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takeoff or continue and get airborne.
      The fieldalength determined by the above considerations is known as "balanced"
field length3 and is schematically shown in Fig. 2.35.
   Estimation of airborne distance and time.   During the airborne phase, the
aircraft is in an accelerated climb. The equations of motion for this phase are
     WdV
T-D-WsinY = g dt
/- W cos }/
and the kinematic equations are given by
                                    x - V cosy
                                   h : V siny
(2.337)
(2.338)
(2.339)
(2.340)
152             PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
For accurate estimatiori of the airborne distance S2, we have to solve the above dif-
ferential equations. However, a simple and approximate estimation of the airborne
distance S2 and the corresponding time t2 can be done by assuming that the flight
path angle y  is constant during the airborne phase. With these assumptions, we have
 hobst
S2 - .                                 (2.341)
         tan y
                      S2
                                  t2 = VI osy
where
                                siny = (T WD) ,='vi
(2.342)
(2.343)
    A typical landing phase consists of the following sequences (Fig. 2.36):  1) a
steady shallow glide approach to the runway holding a constant glide angle y; the
glide angle is held as small as possible so that the rate of sink is kept down to a
minimum (in this way,itis possible to reduce the energy that has to be dissipated at
impact with the ground); 2) a rtlare during which the aircraftis rotated noseup so as
to momentarily achieve alevel fiight condition and to further mirumize the rate of
sink; 3) a touchdown prior to which the pilot may momentarily stall the airplane;
and 4) the ground run during which full reverse thrust (if available), spoilers or
drag parachutes (like the F-15 or the MiG-21 aircraft), and brakes are applied to
produce maximum retardation and bring the aircraft to a complete halt.
   Estimation of airborne distance and time.   Assuming that the glide angle
and velocity are constant during the fnal approach,
H
 hobst
 sz = tm y
tt = VXy
(2.344)
(2.345)
                                         
                          ?-             
┏━━━━━━━━━━━┳━━━━━━━┓
┃                      ┃              ┃
┣━━┳━━┳━━━━━┫              ┃
┃~ J-┃    ┃k..~_ \N  ┃~ .~-- -+~:   ┃
┃!   ┃:,  ┃          ┃ TouchDown :  ┃
┃[b. ┃4   ┃          ┃              ┃
┗━━┻━━┻━━━━━┻━━━━━━━┛
l- S,          --S2~- S3J
Fig.2.36   Schematic diagram ofturplanelanding.
AIRCRAFT PERFORMANCE
153
The approach speed VA iS usually equal to 1.3  Vscdl. Furthermore, we assume that
　
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