Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 3 with increasing camber. The addition of 2% camber results in a 2.0 to 2.5 degree shift in the zero lift angle of attack. The maximum steady-state lift coefficients also increase. In the case of these two sections, there is a 30% increase in the maximum steady-state lift coefficient. Although the drag also increases, in this regime the ability to attain higher lift coefficients generally results in a net gain in lift-to-drag ratio. Due to the introduction of camber, the maximum lift-to-drag ratio increases from 4.5 to 5.4 at Re=1000 and from 9.3 to 11.0 at Re=6000. Within the quasi-linear range, the reduction in lift curve slope with a decrease in the Reynolds number is visible for the NACA 0002, but the effect of reducing the Reynolds number on the NACA 4402 is different. It appears as a drift towards higher zero lift angles of attack as the reduction in Reynolds number uniformly reduces the effective camber of the section across the entire quasi-linear lift range. All but the Re=1000 case eventually suffer from leading edge separation, but the onset is delayed slightly. This is most likely attributed to the increase in the ideal angle of attack that comes with the introduction of camber. The delay in trailing edge separation attributed to reducing the Reynolds number is also visible in the NACA 4402 results. At α=5.0 and Re=6000, separation occurs at 55% chord while at Re=2000 separation is pushed back to 92% chord. The Re=1000 case, at α=5.0, remains fully attached, and at α=7.5, is still attached up to 65% chord. Consideration of the drag polars in Figure 3.12 reveals trends similar to those at higher Reynolds numbers. The addition of camber results in an increase in zero lift drag and an upward shift of the polars towards higher lift coefficients. 36
C l C l 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 NACA 0002 Re=1000 NACA 4402 Re=1000 NACA 0002 Re=2000 NACA 4402 Re=2000 NACA 0002 Re=6000 NACA 4402 Re=6000 0 1 2 3 4 5 6 7 8 9 α (deg.) FIGURE 3.11 Lift curves for the NACA 4402 and NACA 0002. -0.1 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 C d NACA 0002 Re=6000 NACA 4402 Re=6000 NACA 0002 Re=2000 NACA 4402 Re=2000 NACA 0002 Re=1000 NACA 4402 Re=1000 FIGURE 3.12 Drag polars for the NACA 4402 and NACA 0002. Chapter 3 37
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AERODYNAMICS AND DESIGN FOR ULTRA-L
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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 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: FIGURE 3.10 NACA 0002 and NACA 0008
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 and 100: 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
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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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