Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 6 Similar results are found for the two versions of the five-blade 2.2cm diameter rotors. The predicted deflections are shown in Figure 6.30. The large differences result from the variations in the thickness distribution over the first 25% of the blade. The slight change in incidence has negligible effect and in this case the planform and hub diameter is identical for both rotors. Compared to the four-blade rotor this design exhibits roughly twice as much variation across the sampled operating speeds, even though the roots chords and tip speeds are similar. The large mid-span chords of this design contribute to this difference. 128 Aero-Structural Twist (deg.) 0.0 -2.5 -5.0 Original Design Original Design +3 deg. -7.5 -10.0 30,000 RPM 35,000 RPM 40,620 RPM 46,790 RPM 50,760 RPM 0.0 0.2 0.4 0.6 0.8 1.0 r/R FIGURE 6.30 Predicted torsional deflections for two versions of the five-blade 2.2cm rotor.
Thrust (g) 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Reduced-order Method Experiment Reduced-order Method, Original +3 deg. Experiment, Original +3 deg. Modeled w/ Torsional Defl. Modeled w/ Torsional Defl., +3 deg. 10000 20000 30000 RPM 40000 50000 Chapter 6 FIGURE 6.31 Comparison of experimental and predicted thrust with torsional deflections for two versions of the five-blade 2.2cm rotor. The rapid analysis method thrust predictions for the deflected forms are presented with the experimental results and the undeflected predicted performance in Figure 6.31. Here the agreement is not as good as in the four-blade case, but the overall trend is well captured considering that only two iterations on the aerodynamic forces were performed. Performance analysis of these deflected forms reinforces the importance of torsional effects and the ability of the current tools to capture them. It also provides closure on the most anomalous experimental behavior observed over the course of this research. 6.6 Spanwise Thrust and Torque Distributions The experimental results have so far limited the discussion of performance to the gross performance parameters of total thrust and total power required. Three-dimensional 129
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AERODYNAMICS AND DESIGN FOR ULTRA-L
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I certify that I have read this dis
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Abstract Growing interest in micro-
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Nomenclature A Rotor disk area B Nu
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τ Shear stress ω, Ω Rotor angul
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Contents Acknowledgments...........
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Chapter 5..........................
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List of Tables 3.1 Effect of Airfoi
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List of Figures 2.1 Comparison of I
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5.6 Small test fixture in the large
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6.38 Predicted spanwise thrust dist
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Chapter 1 Introduction 1.1 Looking
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Chapter 1 wind-tunnel facilities an
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1.3 Summary of Contributions Chapte
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Chapter 2 Two-Dimensional Computati
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Chapter 2 The artificial compressib
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Chapter 2 The control volume method
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2.2.4 Comparison with Experiment Th
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Chapter 2 to diverge if significant
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2.4 Flow Field Assumptions The INS2
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Chapter 2 The results of these time
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Chapter 3 Analysis and Design of Ai
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Chapter 3 adverse gradient in the p
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The canonical pressure coefficient
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Chapter 3 reaches α=5.0 and a lift
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��
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Cl 0.50 0.40 0.30 0.20 0.10 0.00 -0
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Re=6000 result due to Reynolds numb
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FIGURE 3.10 NACA 0002 and NACA 0008
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C l C l 0.8 0.7 0.6 0.5 0.4 0.3 0.2
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Chapter 3 The maximum L/D for all n
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3.5 Effect of Leading Edge Shape an
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C l 0.60 0.50 0.40 0.30 0.20 0.10 0
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Chapter 3 prominent droop near the
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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
Page 101 and 102: 1. Substrate Preparation 2. Polymer
Page 103 and 104: Chapter 5 surface finish and aids i
Page 105 and 106: FIGURE 5.5 Small test fixture in th
Page 107 and 108: Chapter 5 The direct influence of t
Page 109 and 110: FIGURE 5.9 Large test fixture in th
Page 111 and 112: 5.4.1 Motor Power Supply All tests
Page 113 and 114: Chapter 5 or roughly (+/-) 25% of t
Page 115 and 116: Chapter 5 newly forming blade tip v
Page 117 and 118: FIGURE 5.14 Near-body grid geometry
Page 119 and 120: Chapter 6 Design Examples and Compa
Page 121 and 122: Chapter 6 capable of speeds up to 1
Page 123 and 124: FIGURE 6.2 The Astro Flight Firefly
Page 125 and 126: t/c 0.5 0.4 0.3 0.2 0.1 0.0 FIGURE
Page 127 and 128: c/R 0.0 0.2 0.4 0.6 0.8 1.0 r/R Cha
Page 129 and 130: FIGURE 6.10 Carbon-fiber two-blade
Page 131 and 132: Power Req. (W) 3.5 3.0 2.5 2.0 1.5
Page 133 and 134: Chapter 6 TABLE 6.1 Comparison of p
Page 135 and 136: Electro-mechanical Efficiency 0.20
Page 137 and 138: these variations and possible solut
Page 139 and 140: upper and lower surface corners of
Page 141 and 142: Chapter 6 The Sample-1 rotor exhibi
Page 143 and 144: The static deformations described i
Page 145 and 146: Q( r) This problem is solved as a l
Page 147 and 148: Structural Analyses Chapter 6 The m
Page 149 and 150: Aero-Structural Twist (deg.) 0.00 -
Page 151: Thrust (g) 5 4 3 2 1 0 10000 20000
Page 155 and 156: Torque per unit span (g cm) 0.75 0.
Page 157 and 158: Thrust per unit span (g) 3.5 3.0 2.
Page 159 and 160: V total / ωr 1.0 0.9 0.8 Classical
Page 161 and 162: Torque per unit span (g cm) 0.75 0.
Page 163 and 164: Chapter 6 Recall that this rotor wa
Page 165 and 166: Incidence (deg.) 30 25 20 15 10 5 0
Page 167 and 168: Thrust (g) 9 8 7 6 5 4 3 2 38000 40
Page 169 and 170: 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
Page 173 and 174: C f 0.125 0.100 0.075 0.050 0.025 0
Page 175 and 176: Chapter 7 Micro-Rotorcraft Prototyp
Page 177 and 178: This vehicle does not currently inc
Page 179 and 180: FIGURE 7.2 The 65g prototype electr
Page 181 and 182: 7.4 The 150g Prototype Chapter 7 Th
Page 183 and 184: At hover, with a mass of 153g, the
Page 185 and 186: Using the 150g prototype as an exam
Page 187 and 188: 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
Page 193 and 194: Chapter 8 Conclusions and Recommend
Page 195 and 196: the significant performance gains a
Page 197 and 198: Chapter 8 are also opportunities to
Page 199 and 200: Chapter 8 formation flight, and man
Page 201 and 202: References [1] Spedding, G.R., Liss
Page 203 and 204:
[28] Lamb, Sir Horace, Hydrodynamic
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Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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