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lecture_2 - 16.333 Lecture#2 Static Stability Aircraft...

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16.333: Lecture #2 Static Stability Aircraft Static Stability (longitudinal) Wing/Tail contributions 0
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Fall 2004 16.333 2–1 Static Stability Static stability is all about the initial tendency of a body to return to its equilibrium state after being disturbed To have a statically stable equilibrium point, the vehicle must develop a restoring force/moment to bring it back to the eq. condition Later on we will also deal with dynamic stability , which is concerned with the time history of the motion after the disturbance Can be SS but not DS, but to be DS, must be SS SS is a necessary, but not sufficient condition for DS To investigate the static stability of an aircraft, can analyze response to a disturbance in the angle of attack At eq. pt., expect moment about c.g. to be zero C M cg = 0 If then perturb α up, need a restoring moment that pushes nose back down (negative)
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Fall 2004 16.333 2–2 Classic analysis: Eq at point B A/C 1 is statically stable Conditions for static stability ∂C M C M = 0; < 0 ∂α C M α note that this requires C M | α 0 > 0 Since C L = C L α ( α α 0 ) with C L α > 0 , then an equivalent condition for SS is that ∂C M < 0 ∂C L
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Fall 2004 16.333 2–3 Basic Aerodynamics i w X cg X ac L w Z cg M ac w D w c.g. FRL w Fuselage Reference Line (FRL) Wing mean chord Take reference point for the wing to be the aerodynamic center (roughly the 1/4 chord point) 1 Consider wing contribution to the pitching moment about the c.g. Assume that wing incidence is i w so that, if α w = α F RL + i w , then α F RL = α w i w With x k measured from the leading edge, the moment is: M cg = ( L w cos α F RL + D w sin α F RL )( x cg x ac ) +( L w sin α F RL D w cos α F RL )( z cg ) + M ac w Assuming that α F RL 1 , M cg ( L w + D w α AF RL )( x cg x ac ) +( L w α F RL D w )( z cg ) + M ac w But the second term contributes very little (drop) 1 The aerodynamic center (AC) is the
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