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consumed per unit power per unit time.ln this text, we will use the units of N/kWh
to specify the specific fuel consumption of propeller airplanes. For jet aircraft,
specific fuel consumption is the amount of fuel consumed per unit thrust per unit
time and will have the units of N/Nh.
   For a given altitude, the power developed by a piston (reciprocating) engine
is virtually constant with flight velocity. The only variation of power arises due
to the variation of the ram pressure in the intake manifold with fiight velocity.
However, the power developed by a reciprocating engine decreases with an increase
in altitude because ofa fallin air density. With turbosupercharging, this decrease in
engine power can be minimized up to a certain altitude. The propulsive efficienc}r,
in general, varies with flight velocity. However, if the aircraft is equipped with a
variable-pitch, constant-speed propeller, the propulsive efficiency can be assumed
constant over the design operaoing range. For a given altitude, the thrust developed
Pa
AIRCRAFT PERFORMANCE
v
Ta
N
Ta
v
v
                                             .   b) Jet aircraft
~g. 2.1    Schematic variation ofthrust and power av:ulable with velocity.
70               PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
flight, range and endurance, takeoff, landing,  and turning flights. We will also de-
termine the fiight variables that optimize the point performance of the airplane in
such fiights. We will not be dealing with path performance problems that are es-
sentially problems in variational calculus. Interested readers may refer elsewherei
for more information on path performance problems.
2.2    Equations of Motion for Flight in Vertical Plane
      Let us consider an airplane whose fiight path is contained in a vertical plane as
show in Fig. 2.2. Let V  be the flight velocity that is directed along the tangent to
the flight path: Let the tangent to the flight path'at a given instant of time make an
 angle y with respect to the local horizontal. The angle y  is usually called the flight
path angle. Let 0 be the inclination of the airplane reference line or the zero-lift
line with respect to the local horizontal so thatPthe angle of attack a  - 0 - y. Let
 R be the radius of curvature of the fiight path in the vertical plane.
    The external forces acting on the airplane are lift L acting normal to the flight
 velocity, the drag D parallel to the flightYpath and in opposite direction to the flight
velocity  V, the thrust T in the forward direction mak~:g an angle e with respect to
the flight path, and the weight W in the direction of gravity directed towards the
center of the Earth.
     Resolving the forces along and normal to the flight path, we have
                          W (1V
T cos e - D - W sin y = -7.                               (2.5)
               g dt
                                                    W I/2
                                         T sin e +L - W cos y - -.                                   (2.6)
                  gR
Equations (2.5) and (2.6) describe the accelerated motion of the airplane in a
vertical plane. Generally, the thrust inclination e is ver}t small. Therefore, it is
tal
Fig. 2.2    Forces achng on an airplane in fiightin a verticalplane.
　
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