Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics Volume II Division

ISBN-13: 9783642896286 / Niemiecki / Miękka / 1935 / 368 str.

William Frederick Durand; William Frederick Durand

Opis

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfangen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen fur die historische wie auch die disziplingeschichtliche Forschung zur Verfugung, die jeweils im historischen Kontext betrachtet werden mussen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben."

Spis treści

Division E General Aerodynamic Theory Perfect Fluids.- I. Basic Ideas of Wing Theory: Flow Around an Airfoil.- 1. Introductory Remarks.- 2. Principle Data Characterizing an Airfoil.- 3. Reaction of the Air upon an Airfoil.- 4. Moment of the Reaction of the Air upon an Airfoil.- 5. The Circulatory Flow around an Airfoil.- 6. The Kutta-Joukowski Theorem.- 7. Vortex System Connected with the Circulatory Motion around the Airfoil.- 8. Origin of the Circulation around the Airfoil.- 9. Equivalence of an Airfoil and a System of Vortices.- 10. Connection between Equation (9.8) and the Kutta-Joukowski Theorem.- 11. General Expression for the Induced Resistance.- 12. Reduction Formulae.- 13. Concluding Remarks. Program for the Following Chapters.- II. Theory of Airplane Wings of Infinite Span.- 1. Introduction.- A. Vortex Systems and their Application in the Theory of Thin Airfoils.- 2. Forces Acting on a Fluid in Two-Dimensional Motion.- 3. Forces on a System of Vortex Filaments.- 4. Calculation of the Forces Acting on a Vortex System by the Method of Complex Variables.- 5. Vortex Sheets.- 6. The Velocity Field of the Vortex Sheet in the Complex Form.- 7. The Plane Airfoil.- 8. Theory of Thin Wing Sections (Thin Airfoils).- 9. Munk’s Integral Formulae for the Lift and Moment of a Thin Airfoil.- 10. Simple Types of Thin Airfoils. General Discussion.- 11. Airfoil with Flap.- 12. Two-Dimensional Approximate Biplane Theory.- B. Application of the Theory of Conformai Transformation to the Investigation of the Flow around Airfoil Profiles.- 13. Conformai Transformation.- 14. General Expressions for Lift and Moment.- 15. Metacentric Parabola.- 16. The Joukowski Transformation. Classification of Airfoil Families.- 17. The Joukowski Family of Airfoils.- 18. Graphical Method for Plotting Joukowski Airfoils and Computing Velocity Distribution.- 19. The Kármán-Trefftz Family of Airfoils.- 20. The Mises Family of Airfoils.- 21. Aerodynamic Characteristics of Given Airfoils.- 22. The Theory of Biplanes.- 23. Flow through a Lattice Composed of Airfoils.- 24. Some Examples of the Application of Conformai Transformation to Problems Connected with Airfoils.- III. Mathematical Foundation of the Theory of Wings with Finite Span.- 1. Equations of Motion of the Fluid.- A. Motion of a Perfect Fluid Produced by External Forces.- 2. Motion Produced by Impulsive Forces.- 3. Generation of a Vortex Ring by an Impulsive Pressure Acting over a Circular Area.- 4. Action of Continuous Forces.- 5. Forces Directed Perpendicular to the Original Motion of the Fluid.- 6. Steady Motion under the Action of Forces Independent of the Time. Transformation of the Hydrodynamic Equations.- 7. Solution of the Equations by Successive Approximations.- 8. Solution of the System of Equations (6.2), (6.7).—Determination of q.- 9. Determination of the Components of the Velocity.- Appendix to Section 9.—Remark in Connection with Bernoulli’s Theorem.- 10. Discussion of the Result Obtained—Vorticity.- 11. Forces Parallel to the Direction of the Original Motion.- 12. Forces Directed Normal to the Original Motion—Loaded Line with Uniform Lift Distribution.- 13. Loaded Line in Arbitrary Position and with Variable Lift Distribution.- 14. Introduction of the “Induced Forces” (Second Order Forces) gx, gy, gz.- 15. Continuation. Influence of the “Second Order Forces” g in the Wake.- B. Wake Energy and Induced Drag.- 16. Energy Expended in Producing the Flow Pattern.- 17. Case of Generalized Forces all Parallel to O z.- 18. Reduction of the Integral for the Induced Resistance.—Munk’s Theorems.- 19. General Case of Forces Perpendicular to the Axis O x.- 20. Problems of Minimum Induced Resistance.- 21. Distribution of Generalized Forces Giving a Constant Value of wz ?, wy ? over a Perpendicular Section of the Wake.- 22. Example. Case of the Single Wing.- C. The Field of Induced Velocities.- 23. Expressions for the Calculation of the Velocity Components when the “Generalized Forces” are given.- 24. Expressions for wx, wy, wz in the Case of Uniform Loading.- 25. Approximate Calculation of Induced Velocities (Reduced Span).- 26. Full Expression for the Downwash at Infinity in the Case of Elliptic Loading.- 27. Calculation of the Downwash at the Points of the Load System—Wing Replaced by Loaded Line.- 28. Case of a Loaded Surface of Arbitrary Form.- 29. Remark in Connection with Equations (28.8) and (27.6).- D. The Kutta-Joukowski Theorem.- 30. The Kutta-Joukowski Theorem for Wings of Infinite Span.- 31. The Application of the Kutta-Joukowski Theorem to the Three-Dimensional Case.- 32. Concluding Remarks.—Inverse Problem.- IV. Airfoils and Airfoil Systems of Finite Span.- 1. Introduction.- A. Single Wing.- 2. Case of Elliptic Loading.- 3. General Problem of the Single Wing.- Appendix to Section 3..- Evaluation of the Integral In.- 4. General Relations Expressed with the Aid of the Fourier Coefficients An.- 5. Rectangular Wing of Constant Profile and Constant Angle of Incidence.- 6. Effective Angle of Incidence. Induced Resistance.- 7. Comparison with Other Calculations.- 8. Tapered Airfoils.- 9. Twisted Airfoils.- 10. Influence of Sweep-Back on Pitching Moment.- 11. Airfoil with Ailerons Moved out of Neutral Position. Discontinous Change of Angle of Incidence at Certain Points of the Span.- 12. Iteration Method proposed by Irmgard Lotz.- 13. Airfoils of Moderate or Small Aspect Ratio.—Summary of Blenk’s Theory for the Rectangular Airfoil.- 14. Application to the Inverse Problem. Calculation of the Distribution of the Lift for a Given Airfoil.- 15. Application of Equation III (28.8) to the Calculation of wz.—Formulae for Yawed Rectangular Airfoil.- B. Multiplane Systems.- 16. Minimum Induced Drag of Multiplane Systems.- 17. Closed Rectangular System.- Appendix to Section.- The Schwarz-Christoffel Theorem.- 18. Biplane System with Equal Span for Both Wings.- 19. Single Wing with Shields at Ends.- 20. Airfoil with Gap.- 21. Direct Method for the Calculation of Biplane Systems.- 22. Elliptic Distribution of the Generalized Load for Both Wings.- 23. Final Expression for the Induced Resistance.- 24. Induced Resistance of Triplane Systems.- 25. Detailed Investigation of the Forces Acting on the Wings of a Biplane System.—Mean Values of the Velocity Components along the Wings.- 26. Continuation. Calculation of L1 and L2 when the Geometrical Angles of Incidence of both Wings Are Given.- 27. Refinement of the Theory.—Correction for Curvature of Stream-Lines.- 28. Further Refinement of the Theory.- C. Influence of Boundaries in the Field of Motion around Airfoil Systems.- 29. General Considerations Concerning the Influence of Boundaries.- 30. Example.—Image of a System with Respect to a Single Plane Boundary.- 31. General Treatment of the Influence of a Plane Boundary.- 32. Disturbing Velocities Experienced by the Original System.- 33. Case of a Plane Boundary Perpendicular to the Axis O y.- 34. Boundaries Composed of Systems of Plane Surfaces.- 35. Case of Four Boundaries Forming a Rectangular Prism.- 36. General Considerations on the Influence of Cylindrical or Prismatic Boundaries.- 37. Extension of the Theorem of III 16.- 38. Equation for the Induced Resistance.- 39. Image of a Vortex System with Respect to a Circular Boundary in Two-Dimensional Motion.- 40. Application to the Case of an Airfoil with Uniform Loading.- 41. Symmetrical Biplane.- 42. Calculation of the Windchannel Corrections at an Arbitrary Point of the Field.- 43. Application to a Special Case.- 44. Case of a Channel with Fixed Cylindrical Boundary (Closed Working Section).- 45. Influence of an Internal Cylindrical Boundary upon the Field of Motion around a Loaded Line.- 46. The Problem of Minimum Induced Resistance for a Loaded Line Connected with an Infinite Cylinder.- V. Problems of Non-Uniform and of Curvilinear Motion.- A. Problems of Non-Uniform Motion.- 1. Introduction.- Vortex System Associated with the Variations of the Circulation around an Airfoil.- 2. Equations for the Motion of a Fluid under the Influence of External Forces, if both the Latter and the General Velocity V are Functions of the Time.- 3. Continuation. Equation for the Vorticity.- 4. Circulation around an Airfoil in the Presence of Free Vortices.- 5. Accelerated Rectilinear Motion, Starting from Rest at t = 0.- 6. Airfoil Moving with Constant Velocity Describing Harmonic Oscillations.- 7. Expressions for the Force and the Moment Acting upon the Airfoil.- Appendix to Section 7..- Calculation of the Integrals I and J.- 8. Calculation of the Force Experienced by the Airfoil.- 9. Energy Expended in Producing the Vortex System.- Appendix to Section 9..- Calculation of the Coefficient C in the Expression $$ \gamma = 2\;C/\sqrt {x + c} $$ for the Vorticity in the Neighborhood of the Leading Edge.- B. Curvilinear Motion of an Airfoil.- 10. General Remarks Concerning the Vortex System in the Case of Curvilinear Flight.- 11. The Downward Velocity at the Airfoil, Due to Slightly Curved Vortices.- 12. Determination of the Distribution of the Lift over the Span.- VI. The Development of the Vortex System Downstream of the Airfoil.- 1. Introductory Considerations.- 2. Continuation.- Appendix to Section 2..- On the Influence of Higher Approximations in the Case of a Continuous Distribution of Vorticity.- 3. The Rolling up of the Vortex Sheet behind an Airfoil.- 4. Continuation.—Further Approximations.- 5. Application to the Vortex Sheet behind an Airfoil.- Appendix to Section 5..- Impulse of a System of Vortices.- 6. On the Calculation of the Downward Velocity Experienced by a Tailplane Placed behind a Single Airfoil.- 7. Conclusion.- Appendix to Section 7..- Energy of a Vortex Pair.- VII. Theory of the Wake.- 1. Introductory Remarks.- 2. The Method of Discontinuous Potential Motion.- 3. Discontinuous Potential Motion in the Case of a Straight Airfoil.- 4. Extension of the Theory of the Discontinuous Potential Motion to Curved Boundaries. Method of Levi-Civita.- 5. The Instability of Vortex Sheets.- 6. Stability of Double Rows of Vortices.- 7. The Expression for the Drag.- 8. Oseen’s Theory of the Wake.