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lectures-airplane-stability

# lectures-airplane-stability - 650:460 Aerodynamics Airplane...

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Unformatted text preview: 650:460 Aerodynamics Airplane Stability Prof. Doyle Knight Tel: 732 445 4464, Email: [email protected] Office hours: Tues and Thur, 4:30 pm - 6:00 pm and by appointment Fall 2009 1 Static Stability and Control • Introduction An aircraft is in trim if the sum of the forces and moments about its center of gravity (cg) is zero The center of gravity is the point about which the aircraft could be suspended by a cable in quiescent air and would not rotate Stability of an aircraft is the movement in returning, or tendency to return, to a given state of equilibrium which is referred to as trim Static stability is the tendency of the aircraft to return to a trimmed condition when disturbed Dynamic stability includes the time-dependent behavior of the aircraft when disturbed from its equilibrium condition Static stability is a necessary but not sufficient condition for dynamic stability. 2 Static Stability and Control 3 Static Stability and Control • Longitudinal Static Stability Consider an aircraft at trim condition A If the aircraft angle of attack α is changed to A ′ , there are two possible cases. Point B : This is unstable, since the pitching moment M is positive and therefore will increase α 4 Static Stability and Control • Longitudinal Static Stability Consider an aircraft at trim condition A Point C : This is stable, since the pitching moment M is negative and therefore will decrease α Same analysis holds for an initial negative change in α Thus, longitudinal static stability implies dM cg / d α < 5 Static Stability and Control • Wing-tail combination All angles relative to the zero lift line of the wing or tail Consider the wing at zero angle of attack ( i.e. , no lift on wing) The moment about the cg is M = M ac- l t L t For a positively cambered wing, M ac < 0 and thus L t must be negative, i.e. , the tail incidence angle i t must be downwards. Note that i t > 0 as shown by assumption. 6 Static Stability and Control At non-zero angle of attack for the wing, the moment about cg is M cg = M ac + l w L w- l t L t where l w distance from aerodynamic center to center of gravity (positive if cg is aft of ac) l t distance from center of gravity to tail ( postive if cg is forward of tail) 7 Static Stability and Control Longitudinal static stability dM cg d α < implies l w dL W d α < l t dL t d α This can be achieved by making l w sufficiently small, e.g. , by placing the cg close to (or ahead of) the aerodynamic center, or by making l t sufficiently large 8 Static Stability and Control • Total airplane lift The wing is represented by a rectangular airfoil with mean aerodynamic chord ¯ c = S / b The wing affects the flowfield in the vicinity of the tail 9 Static Stability and Control • Total airplane lift The principal effect is to reduce the angle of attack as seen by the tail α t = α w- i t- ǫ α α where ǫ α = d ǫ/ d α and ǫ is the downwash angle at the tail 10 Static Stability and Control The lift on the wing is L w...
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lectures-airplane-stability - 650:460 Aerodynamics Airplane...

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