Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 7 166 Rotor Solidity 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 40 44 48 52 56 60 64 68 72 76 80 C l / C d FIGURE 7.5 Figure of merit as a function of mean section performance and solidity at C l=1.0. Rotor Solidity 0.30 0.26 0.22 0.18 0.14 0.10 0.06 0.02 0.15 0.11 0.23 0.77 0.19 0.27 0.32 0.81 0.71 0.36 0.44 FIGURE 7.6 Figure of merit as a function of mean section performance and solidity at C l =0.6. 0.72 0.87 0.86 0.74 0.76 0.40 0.52 0.89 0.48 0.82 0.84 0.79 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 C l / C d 0.56 0.68 0.60 0.64 0.72
Chapter 7 For large scale helicopters, Figure 7.5 predicts figure of merit values between 0.80 and 0.87. This agrees reasonably well with the actual values for many full-scale helicopters. The results are seen to be relatively insensitive to airfoil performance. For micro-rotors, Figure 7.6 paints a very different picture. In this regime the figure of merit is highly sensitive to section performance. The two micro-rotor designs considered here, the four- blade 2.5cm diameter rotor and the and the five-blade 2.2cm diameter rotor, have comparatively high solidity values of 24% and 35% respectively, but the upper bound on figure of merit for these rotors appears to be between 0.60 and 0.65 based on the predicted optimal section performance of Chapter 3. Under the best case scenario then, centimeter scale micro-rotors can expect a 20% to 30% reduction in figure of merit relative to large scale helicopter rotors. With the upper limits of performance reasonably well defined, there is still room for improvement and motivation for research and design for centimeter scale rotors. The rotor design examples described here still fall short of this target. The computed and measured values of the figure of merit for the four-blade 2.5cm diameter rotor are provided in Figure 7.7 as a function of the rotor RPM. The rapid analysis method provides the most optimistic estimate of approximately M=0.55, the measured values for this single sample are lower, at approximately M=0.39 for the higher RPM of primary interest. 167
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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
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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
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 and 152: Thrust (g) 5 4 3 2 1 0 10000 20000
Page 153 and 154: Thrust (g) 4.5 4.0 3.5 3.0 2.5 2.0
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: most of the blade. These values are
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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