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We have
I
Em = 2- -
VR -
Substituting, we get E,, - 18.64, Vle - 96.136 m/s so that Um = VR/Cmax] VR =
1.5863.
For maximum rate of climb at sea level,
3u: - 2zou~ - 1= 0
Solving, we obtain zo = 3.5758, which gives sea level thrust To = 30,110.6790 N.
The lift coefficient is given by
2W
C = pS_ R~
- 0.2370
The maximum and minimum velocities in level flight at sea level are given by
llmax ~
- 2.6474
106 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Vnmx = llmax VR
- 254.51 m/s
Umin -
- 0.3770
Vmin : llmin VR
- 36.31 mts
VstaU -
- 60.6135 m/s
The fiight at Vmn iS not possible because Vnun 4Vsrall
We have
Tou0.6Em
z= W
o = (-,,,.) -
With z = 1 at absolute ceiling, we get cr = 0.1196. From standard atmospheric
tables (see Appendix), we get the altitude as approximately equal to 16.8 km.
2.6 Range and Endurance
Cruise flight begins at the end of the climb phase when the airplane has reached
the desired altitude, and cruise fiight ends when the descent phase begins. For
a given amount of fuelload, the horizontal distance covered with respect to the
ground during the cruise flight is called cruise range and does not include any
distance covered during the climb or descent.ln this text, the term range refers to
the cruise range and will be expressed in kilometers.
Range is an important performance measure for commercial transport airplanes
like the Boeing 747 or Airbus 320. Range is also important for military bombers
like e B-52 or the B-l.
From physical considerations, the range will be maximum when the airplane
cruises at that velocity when the ratio of velocity to fuel consumed per unit time
is maximum.
Endurance is the total time that an airplane can remain in the air for a given fuel
load and is usually expressedin hours. The endurance is an important performance
measure for reconnaissance or surveillance airplancs.lt is also of interest to all
aircraft during the loiter, which is defined as that phase of f/ight where the primary
aim is to remain airborne and not worry about the ground distance covered. Long-
range bombers like the B-52 or the B-l may loiter while on an airbome alert. A
fighter aircraft on a combat air patrol mission loiters while guarding the airspace
AIRCRAFT PERFORMANCE
107
from intruding aircraft. When the primary aim is to be airborne, the aircraft is
essentially in level flight, and it will fly at that speed when the fuel consumed per
unit time is a minimum.
In the following sections, we will study the range and endurance of propeller
and jet aircraft and determine the conditions when these quantities assume their
maximum values.
2:6.t Range of a Jet Aircraft
Because the airplane during the cruise is essentially in level fiight, we have
L - W - O (2.137)
T - D - O (2.138)
Kinematic equations are
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