This paper determines the worst-case gust response of a typical airfoil section with a control surface. Matched filter theory is employed in order to compute the gust that produces a maximum response. These results are compared with a tuned one-minus-cosine gust, one of the standard representations of discrete gusts. It is found that the responses obtained by the matched filter theory are about twice as large as those obtained using the one-minus-cosine gust. Moreover, it is found that the hinge stiffness of the control surface can affect the plunging motion.
Nomenclature= aerodynamic force vector caused by the gust,frequency response function of airplane h = plunge displacement, 2bn h y (t) = unit impulse response I α , I β = mass moment of inertia about elastic axis, control surface hinge J 0 (k), J 1 (k) = Bessel function of the first kind K = arbitrary constant k = reduced frequency, ωb/U L = scale of turbulence L G = lift caused by gust L M = lift caused by wing motion L M C , L M NC = lift of the circulatory flow, noncirculatory flow M G α , M G β = moment caused by gust M M α , M M β = moment caused by wing motion m = airfoil total mass n = gust gradient distance in chords p, s = Laplace variable R = ratio of standard deviations S α , S β = static moment T i = aerodynamic coefficient t = time t 0 , τ 0 = arbitrary time shift U= airspeed w G = upwash caused by gust w 0.75c = downwash at 75% chord w 1 − cos = maximum velocity of discrete gust