88               PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
We have
m
h
    v*
a) Eqruvalent air speed
          v
             b) True air speed
Fig.2.12 Levelftighterrvelope.
    T-D
                                                 1
                                   = ~p V2S(CDO +kC~.)
                                                 1
                                 = ~p V2SCDO + (jk,_WS
Equation (2.85) can bc written as follows:
                                      A/r4 _ Tlr2+ B = O
Where
                                   = ~pSCDO
                              .  B = (2kpVg.)
(2.85)
(2.86)
(2.87)
(2.88)
AIRCRAFT PERFORMANCE
SoMng Eq, (2.86), we obtain
Vmax =
Vmin =
~]
(2.89)
(2.90)
Hcywever, a more elegant form of analytical solution can be obtained using the
nondimensional. form ofEqs. (2.27) and (2.28). With y = 0, Eqs. (2.27)'and (2.28)
take the following form,
Then,
U4 _ 2zu2 +1 = 0
 n:1
ILmax = ~
Umin = V
       Vmax - llmax VR
         Vmin -. ILmin VR
(2.91)
(2.92)
(2.93)
(2.94)
(2.95)
(2.96)
(2.97)
Given the variation of thrust available with altitude, using this approach, we can
construct the level fiight envelope for a jet aircraft whose thrust is independent of
flight velocity. At the absolute ceiling, Unun - Umax, which gives z = 1. Physically,
when z - 1, T - Dmn. As said before, at absolute ceiling, level fiight is possible
only at only one speed where the drag is minimum.
   Whether the flight is possible at Vmin depends on the magnitude of the level
flight stalling velocity, which is given by
Vstall -
(2.98)
If Vmm < VstaU, then the airplane cannot fly at Vmin in steady level flight because
it asks for a lift coefficient in excess of CL,max. For such cases, the level flight
solution  Vnun has no physical significance, and  VstaU effectively 'oecomes the low-
speed solution.
      To flyinlevelflight at any speed at aspeed  V  such that V             V  <  'V~x, the pilot
has to throttle the engine so that the drag at this speed equals the thrust available
as schematically shown in Fig. 2.13.
  . AIAA
EDUCATION
SERIES
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TL671,4
.P28
Performance, Stability, Dynamics9
and  Control of Airplanes
Performance, Stability, Dynam.ics,
and  Control  of Airplanes
Bandu N. Pamadi
NASA Langley Researcb Center
Hampton, Mrginia
EDUCATION SERIES
J. S. Przemieniecki
Series Editor-in-Chief
Air Force Institute of Technology
Wright-Patterson Air Force Base, Ohio
Published by
American Institute of Aeronautics and Astronautics, Inc.
　
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