Aircraft Stability Analysis Including Unsteady Aerodynamic Effects

581x0 ( αi) =1+exp(2-6)N α( −σ( α −α∗)2( x ) = a + b x c xC +N αi112( x ) = a + b x c xC +22 ii i2( x ) = a + b x c xC +2ii12iN α& ˆ i 3 3 i 3 i(2-7)N α& ˆ2( x ) = a + b x c xC +N α ˆ & α42 ii i2( x ) = a + b x c xC +i545i45iThe parameters of this formulation that must be identified are:- the polynomial coefficients C N0 , a i , b i , c i of Eqs. (2-7);- transient time-constant τ1, xand time-delay constant τ 2 , α of Eq. (2-2), functions of thewing pitch angle θ0at which the dynamic experimental data are obtained;∗- the parameters α and σ of the logistic equation (2-6) that represent the static positionof the vortex breakdown over the panel. They are left free to vary with the roll angle atwhich the static experimental data was obtained and, therefore, there are one of each ofthese parameters for each static experimental value of the roll angle;- the normal force arms y , y , which are also varying with the roll angle at which thestatic experimental data are obtained.lrThe identification of these parameters is described in further detail in Section 3.3.As shown in Figures 3-4 to 3-9, the responses obtained for this, the first modelinvestigated did not match the experimental data very well. Because of that, a secondunsteady aerodynamic model was developed. Next, we present its description.