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The Experimental Determination of the Moment of Inertia of a Model Airplane Michael Koken [email protected]

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The University of Akron IdeaExchange@UAkron The Dr. Gary B. and Pamela S. Williams Honors Honors Research Projects College Fall 2017 The Experimental Determination of the Moment of Inertia of a Model Airplane Michael Koken [email protected] Please take a moment to share how this work helps you through this survey. Your feedback will be important as we plan further development of our repository. Follow this and additional works at: http://ideaexchange.uakron.edu/honors_research_projects Part of the Aerospace Engineering Commons, Aviation Commons, Civil and Environmental Engineering Commons, Mechanical Engineering Commons, and the Physics Commons Recommended Citation Koken, Michael, "The Experimental Determination of the Moment of Inertia of a Model Airplane" (2017). Honors Research Projects. 585. http://ideaexchange.uakron.edu/honors_research_projects/585 This Honors Research Project is brought to you for free and open access by The Dr. Gary B. and Pamela S. Williams Honors College at IdeaExchange@UAkron, the institutional repository of The nivU ersity of Akron in Akron, Ohio, USA. It has been accepted for inclusion in Honors Research Projects by an authorized administrator of IdeaExchange@UAkron. For more information, please contact [email protected], [email protected]. 2017 THE EXPERIMENTAL DETERMINATION OF A MODEL AIRPLANE KOKEN, MICHAEL THE UNIVERSITY OF AKRON Honors Project TABLE OF CONTENTS List of Tables ................................................................................................................................................. 2 List of Figures ................................................................................................................................................ 3 Chapter 1: Introduction .......................................................................................................................... 4 1.1 Defining the Moment of Inertia .................................................................................................... 4 1.2 The Importance of an Airplane’s Moment of Inertia .................................................................... 4 1.3 Analytically Determining an Object’s Moment of inertia ............................................................. 4 1.4 Experimentally Determining an Objects Moment of Inertia ........................................................ 4 1.5 Project description ........................................................................................................................ 5 Chapter 2: Equipment ............................................................................................................................. 6 Chapter 3: Procedure .............................................................................................................................. 7 Chapter 4: Determination of the Moment of Inertia of a Solid Wooden Block ..................................... 8 4.1 Analytical Determination .............................................................................................................. 8 4.2 Experimental Determination ........................................................................................................ 8 Chapter 5: Determination of the Moment of Inertia of a Model Airplane ............................................. 9 5.1 Yaw, Roll, and Pitch Axes .............................................................................................................. 9 5.2 Experimental Determination ........................................................................................................ 9 Chapter 6: Discussion of Results ........................................................................................................... 10 6.1 Wooden Block Experiment ......................................................................................................... 10 6.2 Model Airplane Experiment ........................................................................................................ 10 Chapter 7: Conclusion ........................................................................................................................... 11 Appendix A: Test Data and Figures from the Wooden Block Experiment .................................................. 12 Appendix B: Test Data and Figures from the Airplane Experiment ............................................................ 13 References .................................................................................................................................................. 15 1 LIST OF TABLES Table 1: Physical properties of wooden block .............................................................................................. 8 Table 2: Measurements of pendulum configuration per axis....................................................................... 8 Table 3: Experimental vs. known measurements of gravity ......................................................................... 8 Table 4: Experimental vs. analytical measurements of the block's moments of inertia .............................. 8 Table 5: Measurements of pendulum configuration for the airplane per axis: ........................................... 9 Table 6:Experimental vs. known measurements of gravity .......................................................................... 9 Table 7: Experimental vs. analytical measurements of the airplane's moments of inertia ......................... 9 Table 8: Time for the block to complete 10 oscillations in a pendulum motion to confirm gravity for each axis .............................................................................................................................................................. 12 Table 9: Time for the block to complete 10 oscillations rotating about said axis to determine the moment of inertia ...................................................................................................................................................... 12 Table 10: Time for the block to complete 10 oscillations in a pendulum motion to confirm gravity for each axis ...................................................................................................................................................... 14 Table 11: Time for the block to complete 10 oscillations rotating about said axis to determine the moment of inertia ....................................................................................................................................... 14 2 LIST OF FIGURES Figure 1: Pendulum configuration ................................................................................................................ 4 Figure 2: Wooden block used for the experiment ........................................................................................ 5 Figure 3: Model airplane used for the experiment ....................................................................................... 5 Figure 4: Pendulum configuration ................................................................................................................ 7 Figure 5: Swinging motion of the pendulum ................................................................................................ 7 Figure 6: Rotation about the object's vertical axis ....................................................................................... 7 Figure 7: Axes and variables used for block .................................................................................................. 8 Figure 8: Setup to determine the moment of inertia about the y-axis of the wooden block ...................... 8 Figure 9: Pendulum configuration ................................................................................................................ 9 Figure 10: Configuration to determine the moment of inertia about the x-axis ........................................ 12 Figure 11: Configuration to determine the moment of inertia about the y-axis ........................................ 12 Figure 12: Configuration to determine the moment of inertia about the z-axis ........................................ 12 Figure 13: Configuration to determine the moment of inertia about the yaw axis ................................... 13 Figure 14:Configuration to determine the moment of inertia about the roll axis ..................................... 13 Figure 15: Configuration to determine the moment of inertia about the pitch axis .................................. 13 Figure 16: Overall configuration to determine the moment of inertia about the yaw axis ....................... 13 3 CHAPTER 1: INTRODUCTION 1.1 Defining the Moment of Inertia The moment of inertia is a quantity that expresses a body’s tendency to resist angular acceleration from torque about a specified axis. It is the sum of the mass of each particle in the body with the square of its distance from the axis of rotation. 1.2 The Importance of an Airplane’s Moment of Inertia In flight, the control surfaces of an aircraft produce aerodynamic forces. These forces are applied at the center of pressure of the control surfaces which are some distance from the aircraft center of gravity and produce torques (or moments) about the principal axes. The torques cause the aircraft to rotate. The ability to vary the amount of the force and the moment allows the pilot to maneuver or to trim the aircraft. 1.3 Analytically Determining an Object’s Moment of inertia The moment of inertia of any object having a shape
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