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             ve
Fig. 2.23    Schematic illustration of cruise altitude for jet aircraft.
AIRCRAFT PERFORMANCE
113
corresponds to the altitude of that Ta curve, which is tangential to the TR curve.
The velocity at this tangential point is the velocity for maximum Breguet range.
Note that this altitude is not the absolute ceiling because TR is based on the initial
weight Wo and not the instantaneous weight."F '
    A similar approach can be used for the constant-altitude range program.
    For jet airplanes, the cruise altitude can also be determined anal.ytically if we
assume: 1) the thrust varies with altitude as T - Too p, where p is a constant
smaller than uruty: and 2) we ignore the variation of specific fuel consumption
with altitude. We have
                                       T - D                             (2.166)
Multiply and divide the right-hand side ofEq. (2.166) by Wo and use the condition
L - Wo to obtain
Toap = W~D
 WOCD
 =C
   WO
 =E
   U = (EWT )'
(2.167)
(2.168)
With this value of cr, the most economical cruise altitude h in kilometers can be
approximately obtained using
                                                   Jz = 44,3(1 - U 0.235)                                   (2.169)
2.6.5  Approximate Estimation of Height Gained During
       Cruise Climb
    This method is based on the assumption that the relations L -. W and T - D
hold at the begiruung and at the end of the constant-velocity cruise.ln other words,
we assume that, at the endpoint of the constant-velocity cruise, the decrease in
thrust and drag caused by increase in altitude compensate each other, and similarly
the decrease in lift (caused by increase in altitude) and weight (caused by fuel
consumption) also balance ea~h other. Furthermore, we ignore any variations in
specific fuel consumption during the cruise.
    Let pi and p f denote densities at the the initial and final altitudes. Then
                                  wo = r~Pi V2SCL
                              WI = ~pf V2SCL
so that
                Wl
                      pf = WOp'i
(2.170)
(2.171)
(2,172)
114                PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
or
                 Wl
                         af = Woal                   (2.173)
The corr.esponding altitude /V in kilometers can be approximately estimated using
the following relation:
                    /if =4zV3(1-cr~.235)             .  (2.174)
so that the height gained is given by
                                           Ah = hf - hi                               (2.175)
　
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