AAE 451 DYNAMICS CONTROL QDR 3 TEAM 4

AAE 451 DYNAMICS & CONTROL QDR 3 TEAM 4 Jared Hutter, Andrew Faust, Matt Bagg, Tony Bradford, Arun Padmanabhan, Gerald Lo, Kelvin Seah December 2, 2003

TEAM 4 OVERVIEW n Aircraft Walk-Around n Tail Re-Sizing n Stability Check n Modal Analysis n 6 -DOF Simulation

TEAM 4 CONCEPT REVIEW Empennage High Wing Horizontal and Vertical Tails S = 39. 3 ft 2 b = 14. 0 ft, c = 2. 8 ft AR = 5 UPDATED Avionics Pod 20 lb; can be positioned front or aft depending on requirements Twin Engine 1. 8 HP each Twin Booms 3 ft apart; 5. 7 ft from Wing MAC to HT MAC

TEAM 4 CONCEPT REVIEW Empennage High Wing Horizontal and Vertical Tails RESIZED S = 39. 3 ft 2 b = 14. 0 ft, c = 2. 8 ft AR = 5 UPDATED Avionics Pod 20 lb; can be positioned front or aft depending on requirements Twin Engine 1. 8 HP each Twin Booms 3 ft apart; 5. 7 ft from Wing MAC to HT MAC

TEAM 4 TAIL RE-SIZING n Horizontal and Vertical Tails were resized using updated Wing Geometry. n Modified Class 1 Approach: ¨ Fixed volume coefficients, get new tail size; ¨ Verified results with OEI yaw-trimming with rudder; ¨ Verified stability of modal responses; ¨ Iterated …

TEAM 4 TAIL RE-SIZING RESULTS VERTICAL TAIL HORIZONTAL TAIL = 9. 01 ft 2 1. 00 ft 1. 68 ft ½ = 1. 80 ft 2 2. 69 ft 1. 19 ft 3. 0 ft 1. 19 ft 5. 37 ft 1. 68 ft Volume Coefficients: Chord-wise Span-wise = 0. 50 • Elevator 0. 84 ft 2. 67 ft = 0. 04 • Rudder 0. 35 c. VT 2. 42 ft

TEAM 4 RUDDER DEFLECTION IN OEI CONDITIONS n Roskam (AAE 421 Textbook) n Required rudder deflection: FAR 23, 25 Limit Max Deflection n DRn. O: = 28 ft/s n Deflection Limit: n FAR 23, 25 requires that 1. 2 for = 0° n In this case, = 29. 57 ft/s Stall Speed Limit = 25°

TEAM 4 MODAL ANALYSIS n n Mode Poles Natural Frequency (rad/sec) Damping Ratio Dutch Roll -0. 86 ± j 1. 50 1. 73 0. 497 Lateral-Directional Subsystem Roll -5. 22 Spiral -0. 84 Side Velocity 0 Mode Poles Natural Frequency (rad/sec) Damping Ratio Phugoid -0. 05 ± j 0. 61 0. 084 0. 616 Longitudinal Subsystem Short Period -7. 59, -34. 80 Altitude ≈0

TEAM 4 MIL-F-8785 C GUIDELINES n Mode Poles Natural Frequency (rad/sec) Damping Ratio Dutch Roll -0. 86 ± j 1. 50 1. 73 0. 497 Lateral-Directional Subsystem Roll -5. 22 Spiral -0. 84 Side Velocity 0 0. 4, OK! 0. 08, OK! Stable, non-oscillatory – OK! Stable, does not diverge – OK! n Mode Poles Natural Frequency (rad/sec) Damping Ratio Phugoid -0. 05 ± j 0. 61 0. 084 0. 616 Longitudinal Subsystem Short Period -7. 59, -34. 80 Altitude ≈0 “Must be heavily damped” – OK!

TEAM 4 6 -DOF SIMULATION n The 6 -DOF motion was simulated in MATLAB. n Assumed flat earth, rigid body and steady winds. n Aircraft was trimmed at loiter conditions, and linearized the system about trim. n Comparisons between nonlinear and linear time responses: ¨ Elevator Step Input, e = 5° ¨ Aileron Step Input, a = 5° ¨ Rudder Step Input, r = 5°

TEAM 4 6 -DOF SIMULATION WITH ELEVATOR STEP INPUT

TEAM 4 6 -DOF SIMULATION WITH AILERON STEP INPUT

TEAM 4 6 -DOF SIMULATION WITH AILERON STEP INPUT

TEAM 4 6 -DOF SIMULATION WITH AILERON STEP INPUT

TEAM 4 6 -DOF SIMULATION WITH RUDDER STEP INPUT

TEAM 4 6 -DOF SIMULATION WITH RUDDER STEP INPUT

AAE 451 QUESTIONS?

AAE 451 APPENDIX

TEAM 4 RUDDER DEFLECTION IN OEI CONDITIONS ref. “Airplane Flight Dynamics and Automatic Flight Controls” (Roskam) Section 4. 2. 6 [rad] where @ 2, 000 ft for fixed pitch [slug/ft 3] V [ft/sec] P [hp] y. T [ft]

TEAM 4 IDENTIFICATION OF POLES n Lateral-Directional Subsystem Dutch Roll Mode n Only pole in this subsystem with both e and m parts. ¨ Roll Mode n Pole is negative; relatively large magnitude. ¨ Spiral Mode n Can be positive (in the case of the Predator), or negative. Small magnitude, so not typically a problem. ¨ Side Velocity Mode n Only pole in this subsystem that has zero magnitude. ¨

TEAM 4 IDENTIFICATION OF POLES n Longitudinal Subsystem Phugoid Mode n Complex conjugate pair. The m parts have a smaller magnitude than that of the other conjugate pair, indicating longer period (lower frequency). e parts are of small value, light damping. ¨ Short Period Mode n Complex conjugate pair. The m parts have a larger magnitude than that of the other conjugate pair, indicating shorter period (higher frequency). e parts are of larger value, heavier damping. ¨ Altitude Pole n Only pole in this subsystem that is purely real. ¨