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Another significant advantage ofthe oblique wing is the absence of aerodynamic
center shift at transonic speeds. On a conventional variable geometry wing at
transonic speeds, the aerodynanuc center moves aft as the wing sweep increases
to reduce the wave drag. This creates more nosedown moment and requires a
large horizontal tail surface to trim the aircraft. This increases the trim drag and
hence affects the performance. With the oblique wing, this problem is considerably
alleviated as one half of the wing sweeps aft and the other half sweeps forward and
the overall aerodynamic center hardly moves. Therefore, a large horizontal tail is
not needed to trim the aircraft in transonic speeds.
The benefits of the oblique wing wereodveumonstrated in flight using the F-8
Crusader aircraft during the mid-1980s.
1.12 Area Rule
Area ruling18,20 is a systematic method of minimizing the transonic/supersonic
wave drag of airplane configurations. Fundamental to this method is the assumption
that, at Mach numbers close to unity and at large distances from the body, distur-
bances and shock waves are indepen~ent of the arrangement of the components and
are only functions of the longitudinal variation of the cross-sectional area. In other
words, the wave drags ofa given wing-body and an equivalent body having an iden-
tical longitudinal cross-sectional area variation (Fig, 1.60) are essentially the same.
For most airplane configurations, adding cross~sectional areas of wing to that of
the fuselage results in a bump in the overall area distribution as shown in Fig. 1.61a.
To obtain the minimum wave drag, the overall distribution should be that for a
smooth body with minimum wave drag. The most obvious way to achieve this is
to remove the cross-sectional area of the wing from the fuselage in that region
where the fuselagejoins the wing. This results in a modifled shape that looks like a
coke bottle. The cross-sectional areas of other components like"vengines, nacelles,
and tail surfaces can be treated in a similar manner:y:Che wave drag of the modified
body is lower than that of the basic configuration as shown in Fig. 1.61b.
For supersonic Mach numbers, cross-sectional areas are to be obtained by taking
planes inc.lined at an angle /r, = sin-l(l/Moo) to the axis of the given body.
The application of area rule resulted in significant transonic/supersonic drag
reductions of several aircraft, One particular example was the Convair F-102
a) Basic wing-body
b) Eqruvalent body
Fig. 1.60 Concept of equivalent body for area rule.
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Fig.1.61 Area-ruleconcept
interceptor aircraft.20,21 Wind-tunnel tests on the original design indicated that
the transonic drag was so high that the aircraft would not be able to f(y past Mach
1. This prediction was foun9'to be true when the prototype aircraft fiew in 1953.
The concept of area rule was then applied, and the fuselage of the F-102 was
redesigned. In the late 1954, the modified F-102 flew past Mach 1 successfully.
After this fiight validation, several aircraft were redesigned on the basis of the area
rule concept. These include the Convair F-106, the Convair'B-58, and the Vought
F8V. Some recent examples are the Air Force B-l and the Boeing 747 aircraft.
It should be noted that with the application of the area rule concept, an aircraft
configuration can be derived to give a minimum wave drag only at one flight Mach
number. At any other flight Mach number, the benefits of area rule may be lost and
the wave drag may bc substantially higher.
Example 1-1
A fiying wing with an area of 27.75 m2 has a NACA 2412 airfoil section. The
weight of the flying wing is 2270.663 kg and the aspect ratio is 6. For level fiight
at an altitude of 1500 m (a = 0.864) and a velocity of 160 km/h, determine the
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