Aircraft Stability Analysis Including Unsteady Aerodynamic Effects

19tˆ =c2V, (1-17)c being a characteristic length, and V the airspeed. It is worthwhile noting that theconvective timec is related to the time it takes for an air molecule to travel along theVwing mean aerodynamic chord. The factor ½ is included in Eq. (1-17) because it wasused to determine the non-dimensional pitch rate in most of the references related tounsteady aerodynamics and flight dynamics. The reason for that is probably just tradition.The mid-chord was historically taken as the coordinate origin for a pitching airfoil inunsteady aerodynamics analysis and, as a natural consequence, the semi-chord wasintroduced as the characteristic length [37],[38].The stability derivatives in Eq. (1-16) are defined as quadratic polynomials of the nondimensionalstate variable x , that isC( x)= a + b x c xaa a+χ χ χa χ2,where a is the type of aerodynamic coefficient, and χ represents the motion variables2 2with respect to which the partial derivatives were taken. In this case, χ = α , qˆ,α , qˆ, αqˆ.In [32] this formulation was used to represent the static hysteresis of an NACA 0018airfoil, reported in [31]. The comparison between wind tunnel data and model responsesfor pitching moment and normal force coefficients can be seen in Figure 1-5 and Figure1-6, respectively. They show that this formulation matches very well experimentalresults.