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   77me for takeoff,
Let
so that
and
 w (I V
g dt =Fcr
     (2.329)
dt - WdV
 8Fa
    a - Fo
b= Fi - Fo
  '[/12
Fa ~ a + I,Jr2
 dt~ WIV
                 g(a + blV 2)
          vJ     Wd V
tI =
=-_~---
            g(a +b V2)
(2.330)
(2.331)
(2.332)
(2,333)
(2.334)
(2.335)
150            PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Then,
t, = (g~l6~-'
2g^~-
(a > 0, b > 0)
                       bi Vi ~
e. .+G:;;v) (a>O,b<0) (2.336)
where bi  =  lbl is the absolute value of b. Here, we have assumed that there is no
wind during the ground run. If the aircraft operates in the presence of wind, the
ground run si  and takeoff time ti  will be quite different. Thve headwind improves
takeoff performance, whereas the tailwind degrades it.
      If the airplane is to takeoff under crosswind condittons, the airplane drag has to
be estimated for sideslip conditions. With sideslip, the drag will be higher, and, as
a result  the ground run si and corresponding time ti willbe higher compared to the
case of zero sideslip. Furthermore, the pilot has to operate the rudder to prevent the
airplane from aligning itself along the resultant velocity vector as schematically
shown in Fig. 2.34. The aircraft attempts to align along the resultant velocity on
account ofits inherent directional stability, which we will study in Chapter 3.
   Aborted takeoff.  Sometimes, takeoff may have to be aborted because an
engine failure occurs during the ground run. Adn immediate detection of an engine
failure may not always be possible, and the pilot may not notice it until the aircraft
has gained some ground speed. To account for such unforeseen situations, a certain
 speed called critical speed  Vcr iS defined for each aircraft to assist the pilotin making
a decision whether to abort or continue the takeoff.lf an engine failure is detected
at speeds below the critical speed, the pilot is advised to abort the takeoff because
he still has enough runway length left to bring the aircraft to a complete stop. If
                         
              ~     ~    
┏━━┳━━┳━━┳━━┓
┃,   ┃(   ┃.   ┃/   ┃
┃    ┃    ┃    ┃ N  ┃
┃~   ┃    ┃    ┃[-  ┃
┃    ┃    ┃.   ┃    ┃
┃~   ┃    ┃    ┃~   ┃
┃    ┃    ┃    ┃--- ┃
┣━━┻━━╋━━┻━━┫
┃r-    \{  ┃}/-l      ┃
┃4-        ┃          ┃
┣━━━━━╋━━━━━┫
┃          ┃          ┃
┗━━━━━┻━━━━━┛
NS = NR
   Ns - Stibillty
        Yawinqi Moment
Nr ~ ~tiwing ~4omtnt
     Duc to Ruddcr
yr - Side Force
      Due to Ruddcr
V ctlrn b
   V.
 Vcr
E
AfRCRAFT PERFORMANCE
S.+ S2  = Normal  Take-off  Oista .ce
A + B   = Balinced  Field  Length
Stop
Fig. 2.35    Normal takeoff distance and balanced field length.
151
engine failure is detected at speeds exceeding the critical speed, then he is advised
to continue the takeoff and get airborne because the available runway length may
not be sufficient to bring the aircraft to a safe halt. Once a:irborne, he will have to
assess the nature and severity of the situation and take appropriate action. If an
engine failure is detected at V  -  Vcr, he has both opf.ions. He can either abort the
　
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