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power. We observe that the R/C is maximum when the specific excess power is
maximum.
  Ana/ytical so/ution for ckmbing fkght of prope/ler aircraH.  For propeller
aircraft whose power developed by the engine P(kW) and propulsive efficiency
r7p are independent of flight velocity, Eq. (2.104) takes the form
                (Rl C) = V:= (k  7p P(kW) ~ ~pSCDOV3 _ 2k WV. )               (2.105)
                pSV
For maximum R/C,
or
d(RlC)  3      2kW2
   d~ = -2/p SCDO \/2 + 2tj_S j
          - 0                                         (2.106)
                  1
VR/C,max _
                                                   = ~ VR                                        (2.107)
                                                                 4
                           N
It may be observed that the speed at which the rate of climb is maximum is the
same as the speed at which the power required in level fiight is minimum. The
two speeds are the same because, for the propeller aircraft, we have assumed that
the power available is independent of forward speed. Thus, essentially, the speed

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96               PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
at which excess power is maximum becomes the same as that when the power
required is minimum,i.c., VR/C.,max = Vmp.
    Substitution in Eq. (2.105) gives
where
(Rl C)max = k'r7p P'(kW) - 0 8~16PEm                      (2.108)
                                                          Pl
The climb angle is given by
    h
y=v
 RlC
=V
   rl. P(kW)
P'(kW)= W
(2.109)
_ k'r7pP'(kW)    1             2kW
  V _2WpSCDOtr2_2S1,  (2.110)
For steepest climb,i.e., when (y - Ymax),
            dy = k~7pP'(kW)  pSCDO'V   kW
           dV =     V2       w LV+D:sf3
                          - O                                                  (2.111)
This equation is of the form V4 +a V +b = 0, where
                                                          k'r7p P'(kW)
　
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