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1. (25 pts.) The slope of the Cm vs. CL curve of a conventional aircraft at a specific flight condition is −0.15 and its pitching moment at zero lift is 0.08. The aircraft’s wing has an aspect ratio of 6 with a thin airfoil profile and zero-lift angle of attack of −2o . a. Determine the trim lift coefficient at this flight condition. b. What is its trim angle of attack assuming wing is the main lift generator of the aircraft? c. Does this aircraft possess static longitudinal stability? Briefly explain your answer. d. If the pitching moment characteristics of this aircraft in the above flight condition is expressed in a Cm vs. α curve, determine the slope of the curve and the value of Cm at zero angle of attack. 2. (25 pts.) A canard-wing configuration of an aircraft is sketched in the Figure below. The canard and wing are geometrically similar and are made from the same airfoil section. The dimensional relationships between the canard (subscript c) and the wing (subscript w) are as follows: , 0.2 , 0.45 AR AR S S c c c w c w c w a. Develop an expression for the pitching moment coefficient about the center of gravity. Neglect the upwash/downwash effects between the lifting surfaces and the drag contribution to the pitching moment. Also assume small angles. b. Find the location of the CG where 0 Cm , assuming canard efficiency of 1. Note: this point is called neutral point, and it is similar in concept to aerodynamic center of an airfoil. c. For the aircraft to be statically stable longitudinally, should the center of gravity be forward or aft of the neutral point. Briefly provide an explanation for your answer. 3. (50 pts.) The longitudinal data of a business jet aircraft flying in subsonic speed is given below. The CG of the aircraft is at 25% MAC ( 0.25c ). Note that because the sweep angle (Λ) on the wing and tail, CL for the wing and tail should be corrected according to , , no sweep cos C C L L 2 The variation of the fuselage width and camber angle as a function of the axial location along the fuselage is shown in the following table: Assume the pitching moment contribution of each aircraft component varies linearly with angle of attack according to 0 + C C C m m m . Determine for the flying condition above: a. the wing contribution to the aircraft pitching moment. b. the tail contribution to the aircraft pitching moment (assume 0 0, 3 , 1 w t i i ). c. the fuselage contribution to the aircraft pitching moment (assume 14.1 ft h l ). d. the total aircraft pitching moment, assuming contributions from wing, tail, and fuselage only. Is this aircraft statically stable and trimmable longitudinally? Briefly explain. e. Sketch the various contributions above, including the total pitching moment, on a vs. Cm graph (use a graph paper or using a plotting software).

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Aircraft Stability and Control
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