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of 25 deg, sideslip of -5 deg, and a bank angle of 5 deg. The internal strain gage
balance records an axial force of 25 lb, a side force of -3 lb, and a normal force
of -75 lb with respect to the model axes system. Determine the effective angle
of attack, effective sideslip, lift, and drag forces acting on the model.
4.7 An airplane is flying at a velocity of 150' ft/s at an angle of attack of 12 deg
and sideslip of 2 deg. It has angular velocities in pitch, roll, and yaw measured by
onboard rate gyros as 10 deg/s, 5 deg/s, and 10 deg/s, respectively. Determine the
angular velocity rates ct, B, and @ associated with the wind axes system.
4.8 Given p = 10 deg/s, q = 5 deg/s, and r = 10 deg/s, determine C2{lt, and g2:b.
4.9 An aircraft is in a spin at an angle of attack of 60 deg. Assuming that the
spin rate about a vertical axis through the center of gravity is 40 deg/s, plot the
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438 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
time history of Euler angles using (a) method of Euler angles, (b) the method of
direction cosines, and (c) the quaternions.
4.10 Determine the missing elements (marked xx) of the following direction
cosine matrices:
0.1587 xx
(a) DCMi - 0.8595 -0.1218
xx 0.4963
xx 0.5283
(b) DCM2 = -0.5253 xx
0.0888 xx
4.11 An acrobatic aircraft flying at 150 m/s and a 30-deg angle of attack, executes
a body axis roll at a rate of 150 deg/s. Determine the accelerations measured by
onboard accelerometers.
4*12 An airplane fiying at an angle of attack below stall angle is in a steady roll
at a rate po deg/s. Derive the equations of motion for small disturbance motion.
4.13 An aircraft weighs 50,000 N and is in a steady level flight at 150 m/s
at sea level. The drag polar is given by CD = 0.018+0.024Cl.. The lift-curve
slope of the wings is 0.095/deg, and the wing mean aerodynamic chord is 2.5 m.
The lift-curve slope of the horizontal tail is 0.06/deg. As9uming a tail efficiency
of 0.9, estimate the stability derivatives Cxu, Czu, Cxa, Cza, Czq, Cztr, and Cma.
[Answer: Cxu -.-0.03697, Cz" =-0.2844, Cxa -.0.1047, Cza -.-0.11348,
Czq ~ ~3.5373, Cz& = -1.2476, Cmq = -8.5548, and C,na, - -2.9942. All val-
ues are per radian.]
4.14 For the wing-body ofExample 4.12,estimate the stability derivatives CLq,
Cmq, CLa, and CmCr at a Mach number of 0.4.
4.15 For an aircraft wing with Ieading-edge sweep 30 deg, aspect ratio 4, lift-
curve slope O.l/deg, dihedral angle 3 deg, taper ratio 0.5, CDD = 0.021, CDa,l -
0.0012/deg, and span 10 m, estimate the stability derivatives Ctp, Cnp, CLr, and
Cnr at M - 0.3 and a -. 8 deg using strip theory and compare your results with
those obtained using Datcom methods. Assume that the center ofgravity (moment
reference point) is located 0.2G ahead of the aerodynarnic center and the wing
root chord is located I m below the center of gravity (zw - 1.0 m).
4.16 Estimate the vertical tailcontribution to C,P, Cnp, C,r, Cnr, Cyr,, Ci/.i dand Clt,
for an aircraft with following data: wing sweep = 30 deg, wing mean aerodynamic
chord c = 2.5 m, wing dihedral = 3 deg, wing aspect ratio = 4, wing taper ratio =
0.5, wing span : 12 m,vertical taillength - 2.5 c,ay = 0.08/deg, zv = 0.85 m, and
ratio of vertical tail area to wing area = 0.25. Assume vertical tail parameter k =
0.84 and that-the aircraft is operating at an angle of attack of 6 deg and M N O.l0.
[Answer: Clp = -0.001908, Cnp ~ -0.06191, CLr - 0.0185, Cnr - -0.09464,
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