Aircraft Stability Analysis Including Unsteady Aerodynamic Effects

23In equation (1-19)∗αwdescribes the location of this function, σwis the slope factor, andαwiis the local angle of attack of the wing panel at a location along the wing span at adistancel wfrom the axis of the fuselage. In this work the primary concern is with purerolling oscillatory motions. For this kind of motion the local velocity components at thatlocation can be expressed in the body-axis system as (see Appendix A.2),uw= V Tcosθ 0v = V sinθsinφw T 0(1-20)ww= V sinθcosφl & φT0m wwhere the negative sign corresponds to the left wing panel while the plus sign to the rightwing panel. The angle of attack and the sideslip angle are defined as,wα = tan −1u(1-21)β = sin−1u2v+ v2+ w2Subtituting (1-20) into (1-21), the local angle of attack values for the left and right wingpanels can be calculated throughααwlwr= tan= tan−1−1⎛⎜ tanθ0cosφ−⎝V⎛⎜ tanθ0cosφ+⎝VTTl & ⎞wφ⎟cosθ0⎠l & ⎞wφ⎟cosθ0⎠(1-22)The output of the system (1-18) iswing panel. The derivativesC Nwi, the normal force coefficient on the left or rightC α( x ) and ( x )NwiwiC α&are modeled as,Nwiwi