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162 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
for a properly banked turn in a horizontal plane. [Answer: (a) co -. 14.8285 deg/s,
(b) V = 70.3948 deg, (c) ct -. 18.2 deg, and (d) E - 7.9477J
2.23 A light combat aircraft powered by ajet engine weighs 70,000 N and has a
wing area of25 m2, CD = 0.015+0.06CZ,and CL, x = 1.4.The structurallimit
load factor is 8.0. Determine (a) the bank angle, (b) lift coefficient, (c) lift-to-drag
ratio, (d) radius of turn, and (e) load factor developed when the aircraft flying at
300 km/h completes a 180 deg turn at sea level in 15 s. (f) What is the thrust
required? [Answer: (a) /L - 60.656 deg, (b) CL = 1.3433, (c) E - 10.8975,
(d) R = 397.9615 m, (e) n -. 2.0406, and (f) T -. 13,111.32 N.]
2.24 A light turbojet aircraft powered by ajet engine weighs 50,000 N and has
a maximum thrust of 6000 N at sea level. The wing loading is 1500 N/m2, CD =
0.020 + 0.08CZ, and CL,rmx - 1.8. The maximum permissible load factor is 2.5.
Determine (a) the bank angle, (b) lift coefficient, (c) lift-to-drag ratio, (d) rate of
turn, and (e) load factor developed when the aircraft makes a coordinated sealevel
turn of 1500 m radius using full thrusL [Answer: This problem has two solutions:
1) (a) p,- 59.0639 deg, (b) CL - 0.1940, (c) E -.8.4308, (d) co = 5.9856 deg/s,
and (e) n = 1.9452, and 2) (a) p, = 10.9143 deg, (b) CL - 0.8790, (c) E - 10.7444,
(d) co -. 2.0348 deg/s, and (e) n = 1.0184.]
2.25 A light combat aircraft weighs 75,000 N and has a wing area of 27 1112.
The maximum lift coefficient with high-lift devices is 1.8, and the structurallimit
load factor is 6.0. While flying at 250 km/h, the aircraft makes a 90 deg turn in
8 s at sea level holding a constant altitude and at an angle of attack such that
the lift-to-drag ratio is 8.0. Find (a) the banlc angle, (b) load factor, (c) radius of
turn, and (d) the thrust required. [Answer: (a) y : 54.26 deg, (b) n - J.7120,
(c) R - 353.7665 m, and (d) T - 16,050 N.]
2.26 Determine the thrust required for a turbojet aircraft weighing 85,000 N
with a wing area of 32 mz, CL. x = 1.50, CD ~ 0.04 + 0.0833CZ, and nmn =
6.0, so that it can execute a sea level coordinated 90 deg turn in 6 s. [Answer:
31,688.028 N.]
2.27 A turbojet aircraft weighs 68,000 N and has a thrust-to-weight ratio of 0.6.
Assuming S-: 24 m2, CD -- 0.025 + 0.07CZ, CL,max = 1.20, and nUm - 8.0,
determine the minimum time to make a 180 deg tum while operating at an altitude
of 2250 m (cr = 0.80) for (a) holding constant altitude and (b) permitting loss of
altitude. (c) Determine the heightlostin case 2. [Answer: (a) 9.9846 s, (b) 7.9210 s,
and (c) 371.1758 m.]
AIRCRAFT PERFORMANCE
163
2.28 Show that the reduction in takeoff ground run in the presence of a headwind
is approximately given by Asi - (2 Vw/ Vi)si.
2.30 Assuming an obstacle height of 15 m, find total takeoff distance and time
for the aircraft in Exercise 2.29.
2.31 A light combat aircraft weighs 78,480 N and has a wing area of 25 II12,
lift-curve slope of 0.06 per deg, CL,max = 0.95, and CD - 0.0254 + 0.178CZ.
This aircraft is required to land at an airstrip located at an altitude of 1000 m
(cr = 0.9074). Assuming that the coefficient of friction between the tires and the
runway is equal to 0.02 and approach glide angle is 3.5 deg, estimate (a) airborne
distance (including flare) and (b) ground run.
Assume that fiaps are lowered at touchdown and grve an increase in C/,max
of 0.45 and an increase in CD of 0.05. Further assume that the brakes are ap-
plied simultaneously grving an increment in frictionaJ coefficient of 0.4. [Answer:
(a) 294.0329 m and (b) 1408.5 m.l
3.1 Introduction
3
Static Stability and Control
The airplane is a dynamic system with six degrees offreedom, threein translation
and three in rotation. In general, airplane motion is characterized by three linear
and three angular accelerations under the action of gravitational, inertial, and
aerodynanuc and propulsive forces and moments. We will study such a dynamic
system in Chapters 4 and 6. However, a significant portion of the airplane's flight
envelope consists of steady flight conditions such as cruise, climb, or glide. For
such fiight conditions, the principles of static equilibrium can be applied. This
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