1. March 10, 20051 Dynamics & Controls 2 PDR Michael Caldwell Jeff Haddin Asif Hossain James Kobyra John McKinnis Kathleen Mondino Andrew Rodenbeck Jason Tang Joe Taylor Tyler Wilhelm AAE 451: Team 2

2. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 2 Overview Aircraft 3-View Trim Diagram Loop Closure Description Block Diagram Aircraft Transfer Function Pitch Rate Gyro Transfer Function Servo Transfer Function Gain Calculation Root Locus, Bode, and Nyquist Plot

3. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 3 Mission Requirements 15 min. endurance Take-off distance ≤ 60 ft. V stall ≤ 15 ft/s V loiter ≤ 25 ft/s 35 ft. turn radius Aircraft 3-View

4. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 4 Effect of Control Surface Deflection: Lift Roskam,Jan, Airplane Design PartVI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000

5. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 5 Effect of Control Surface Deflection: Pitching Moment Roskam,Jan, Airplane Design PartVI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000

6. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 6 Trim Diagram C L Max Trimmed Maximum C L (x ref = x cg ) α CL Max α = 0 o

7. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 7 Loop Closure Description Pitch Rate feedback to the Elevator Objectives: 1) Establish longitudinal stability by using pitch rate feedback by varying damping ratio of the short period mode from 0.83 to 0.99. 2) Numerical values for all physical constants in the transfer functions.

8. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 8 Block Diagram H e (s) q(s)/  e (s) H (s)K  Pilot Input Elevator Servo Aircraft  e (s ) q(s) + _ Pitch Rate Gyro Feedback Gain

9. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 9 Dynamic Models Aircraft Transfer Function

10. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 10 Longitudinal Non-Dimensional Stability Derivatives Pitching moment coefficient due to elevator deflection Pitching moment coefficient due to angle of attack Pitching moment coefficient due to rate of change of angle of attack Pitching moment coefficient due to pitch rate Lift coefficient due to elevator deflection = -0.029 = -0.008 = -0.518 = -0.011 = -11.72 Equation Description Value

11. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 11 Longitudinal Dimensional Stability Derivatives Pitch angular acceleration per unit elevator angle Vertical acceleration per unit elevator angle Pitch angular acceleration per unit angle of attack Pitch angular acceleration per unit rate of change of AOA Vertical acceleration per unit angle of attack Pitch angular acceleration per unit pitch rate Equation Description Value = -30.04 [(rad/s 2 )/rad] = -32.39 [(ft/s 2 )/rad] = -0.007 [(rad/s 2 )/rad] = -9.13 [(rad/s 2 )/(rad/s)] = -243.25 [(ft/s 2 )/rad] = -8.61 [(rad/s 2 )/(rad/s)]

12. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 12 Dynamic Models Aircraft Transfer Function (short Period Approx.) Aircraft Transfer Function (Flat Earth Predator)

13. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 13 Natural Frequency and Damping Ratio Undamped Natural Frequency Damping Ratio

14. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 14 Dynamic Models Pitch Rate Gyro Transfer Function Futaba GYA350 Gyro :  The Gyro Mixer  The Gyroscope or Sensor  The Switch/Gain Control Unit (SW Unit)

15. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 15 Dynamic Models Servo Transfer Function Hitec HS-55 Economy Sub Micro Servos The servo is used to convert voltage (  v ) to elevator deflection (  e )

16. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 16 Gain Calculation, k First Trial: Determine k by trial and error: - Using the modified DesignPitch.m file - Matlab code to approximate short period mode Second Trial: - Flat Earth Predator - SISOTOOL k = 0.0857

17. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 17 Root Locus

18. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 18 Root Locus

19. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 19 Gain Calculation, k For k = 0 For k = 0.0857

20. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 20 Bode Plot

21. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 21 Nyquist Plot

22. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 22 Questions ?

23. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 23 Appendix

24. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 24 Tail Sizing Comparison Class 1 SizingClass 2 Sizing Canard Area S ht 1.432 ft 2 1.557 ft 2 Vertical Tail Area S vt (each) 0.915 ft 2 0.912 ft 2

25. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 25 Control Surface Sizing Span (ft)Chord (ft)Area (ft 2 ) Aileron 2.620.200.524 Elevator 1.920.330.634 Rudder (each) 0.820.500.410

26. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 26 Control Surface Comparison Team 2 Spring 2005 Team 1 Fall 2004 Team 4 Fall 2004 Aileron Area Wing Area 0.1000.204.0102 Elevator Area Canard Area 0.4420.1980.258 Rudder Area Vtail Area 0.4480.4000.326 *Areas compared – Ongoing Research for Moments

27. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 27 Actual Static Margin X cg = 1.70 ft X np = 1.85 ft Static Margin = 14.80%

28. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 28 Variation of Yawing Moment Coefficient with Sideslip Angle Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

29. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 29 Variation of Rolling Moment Coefficient with Sideslip Angle Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

30. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 30 Variation of Pitching Moment Coefficient with Elevator Angle Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

31. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 31 Variation of Yawing Moment Coefficient with Rudder Deflection Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

32. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 32 Variation of Rolling Moment Coefficient with Aileron Deflection Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

33. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 33 Longitudinal Static Stability Aircraft starting from straight, level, trimmed flight with small perturbations has two independent natural motions acting about an aircraft’s pitch axis. Longitudinal Modes: 1. Short Period Mode (Heavy damping and high frequency) 2. Phugoid Mode (Less damping and low frequency)

34. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 34 Longitudinal Static Stability Short Period Mode:

35. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 35 Longitudinal Static Stability Phugoid Mode:

36. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 36 Longitudinal Static Stability Short Period Mode Phugoid Mode

37. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 37 Lateral Directional Stability Lateral directional EOMs can be expressed by a second order differential equation and two first order differential equations. Lateral-directional Modes: 1. Dutch Roll Mode 2. Spiral Mode 3. Roll Mode

38. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 38 Lateral Directional Stability Dutch Roll mode:

39. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 39 Lateral Directional Stability Dutch Roll mode: Spiral Mode: Roll Mode:

40. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ]123456789101112131415161718192021 March 10, 2005 40 Lateral Directional Stability Desired spiral mode time constant is excess of 20 seconds Desired roll mode time constant is 0.5 to 3 seconds