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

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Planetary Exploration Using Biomimetics An Entomopter for Flight on Mars superimposed onto the model proposed by Eric Reissner [222]. Since the model proposed by Theoderson involves a harmonic motion analysis with real and imaginary parts, it was decided that motion in two degrees of freedom would be modeled as real parts and equations provided by Azuma [12] would be used. The formulation was initially done for a baseline configuration, and once the model was formulated and validated by CFD results, the analytical model was used to explore the design space based on a parametric analysis. This model does not account for the airfoil shape, instead being considered as a thin flat plate, which is close to the actual case as the proposed wing design is very thin, however, camber effects are also not taken into account. The three dimensional effects for wing planform shape, sweep, and change of chord length with span is modeled in terms of correction factors for both flapping and pitch motion. These correction factors are then added to the results of the two dimensional model to complete the analysis. Having considered the nature of the modeling, the next step was to select the engineering metrics which should comprise evaluation criteria for analysis and design. Basically lift and thrust are the main factors, and the net lift should be able to support the weight of the vehicle and net thrust should provide the forward flight capability. In addition to these two, the moment and power required are the other key metrics. All these things in non dimensional form for their respective coefficients were selected as the key responses, in order to assess the flight worthiness of the flapping wing Entomopter on Mars. After having selected the key responses, the next step is selection of key variables that are sensitive to the variability of these responses. The variables are: • Wing span • Chord length • Flapping frequency in Hertz • Flapping amplitude • Pivot location from leading edge • Angle of attack • Pitch amplitude • Phase between pitch and plunge • Free stream density • Free stream velocity • Free stream kinematic viscosity The model is unsteady and the responses are varying within each time period of motion, however, motion is harmonic and is the same for each time period. To simplify the model, flow is assumed inviscid, thereby eliminating the viscosity variable. Also the density of Mars lower atmosphere is assumed constant for nap-of-the-planet flight. 3.3.3.4 Detailed Aerodynamic Analysis The problem of determining the aerodynamic forces on an airfoil moving in simple harmonic motion about an equilibrium position is very detailed, and is fully derived in Reference [254]. At this point, a qualitative explanation of basic concepts is attempted. 124 Phase II Final Report
Chapter 3.0 Vehicle Design 3.3 Wing Aerodynamics Consider the forces acting on a thin airfoil, of infinite aspect ratio, moving with constant velocity in a perfect fluid and with constant angle of attack. From elementary aerodynamics it is deduced that the net forces acting on such an airfoil are those associated with the circulation of the fluid around the airfoil. The circulation for the steady state condition is proportional to the velocity, angle of attack, and chord length. However, for the case of unsteady motion the lift on the airfoil section is no longer a simple function of the circulation. For one thing, it can be easily shown that any plate accelerated in a fluid exerts forces and moments even in the absence of circulation. Thus, even at zero forward velocity for an airfoil performing simple harmonic motion, the fluid will exert forces and moments on the airfoil section due to the acceleration and deceleration of the fluid moving with the airfoil. These can be considered aerodynamic inertia forces. A second important contribution to the lift for the case of unsteady motion is known as the quasi steady lift. This is the lift which would be produced by the motion of the airfoil if the circulation pattern behind it (i.e., the wake) had no effect. It represents the force that would be produced if the instantaneous velocity and angle of attack of the airfoil were permanently maintained. The lift can then be considered to vary and to be a function of the instantaneous configuration of the system. In general, every change of the state of motion of the airfoil is accompanied by a change in circulation around it. Furthermore, every change in circulation about an airfoil section is accompanied by a vortex shed from the trailing edge of the airfoil. For the change of a continuously changing circulation, such as for a simple harmonic motion, a continuous band of shed vortices develop behind the airfoil section. These shed vortices (or the vortex sheet) produce vertical velocities in the neighborhood of the airfoil. The periodic force is a function of this vortex sheet, the distributed vortex strength of which is another periodic function in terms of reduced frequency parameter (k). This will be explained in more detail below. Thus from the qualitative discussion above, it can be deduced that lift on a flapping airfoil is a function of free stream velocity and periodic functions of plunge and pitching motion. Now after having discussed the problem qualitatively, the different assumptions made to simplify the model and equations formulated as a result of this analytical model, will be explained. This will be followed by the results thus obtained. 3.3.3.5 Assumptions 1. The flow is assumed to be by a perfect gas, which behaves in accordance with a perfect gas law, with constant specific heat values over a reasonable range of temperature and pressure. 2. No friction is considered internally or externally; so for the required power analysis, a factor must be added to account for frictional losses. 3. Irrotational flow such that all fluid particles have zero angular momentum about the center of gravity axis. 4. The basic model only encompasses the two dimensional airfoil effects with infinite span. This will be modified to include the three dimensional finite span effects and planform shape by inclusion of Reissner's correction factors. 5. The model is based on non stationery potential flow theory, and no deviations from potential flow are being considered. 125
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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 3.5 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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