Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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xvi 6.5.1 Static Structural Deformations ................................................................ 114 6.5.2 Operational Deformations ....................................................................... 119 6.6 Spanwise Thrust and Torque Distributions ..................................................... 129 6.7 Modeling Effects on Performance Estimation.................................................. 132 6.7.1 Effect of Swirl Modeling on Performance Estimation ............................ 132 6.7.2 Effect of Wake Modeling on Performance Estimation............................ 135 6.8 Modeling Effects on Design Configuration...................................................... 139 6.8.1 Effect of Swirl Modeling on Design........................................................ 139 6.8.2 Effect of Wake Modeling on Design....................................................... 144 6.9 Three-Dimensional Boundary Layer Effects.................................................... 147 Chapter 7 ...................................................................................................151 Micro-Rotorcraft Prototypes 7.1 Introduction....................................................................................................... 151 7.2 The 15g Prototype............................................................................................. 151 7.3 The 65g Prototype............................................................................................. 154 7.4 The 150g Prototype........................................................................................... 157 7.5 Insights Gained, Limiting Technologies, and the Potential for Future Development ......................................................................................... 159 7.5.1 Emerging Battery Technologies .............................................................. 160 7.5.2 Electro-mechanical Efficiency................................................................. 161 7.5.3 Rotor Aerodynamic Efficiency................................................................ 162 Chapter 8 ...................................................................................................169 Conclusions and Recommendations 8.1 Summary of Results and Contributions in the Area of Two-Dimensional Aerodynamics..................................................................... 169 8.2 Summary of Results and Contributions in the Area of Ultra-Low Reynolds Number Rotors................................................................ 171 8.3 Consideration of Future Work.......................................................................... 172 References .................................................................................................177
List of Tables 3.1 Effect of Airfoil Thickness Ratio and Reynolds Number on Zero Lift Drag. ....... 31 3.2 Effect of Camber Variations on L/D for a 2% Thick Airfoil. ................................ 39 6.1 Comparison of predicted thrust and power required at three operating points. ... 109 7.1 Mass allocation for the 15g prototype electric rotorcraft..................................... 153 7.2 Mass allocation for the 65g prototype electric rotorcraft..................................... 154 7.3 Mass allocation and payload estimate for the 150g prototype electric rotorcraft.................................................................................. 158 7.4 Summary of physical and performance data for three prototype electric rotorcraft.................................................................................. 160 xvii
Page 1 and 2: AERODYNAMICS AND DESIGN FOR ULTRA-L
Page 3: I certify that I have read this dis
Page 7 and 8: Abstract Growing interest in micro-
Page 9 and 10: Nomenclature A Rotor disk area B Nu
Page 11 and 12: τ Shear stress ω, Ω Rotor angul
Page 13 and 14: Contents Acknowledgments...........
Page 15: Chapter 5..........................
Page 19 and 20: List of Figures 2.1 Comparison of I
Page 21 and 22: 5.6 Small test fixture in the large
Page 23 and 24: 6.38 Predicted spanwise thrust dist
Page 25 and 26: Chapter 1 Introduction 1.1 Looking
Page 27 and 28: Chapter 1 wind-tunnel facilities an
Page 29 and 30: 1.3 Summary of Contributions Chapte
Page 31 and 32: Chapter 2 Two-Dimensional Computati
Page 33 and 34: Chapter 2 The artificial compressib
Page 35 and 36: Chapter 2 The control volume method
Page 37 and 38: 2.2.4 Comparison with Experiment Th
Page 39 and 40: Chapter 2 to diverge if significant
Page 41 and 42: 2.4 Flow Field Assumptions The INS2
Page 43 and 44: Chapter 2 The results of these time
Page 45 and 46: Chapter 3 Analysis and Design of Ai
Page 47 and 48: Chapter 3 adverse gradient in the p
Page 49 and 50: The canonical pressure coefficient
Page 51 and 52: Chapter 3 reaches α=5.0 and a lift
Page 53 and 54: ��
Page 55 and 56: Cl 0.50 0.40 0.30 0.20 0.10 0.00 -0
Page 57 and 58: Re=6000 result due to Reynolds numb
Page 59 and 60: FIGURE 3.10 NACA 0002 and NACA 0008
Page 61 and 62: C l C l 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Page 63 and 64: Chapter 3 The maximum L/D for all n
Page 65 and 66: 3.5 Effect of Leading Edge Shape an
Page 67 and 68:
C l 0.60 0.50 0.40 0.30 0.20 0.10 0
Page 69 and 70:
Chapter 3 prominent droop near the
Page 71 and 72:
Chapter 3 Small improvements in lif
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Chapter 4 Hybrid Method for Rotor D
Page 75 and 76:
Q/r D L Chapter 4 FIGURE 4.1 Typica
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4.2.3 Elimination of Trigonometric
Page 79 and 80:
Chapter 4 applications of interest
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4.2.7 The Distinction Between the A
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Chapter 4 Two input parameters dete
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Chapter 4 simplification, particula
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4.3.3 Conservation of Angular Momen
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Chapter 4 moves downstream is less
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Chapter 4 of the pitch angle at the
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FIGURE 4.6 Converged wake streamlin
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Chapter 4 idealized models. The met
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��
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Chapter 5 Overview of Experimental
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1. Substrate Preparation 2. Polymer
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Chapter 5 surface finish and aids i
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FIGURE 5.5 Small test fixture in th
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Chapter 5 The direct influence of t
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FIGURE 5.9 Large test fixture in th
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5.4.1 Motor Power Supply All tests
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Chapter 5 or roughly (+/-) 25% of t
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Chapter 5 newly forming blade tip v
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FIGURE 5.14 Near-body grid geometry
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Chapter 6 Design Examples and Compa
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Chapter 6 capable of speeds up to 1
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FIGURE 6.2 The Astro Flight Firefly
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t/c 0.5 0.4 0.3 0.2 0.1 0.0 FIGURE
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c/R 0.0 0.2 0.4 0.6 0.8 1.0 r/R Cha
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FIGURE 6.10 Carbon-fiber two-blade
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Power Req. (W) 3.5 3.0 2.5 2.0 1.5
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Chapter 6 TABLE 6.1 Comparison of p
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Electro-mechanical Efficiency 0.20
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these variations and possible solut
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upper and lower surface corners of
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Chapter 6 The Sample-1 rotor exhibi
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The static deformations described i
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Q( r) This problem is solved as a l
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Structural Analyses Chapter 6 The m
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Aero-Structural Twist (deg.) 0.00 -
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Thrust (g) 5 4 3 2 1 0 10000 20000
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Thrust (g) 4.5 4.0 3.5 3.0 2.5 2.0
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Torque per unit span (g cm) 0.75 0.
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Thrust per unit span (g) 3.5 3.0 2.
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V total / ωr 1.0 0.9 0.8 Classical
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Torque per unit span (g cm) 0.75 0.
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Chapter 6 Recall that this rotor wa
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Incidence (deg.) 30 25 20 15 10 5 0
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Thrust (g) 9 8 7 6 5 4 3 2 38000 40
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x/R 0.4 0.2 0.0 -0.2 Chapter 6 FIGU
Page 171 and 172:
Cl 0.64 0.62 0.60 0.58 0.0 0.2 0.4
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C f 0.125 0.100 0.075 0.050 0.025 0
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Chapter 7 Micro-Rotorcraft Prototyp
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This vehicle does not currently inc
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FIGURE 7.2 The 65g prototype electr
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7.4 The 150g Prototype Chapter 7 Th
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At hover, with a mass of 153g, the
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Using the 150g prototype as an exam
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Chapter 7 Basic rotor theory has be
Page 189 and 190:
most of the blade. These values are
Page 191 and 192:
Chapter 7 For large scale helicopte
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Chapter 8 Conclusions and Recommend
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the significant performance gains a
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Chapter 8 are also opportunities to
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Chapter 8 formation flight, and man
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References [1] Spedding, G.R., Liss
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[28] Lamb, Sir Horace, Hydrodynamic
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Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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