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

2. OVERVIEW Aircraft Walk-Around Tail Re-Sizing Stability Check
Modal Analysis
6-DOF Simulation

3. 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

4. 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

5. 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 …

6. 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 ft ft
Rudder cVT ft

7. 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, = ft/s
FAR 23, 25 Limit
Max Deflection
1.2
Stall Speed Limit

8. 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,
Altitude
≈ 0

9. 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
± j 0.61
0.084
0.616
Short Period
-7.59,
Altitude
≈ 0
“Must be heavily damped” – OK!

10. 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°

11. 6-DOF SIMULATION WITH ELEVATOR STEP INPUT

12. 6-DOF SIMULATION WITH AILERON STEP INPUT

13. 6-DOF SIMULATION WITH AILERON STEP INPUT

14. 6-DOF SIMULATION WITH AILERON STEP INPUT

15. 6-DOF SIMULATION WITH RUDDER STEP INPUT

16. 6-DOF SIMULATION WITH RUDDER STEP INPUT

17. QUESTIONS?

18. APPENDIX

19. 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

20. 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.

21. 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.