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ing all these factors while optimizing the flight path performance is a complex
mathematical problem.
However, the problem was simplified by assuming that 1) the airjplane has a
parabolic drag polar and alinear lift coe:fficient and 2) the power developed by the
piston engine, the propulsive efficiency ofthe piston-props, and the thrust produced
by the jet aircraft are independent of flight velocity. With these assumpf:ons, the
performance problems of propeller and jet aircraft become amenable to the meth-
ods of ordinary calculus. Although the equations for the performance ofjet aircraft
have analytical closed form solutions, most of those for propeller aircraft do not
have analytical solutions. One has to solve them graphically or numerically.
This approach gives us so-called point performance cha;aycteristics. We have ob-
tained conditions that optimize the point performance in various flight conditions.
Even though this metrhod docs not deal with the path performance of the aircraft,
it gives a very useful underst,anding of the physical parameters of the airplane that
play key roles in improving its path performance.
References
1Vinh, N. X., Opirmat Trajectories rn Armospheric Flight, Elsevier, New York, 1981.
2Guntson, B., and Spick, M., Modem Aircombat, Crescent, New York, 1983.
AIRCRAFT PERFORMANCE
159
3McCormick, B. W., Aerodynamics, Aeronautics, cmd Flight Mechanics, Wiley, New
York, 1979.
4Boyle, D., "Windshear, Taming the Killer:'Interavia, Jan. 1985, pp. 65-66.
SLewis, M. S., "Sensing a Change in the Wind:' Aerospace A,nerica, Jan. 1993, p. 20.
6Mulgund, S. S., and Stengel, R. F., "Target Pitch Angle for the Microburst Escape
Maneuver," Jozrmal of Aircraft, Vol. 30, No. 6, 1993, pp. 826-832.
:rStengel, R. F., "Solving the Pilot's Wind Shear Problem:' Aerospace America, March
1985, pp. 82-85.
Problems
2.1 Show that the maximum endurance ofa glideris given by
3
tmax = 2+-~V (h~ -hf)
2.2 A glider weighs 4500 N and has a wing loading of 600 N/m2, and its drag
polar is given by CD = 0-01 + 0.022C2. It is launched from a height of 400 m in
still air. Find (a) greatest possible ground distance it can cover, (b) the max:imum
time it can remain in air, and (c) effect of 10 m/s tailwind for each of the above two
cases. [Answer: (a) 13.484 km, (b) 6.72 min, and (c) AR -. 3.52 km and At -. 0.]
2.3 A certain airplane weighs 44,440 N and has a wing loading of 1433.55 N/m2.
The drag polaris given by CD = 0,02+0.04CZ and CL,max = 1,2. For a power-off
glide from 600 m, determine (a) the maxunum distance it can cover and (b) the
maximum timeit can remain in the air. [Answer: (a) 16.6066 km and (b) 210.125 s.]
2.4 A piston-prop aircraft has a wing loading of 1600 N/m2, and its drag polar
is given by CD - 0.025 + 0.05CZ. The maximum Jift coe:fficient is 1.5. The
reciprocating engine develops 750 kW at sea level, and the propulsive ef'ficiency
of the engine-propeller c. ombination is 0.85. Draw the power-available and power-
required curves at sea level. Determine the maximum and minimum speeds for
level fiight at sea level.
What is the minimum power required for level fiight at sea level? Determine the
corresponding velocity and lift coefficient.
2.5 A light turbojet airplane weighs 30,000 N, has a wing loading of 1000 N/m2,
and produces a sea level thrust of 4000 N. The thrust varies with altitude as
T = Toa0.8. Assuming CD - 0.015 +0.024CZ and CL, . = 1.4, find (a) maxi-
mum and mirumum speeds in level flight at sea level and (b) the absolute ceiling
of the airplane. [Answer: (a) 119.2149 m/s and 32.9914 m/s and (b) 13.30 km.l
2.6 Whatis the thrust required for a turbojet airplane weighing 50,000 N, with a
wing loading of 1800 N/m2 and a maximum sea level fiight speed of 241.83 m/s?
Assume CD = 0.02 + 0.04CZ, and CL,rmx = 1.5. [Answer: 20,000 N.]
2.7 For the propeller airplane of Exercise 2.4, determine, the maximum climb
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