You are a flight test engineer who wants to find the aerodynamic center of an aircraft that can be de- scribed using the longitudinal model studied in class. You have access to accurate aircraft weight, balance and geometry data as well as in-flight telemetry of the aircraft's elevator deflection and dynamic pressure. Furthermore, you have a means of shifting the aircraft's center of gravity. In this problem, we explore the relationship between Tac, Teg, detrim and Crim to show how one can compute Tac given the data described above. 1. If the weight of the aircraft is W and the wing planform area is S, what is the trimmed lift coefficient, CLtrim for steady level flight at a dynamic pressure q? 2. In class, we derived an expression for dem Using that and your answer to the previous part, find an expression for detrim/dCLtrim in terms of CL CL, CM and CM* 3. Write an expression for CM, in terms of Tac, Teg and CL 4. Write an expression for CM, in terms of Teg, Tac, and CLS 5. Use your answers from parts 3 and 4 to find an expression for (CMCL - CMS, CL.) in terms of CL CL Tac and Tact 6. Use your answers from parts 2, 3 and 5 to show that detrim dC Ltrim -(Tac-Teg) CLS (Tac-Tac)" (1) 7. If this aircraft is statically stable, is de positive or negative? Explain by analyzing the signs of (Tac Teg), CLs, and (Tac-Tac). - dC Larim You've finished your analysis! Note that equation (1) is a linear function of Teg; the remaining variables do not vary as you move the CG. This means that if we measure doetrim/dC Lim for different CG locations, we can fit a line to the data and extrapolate from that line to find what value of Teg would satisfy doctim/dC Ltrim = 0. This value is the aircraft's aerodynamic center, Tac. For a fixed CG, to find doerim/dCLim we can choose an altitude and record what de is required to trim the aircraft at different airspeeds. Each airspeed at the fixed altitude will correspond to different dynamic pressures, which each correspond to different values of CLim by the relation you derived in part 1. Thus, we can fit a line to our derim VS CLtrim data to compute detrim/dCrim for that CG location.