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Submit a ProposalAerodynamics for Sixth Generation Aircraft Design
 | Forward and Inverse Transonic and Shear Flow Models for Close Ground Effect By Wilson C. Chin Copyright: 2026 | Expected Pub Date: 2026 ISBN: 9781394470198 | Hardcover | 524 pages Price: $225 USD  |
One Line Description
Uniting classical fluid dynamics with cutting-edge AI, this definitive guide empowers aerospace engineers and defense strategists to master the transition from traditional airframe aerodynamics to stealth-driven, sixth-generation aircraft design.
Description
Commercial aircraft feature prominent fuselages, long wings extending perpendicular to the body, and movable control surfaces that manage lift, stability, and navigation during takeoff and landing. In contrast, sixth-generation aircraft abandon traditional airframe separation in favor of a blended wing-body design that drastically reduces radar cross-section, maximizes aerodynamic efficiency at high speeds, and redefines maneuverability. Building on the foundational contributions of Earll Murman, this volume bridges classical aerodynamic theory with modern computational breakthroughs. It addresses critical engineering challenges alongside their military and geopolitical ramifications, demonstrating how classical mathematics, artificial intelligence, and machine learning can unite to drive high-level strategic analysis. The text examines both forward aerodynamic problems, where given shapes yield calculated pressure distributions, and inverse problems, which determine optimal airframe geometry from target pressure profiles. Furthermore, it highlights the integrative power of combining advanced large language models like DeepSeek with classical fluid dynamics, complete with a detailed five-page LLM diagnostic report that illustrates this hybrid approach in action. Bridging foundational physics and next-generation innovation, this text is an essential guide for aerospace engineers, defense strategists, and researchers ready to master the future of flight.
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Commercial aircraft feature prominent fuselages, long wings extending perpendicular to the body, and movable control surfaces that manage lift, stability, and navigation during takeoff and landing. In contrast, sixth-generation aircraft abandon traditional airframe separation in favor of a blended wing-body design that drastically reduces radar cross-section, maximizes aerodynamic efficiency at high speeds, and redefines maneuverability. Building on the foundational contributions of Earll Murman, this volume bridges classical aerodynamic theory with modern computational breakthroughs. It addresses critical engineering challenges alongside their military and geopolitical ramifications, demonstrating how classical mathematics, artificial intelligence, and machine learning can unite to drive high-level strategic analysis. The text examines both forward aerodynamic problems, where given shapes yield calculated pressure distributions, and inverse problems, which determine optimal airframe geometry from target pressure profiles. Furthermore, it highlights the integrative power of combining advanced large language models like DeepSeek with classical fluid dynamics, complete with a detailed five-page LLM diagnostic report that illustrates this hybrid approach in action. Bridging foundational physics and next-generation innovation, this text is an essential guide for aerospace engineers, defense strategists, and researchers ready to master the future of flight.
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Author / Editor Details
Wilson C. Chin, PhD earned his Ph.D. from the Massachusetts Institute of Technology (MIT), and later served as a member of Boeing, Pratt and Whitney, and NASA. His extensive work involves the optimal engine and airframe integration of PWA engines with Airbus jumbo jets and streamlining systems operations. He is the author of one award-winning book and has published numerous articles in international journals of repute.
Wilson C. Chin, PhD earned his Ph.D. from the Massachusetts Institute of Technology (MIT), and later served as a member of Boeing, Pratt and Whitney, and NASA. His extensive work involves the optimal engine and airframe integration of PWA engines with Airbus jumbo jets and streamlining systems operations. He is the author of one award-winning book and has published numerous articles in international journals of repute.
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Table of Contents
Preface
Acknowledgements
1. Overview and Modeling Perspectives
1. Perspectives in Aerodynamic Flow Modeling
1.1 Conventional Potential Flow Analysis – A Foundational Building Block
1.2 Conventional versus Conservation Law Approaches
1.3 Author Background and Context
1.4 Avoiding Semantic Traps, Thinking Outside the Box
1.5 Mathematics and Numerical Methods Review
1.6 Delta Wings, Lambda Planforms, Vortex Roll-up, Euler and Navier-Stokes Solvers
1.7 References
2. New Analytical Methods for Thin Subsonic Airfoil Design
2.1 Introduction and Objectives
2.2 Analytical Derivations
2.3 Discussion and Conclusions
2.4 References
3. Inverse Problems in Transonic Irrotational Supercritical Flow with Shockwaves
3.1 Fluid Dynamics Overview and Motivating Ideas 53
3.2 Streamfunction Formulation 58
3.3 Numerical Procedure 62
3.4 Calculated Results 64
3.5 Discussion and Closing Remarks 67
3.6 References
4. Class of Shockfree Airfoils Producing the Same Surface
Pressure
4.1 Motivating Ideas
4.2 Analysis Summary
4.3 Discussion and Conclusion
4.4 References
5. Inverse Formulations for Three-Dimensional Problems
5.1 Introduction 81
5.2 Constant Density Planar Flows 83
5.3 Constant Density Flows Past Finite Wings 85
5.4 Compressible Flows Past Finite Wings 88
5.5 Flows in Fans and Cascades 90
5.6 Axisymmetric Compressible Flows 90
5.7 Sample Calculations 92
5.8 Closing Remarks 96
5.9 References
6. Methods for Planar, Inviscid and Incompressible Shear Flow
6.2 Planar Flows with Constant Vorticity: Inverse Problems 103
6.3 Planar Flows: Direct Formulations 105
6.4 Some Planar Analytical Solutions 105
6.5 Analogy To Ringwing Potential Flows 107
6.6 Source and Vortex Interactlons for Ringwings 108
6.7 Airfoils in General Parallel Shear Flow 109
6.8 Numerical Results 113
6.9 Closing Remarks 117
6.10 References
7. Unified Formulations for Inviscid Transonic, Supercritical and Rotational Flows
7.1 Compressible Irrotational Flow and Deepseek-R1 Evaluation
7.2 Deepseek-R1 Insights on Rotational Streamfunction Shear Flow Models
7.3 Simple Integrated Formulations for Transonic Shear Flow
(Non-Euler Equation Models)
7.4 Transonic Forward and Inverse Formulations in Parallel Shear Flow
7.5 Closing Remarks and Research Summary
7.6 References
8. Aerodynamic Modeling Concepts and Algorithm Development
8.1 Basic Challenges in Laplace Equation Solutions
8.2 Motivation – Solution Algorithm for Constant Density and
More Complicated Flows
8.3 Shear Flow Modeling Ideas, Models and Formulas
8.3.1 Classical Transonic Irrotational Model Without Shear Flow
8.3.2 On Potentials and Streamfunctions at Nonzero Mach Numbers
8.3.3 Constant Density Flows with Strong Parallel Background Shear
8.3.4 Compressible Flows with Strong Parallel Background Shear
8.3.5 Dimensionless Numbers and Boundary Value Problems
8.4 Closing Comments Prior to Example Calculations
8.4.1 Note 1 – Perspectives on Fluid Dynamics Education
8.4.2 Note 2 – Potential Flow “Forward” Analysis and Inverse Extensions
8.4.3 Note 3 – Inverse Formulations
8.4.4 Note 4 – Computational Details
8.5 References
9. Validations and Applications in Multiple Physical Limits
9-1. Forward 2D Analysis Problems, Validations and Calculated Solutions
Forward, Analysis or Direct 2D Problems
Example 9-1. Flat plate camber line in large and smaller boxes, first irrotational (MOD-16), then with background parallel shear flow, all runs Mach 0.0 (MOD-16-SHR)
Example 9-2. Thickness distribution in large and smaller boxes, no parallel shear, all runs Mach 0.0 (MOD-15)
Example 9-3. Airfoil CL versus height in ground effect, without and with parallel shear flow with applications to “Wing in Ground” (WIG) aircraft design, all runs Mach 0.0 (MOD-16, MOD-16-SHR)
Example 9-4. Centered unpitched biconvex and flat plate airfoils – pressure distributions, shockwave formation and movement, numerical stability for Mach numbers 0-0.95 (MOD-18)
Example 9-5. Centered biconvex airfoil, transonic flow with parallel shear U(y) (MOD-18-SHR)
Example 9-6. Runs 1-4. Unpitched biconvex, pitched flat plate, Mach 0 and 0.85, with and without shear in infinite media, with and without close ground effect (MOD-19, prior codes combined)
Example 9-7. Discriminant plot, subsonic and supersonic zone definition (MOD-19)
Example 9-8. Trailing edge Kutta condition enforcement (MOD-19)
Example 9-9. Integrated forward, potential-like numerical algorithm in two-dimensional, nonlinear transonic flow in the presence of parallel shear velocity U(y) function (MOD-22)
Example 9-10. Prandtl-Glauert pressure similitude (MOD-22)
9-2. Inverse or Indirect 2D Problems, Validations and Calculated Solutions
Inverse, Design or Indirect 2D Problems
Example 9-11. Exact solution validations - Inverse symmetric and antisymmetric Cp inputs at M∞ = 0 without shear (MOD18-SF-16B)
Example 9-12. Inverse shape prediction, Cp = - 0.2 constant upper and lower surfaces, constant density flow and strong background parallel shear flow at Mach 0 (MOD18-SF-16B)
Example 9-13. Inverse calculations for symmetric Cp surface distributions with different degrees of trailing edge closure at Mach 0 without shear (MOD18-SF-16B)
Example 9-14. Inverse irrotational calculations for symmetric Cp = -0.2 surface distributions with trailing edge closure at different Mach numbers (MOD18-SF-16B)
Example 9-15. Inverse irrotational calculations for symmetric Cp = -0.2 at Mach 0, with proximity to ground plane varied (for Wing in Ground, “WIG” applications) (MOD18-SF-16B)
Example 9-16. Inverse airfoil design, irrotational, subsonic to high transonic with “shape shock,” symmetric Cp = -0.2 fixed, chord centered vertically in a large box (MOD18-SF-16B)
Example 9-17. Inverse airfoil design, M = 0.3 and positive shear level both fixed, symmetric Cp = -0.2 fixed, distance to ground decreases from chord centered vertically in large box (top) to near ground proximity (bottom) (MOD18-SF-16B)
Example 9-18. Inverse airfoil design, M = 0.4 and vertically centered all runs, symmetric Cp = -0.2 fixed, positive shear level increases downward (MOD18-SF-16B)
9-3. Forward and Inverse 3D Problems, Special Projects and
Calculated Solutions
Example 9-19. Three-dimensionality, nonlinearities and ground effect models (MOD22-3D-9)
Example 9-20. High aspect ratio wing at Mach 0 (MOD22-3D-9)
Example 9-21. High aspect ratio wing at Mach 0.9 showing shock capture (MOD22-3D-9)
Example 9-22. High aspect ratio wing calculations, at high Mach number with shock, positive wind shear, and strong ground effect (MOD22-3D-9)
Example 9-23. Simplified grids for swept delta and NASA oblique wings (MOD22-3DSWP-1)
Example 9-24. Inverse shape prediction – 3D modeling concepts, rectangular planform baseline calculation, closed trailing edges (MOD18-SF3D-5)
Example 9-25. Inverse shape prediction – Delta wings, background shear flow, close ground effect, opened trailing edges with mass outflow (MOD18-SFSWP-1)
Example 9-3. Airfoil CL versus height in ground effect, without and with shear flow, Mach 0.0 with applications to “Wing in Ground” (WIG) aircraft design (MOD-16, MOD-16-SHR).
Example 9-27. Inverse problem – High sweep delta wing, irrotational, centered, high Mach number, strong supersonic zone, “shape shock” and closed trailing edge (MOD18-SFSWP-1)
Example 9-28. Model problem – “Wing in Ground” (WIG), proximity, shear and nonlinear effects (MOD-22)
Example 9-29. Meshing strategy – H-20 and similar bomber planforms (MOD18-SFSWP-1)
Example 9-30. Cylindrical flow strategies – Ringwings, inlet/nacelles and mixers (calculated results from modified rectangular wing algorithms – compare similarities in Equations 9-1a,b and 9-21,b)
Example 9-31. Forward 3D problems for simple delta and lambda planforms at Mach 0.7, Lockheed Vectis, China H-20 Stealth Bomber and CH-7 Stealth Drone (MOD22-3DSWP-2)
Example 9-32. Inverse 3D problems for simple delta and lambda planforms at Mach 0.7, Lockheed Vectis, China H-20 Stealth Bomber and CH-7 Stealth Drone (MOD18-SFSWP-2)
9-4. Development Philosophy and Closing Remarks
9-5. References
9-6. Appendixes (AL/ML generated results set in Calibri font)
Appendixes 4 and 5 derive the linear disturbance streamfunction equation with transonic compressibility and shear. Appendixes 5, 6 and 7 derive the transonic streamfunction equation with the correct nonlinear terms for
irrotational flows. Almost three dozen detailed calculated
examples solving a unified model are provided in Chapter 9.
All results are new to the aerodynamics literature.
Appendix 1, Three-Dimensional Constant Density Flows
Appendix 2, Planar Compressible Shear Flow of a Gas
Appendix 3, Deepseek-R1 Conversational Query-4 and Modeling Results
Appendix 4, Deepseek-R1 Conversational Query-5
Appendix 5, Deepseek-R1, Transonic Small Disturbance Streamfunction for Irrotational Flow
Appendix 6, Deepseek-R1, Revisited, Llama-4-Scout-Nitro and GPT-4.1 Transonic Small Disturbance Streamfunction for Irrotational Flow
Appendix 7, ChatGPT - Transonic Small-Disturbance Streamfunction Irrotational Equation
Appendix 8, Deepseek-R1 - Opinions on Industry, Military and Geopolitical Impact
10. Focused Tutorials and Glossary
Cumulative References
Index
About the Author
Back to Top
Preface
Acknowledgements
1. Overview and Modeling Perspectives
1. Perspectives in Aerodynamic Flow Modeling
1.1 Conventional Potential Flow Analysis – A Foundational Building Block
1.2 Conventional versus Conservation Law Approaches
1.3 Author Background and Context
1.4 Avoiding Semantic Traps, Thinking Outside the Box
1.5 Mathematics and Numerical Methods Review
1.6 Delta Wings, Lambda Planforms, Vortex Roll-up, Euler and Navier-Stokes Solvers
1.7 References
2. New Analytical Methods for Thin Subsonic Airfoil Design
2.1 Introduction and Objectives
2.2 Analytical Derivations
2.3 Discussion and Conclusions
2.4 References
3. Inverse Problems in Transonic Irrotational Supercritical Flow with Shockwaves
3.1 Fluid Dynamics Overview and Motivating Ideas 53
3.2 Streamfunction Formulation 58
3.3 Numerical Procedure 62
3.4 Calculated Results 64
3.5 Discussion and Closing Remarks 67
3.6 References
4. Class of Shockfree Airfoils Producing the Same Surface
Pressure
4.1 Motivating Ideas
4.2 Analysis Summary
4.3 Discussion and Conclusion
4.4 References
5. Inverse Formulations for Three-Dimensional Problems
5.1 Introduction 81
5.2 Constant Density Planar Flows 83
5.3 Constant Density Flows Past Finite Wings 85
5.4 Compressible Flows Past Finite Wings 88
5.5 Flows in Fans and Cascades 90
5.6 Axisymmetric Compressible Flows 90
5.7 Sample Calculations 92
5.8 Closing Remarks 96
5.9 References
6. Methods for Planar, Inviscid and Incompressible Shear Flow
6.2 Planar Flows with Constant Vorticity: Inverse Problems 103
6.3 Planar Flows: Direct Formulations 105
6.4 Some Planar Analytical Solutions 105
6.5 Analogy To Ringwing Potential Flows 107
6.6 Source and Vortex Interactlons for Ringwings 108
6.7 Airfoils in General Parallel Shear Flow 109
6.8 Numerical Results 113
6.9 Closing Remarks 117
6.10 References
7. Unified Formulations for Inviscid Transonic, Supercritical and Rotational Flows
7.1 Compressible Irrotational Flow and Deepseek-R1 Evaluation
7.2 Deepseek-R1 Insights on Rotational Streamfunction Shear Flow Models
7.3 Simple Integrated Formulations for Transonic Shear Flow
(Non-Euler Equation Models)
7.4 Transonic Forward and Inverse Formulations in Parallel Shear Flow
7.5 Closing Remarks and Research Summary
7.6 References
8. Aerodynamic Modeling Concepts and Algorithm Development
8.1 Basic Challenges in Laplace Equation Solutions
8.2 Motivation – Solution Algorithm for Constant Density and
More Complicated Flows
8.3 Shear Flow Modeling Ideas, Models and Formulas
8.3.1 Classical Transonic Irrotational Model Without Shear Flow
8.3.2 On Potentials and Streamfunctions at Nonzero Mach Numbers
8.3.3 Constant Density Flows with Strong Parallel Background Shear
8.3.4 Compressible Flows with Strong Parallel Background Shear
8.3.5 Dimensionless Numbers and Boundary Value Problems
8.4 Closing Comments Prior to Example Calculations
8.4.1 Note 1 – Perspectives on Fluid Dynamics Education
8.4.2 Note 2 – Potential Flow “Forward” Analysis and Inverse Extensions
8.4.3 Note 3 – Inverse Formulations
8.4.4 Note 4 – Computational Details
8.5 References
9. Validations and Applications in Multiple Physical Limits
9-1. Forward 2D Analysis Problems, Validations and Calculated Solutions
Forward, Analysis or Direct 2D Problems
Example 9-1. Flat plate camber line in large and smaller boxes, first irrotational (MOD-16), then with background parallel shear flow, all runs Mach 0.0 (MOD-16-SHR)
Example 9-2. Thickness distribution in large and smaller boxes, no parallel shear, all runs Mach 0.0 (MOD-15)
Example 9-3. Airfoil CL versus height in ground effect, without and with parallel shear flow with applications to “Wing in Ground” (WIG) aircraft design, all runs Mach 0.0 (MOD-16, MOD-16-SHR)
Example 9-4. Centered unpitched biconvex and flat plate airfoils – pressure distributions, shockwave formation and movement, numerical stability for Mach numbers 0-0.95 (MOD-18)
Example 9-5. Centered biconvex airfoil, transonic flow with parallel shear U(y) (MOD-18-SHR)
Example 9-6. Runs 1-4. Unpitched biconvex, pitched flat plate, Mach 0 and 0.85, with and without shear in infinite media, with and without close ground effect (MOD-19, prior codes combined)
Example 9-7. Discriminant plot, subsonic and supersonic zone definition (MOD-19)
Example 9-8. Trailing edge Kutta condition enforcement (MOD-19)
Example 9-9. Integrated forward, potential-like numerical algorithm in two-dimensional, nonlinear transonic flow in the presence of parallel shear velocity U(y) function (MOD-22)
Example 9-10. Prandtl-Glauert pressure similitude (MOD-22)
9-2. Inverse or Indirect 2D Problems, Validations and Calculated Solutions
Inverse, Design or Indirect 2D Problems
Example 9-11. Exact solution validations - Inverse symmetric and antisymmetric Cp inputs at M∞ = 0 without shear (MOD18-SF-16B)
Example 9-12. Inverse shape prediction, Cp = - 0.2 constant upper and lower surfaces, constant density flow and strong background parallel shear flow at Mach 0 (MOD18-SF-16B)
Example 9-13. Inverse calculations for symmetric Cp surface distributions with different degrees of trailing edge closure at Mach 0 without shear (MOD18-SF-16B)
Example 9-14. Inverse irrotational calculations for symmetric Cp = -0.2 surface distributions with trailing edge closure at different Mach numbers (MOD18-SF-16B)
Example 9-15. Inverse irrotational calculations for symmetric Cp = -0.2 at Mach 0, with proximity to ground plane varied (for Wing in Ground, “WIG” applications) (MOD18-SF-16B)
Example 9-16. Inverse airfoil design, irrotational, subsonic to high transonic with “shape shock,” symmetric Cp = -0.2 fixed, chord centered vertically in a large box (MOD18-SF-16B)
Example 9-17. Inverse airfoil design, M = 0.3 and positive shear level both fixed, symmetric Cp = -0.2 fixed, distance to ground decreases from chord centered vertically in large box (top) to near ground proximity (bottom) (MOD18-SF-16B)
Example 9-18. Inverse airfoil design, M = 0.4 and vertically centered all runs, symmetric Cp = -0.2 fixed, positive shear level increases downward (MOD18-SF-16B)
9-3. Forward and Inverse 3D Problems, Special Projects and
Calculated Solutions
Example 9-19. Three-dimensionality, nonlinearities and ground effect models (MOD22-3D-9)
Example 9-20. High aspect ratio wing at Mach 0 (MOD22-3D-9)
Example 9-21. High aspect ratio wing at Mach 0.9 showing shock capture (MOD22-3D-9)
Example 9-22. High aspect ratio wing calculations, at high Mach number with shock, positive wind shear, and strong ground effect (MOD22-3D-9)
Example 9-23. Simplified grids for swept delta and NASA oblique wings (MOD22-3DSWP-1)
Example 9-24. Inverse shape prediction – 3D modeling concepts, rectangular planform baseline calculation, closed trailing edges (MOD18-SF3D-5)
Example 9-25. Inverse shape prediction – Delta wings, background shear flow, close ground effect, opened trailing edges with mass outflow (MOD18-SFSWP-1)
Example 9-3. Airfoil CL versus height in ground effect, without and with shear flow, Mach 0.0 with applications to “Wing in Ground” (WIG) aircraft design (MOD-16, MOD-16-SHR).
Example 9-27. Inverse problem – High sweep delta wing, irrotational, centered, high Mach number, strong supersonic zone, “shape shock” and closed trailing edge (MOD18-SFSWP-1)
Example 9-28. Model problem – “Wing in Ground” (WIG), proximity, shear and nonlinear effects (MOD-22)
Example 9-29. Meshing strategy – H-20 and similar bomber planforms (MOD18-SFSWP-1)
Example 9-30. Cylindrical flow strategies – Ringwings, inlet/nacelles and mixers (calculated results from modified rectangular wing algorithms – compare similarities in Equations 9-1a,b and 9-21,b)
Example 9-31. Forward 3D problems for simple delta and lambda planforms at Mach 0.7, Lockheed Vectis, China H-20 Stealth Bomber and CH-7 Stealth Drone (MOD22-3DSWP-2)
Example 9-32. Inverse 3D problems for simple delta and lambda planforms at Mach 0.7, Lockheed Vectis, China H-20 Stealth Bomber and CH-7 Stealth Drone (MOD18-SFSWP-2)
9-4. Development Philosophy and Closing Remarks
9-5. References
9-6. Appendixes (AL/ML generated results set in Calibri font)
Appendixes 4 and 5 derive the linear disturbance streamfunction equation with transonic compressibility and shear. Appendixes 5, 6 and 7 derive the transonic streamfunction equation with the correct nonlinear terms for
irrotational flows. Almost three dozen detailed calculated
examples solving a unified model are provided in Chapter 9.
All results are new to the aerodynamics literature.
Appendix 1, Three-Dimensional Constant Density Flows
Appendix 2, Planar Compressible Shear Flow of a Gas
Appendix 3, Deepseek-R1 Conversational Query-4 and Modeling Results
Appendix 4, Deepseek-R1 Conversational Query-5
Appendix 5, Deepseek-R1, Transonic Small Disturbance Streamfunction for Irrotational Flow
Appendix 6, Deepseek-R1, Revisited, Llama-4-Scout-Nitro and GPT-4.1 Transonic Small Disturbance Streamfunction for Irrotational Flow
Appendix 7, ChatGPT - Transonic Small-Disturbance Streamfunction Irrotational Equation
Appendix 8, Deepseek-R1 - Opinions on Industry, Military and Geopolitical Impact
10. Focused Tutorials and Glossary
Cumulative References
Index
About the Author
Back to Top