Aircraft Stability Analysis Including Unsteady Aerodynamic Effects

71When the quasi-static sequences of experimental data are considered, the error costfunctionsto be minimized are as follows,j= 1 i=1r[ ] 2θ , φ xN Mr 1ε ( ) ˆCNxC = ∑∑ CN( θ0 i, φj) − CN(0ij,NC)NM * Nr( x ) =1 C ∑∑[ Cˆl( θi j) − Cl(i jxC ]l0, φ θ0, φ ,rlN M 2εCl)M * Nj= 1 i=1(3-1)(3-2)where each value of the roll angle in the sequence φj, j = 1,2, ... , N has a correspondingsequence of values for the wind tunnel sting pitch angle θ0i, i = 1,2, ... , M, as shown inFigures 1-17 and 1-18. At these points, the wind tunnel measurements are{ Cˆ( θ , φ ),Cˆ( θ , φ );i = 1,2,..., M ; j 1,2 N}N 0 i j l 0ij= ,...,, while the model responses determinedat the same points for a given sets x r C, x rN Cof model parameters arelrr{ CN ( θiφj, x ),Cl( θi, φj, xC);i = 1,2,..., M;j 1,2,...,N}.0,C N 0=lWhen the published values of wind tunnel dynamic measurements at unsteady flowconditions are used to identify parameters, one roll angle time history { ( t ),0 ≤ t ≤ T }φ ,iiFsuch that0 = t1< t2< ... < ti< ti+ 1< ... < tL= TF, is taken for each fixed value of the stingpitch angle θ0in the sequenceθ0 k, k = 1, 2, ... , K . If the corresponding dynamic windtunnel measurements of the rolling moment coefficient can be represented by{ Cˆ( ( t , θ ));i = 1,2,..., L;k 1,2 K}φ and the values of the model responses calculatedl i 0= ,...,at the same points for given set x r dynof model parameters arer{ C ( φ ( t , θ0 ),x); i 1,2,..., L;k = 1,2 K= }, the error cost-function for the dynamic phasel i,...,of the identification is