Aircraft dynamics mode simulation
- 1. SIMULATION OF AIRCRAFT DYNAMICS- LONGITUDINAL MODE Minor Project
- 2. Group description Name Roll No. Batch Mahendra Gehlot 15/551 A1 Mousam Kumari 15/562 A1 Krishna Shekhawat 15/544 A1 Ishank Srivastava 15/679 A1 Under the supervision of – Mr. Mohammed Shahid Assistant Professor Rajasthan Technical University, Kota Submitted to- Mr. Brijesh Tripathi Mr. Anshul Khandelwal
- 3. Objectives • Simulation of Aircraft Dynamics (Longitudinal Mode) for Boeing 747. • Error calculation of exact solution to approximate solution for short and phugoid mode. • Visualization of Aircraft Dynamic time history of various parameter of longitudinal mode for exact solution (Boeing 747).
- 4. Project outline Aircraft Equations of motion Decoupling of EOM Longitudinal EOM Selection of aircraft Step 1 Mathematical Modelling on MATLAB Short Period Approximation Phugoid Period Approximation Step 2 Simulink Model Results Error Calculation Step 3 Visualisation of Simulation Conclusion Step 4
- 5. Introduction Aircraft Stability Static Stability Dynamic Stability Aircraft stability - Ability of aircraft to correct for conditions that are acting on it Initial tendency of an aircraft to return to its original position when it’s disturbed How airplane responds over time to disturbance
- 6. Various Modes of Dynamics Stability Longitudinal mode - Phugoid (longer period) oscillations - Short period oscillations Lateral-Directional Modes - Roll subsidence mode - Dutch roll mode - Spiral divergence
- 7. Aircraft Equations of Motion There are six equation of motion of aircraft consist of: - Longitudinal Equation of Motion - Lateral and Direction Equation of Motion • The six aircraft equation of motion (EOM) can be decoupled into two sets of three equations. • These are the three longitudinal EOM and the three lateral-directional EOM. • This is convenient in that it requires only three equations to be solved simultaneously for many flight conditions.
- 8. Longitudinal Equations of Motion One way of the thinking of the longitudinal EOM is to picture an aircraft with its xz plane coincident with an xz plane fixed in space. Longitudinal motion consists of those movements where aircraft would only move within that xz plane, that is, translation in the x direction, translation in the z direction and rotation about y axis.
- 9. Longitudinal Equations of Motion The three longitudinal EOM consist of the x force, and z force, and y moment equations Where U,V, and W are the velocities in the x, y, and z body axes, respectively. P,Q, and R are the roll, pitch and yaw rates respectively.
- 10. Simulation Model : Boeing 747-200
- 11. Approximations Short Period Approximation The period is so short that the speed does not have time to change, so the oscillation is essentially an angle-of- attack variation. The motion is a rapid pitching of the aircraft about the centre of gravity. Its damping ratio and natural frequency is high. Percentage error from exact Solution is negligible. Phugoid Approximation Large-amplitude variation of air-speed, pitch angle, and altitude, but almost no angle-of-attack variation. It has a nearly constant angle of attack but varying pitch, caused by a repeated exchange of airspeed and altitude. Its damping ratio and natural frequency is low. Percentage error is approximately 30- 40% compared with exact solution.
- 12. Simulink Model (linear) – extended from MATLAB workspace
- 13. Exact Solution
- 14. Exact Solution
- 15. Results Exact Solution Mode Natural Frequency Damping Ratio Short Period 1.3201 0.3555 Phugoid 0.0333 0.9625 Approximate Solution Mode Natural Frequency Damping Ratio Short Period 1.3328 0.3530 Phugoid 0.0452 0.7307 Percentage Error in Approximate Solution Mode Natural Frequency Damping Ratio Short Period 0.96 0.70 Phugoid 35.73 24.08
- 16. Conclusion The phugoid approximations provide poor estimates while the short period approximations are accurate. Time taken in short period mode to reach the equilibrium is 40-50 seconds after being disturbed and 280-300 seconds for phugoid mode.
Editor's Notes
- #2: NOTE: Want a different image on this slide? Select the picture and delete it. Now click the Pictures icon in the placeholder to insert your own image.