Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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6.20 Comparison of laser scanning incidence data and quadratic fit with error xxii bounds for one blade of the Sample-1 four-blade 2.5cm rotor. ........................... 116 6.21 Sample-1 blade incidence distributions based on quadratic fitting of laser-scan data.................................................................................................. 117 6.22 Sample-2 blade incidence distributions based on quadratic fitting of laser-scan data.................................................................................................. 118 6.23 Sample-3 blade incidence distributions based on quadratic fitting of laser-scan data.................................................................................................. 118 6.24 Depiction of a chord-wise blade element for a rotational torsional deflection model................................................................................................... 121 6.25 Predicted torsional deflections for large-hub four-blade rotors. .......................... 124 6.26 Predicted torsional deflections with and without aerodynamic effects................ 125 6.27 Predicted torsional deflections for large-hub and small-hub four-blade rotors. .. 126 6.28 Comparison of experimental and predicted thrust with torsional deflections...... 127 6.29 Comparison of experimental and predicted power required with torsional deflections. ........................................................................................................... 127 6.30 Predicted torsional deflections for two versions of the five-blade 2.2cm rotor. .. 128 6.31 Comparison of experimental and predicted thrust with torsional deflections for two versions of the five-blade 2.2cm rotor..................................................... 129 6.32 OVERFLOW-D and rapid analysis method spanwise thrust distributions for the four-blade 2.5cm rotor. ............................................................................. 130 6.33 OVERFLOW-D and rapid analysis method spanwise torque distributions for the four-blade 2.5cm rotor. ............................................................................. 131 6.34 Predicted spanwise thrust distributions for the four-blade 2.5cm rotor using three different viscous swirl models..................................................................... 132 6.35 Predicted spanwise torque distributions for the 4-blade 2.5cm rotor using three different viscous swirl models..................................................................... 133 6.36 Predicted inflow angles using three different viscous swirl models. ................... 134 6.37 Local relative flow velocities using three different viscous swirl models. .......... 135
6.38 Predicted spanwise thrust distributions for the four-blade 2.5cm rotor using two different wake models. .................................................................................. 136 6.39 Predicted spanwise torque distributions for the four-blade 2.5cm rotor using two different wake models. ......................................................................................... 137 6.40 Local relative flow velocities using two different wake models.......................... 138 6.41 Predicted inflow angles using two different wake models................................... 138 6.42 Blade planforms obtained by applying the rapid design tool with three different viscous swirl models in conjunction with the classical Prandtl tip loss correction..................................................................................... 140 6.43 Blade incidence distributions obtained by applying the rapid design tool with three different viscous swirl models in conjunction with the classical Prandtl tip loss correction..................................................................................... 141 6.44 Predicted thrust for three different 2.5cm diameter rotor designs utilizing various viscous swirl models................................................................................ 143 6.45 Predicted power required for three different 2.5cm diameter rotor designs utilizing various viscous swirl models. ................................................................ 143 6.46 Blade planforms obtained by applying the rapid design tool with two different wake models in conjunction with the angular momentum swirl correction. ....... 145 6.47 Blade incidence distributions obtained by applying the rapid design tool with two different wake models in conjunction with the angular momentum swirl correction..................................................................................................... 146 6.48 Lift coefficient distributions predicted by the rapid analysis tool for three different rotor designs emphasizing the effect different wake models. ............... 147 6.49 Chordline pressure distribution at r/R=0.48, 50k RPM. ...................................... 148 6.50 Distribution of the chord-wise component of skin friction at r/R=0.48, 50k RPM. ......................................................................................... 149 7.1 The 15g prototype electric rotorcraft. .................................................................. 152 7.2 The 65g prototype electric rotorcraft, remote control version. ............................ 155 7.3 The 65g prototype electric rotorcraft, microprocessor version. ........................... 155 7.4 The 150g prototype electric rotorcraft. ................................................................ 157 xxiii
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 and 16: Chapter 5..........................
Page 17 and 18: List of Tables 3.1 Effect of Airfoi
Page 19 and 20: List of Figures 2.1 Comparison of I
Page 21: 5.6 Small test fixture in the large
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
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Q/r D L Chapter 4 FIGURE 4.1 Typica
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4.2.3 Elimination of Trigonometric
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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
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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
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most of the blade. These values are
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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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