Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 6 efficiencies are only a part of the total electo-mechanical efficiency of the power and propulsion system, battery, wiring harness, and controller efficiencies further reduced the total system efficiency. For their small size, these motors provide very good performance both in terms of torque production and high rotational speeds. One limitation of this three-pole stepper motor is the need for additional circuitry to cycle power through the motor coils. This adds mass to the system; in the final configuration of the 15g vehicle, the controllers represent a mass fraction of 20% to 30%. Simple circuitry is required to run the motor without feedback, but the motor efficiency is greatly reduced and the maximum RPM under load drops considerably, in this case from well over 50,000 RPM to below 25,000 RPM. Feedback is required to account for phase lags in the coil/shaft position induced by the rotational inertia of the shaft and rotor, friction, and aerodynamic drag. The feedback circuitry does not add considerably to the mass, but the complexity of the circuity increases. Small traditional or coreless DC motors, such a pager motors, are not a viable alternative. Although they require no additional circuity, these motors provide insufficient torque and rotational speed at his scale. Their efficiencies are also typically much lower, often as low as 5% to 10%. It may be possible that a design-specific traditional DC motor could be built with performance closer to the level of the 5mm Smoovy, but this is beyond the scope of this work. 6.2.2 Astroflight Firefly Motor The ten inch diameter rotor is powered by the Astroflight Firefly coreless DC motor with an integrated 16:1 gearbox, Model #800 [39]. This motor and gearbox have a combined mass of 12g and a manufacturer’s indicated efficiency of 83%. The Firefly and gearbox are pictured in Figure 6.2. This, once again, is not the total system electro-mechanical efficiency, simply that of the motor and gear box. This factor of two to four increase in efficiency relative to the 5mm Smoovy illustrates some of the practical difficulties associated with developing very small flight vehicles. In each case these motors represent the upper levels of performance at their respective scales. 98
FIGURE 6.2 The Astro Flight Firefly 800 with 16:1 gearbox, inch scale. The output power / RPM curve used for design with the Firefly motor has been Chapter 6 theoretically derived from motor characteristics provided by the manufacturer using a model of an idealized DC motor [40]. 6.3 Rotor Design Specifications 6.3.1 Five-Blade 2.2cm Diameter Rotor This rotor is the first manufactured and tested for the 5mm Smoovy three-phase stepper motor. It utilizes a NACA 4402 camberline with a nominal 2% constant thickness profile. It was developed using a predecessor to the current design tool and incorporates the angular momentum swirl model, Prandtl tip loss correction, and 2-D drag polars based on INS2d analyses. The diameter and blade count have been chosen by a parametric study completed with the same code. This rotor is pictured in Figure 6.3. 99
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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
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
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: Chapter 6 capable of speeds up to 1
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 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
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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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