DYNAMICS & CONTROL QDR 3 TEAM 4 Jared Hutter, Andrew Faust, Matt Bagg, Tony Bradford, Arun Padmanabhan, Gerald Lo, Kelvin Seah December 2, 2003
OVERVIEW Aircraft Walk-Around Tail Re-Sizing Stability Check Modal Analysis 6-DOF Simulation
CONCEPT REVIEW Empennage High Wing UPDATED Avionics Pod Twin Booms Horizontal and Vertical Tails High Wing S = 39.3 ft2 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 Booms 3 ft apart; 5.7 ft from Wing MAC to HT MAC Twin Engine 1.8 HP each
CONCEPT REVIEW Empennage RESIZED High Wing UPDATED Avionics Pod Horizontal and Vertical Tails RESIZED High Wing S = 39.3 ft2 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 Booms 3 ft apart; 5.7 ft from Wing MAC to HT MAC Twin Engine 1.8 HP each
TAIL RE-SIZING Horizontal and Vertical Tails were resized using updated Wing Geometry. 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 …
TAIL RE-SIZING RESULTS HORIZONTAL TAIL VERTICAL TAIL = 9.01 ft2 1.00 ft 1.68 ft ½ = 1.80 ft2 2.69 ft 1.19 ft 3.0 ft 1.19 ft 5.37 ft 1.68 ft Volume Coefficients: = 0.50 = 0.04 Chord-wise Span-wise Elevator 0.84 ft 2.67 ft Rudder 0.35 cVT 2.42 ft
RUDDER DEFLECTION IN OEI CONDITIONS Roskam (AAE 421 Textbook) Required rudder deflection: DRnO: = 28 ft/s Deflection Limit: = 25° FAR 23, 25 requires that for = 0° In this case, = 29.57 ft/s FAR 23, 25 Limit Max Deflection 1.2 Stall Speed Limit
MODAL ANALYSIS Lateral-Directional Subsystem Longitudinal Subsystem Mode Poles Natural Frequency (rad/sec) Damping Ratio Dutch Roll -0.86 ± j 1.50 1.73 0.497 Roll -5.22 Spiral -0.84 Side Velocity Mode Poles Natural Frequency (rad/sec) Damping Ratio Phugoid -0.05 ± j 0.61 0.084 0.616 Short Period -7.59, -34.80 Altitude ≈ 0
MIL-F-8785C GUIDELINES Lateral-Directional Subsystem Longitudinal Subsystem Mode Poles Natural Frequency (rad/sec) Damping Ratio Dutch Roll -0.86 ± j 1.50 1.73 0.497 Roll -5.22 Spiral -0.84 Side Velocity 0.4, OK! 0.08, OK! Stable, non-oscillatory – OK! Stable, does not diverge – OK! Mode Poles Natural Frequency (rad/sec) Damping Ratio Phugoid -0.05 ± j 0.61 0.084 0.616 Short Period -7.59, -34.80 Altitude ≈ 0 “Must be heavily damped” – OK!
6-DOF SIMULATION The 6-DOF motion was simulated in MATLAB. Assumed flat earth, rigid body and steady winds. Aircraft was trimmed at loiter conditions, and linearized the system about trim. Comparisons between nonlinear and linear time responses: Elevator Step Input, e = 5° Aileron Step Input, a = 5° Rudder Step Input, r = 5°
6-DOF SIMULATION WITH ELEVATOR STEP INPUT
6-DOF SIMULATION WITH AILERON STEP INPUT
6-DOF SIMULATION WITH AILERON STEP INPUT
6-DOF SIMULATION WITH AILERON STEP INPUT
6-DOF SIMULATION WITH RUDDER STEP INPUT
6-DOF SIMULATION WITH RUDDER STEP INPUT
QUESTIONS?
APPENDIX
RUDDER DEFLECTION IN OEI CONDITIONS ref. “Airplane Flight Dynamics and Automatic Flight Controls” (Roskam) Section 4.2.6 [rad] where @ 2,000 ft [slug/ft3] V [ft/sec] P [hp] yT [ft] for fixed pitch
IDENTIFICATION OF POLES Lateral-Directional Subsystem Dutch Roll Mode Only pole in this subsystem with both e and m parts. Roll Mode Pole is negative; relatively large magnitude. Spiral Mode Can be positive (in the case of the Predator), or negative. Small magnitude, so not typically a problem. Side Velocity Mode Only pole in this subsystem that has zero magnitude.
IDENTIFICATION OF POLES Longitudinal Subsystem Phugoid Mode 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 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 Only pole in this subsystem that is purely real.