Phase II Final Report - NASA's Institute for Advanced Concepts

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Planetary Exploration Using Biomimetics An Entomopter for Flight on Mars Cm = Coefficient of Moment Cp = Coefficient of Power Required. Table 3-8: List of Symbols (Continued) 3.3.3.7 Model Formulation for Baseline Case It was assumed that the planform shape of the Entomopter wing is fixed in three dimensions and for parametric analysis, as we change the span of the wing, the chord length will vary all along the wing, so the shape of the planform is just defined by one parameter: span. Also it is assumed that the axis of rotation ("a") is constant. Hence, the total number of variables considered reduce to five: span, velocity, flapping frequency, flapping amplitude, and pitch amplitude. A cycle is defined as one complete upbeat and one downbeat, starting with h = 0 at t = 0, and then it moves (upwards) to -hamp at 1/4 time period, and then starts the down beat, continuing until the 3/4 time period. In the final 1/4 time period, it comes back to the zero position. The angle of attack stays constant during the upbeat and downbeat and it flips during the 1/20th portion of time period at the extremes of the upbeat and down beat. A computer code was written in Mathcad 2000 to evaluate these results. The values and equations used for baseline case are as follows: (NOTE: the notation used below ":=" means "defined as".) V:= 14 freq := 16 Plamp := 75 Pitamp := 8 sspan span := 2 a:= −0.25 ω := 4⋅ freq ⋅ Plamp ⋅ ⎛ ⎜ ⎝ π 180 hamp := sspan ⋅ sin Plamp ⋅ αamp := Pitamp ⋅ t := 0 , 100⋅ freq π 180 1 100⋅ freq π 180 ⎞ ⎠ 1 .. freq Since the instantaneous flapping height changes linearly, it was decided that different coefficients would be calculated for the first quarter cycle, then from 1/4 until 3/4 and finally for the last quarter of the cycle. This will give close to linear change effects. A similar approach was adopted for pitching motion coefficients and different coefficients were evaluated for flipping from positive to negative and vice versa. These coefficients were determined by solving a system of nonlinear simultaneous equations. ( ) h01 + h11 ⋅ cos φh1 0 128 Phase II Final Report
Chapter 3.0 Vehicle Design 3.3 Wing Aerodynamics h01 + h11 ⋅ cos ⎛ ⎜ ⎝ ω 8 ⋅ freq + φh1 ⎛ ⎝ ( ) ⎞ ⎠ −hamp 2 ω h01 + h11 ⋅ cos ⎜ + φh1 −hamp 4 ⋅ freq Coeff1 := Find h11, φh1, h01 ⎛ ⎝ ω h02 + h12 ⋅ cos ⎜ + φh2 −hamp 4 ⋅ freq ⎛ ⎝ The flapping motion produced is shown in Figure 3-118. ⎞ ⎠ ⎞ ⎠ ⎞ ⎠ ω h02 + h12 ⋅ cos⎜ + φh2 0 2 ⋅ freq ⎛ ⎝ ( ) 3 ⋅ ω h02 + h12 ⋅ cos⎜ + φh2 hamp 4 ⋅ freq Coeff2 := Find h12, φh2, h02 ⎛ ⎝ 3 ⋅ ω h03 + h13 ⋅ cos⎜ + φh3 hamp 4 ⋅ freq h03 + h13 ⋅ cos ⎛ ⎜ ⎝ ⎛ ⎝ 7 ⋅ ω 8⋅ freq + φh3 ⎞ ⎠ ⎞ ⎠ ⎞ ⎠ ⎞ ⎠ ω h03 + h13 ⋅ cos⎜ + φh3 0 freq ( ) Coeff5 := Find h13, φh3, h03 ⎛ ⎝ ⎛ ⎜ ⎝ ⎛ ⎜ ⎝ ⎛ ⎝ hamp 2 1 1 3 h0() t := if⎜ t≤ , Coeff1 2 , if⎜ t > ∧ t ≤ , Coeff2 2 , Coeff5 2 4 ⋅ freq 4 ⋅ freq 4 ⋅ freq ⎛ ⎝ 1 1 3 h1() t := if t≤ , Coeff1 0 , if⎜ t > ∧ t ≤ , Coeff2 0 , Coeff5 0 4 ⋅ freq 4 ⋅ freq 4 ⋅ freq ⎛ ⎝ 1 1 3 φh() t := if t≤ , Coeff1 1 , if⎜ t > ∧ t ≤ , Coeff2 1 , Coeff5 1 4 ⋅ freq 4 ⋅ freq 4 ⋅ freq ( ) ht ():= h0t () + h1t () ⋅ cos ω ⋅ t + φht () ⎞⎞ ⎠⎠ ⎞⎞ ⎠⎠ ⎞⎞ ⎠⎠ 129
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Planetary Exploration Using Biomime
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Table of Contents Table of Contents
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List of Tables List of Tables Table
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List of Figures List of Figures Fig
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List of Figures Figure 3-54: Pressu
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List of Figures Figure 3-138: Stere
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List of Figures Figure 4-24: Averag
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List of Contributors List of Contri
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Executive Summary Executive Summary
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Chapter 1.0 Introduction Chapter 1.
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Chapter 1.0 Introduction Figure 1-2
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Chapter 1.0 Introduction 1.1 Histor
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Chapter 1.0 Introduction 1.2 Origin
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Chapter 1.0 Introduction 1.3 Missio
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1.3.3.1 Surface Imaging The Entomop
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Chapter 2.0 Entomopter Configuratio
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Chapter 3.0 Vehicle Design 3.1 Wing
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Chapter 3.0 Vehicle Design 3.5 Fuel
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Chapter 3.0 Vehicle Design 3.6 Powe
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Chapter 4.0 Entomopter Flight Opera
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Chapter 5.0 Potential Payload Funct
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Chapter 6.0 Media Exposure 6.1 Intr
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Chapter 6.0 Media Exposure 6.3 Onli
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Chapter 6.0 Media Exposure 6.6 Spec
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Chapter 7.0 Conclusion Chapter 7.0
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Appendix A: Mars Atmosphere Data JP
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Appendix A: Mars Atmosphere Data Ge
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Appendix A: Mars Atmosphere Data Ge
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Appendix A: Mars Atmosphere Data Ma
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Appendix B: Sizing Results Appendix
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Appendix B: Sizing Results 30 Wing
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Appendix B: Sizing Results 16 Wing
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Appendix B: Sizing Results Length 0
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Appendix B: Sizing Results Lenght 0
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Appendix C: List of References Appe
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Appendix C: List of References 41.
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Phase II Final Report - NASA's Institute for Advanced Concepts

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