1. Nonlinear and Time-Dependent Aerodynamics: Implications for Testing and Flight Mechanics Analysis Jerry E. Jenkins Voluntary Emeritus Corps AFRL Wright-Patterson AFB, OH

2. The Delta Wing Model

3. Free-to-Roll Tests Instantaneous motion state insufficient Bypasses stable trim points

4. Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA-97-0742 Free-to-Roll tests perplexing results –Aerodynamic responses at moderate angles of attack Not determined by instantaneous motion state Highly dependent on motion history

5. Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA-97-0742 Free-to-Roll tests perplexing results –Aerodynamic responses at moderate angles of attack Often not determined by instantaneous motion state Highly dependent on motion history Viscous effects superimposed on potential flow –L. E. Vortex system structure –Vortex breakdown dynamics

6. Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA-97-0742 Flow Structure The steady-state flow-field can become unstable –At some flight conditions (Critical States) –Bifurcations in static force and moment characteristics

7. Critical States

8. Flow Structure & Bifurcations Left Wing

9. Flow Structure & Bifurcations Right Wing

10. Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA-97-0742 Flow Structure The steady-state flow-field can become unstable –At some flight conditions (Critical States) –Bifurcations in static force and moment characteristics Must transition to a new stable state when perturbed –Can require a considerable amount of time –Static tests give us no clue as to how long

11. Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA-97-0742 Flow Dynamics Flow processes acting on at least three time scales –Transitions between equilibrium states –Potential flow phenomena –Vortex breakdown movement in response to the motion

12. Ramp Across a Critical State 65 o Delta Wing

13. Attached and Vortical Flow Contributions

14. Can isolate CS transients including motion history

15. Harmonic Motion With and Without Critical State Encounters Rolling Moment Pitching Moment k = 0.02 & 0.14

16. Harmonic Motion With and Without Critical State Encounters Rolling Moment Pitching Moment k = 0.02 & 0.14

17. Static Nonlinearities - AIAA 2004-5275 Region 1 2 3 4 Region 5

18. Multiple Time Scales in Linear Region AIAA 2004-5275 Slow responses cannot keep up with rapid motions

19. Broadband Input Allwine, et. al., “Nonlinear Modeling of Unsteady Aerodynamics at High Angle of Attack,” AIAA 2004-5275

20. Multiple Time Scales (F-16XL) AIAA 2001-4016 Variation of in-phase & out-of-phase components Lift-Curve slope Lift due to pitch rate Reduced freq.

21. Schroeder sweep Murphy, P.C., and Klein, V., “Estimation of Aircraft Unsteady Aerodynamic Parameters from Dynamic Wind Tunnel Testing,” AIAA 2001-4016

22. Langley Fighter Model

23. Roll-Damping “Derivative” AIAA-2004-5273

24. Nonlinear & Unsteady Aero Characteristics: Summary Free-to-Roll tests difficult to explain results –Aerodynamic responses at moderate angles of attack Often not determined by instantaneous motion state Highly dependent on motion history Traced to leading edge vortex system dynamics –Vortex system structure –Vortex breakdown phenomenon Response characteristics not unique to delta wings –Static discontinuities, i.e. flow-field instabilities –Multiple time scales

25. Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint Unsteady Aero prescribed motion Flight Mechanics motion is unknown a priori –Stability and Control –Flight Control System Design

26. Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint Unsteady Aero prescribed motion Flight Mechanics motion is unknown a priori –Stability and Control –Flight Control System Design Small-amplitude dynamic data inadequate –Stability “derivatives” –Exhibit frequency and amplitude dependence –Powerless to describe the aerodynamics

27. Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint Unsteady Aero prescribed motion Flight Mechanics motion is unknown a priori –Stability and Control –Flight Control System Design Small-amplitude dynamic data inadequate –Stability “derivatives” –Exhibit frequency and amplitude dependence –Powerless to describe the aerodynamics Need math models for aerodynamics –Applicable to arbitrary motions –Functions of the translational and rotational DOF

28. Nonlinear & Unsteady Aero Characteristics: AIAA-97-0742 AIAA-2001-4016 AIAA-2004-5273 Results were for single DOF motions in wind tunnel Understanding requires that we –acknowledge the existence of multiple time scales –Consider the individual effects of translation and rotation –Include lags present in both responses

29. Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached? Assumptions: –Square-Cube Law holds

30. Vehicle Inertia Variation with Mass

31. Vehicle Weight Variation with Wing Area

32. Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached? Assumptions: –Square-Cube Law holds –Want to fly in similar C L range Conclusions:

33. Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached? Assumptions: –Square-Cube Law holds –Want to fly in similar C L range –Hold non-dimensional derivatives constant i.e. ignore R e effects Conclusions:

34. Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached? Consequences: –Magnitude of atmospheric disturbances do not scale Relative angular disturbances, –Responses to disturbances up to not attenuated Control system rates must increase –Sensor sampling rates –Servo response times –Aerodynamic effects Convective time lags unaltered Separated, vortex dominated flows ( low )

35. Static Test Recommendations Closely spaced static data –Critical state detection Examine all components of the force and moment –Critical States are flow field events Make sweeps should in both directions –Hysteresis detection –Another indication of critical states

36. Dynamic Test Recommendations Structure dynamic tests based on static test results

37. Dynamic Test Recommendations Structure dynamic tests based on static test results Filtering (except anti-aliasing) should not be used –Ensemble averaging recommended

38. Dynamic Test Recommendations Structure dynamic tests based on static test results Filtering (except anti-aliasing) should not be used –Ensemble averaging recommended Record the complete response –potential nonlinear effects -- Linearize off line

39. Dynamic Test Recommendations Structure dynamic tests based on static test results Filtering (except anti-aliasing) should not be used –Ensemble averaging recommended Record the complete response –potential nonlinear effects -- Linearize off line Cover wide range reduced frequencies –Try to saturate the viscous effects –Extract both "static" and dynamic stability derivatives –Frequency dependence multiple time scales

40. Linear Aero Model from Broadband Data AIAA 2004-5275 Linear system ID works quite well

41. Dynamic Test Recommendations Structure dynamic tests based on static test results Filtering (except anti-aliasing) should not be used –Ensemble averaging recommended Record the complete response –potential nonlinear effects -- Linearize off line Cover wide range reduced frequencies –Try to saturate the viscous effects –Extract both "static" and dynamic stability derivatives –Frequency dependence multiple time scales Ramp and hold motions invaluable –Isolate critical state transients –Provide quantitative measures for response times –Examine history effects. –Consider other types of "motion and hold" experiments

42. Ramp-Between-Harmonics

43. Nonlinear Model Constructed from SSM’s AIAA 2004-5275