Canard & Wing Airfoils

157 Pages·2014·2.85 MB·English

by  Ghalami, Mahdi

CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

STATIC PITCH STABILITY OF CANARD CONFIGURED AIRCRAFT

A thesis submitted in partial fulfillment requirements
For the degree of Master of Science in
Mechanical Engineering

By
Mahdi Ghalami

December 2013
The thesis of Mahdi Ghalami is approved:

Stewart Prince, Ph.D. Date

George Youssef, Ph.D. Date

Timothy Fox, Chair Date

California State University, Northridge
ii
Acknowledgement

Dedicated to Sahar
My love, my life, and my wife
For all her love, supports, and understanding

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Table of Contents
Signature Page .................................................................................................................... ii
Acknowledgement ............................................................................................................. iii
List of Figures .................................................................................................................. viii
List of Symbols ................................................................................................................ xiii
Abstract ............................................................................................................................. xv
1. Introduction ................................................................................................................. 1
1.1 Stability ................................................................................................................ 1
1.2 Stable Flight ......................................................................................................... 4
1.3 Canard Concept .................................................................................................... 7
2. Design and Analysis .................................................................................................. 11
2.1 Canard Configuration ......................................................................................... 11
2.2 Airfoil ................................................................................................................. 13
2.3 Reynolds Number ............................................................................................... 18
2.4 Finite Wing ......................................................................................................... 24
2.5 Finite Wing Moment Coefficient (CM) .............................................................. 26
2.6 Finite Wing Lift Coefficient (CL) ....................................................................... 27
2.7 Finite Wing Drag Coefficient (CD) .................................................................... 31
2.8 Parasite Drag of Non-Aerodynamic Parts .......................................................... 33
2.9 Aircraft Actual Lift............................................................................................. 36
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2.10 Aircraft Actual Drag........................................................................................... 38
2.11 Drag Polar .......................................................................................................... 39
2.12 Pitch Static Stability Criteria .............................................................................. 42
2.13 Equilibrium Flight .............................................................................................. 46
2.14 Aircraft Moment Coefficient (CM) .................................................................... 47
2.15 Finding CG Location .......................................................................................... 49
2.16 Pitch Static Stability ........................................................................................... 51
2.17 Aerodynamic Center or Neutral Point (NP) ....................................................... 52
2.18 Static Margin(SM).............................................................................................. 54
3. Excel Spreadsheets .................................................................................................... 57
3.1 Inputs .................................................................................................................. 57
3.2 Aerodynamic Characteristics of Airfoils............................................................ 60
3.3 3D Lift Curve Requirements .............................................................................. 63
3.4 AR Impact on Lift Curves .................................................................................. 65
3.5 3D Aerodynamic Characteristics ....................................................................... 66
3.6 Parasite Drag ...................................................................................................... 69
3.7 Drag Polar and Aerodynamic Efficiency Plots .................................................. 71
3.8 Cruise Optimization ........................................................................................... 71
3.9 Center of Gravity ................................................................................................ 72
3.10 Static Margin ...................................................................................................... 73
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3.11 Optimization ....................................................................................................... 73
4. Results ....................................................................................................................... 74
4.1 Airfoil Selection ................................................................................................. 74
4.2 Canard and Wing Airfoil Comparison ............................................................... 80
4.3 Canard 2D vs. 3D models .................................................................................. 82
4.4 Wing 2D vs. 3D models ..................................................................................... 84
4.5 Aspect Ratio Impact on Lift Slope ..................................................................... 86
4.6 Wing and Canard Comparison ........................................................................... 87
4.7 Aircraft Lift and Drag Coefficients .................................................................... 89
4.8 Aircraft Drag Polar ............................................................................................. 91
4.9 Aircraft Cruise Condition ................................................................................... 92
4.10 Cruise Optimization ........................................................................................... 94
4.11 Angle of Incidence Results ................................................................................ 95
4.12 CG Location ....................................................................................................... 99
4.13 Static Margin .................................................................................................... 100
4.14 Optimization ..................................................................................................... 100
5. Conclusion ............................................................................................................... 113
Bibliography ................................................................................................................... 115
Appendices ...................................................................................................................... 117
Appendix A. Excel Spreadsheets ................................................................................ 117
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Appendix B. Aircraft Lift Coefficient Equation ......................................................... 138
Appendix C. Aircraft Drag Coefficient Equation ....................................................... 139
Appendix D. Aircraft Moment Coefficient Equation.................................................. 141

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List of Figures
Figure 1-1 Stable stability [3] ............................................................................................... 1
Figure 1-2 Unstable stability [3]........................................................................................... 2
Figure 1-3 Neutral stability [3] ............................................................................................. 2
Figure 1-4 Aperiodic dynamic stability [3] .......................................................................... 3
Figure 1-5 Damped oscillation Dynamic Stability [3].......................................................... 3
Figure 1-6 Increasing oscillation dynamic stability [3] ........................................................ 3
Figure 1-7 Aircraft’s axes with translational and rotational motions ................................. 4
Figure 1-8 Moments and forces .......................................................................................... 6
Figure 1-9 Flyer one (National Air and Space Museum) .................................................. 8
Figure 1-10 Rutan’s Voyager design (National Air and Space Museum) .......................... 9
Figure 1-11 Rutan’s VariEz design (Courtesy of National Air and Space Museum) ......... 9
Figure 1-12 Canard Design of CSUN 2011 Aeronautics Team ....................................... 10
Figure 2-1 Earlier stall; for canard (a), and wing (b) ........................................................ 11
Figure 2-2 Earlier hitting zero lift; for wing (a), and canard (b)....................................... 12
Figure 2-3 Airfoil section [3] ............................................................................................. 13
Figure 2-4 Airfoil terms [3] ................................................................................................ 14
Figure 2-5 Low speed airfoil types (Drawn by Profili Software [10]) ............................... 14
Figure 2-6 Definition of forces, moment, and relative wind ............................................ 15
Figure 2-7 NACA 2412 airfoil plots [7] ............................................................................. 16
Figure 2-8 Cambered airfoil vs. symmetric airfoil [9] ....................................................... 17
Figure 2-9 Transition from laminar to turbulent [3] ........................................................... 19
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Figure 2-10 c vs. α curves at different Re number of airfoil E210 (Drawn by Profili
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Software [10]) ..................................................................................................................... 20
Figure 2-11 c vs. AOA curve of some airfoils at same Re number of 250,000 (Drawn by
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Profili Software [10]) .......................................................................................................... 21
Figure 2-12 c vs. AOA curve at different Re number for wing and canard airfoils (Drawn
l
by Profili Software [10]) ..................................................................................................... 23
Figure 2-13 Infinite wing [3] .............................................................................................. 24
Figure 2-14 Wing vortices on a finite wing ...................................................................... 25
Figure 2-15 Origin of induced drag [3] .............................................................................. 26
Figure 2-16 AR impact on cl vs. AOA curve .................................................................... 28
Figure 2-17 Airfoil LE sharpness parameter [11] ............................................................... 30
Figure 2-18 Angle of attack increment for maximum lift coefficient [11] ......................... 30
Figure 2-19 Drag polar...................................................................................................... 40
Figure 2-20 Aerodynamic efficiency (E or L/D) vs. AOA ............................................... 41
Figure 2-21 Aircraft in steady, equilibrium flight at its trim angle .................................. 42
Figure 2-22 Nose up disturbance ...................................................................................... 43
Figure 2-23 Nose down disturbance ................................................................................. 43
Figure 2-24 Moment coefficient vs. AOA curve with a negative slope ........................... 44
Figure 2-25 Moment coefficient curve with a positive slope ........................................... 45
Figure 2-26 Statically unstable flight ................................................................................ 45
Figure 2-27 Forces and moments ...................................................................................... 46
Figure 2-28 Moments, forces and their distances from CG .............................................. 47
Figure 2-29 Impact of NP location on CM curve slope ..................................................... 53
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Figure 2-30 Importance of lift center location, behind the CG [3] .................................... 54
Figure 3-1 c vs. α curves of airfoil FX63-137(Re=130,000), and SD7062 (Re=350,000)
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........................................................................................................................................... 61
Figure 3-2 Airfoil SD7062 lift characters ......................................................................... 62
Figure 3-3 AR impact on the lift slope ............................................................................. 65
Figure 3-4 Angle of incidence impact .............................................................................. 67
Figure 4-1 cl vs. α curve of airfoil FX63-137 at Re number of 130,000 .......................... 74
Figure 4-2 cd vs. α curve of airfoil FX63-137 at Re number of 130,000 .......................... 75
Figure 4-3 cl/cd vs. α curve of airfoil FX63-137 at Re number of 130,000 ...................... 75
Figure 4-4 cl vs. cd curve of airfoil FX63-137 at Re number of 130,000 ......................... 76
Figure 4-5 cm vs. α curve of airfoil FX63-137 at Re number of 130,000 ......................... 76
Figure 4-6 cl vs. α curve of airfoil SD7062 at Re number of 350,000 .............................. 77
Figure 4-7 cd vs. α curve of airfoil SD7062 at Re number of 350,000 ............................. 78
Figure 4-8 cl/cd vs. α curve of airfoil SD7062 at Re number of 350,000 ......................... 78
Figure 4-9 cl vs. cd curve of airfoil SD7062 at Re number of 350,000 ............................. 79
Figure 4-10 cm vs. α curve of airfoil SD7062 at Re number of 350,000 .......................... 79
Figure 4-11 c vs. α curves of airfoil FX63-137(Re=130,000), and SD7062 (Re=350,000)
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........................................................................................................................................... 80
Figure 4-12 c vs. α curves of airfoil FX63-137(Re=130,000), and SD7062 (Re=350,000)
d
........................................................................................................................................... 81
Figure 4-13 cl/cd vs. α curves of FX63-137(Re=130,000), and SD7062 (Re=350,000) .. 81
Figure 4-14 c vs. α curves of airfoil FX63-137(Re=130,000), and SD7062 (Re=350,000)
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........................................................................................................................................... 82
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