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«by: Alexander M. Benoliel Thesis submitted to the faculty of the Virginia Polytechnic Institute & State University in partial fulfillment of the ...»

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Alexander M. Benoliel

Thesis submitted to the faculty of the

Virginia Polytechnic Institute & State University

in partial fulfillment of the requirements for the degree of

Master of Science


Aerospace Engineering



William H. Mason, Committee Chairman ________________________________ ________________________________

Bernard Grossman Mark R. Anderson May 1994 Blacksburg, Virginia



by Alexander M. Benoliel Committee Chairman: William H. Mason Aerospace & Ocean Engineering (ABSTRACT) Low aspect ratio, highly-swept cranked arrow wing planforms are often proposed for highspeed civil transports. These wing planforms offer low supersonic drag without suffering greatly from low lift/drag ratios in low-speed flight. They can, however, suffer from pitchup at modest angles of attack (as low as 5˚) during low-speed flight due to leading edge vortex influence, flow separation and vortex breakdown. The work presented here describes an investigation conducted to study past research on the longitudinal aerodynamic characteristics of highly-swept cranked wing planforms, the development of a new method to estimate pitch-up of these configurations, and the applications of this new method to the analysis of tail designs for trim at high lift coefficients. The survey of past research placed emphasis on 1) understanding the problem of pitch-up, 2) ascertaining the effects of leading and trailing edge flaps, and 3) determining the benefits and shortfalls of tail, tailless, and canard configurations. The estimation method used a vortex lattice method to calculate the inviscid flow solution. Then, the results were adjusted to account for flow separation on the outboard wing section by imposing a limit on the equivalent 2-D sectional lift coefficient. The new method offered a means of making low cost estimates of the nonlinear pitching moment characteristics of slender, cranked arrow wing configurations with increased accuracy compared to conventional linear methods. Numerous comparisons with data are included. The new method was applied toanalyze the trim requirement of slender wing designs generated by an aircraft configuration optimization and design program. The effects of trailing edge flaps and horizontal tail on the trimmed lift coefficient was demonstrated. Finally, recommendations were made to the application of this new method to multidisciplinary design optimization methods.

Acknowledgments This work would not have been possible without the tireless efforts of my faculty advisor, Dr. William H. Mason. I would like to thank Dr. Mason and the other committee members, Dr. Bernard Grossman and Dr. Mark Anderson for their support and encouragement. A portion of this work was developed at NASA Langley Research Center and I would like to thank Dr. Harry Carlson, Dr. John Lamar, and Dr. Michael Mann for their help and suggestions in the theoretical analyses, the support of Mr. Peter Coen and the members of the Vehicle Integration Branch, the assistance of Mr. Kevin Kjerstad of the Subsonic Aerodynamics Branch, and Mr. David Hahne of the Flight Dynamics Branch.

Also, Dr. Dhanvada Rao at Vigyan and Dr. William Wentz at the National Institute for Aviation Research were helpful in supplying me information on the experimental investigations of swept wing configurations, and Mr. Nathan Kirschbaum at Virginia Tech and Mr. Leroy Spearman at NASA Langley for their insight into the various supersonic transport programs conducted in the past. This work was supported by the NASA/Universities Space Research Association/Advanced Design Program (and the Vehicle Integration Branch at NASA Langley Research Center)

iii Table of Contents



Table of Contents

List of Figures

List of Symbols

1. Introduction to Low Aspect Ratio Planforms Designed for High-Speed Flight...............1

1.1 Past Research

2. Aerodynamic Pitch-Up

2.1 Theorized Reasons for Pitch-Up

2.2 Influence of Geometry on Pitch-Up

2.3 Further Considerations

2.4 Pitch-Up Alleviation

3. High-Lift for Slender Wings

3.1 Leading Edge Flap Effects

3.2 Trailing Edge Flap Effects

4. Theoretical Estimation Methods

4.1 A New Method to Estimate Pitch-Up

4.2 Results

4.2.1 Leading Edge Vortex Considerations

4.2.2 Horizontal Tail and Flap Effect Analysis

4.3 Method Limitations

5. Tail/Tailless/Canard Configurations

6. Extensions to Multidisciplinary Design Optimization Methodology for HSCT Configurations

6.1 Application to Multidisciplinary Design Optimization Process

7. Conclusions & Recommendations


Appendix A: Annotated Bibliography

A.1 Experimental Investigations of Supersonic Transports

A.2 Experimental Investigations Related to Supersonic Cruise Planforms............63 A.3 Theoretical Investigations

A.4 Configuration Design

A.5 Reference Reports

A.6 Control Issues

Appendix B: Summary of Experimental Studies

Appendix C: Instructions for the Implementation of the APE Method


–  –  –

1. SCAT Program developed configurations (not to scale).

2. Lift and pitching moment for a McDonnell Douglas 71˚/57˚ sweep cambered and twisted cranked arrow wing

3. Leading edge vortex features on highly swept wings.

4. Variation of pitching moment for a 75˚ sweep arrow wing with varying trailing edge notches.

5. Modified F-16XL predecessor model

6. Effect of leading edge radius on lift and pitching moment on the SCAT-15F.............8

7. Effects of Reynolds number on the inflection lift coefficient for wings incorporating round and sharp leading edges. Λc/4 = 50˚

8. Pylon Vortex Generator Design.

9. Pylon Vortex Generators at 25% and 50% chord

10. Spanwise blowing study 70˚/50˚ sweep model

11. Effect of spanwise blowing on a cranked delta wing

12. Effect of leading edge flap deflection for a 74˚/70.5˚/60˚ sweep untwisted, uncambered cranked arrow wing similar in planform to the AST-200.

13. Effects of a multi-segmented flap for a 74˚/70.5˚/60˚ sweep cambered and twisted cranked arrow wing planform

14. Trailing edge flap effectiveness for a 70˚/48.8˚ sweep uncambered, untwisted cranked arrow wing planform with δLE = 20˚

15. Increments in lift and pitching moment for various trailing edge flap deflections for a 70˚/48.8˚ sweep flat cranked arrow wing

16. 2-D sectional lift coefficient for a 71˚/57˚ sweep wing calculated with Aero2s.........19

17. Comparison of lift and pitching moment estimation methods for a 71˚/57˚ sweep cambered and twisted cranked arrow wing (δTail = 0˚).

18. 74˚/48˚ sweep wing-body combination, comparison to experimental data................21

19. Comparison of estimation methods for an F-16XL (70˚/50˚ sweep) model test.......22

–  –  –

21. Pressure distribution used to calculate the contribution of vortex lift

22. Vortex placement comparison between theoretical estimates and experiment...........25

23. Effects of limiting the vortex effects to the wing only for a 74˚/70.5˚/60˚ sweep wing similar in planform to the AST-200. Limited vortex begins at wing root and does not extend into fuselage region

24. Comparison of lift and pitching moment estimation methods for a 70˚/48.8˚ sweep uncambered and untwisted cranked arrow wing. Estimates made before “limited vortex” modification

25. Effects of limiting the vortex effects to the wing only for a 70˚/48.8˚ sweep uncambered and untwisted cranked arrow wing. Limited vortex begins at wing root and does not to extend into fuselage region

26. Comparison of lift and pitching moment estimation methods for a 71˚/57˚ sweep cambered and twisted cranked arrow wing with flaps deflected (δTail = 0˚, dTE = 30˚, δLE = 13˚/34˚/35˚/35˚/19˚/29˚).

27. Comparison of lift and pitching moment estimation methods for a 71˚/57˚ sweep cambered and twisted cranked arrow wing with flaps deflected and tail removed (δTE = 30˚, δLE = 13˚/34˚/35˚/35˚/19˚/29˚).

28. Comparison of lift and pitching moment estimation methods for a 71˚/57˚ sweep cambered and twisted cranked arrow wing without flaps and horizontal tail removed

29. Comparison of lift and pitching moment estimation methods for a 71˚/57˚ sweep cambered and twisted cranked arrow wing with flaps deflected (δTail = -10˚, δTE = 30˚, δLE = 13˚/34˚/35˚/35˚/19˚/29˚)

30. Comparison of estimation methods for an F-16XL (70˚/50˚ sweep) model test (δLE = 28˚/38˚/40˚/20˚, δTE = 30˚/0˚)

31. 74˚/48˚ sweep wing-body combination with trailing edge flaps deflected (δTE = 15˚)

32. Comparison of lift and pitching moment estimation methods for a 74˚/70.5˚/60˚ sweep uncambered and untwisted cranked arrow wing similar in planform to the AST-200 with leading and trailing edge flaps deflected (δLE = 30˚, δTE = 30˚)......32

33. Comparison of lift and pitching moment estimation methods for a 70˚/48.8˚ sweep uncambered and untwisted cranked arrow wing with flaps deflected (δLE = 20˚, δTE = 30˚)

–  –  –

34. F-16XL model shown with baseline and HSCT planform configurations................34

35. Effects of apex modifications to the F-16XL aerodynamic characteristics (data taken from an unpublished test)

36. Two-dimensional airfoil aerodynamic characteristics for an NACA 63-006 airfoil section

37. Economic impact of increasing the maximum lift coefficient of a transport aircraft limited in weight by the available field length

38. Effects of canard on lateral/directional stability and control

39. Configurations developed during a multidisciplinary design optimization program

40. Aerodynamic characteristics of the baseline and optimized planforms

41. Effects of adding a trailing edge flap (δTE = 30˚) to the optimized planform.

Analysis performed with the APE method.

42. Aerodynamic performance of a trailing edge flap and horizontal tail combination (δTail = -5˚, δTE = 30˚) calculated with the APE method

43. Comparison of the trimmed tail and tailless configurations calculated with the APE method

44. Analysis of the tailless configuration without the APE method.

45. Effects of changing the center of gravity location for a configuration (δTE = 30˚) on the trimmed lift coefficient. Results for initial flap deflected case (δTail = -5˚) were computed with a center of gravity position equal to 175 ft aft of the nose........47

–  –  –

A aspect ratio α angle of attack (measured in the wind axis coordinate system) c chord length Ca sectional axial force coefficient CD total aircraft drag coefficient Cl sectional lift coefficient CL total aircraft lift coefficient Cl2D two dimensional lift coefficient Clmax maximum two dimensional equivalent airfoil lift coefficient lift curve slope, ∂CL/∂α C Lα Cm sectional pitching moment coefficient CM total aircraft pitching moment coefficient Cn sectional normal force coefficient Cp pressure coefficient ∂CM/∂CL slope of pitching moment curve defining the stability of the aircraft δ LE leading edge flap deflection in degrees (positive down) δ TE trailing edge flap deflection in degrees (positive down) δ Tail all moving horizontal tail deflection in degrees (positive down) k vortex lift factor λ taper ratio Λ wing sweep angle M Mach number Re Reynolds number x distance from the leading edge along the local chord of a particular wing section viii

1. Introduction to Low Aspect Ratio Planforms Designed for High-Speed Flight Low aspect ratio wings with highly swept leading edges are the common choice for supersonic cruise transport aircraft configurations because of their low drag benefits in supersonic flight.1 However, these planforms generally have poor low-speed aerodynamic characteristics such as low lift/drag ratios and low lift curve slopes, CLα. To compensate for the deficiencies of these wings, cranked arrow planforms are used in which a lower sweep outboard section is employed. This improves the low speed lift/drag ratio, increases the CLα and reduces the aerodynamic center shift from subsonic to supersonic flight conditions.1 Unlike pure delta wings, at low speeds, these wings are susceptible to pitch-up in the high angle of attack flight regime. Pitch-up can occur at angles of attack as low as 5˚.

Pitch-up is a result of non-linear aerodynamic effects, which include leading edge vortex flow, outer wing stall, and vortex breakdown. These effects are difficult to model with linear aerodynamic methods and continue to pose a challenge for CFD. It is important for configuration designers to be aware of the factors that can cause pitch-up and to determine the effectiveness of leading and trailing edge flaps in reducing pitch-up, providing adequate pitch control, and increasing low speed lift. Recently, Nelson2 described the importance of non-linear aerodynamic characteristics in his study of High-Speed Civil Transport (HSCT) planform effects on off-design aerodynamics. Nelson noted that although highly swept arrow wing configurations were optimum for supersonic cruise performance, they suffered from low-speed, high angle of attack problems, such as pitch-up.

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