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5 m, tip chord of 2 m, and semispan of 10 m, determine the aspect ratio, mean
aerodynanuc chord, and spanwise location of the mean aerodynanuc chord.
1.4 Estimate the skin-friction coefficient for a fiat plate wing of 4 m chord and
10 m span exposed to an airstream of 75 m/s. Assume that the boundary-layer
transition occurs at 50% chord and v:1.5 x 10-5 j112/S.
1.5 Determine the wave-drag coefficient of a double wedge airfoil of 6% thick-
ness ratio held at an angle of attack of 4 deg and a Mach number of 3.
1.6 The critical Mach number of a two~dimensional rectangular wing is 0.75.
What will be the critical Mach number of tlus wing if the leading edge is swept
back at 45 deg?
2
Aircraft Perforn~ance
2.1 Introduction
An akl?lane is a fiying machine. Like any other machine, it is judged by its
performance. Some of the questions that usually come to nund are How fast can
itllyl How high can itlfyl How fast and how steep can it climbl How far can it
go with a tank-load of fuell What length of runway does it need for takeo[-f and
landingl How sharp and how [ast can it turnl Answers to these and many other
questions form the subject matter of aircraft performance.
Performance characteristics depend on the weight of the airplane, aerodynamic
characteristics of the airframe, and the thrust or the power developed by the pow-
erplant. For a given airplane configuration, aerodynamic characteristics depend on
angle of aaack/sideslip, Mach number, and Reynolds number. The thrust/power
characteristics of the powerplant depend on altitude, flight velocity, and engine
operating conditions. Therefore, in general, it is not possible to analytically es-
timate airplane performance considering the arbitrary variations of aerodynamic
and propulsive characteristics. Prior to the arrival of modern digical computers,
it was common practice to use graphical methods for performance evaluations.
Using high-speed computers, these calculations, which once took several hours
or days, can now be performed in a matter of a few minutes with much more
precision and accuracy. However, we are not going to discuss these computational
methods of performance estimation. Instead, we will introduce some simplifying
assumptions so that performance calculations become amenable to the methods of
ordinary calculus.
We assume that the aerodynamic forces acting on the airplane are given in the
coefficient form as follows:
CL -. aa
CD = CDO +kC2
(2.1)
(2.2)
Here, CL iS the lift coefficient, a is the lift-curve slope, CD iS the drag coefficient,
C.DO iS the zero-lift drag coefficient, and kCZ is the induced-drag term. Usually,
CDi iS used to denote the induced-drag coefficient so that we have
CDi = kC~.
(2.3)
The variation of the drag coefficient as given by Eq. (2.2) is often called the
parabolic drag polar of the airplane.
At low speeds, CDO includes skin-friction and pressure drag of all wetted (ex-
posed to airflow) components of the airplane. At high speeds, another form of
zero-lift drag arises, which is known as the wave drag. Therefore, for high sub-
sonic and supersonic airplanes, the term CDO will also include the wave drag. The
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68 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
induced- drag term CD, iS primarily the drag due to lift. However, it also includes
those parts of the skin-friction and pressure drag that vary with angle of attack
The induced-drag parameter k in Eq. (2.2) is given by
~
. 1
k - - (2.4)
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