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co = g ~T-_f
Height lost in one complete turn is given by
Ah = (~h) t27r
= (V y)t2,r
2T( T/2y
= g ff//-=l
_ 47rtl2(]
= pg-/~-~) (C/:) (2.298)
For a given load factor n, we observe that the height lost per turn is minimum when
the glider flies at an angle of attack when CDICZ is a minimum, which happens
whe7C, = C~.max-
General turning flight of aircraft. The maximum rate of turn generated by
an airplane in a coordinated, constant-altitude turn is called the MSTR because
the aircraft can produce such a turn rate continuously for some time. However, the
aircraft can generate still higher rates of turn ifit is permitted to lose altitude so that
it can make use ofits height or the potential energy in addition to the aerodynamic
and propulsive forces. The turn rate so generated can be much higher than MSTR
and is called the maximum instantaneous tum rate or the maximum attainable tum
rate (MATR). A high value of MATR is a good measure of the air superiority of
AIRCRAFT PERFORMANCE
137
combat aircraft because it is of crucial importance in close encounters where a
pilot getting first point-and-shoot capability has a better chance to win. Because
the aircraft will rapidly lose altitude during this maneuver,it is necessary for a pilot
to have enough height margin before he initiates this maneuver.ln the following,
we will study this t)rpe of tunung flight, assuming that the sideslip is zero and
the flight velocity is approximately constant. We will consider only the jet aircraft
here. A similar approach can be used for propeller aircraft.
Equations (2.190-2.192) take the following form:
We have
Then,
T-D- Wsiny =O
L cos p, - W cos y - 0
WV2COS2y = 0
L sin ,r. -
gR
D=2Vg (,2+-,)
V cos y
co= R
, T-D
smy= W
cos y
n -.:
COS /,L
f/2 cos )t
tan/r,- Rg
-
cos y
co = gc-;-
R= _, . _
lV =
(2.299)
(2.300)
(2.301)
(2.302)
(2.303)
(2.304)
(2.305)
(2.306)
(2.307)
(2.308)
(2.309)
138 PERFORMANCE, STABIUTY, DYNAMICS, AND CONTROL
V
Fig. 2 28 Schematicillustrahon ofcorner \relocit)r turn.
From above relations, we observe that, for a given value of thrust T and aero-
dynamic efficiency Em, the turning performance improves with increase in load
factor n and lift coefficient CL but only to be limited by the aerodynamic limit
CL,max and the structurallimit nmn.
Assuming that the fiight path angle y is small, let us plot the variation of turn
rate to with velocity V for various values ofload factor n as shown in Fig. 2.28.
The curve corresponding to n = nhm represents the structural boundary and that
corresponding to CL,max represents the aerodynamic boundary. The velocity at
the intrersection of these two boundaries is called the comer vclocit)r. This is the
velocity for maximum instantaneous turn rate or MATR. For a typical fighter
aircrafi, the corner velocity is about 300-350 kn (550-650 km/h).vln a classical
tuming dogfight situation, the pilot who gets to his comer velocity first usually
gains an upper hand and has a better chance for first point-and-shoot capability.
In the following, we will consider the turning flight at corner velocity.
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