1. February 24, 20051 Dynamics & Controls 1 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. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 2 Overview Tail Sizing (Class 1) Control Surface Sizing Tail Sizing (Class 2) Center of Gravity Aerodynamic Centers Static Margin Dihedral Angle Stability Longitudinal Static Stability and Modes Lateral Directional Stability and Modes

3. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 3 Aircraft 3-View Mission Requirements 15 min. endurance Take-off distance ≤ 60 ft. V stall ≤ 15 ft./s V loiter ≤ 25 ft./s 35 ft. turn radius

4. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 4 Tail Sizing (Class 1) Tail Areas  S HT = c HT C w S w /L HT  S VT = c VT b w S w /L VT c HT = Horizontal tail volume coefficient c VT = Vertical tail volume coefficient C w = Wing mean chord S w = Wing planform area L HT = Horizontal tail moment arm L VT = Vertical tail moment arm

5. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 5 Tail Sizing (Class 1) Constants  c HT = 0.50  c VT = 0.05  C w = 1 ft  S w = 5.24 ft  L HT = 1.83 ft  L VT = 0.75 ft Horizontal tail  Area = 1.432 ft 2 Vertical tail (canard)  Area = 0.915 ft 2 (each)

6. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 6 Control Surface Sizing Typical Values (Raymer)  Aileron 50-90% span & 15-25% chord  Elevator 90% span & 25-50% chord  Rudder 90% span & 25-50% chord

7. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 7 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

8. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 8 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

9. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 9 Tail Sizing (Class 2) Horizontal Tail  Plot X cg and X ac versus S ht  S ht = 1.557 ft 2 15%

10. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 10 Tail Sizing (Class 2) Vertical Tail  Plot X cg and X ac versus S ht  S ht = 0.912 ft 2

11. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 11 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

12. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 12 Center of Gravity Canard/Batteries Propeller Motor Booms Receiver & Servos Wing Fuselage Speed Controller Vertical Tail CG CG at 1.7077 ft from leading edge

13. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 13 Aerodynamic Centers Aerodynamic centers of wing and canard each at the quarter- chord position

14. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 14 Aircraft Neutral Point C L  = Wing Lift curve slope X acw = Location of Wing Aerodynamic Center C m  fus =Fuselage pitching moment  h = Ratio of tail dynamic pressure to freestream dynamic pressure C L  h = Horizontal Tail Lift curve slope X ach = Location of Horizontal tail Aerodynamic Center

15. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 15 Desired Static Margin Static Margin (Raymer)  Typical Fighter Jet: 0-5%  Typical Transport Aircraft = 5-10%  Model aircraft usually more stable Goal: Static Margin = 15%

16. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 16 Actual Static Margin X cg = 1.70 ft X np = 1.85 ft Static Margin = 14.80%

17. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 17 Dihedral Angle Equivalent V-Dihedral (EVD) It is helpful to express required and actual dihedral of an aircraft in terms of “Equivalent V-dihedral.”

18. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 18 Dihedral Angle Outer Panel Dihedral Wing: 4 deg outer panel dihedral, B=4 deg and x at 0.9 ft Canard: -4 deg outer panel dihedral, B=4 deg and x at 0.08 ft

19. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 19 Dihedral Angle EVD of the wing and canard: Wing EVD: Canard EVD:

20. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 20 Effective Wing Area “Effective wing area that is contributing to the lift:

21. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 21 Stability Characteristic Equation Roots of the characteristic equation,

22. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 22 Stability Longitudinal Static Stability Lateral Directional Stability

23. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 23 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)

24. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 24 Longitudinal Static Stability Short Period Mode:

25. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 25 Longitudinal Static Stability Phugoid Mode:

26. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 26 Longitudinal Static Stability Short Period Mode Phugoid Mode

27. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 27 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

28. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 28 Lateral Directional Stability Dutch Roll mode:

29. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 29 Lateral Directional Stability Dutch Roll mode: Spiral Mode: Roll Mode:

30. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 30 Lateral Directional Stability Desired spiral mode time constant is excess of 20 seconds Desired roll mode time constant is 0.5 to 3 seconds

31. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 31 Summary Tail Sizing (class 1 & 2) Control surface sizing Aerodynamic center and C.G. Locations Dihedral Angles Longitudinal Static Stability and modes Lateral Directional Stability and modes

32. [ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]Overview3-View12123123CG121212341212341234Summary February 24, 2005 32 Questions Polygonia interrogationis known as Question Mark