Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 5 5.2 Rotor Manufacturing 5.2.1 Shape Deposition Manufacturing Three different methods have been used in the manufacturing of the rotor prototypes. The smaller rotors are fabricated by the Rapid Prototyping Laboratory at Stanford University. The rotors constructed of epoxy resin have been built using the Shape Deposition Manufacturing (SDM) process [31]. A pictorial summary of this method is shown in Figure 5.1. This method can yield very accurate geometries during manufacturing within certain limitations, but in the case of these micro-rotors, the accuracy of the specified geometry after handling and use has proven to be a problem. Each blade has a minimum thickness of only 20 mils, but the desired camberline is accurately reproduced as seen in Figure 5.2. The blade airfoil geometry is the result of the two-dimensional airfoil optimization at Re = 6000. The NACA four-digit thickness distribution is clearly not reproduced in this case. The desire to minimize section thickness is tempered by manufacturing minimum gage constraints. If the design exceeds these minimums the tooling forces may deform or tear away the part. The trade is then between a thicker airfoil section with a more conventional thickness distribution, or a constant thickness section at minimum gage. The results of Chapter 3 indicate that the latter is preferred. A second cross-section, in this case a NACA 4402 camberline, is shown in Figure 5.3. In both cases the constant thickness regions are approximately 2% chord, representing this minimum gage constraint. In this case, some shaping of the leading and trailing edge regions is visible. This is achieved by reversing the manufacturing orientation such that the kerf of the tool at the bounding tool paths provides beneficial shaping. A comprehensive discussion of the manufacturing aspects of the mesicopter project is provided by Cheng [32]. It is important to recall that, as shown in Chapter 3, the camberline is the primary determinant of performance for very thin sections. 76
1. Substrate Preparation 2. Polymer Casting 3. Surface Flattening 4. Shaping Part Material to Net Shape �� 5. Substrate Removal FIGURE 5.1 Summary of rotor SDM process (from Ref. 32) �� FIGURE 5.2 Specified airfoil and blade section photomicrograph. Chapter 5 77
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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
Page 49 and 50: The canonical pressure coefficient
Page 51 and 52: Chapter 3 reaches α=5.0 and a lift
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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
Page 73 and 74: Chapter 4 Hybrid Method for Rotor D
Page 75 and 76: Q/r D L Chapter 4 FIGURE 4.1 Typica
Page 77 and 78: 4.2.3 Elimination of Trigonometric
Page 79 and 80: Chapter 4 applications of interest
Page 81 and 82: 4.2.7 The Distinction Between the A
Page 83 and 84: Chapter 4 Two input parameters dete
Page 85 and 86: Chapter 4 simplification, particula
Page 87 and 88: 4.3.3 Conservation of Angular Momen
Page 89 and 90: Chapter 4 moves downstream is less
Page 91 and 92: Chapter 4 of the pitch angle at the
Page 93 and 94: FIGURE 4.6 Converged wake streamlin
Page 95 and 96: Chapter 4 idealized models. The met
Page 97 and 98: ��
Page 99: Chapter 5 Overview of Experimental
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 -
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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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