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1. Roll-rate response of an aircraft to a 5°-step aileron input is shown in the figure below. Some relevant information about the aircraft characteristics can be seen in the figure as well. a. Estimate the aileron control power L6. and the roll damping parameter Lp based on the response shown assuming the motion can be approximated well by pure-rolling motion. Hint: Time constant can also be defined as the time for the step response to rise to 63% of its steady-state value. b. Determine differential equation describing the rolling motion of the aircraft. 6 V-224ftisec 4 Plt 2 48 0.00205 1 2 3 Time sec 2. The Dutch roll motion of an aircraft can be approximated using the following equation: Y, Ys 110 AS, No N, N° where B is the angle of sideslip (in rad), r is the yaw rate (0 in rad/s), and 8, is the rudder deflection (in rad). The numerical values of the aircraft parameters are as follows: Yn=-7.8 ft/s² Y, -2.47 ft/s Ys -5.236 ft/s² N=0.64/s² N, -0.34 N° -0.616/s un=154 ft/s a. Determine the Dutch roll eigenvalues. What are its damping ratio and undamped natural frequency? Is the Dutch roll motion stable? b. Obtain the transfer function from & to B C ) using MATLAB. B(s) s,(s) 1 c. Plot and submit the B and r responses given the initial conditions: (AB(0) Ar(0)} - {0.1 o) From the plot, estimate the period and the time to half amplitude. d. Plot and submit the B and l' responses due to a 0.1 rad-step rudder input, assuming zero initial conditions. 3. The lateral-directional derivatives of Navion general aviation airplane flying at 0.158 Mach number in sea-level condition are given below. a. Determine the lateral-directional state-space equations of motion for the Navion in the specified flying condition. b. Determine the characteristic equation of the Navion's lateral-directional motion. c. Calculate the eigenvalues of the longitudinal flight motion. Identify the natural modes of the motion, and for each natural mode, calculate its relevant parameters (time constant for a 1s-order mode; frequency and damping ratio for a 2nd-order mode). Describe also the motion associated with each natural mode and determine the overall stability of the aircraft's lateral-directional motion. d. Plot and submit the free responses of B, P and r with respect to the initial condition B(0) 2° and zero for the other variables. Navion airplane properties Altitude (ft) 0 (sea level) Flight speed (un ft/s) 176 Nominal pitch angle (deg) (slug.ft² Lateral-directional derivatives Y6 (f1/s²) -45.72 L, (1/s²) 16.02 N (1/s²) 4.49 -8.4 N, (1/s) -0.35 Y. (tt/s) L, (1/s) 2.19 N, (1/s) -0.76 Ys (ft/s²) 8.12 (1/s²) -29.01 Lg (1/s²) 23.16 Ns (1/s²) -0.221 Ns. (1/s²) -4.55

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Aircraft Stability and Control
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