and helped to delay
compressibility effects. This effort lead to the design of more highly swept wings
for the Me 262 aircraft. Thus, the Me 262 program was the first systematic effort
towards the design of modern swept-wing aircraft.
The concept of wing sweep is a powerful method ofdelaying the adverse effects
of compressibility and pushing tlre critical Mach number to much higher values
and even beyond Mach 1. The fundamentalidea is that only the component, of the
freestream velocity normal to the wing leading edge Vm cos A affects the pressure
distribution. The spanwise component Voo sin A (Fig. 1.49) does not alter the pres-
sure distribution. The only effect the spanwise component has is on skin-friction
drag, Therefore, the freestream Mach -number at wh/9h the critical condition (local
sonic velocity) occurs on the wing is increased by a factor l/cos A compared to
a straight-unswept wing. In other words, if MLr is the critical Mach number for
a straight wing:t~en the critical Mach number for a swept wing having identical
airfoil section is equal to Mcr]cos A. This is true whether the wing is swept-back
or swept-forward as shown in Figs. 1.49a and 1.49b.
The leading edge of a swept wing is said to be subsonic if the component
of velocity normal to the leading edge is below the sonic velocity or the corre-
sponding Mach number is less than unity. Therefore, the leading edge is sub~
sonic if it is swept behind the Mach cone as shown in Fig. 1.50a. Similarly, if
the component of velocity normal to the leading edge is above the sonic velocity,
the wing leading edge is said to be supersonic. Therefore, the wing leading edge
is supersonic if the leading edge sweep angle is smaller than the Mach angle
AL as shown in Fig. 1.50b. We shall make use of these definitions later in the
text when we discuss the determination of wing lift and pitching-moment coeffi-
cients in the chapter on static stability and control. The wa've drag is usually
much smaller for wings whose leading edges are swept behind the Mach cone.
48 PERFORMANCE, STABILITY, DYNAMICS: AND CONTROL
a) Swept-back wing
b) Swept-forward wing
Fig. 1.49 Schematic illustration of effect of wing sweep.
--
REVIEW OF BASIC AERODYNAMIC PRINCIPLES 49
/
/
t
/
a) Subsonic leading edge
--
b) Supersonic leading edge
Fig.1.50 Subsoruc and supersorucleading edges.
A > Lr
A < Li
To demonstrate the advantage of sweep, consider two aircraft, one straight wing
and the other swept-back wing. We assume that the gross weight, wing area, and
airfoil section ofboth aircraft are identical. Furthermore, assume that both aircraft
are required to operate at the same values of normal dynamic pressure, lift, and
drag forces.
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