Aircraft Stability Analysis Including Unsteady Aerodynamic Effects

65C2( ν ) = a + b ν c νN i 6 6 i+φ 6 iC ( v ) = a + b v + c v2N φ3 i 7 7 i 7 iC ( v ) = a + b v + c v2N φ5 i 8 8 i 8 iC +N2( vi) = a9+ b9vic9viφ & (2-33)C ( v ) = a + b v + cN23 i 10 10 i 10 ivφ & 2C ( v ) = a + b v + cN2 φ i 11 11 i 11 ivφ & 2C ( v ) = a + b v + cN φ & φ2 i 12 12 i 12 ivV = free stream airspeed.The coefficientsa , b , cjjj, are functions of the angle of attack, and are determined by aleast-squares fit with the experimental data. The expansion terms in Eq. (2-31) werepicked in order to match the expansion developed by Konstadinopoulos, Mook, andNayfeh for ( φ)C in [53].lThe parameters to be identified using wind tunnel data for this postulated model aredependent on the pitch angle θ0at which the identification is done. They are:- the polynomial coefficients C N0 , a j , b j , c j, j = 1,2,3,4, 5 of Eqs. (2-29) and (2-30);- the polynomial coefficients a j , b j , c j , j = 6,7, 8 ,9,10,11,12 of Eqs. (2-31) and (2-33);- transient time-constants τ1x, τ1y, τ1vappearing respectively in Eqs. (2-13), (2-14), and(2-15);- time-delay constants τ , α2, τ , φ2from Eqs. (2-21) and (2-24);