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2017

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Articles 331 - 360 of 470

Full-Text Articles in Aerospace Engineering

Find Your Center, Nihad E. Daidzic Apr 2017

Find Your Center, Nihad E. Daidzic

Aviation Department Publications

No abstract provided.


Satellite Sequencing Optimization And Observational Orbit Determination Using Genetic Algorithms, Andrew W. Verstraete Apr 2017

Satellite Sequencing Optimization And Observational Orbit Determination Using Genetic Algorithms, Andrew W. Verstraete

Masters Theses

The problem of mission design for a robotic servicing satellite in geosynchronous Earth orbit (GEO) was investigated. A representative set of potential client satellites was selected, and operational needs were randomly assigned based on the average number of GEO retirements, anomalies, and repositioning maneuvers that currently occur each year. An objective function was developed to represent the value of servicing mission sequences, including client fees, time penalties, and operational risk. A genetic algorithm was then used to find sequences of operations on the potential client set that maximized the objective function’s value. Scenarios were analyzed with the database of satellites …


Biomass Cookstoves: An Empirical Study Into The Relationship Between Thermal Efficiency And Tending Practices For The Developing World, Erin Peiffer Apr 2017

Biomass Cookstoves: An Empirical Study Into The Relationship Between Thermal Efficiency And Tending Practices For The Developing World, Erin Peiffer

Honors Theses

More than 2 billion people in the world use biomass stoves for cooking and heating their homes. Due to incomplete combustion, toxic byproducts such as soot, nitrous oxides and carbon monoxide gasses form. These toxic substances contribute to pollution and can lead to serious health issues over time if inhaled leading to approximately 4 million premature deaths each year. The formation of these toxic substances can be mitigated, in part, through the introduction of increased turbulence intensity allowing for the so-called “well-stirred combustion regime”. Here we will be exploring the health, environmental, and social effects of biomass combustion in the …


Design Of An Opposed-Piston, Opposed-Stroke Diesel Engine For Use In Utility Aircraft, Luke Kozal Apr 2017

Design Of An Opposed-Piston, Opposed-Stroke Diesel Engine For Use In Utility Aircraft, Luke Kozal

Honors Theses

The objective of this thesis was to determine the feasibility of using an opposed-piston, opposed-stroke, diesel engine in utility aircraft. Utility aircraft are aircraft that have a maximal takeoff weight of 12,500lbs. These aircraft are often used for transportation of cargo and other goods. In order to handle that weight, many of the aircraft are powered by turboprop engines. Turboprop engines are a style of jet engine with power capabilities ranging from 500 to several thousand horsepower (hp). They are expensive engines, and in the case of the Piper Mirage, substituting the piston engine with a turboprop engine can increase …


Development Of An Analysis And Design Optimization Framework For Marine Propellers, Ashish C. Tamhane Apr 2017

Development Of An Analysis And Design Optimization Framework For Marine Propellers, Ashish C. Tamhane

Mechanical & Aerospace Engineering Theses & Dissertations

In this thesis, a framework for the analysis and design optimization of ship propellers is developed. This framework can be utilized as an efficient synthesis tool in order to determine the main geometric characteristics of the propeller but also to provide the designer with the capability to optimize the shape of the blade sections based on their specific criteria.

A hybrid lifting-line method with lifting-surface corrections to account for the three-dimensional flow effects has been developed. The prediction of the correction factors is achieved using Artificial Neural Networks and Support Vector Regression. This approach results in increased approximation accuracy compared …


An Evaluation Of The Relationships Between Collegiate Aviation Safety Management System Initiative, Self-Efficacy, Transformational Safety Leadership And Safety Behavior Mediated By Safety Motivation, Daniel Kwasi Adjekum Apr 2017

An Evaluation Of The Relationships Between Collegiate Aviation Safety Management System Initiative, Self-Efficacy, Transformational Safety Leadership And Safety Behavior Mediated By Safety Motivation, Daniel Kwasi Adjekum

Aviation Faculty Publications

The study conceptualized Safety Management System (SMS) initiative, self-efficacy, and transformational safety leadership as constructs that relates to safety behavior (measured by safety compliance and safety participation) when mediated by safety motivation using a quantitative approach. Structural equation modeling techniques was used to derive a final measurement model that fit the empirical data and was used to test the study hypotheses. Utilizing a sample of 282 collegiate flight students and instructors from a large public university in the US, a 46-item survey was used to measure respondent’s perceptions on the study variables. The results indicate that perceptions of SMS policy …


An Investigation Into The Potential Benefits Of Distributed Electric Propulsion On Small Uavs At Low Reynolds Numbers, Engin Baris Apr 2017

An Investigation Into The Potential Benefits Of Distributed Electric Propulsion On Small Uavs At Low Reynolds Numbers, Engin Baris

Mechanical & Aerospace Engineering Theses & Dissertations

Distributed electric propulsion systems benefit from the inherent scale independence of electric propulsion. This property allows the designer to place multiple small electric motors along the wing of an aircraft instead of using a single or several internal combustion motors with gear boxes or other power train components. Aircraft operating at low Reynolds numbers are ideal candidates for benefiting from increased local flow velocities as provided by distributed propulsion systems.

In this study, a distributed electric propulsion system made up of eight motor/propellers was integrated into the leading edge of a small fixed wing-body model to investigate the expected improvements …


Adopting Unmanned Flight Operations Into Controlled Airspace, Jennah C. Perry, Johnny Young, Jacqueline Luedtke, Benjamin Cook, Holly Hughes, Allison M. Little, Kyle Wilkerson Apr 2017

Adopting Unmanned Flight Operations Into Controlled Airspace, Jennah C. Perry, Johnny Young, Jacqueline Luedtke, Benjamin Cook, Holly Hughes, Allison M. Little, Kyle Wilkerson

Publications

Unmanned aircraft activity is becoming more common within the National Airspace System (NAS) and is expected to dominate the NAS in the near future. Specific procedures for adopting unmanned aircraft into the National Airspace System (NAS).

A variation of the Military Grid Reference System was developed and digitally overlaid onto the radar display. To incorporate this grid system, a customized flight plan database was created for the storage of operator submitted flight plans. Instead of verbal communication, a computer chat system is used for communication because of the low altitude operations in the field.

The Federal Aviation Administration (FAA) has …


Investigating The Potential Of Using Off-Axis 3d Woven Composites In Composite Joints’ Applications, Mohamed Nasr Saleh, Ying Wang, Arief Yudhanto, Adam Joesbury, Prasad Potluri, Gilles Lubineau, Constantinos Soutis Apr 2017

Investigating The Potential Of Using Off-Axis 3d Woven Composites In Composite Joints’ Applications, Mohamed Nasr Saleh, Ying Wang, Arief Yudhanto, Adam Joesbury, Prasad Potluri, Gilles Lubineau, Constantinos Soutis

Mechanical and Aerospace Engineering Faculty Research & Creative Works

The effect of circular notch has been evaluated for three different architectures of three-dimensional (3D) carbon fiber woven composites (orthogonal, ORT; layer-to-layer, LTL; angle interlock, AI) through open-hole quasi-static tension and double-lap bearing strength tests in the off-axis (45°) direction. Damage characterization is monitored using Digital Image correlation (DIC) for open-hole testing and X-ray Computed Tomography (CT) for double-lap bearing strength test. The off-axis notched 3D woven composites exhibit minor reduction (less than 10 %) of the notched strength compared to the un-notched strength. DIC strain contour clearly show stress/strain localization regions around the hole periphery and stress/strain redistribution away …


Effect Of The Wake Structure On Drag Coefficient For A Thin Flexible Wire, Harika Gurram Apr 2017

Effect Of The Wake Structure On Drag Coefficient For A Thin Flexible Wire, Harika Gurram

Theses and Dissertations

The present research work focuses on investigating the effect of wake structure on the drag coefficient of a thin flexible wire. Previous researchers have investigated the flow characteristics around the cylinder and estimated the drag coefficient for different Reynold’s number range. The flow transition characteristics in the boundary layer and its effect on the drag coefficient were described. These studies were performed on a non-deformable cylinder. The present work focuses on the drag characteristics of thin flexible cylinders whose diameter is on the order of microns. The results showed up to 30% lower value than reported literature drag coefficient values …


Utilizing Guided Simulation In Conjunction With Digital Learning Tools In Air Traffic Control Training To Enhance Learning At The Collegiate Level, Allison Little, Benjamin Cook, Holly Hughes, Kyle Wilkerson Mar 2017

Utilizing Guided Simulation In Conjunction With Digital Learning Tools In Air Traffic Control Training To Enhance Learning At The Collegiate Level, Allison Little, Benjamin Cook, Holly Hughes, Kyle Wilkerson

Discovery Day - Prescott

Students in an air traffic control program are required to learn and apply advance knowledge and skills in a limited time frame. All students learn at different rates as well as through different learning styles. Swivl is a video capture tool designed to enhance student learning by allowing students to refer back to their individual classroom lab training session videos via an online portal. Swivl is being utilized in two ATC lab courses. During this research, two technological shortcomings were discovered: (1) Swivl lacks the ability to capture audio from the COA’s existing communication software and (2) Swivl cannot focus …


Integrating Unmanned Aircraft Operations Into The National Airspace System, Benjamin Cook, Holly Hughes, Kyle Wilkerson, Allison Little Mar 2017

Integrating Unmanned Aircraft Operations Into The National Airspace System, Benjamin Cook, Holly Hughes, Kyle Wilkerson, Allison Little

Discovery Day - Prescott

Unmanned Aircraft Systems (UAS) are expected to dominate the National Airspace System (NAS) in the near future. One particular barrier preventing the integration of unmanned aircraft into the NAS is the lack of standardized procedures for distinguishing and communicating with remote UAS operators. In preparation for adopting unmanned flight operations into a complex control system, it is important to identify solutions to effectively control UAS in the NAS. To achieve simultaneous safe manned and unmanned aircraft operations in the NAS, the Joint UAS and ATC Team (JUAT) at Embry-Riddle Aeronautical University (ERAU) are developing a system that could be used …


Integrating Unmanned Aircraft Operations Into The National Airspace System, Benjamin Cook, Holly Hughes, Allison Little, Kyle Wilkerson, Jennah C. Perry, Johnny Young, Jacqueline Luedtke Mar 2017

Integrating Unmanned Aircraft Operations Into The National Airspace System, Benjamin Cook, Holly Hughes, Allison Little, Kyle Wilkerson, Jennah C. Perry, Johnny Young, Jacqueline Luedtke

Publications

Commercial unmanned aircraft systems (UAS) are expected to dominate the National Airspace System (NAS) in the years to come. One particular barrier preventing integration of UAS into the NAS is the lack of standardized procedures for separating aircraft and communicating with ATC. In preparation for adopting unmanned flight operations into a complex control system, it is important to identify solutions to effectively control UAS in the NAS.

The Joint UAS and ATC Team (JUAT) group has designed several simulated ATC scenarios in order to determine effective solutions for integration. Through the use of digitized radar display overlays that replicate the …


Relating Film Cooling Performance Between Ambient And Near Engine Temperatures, Christopher J. Vorgert Mar 2017

Relating Film Cooling Performance Between Ambient And Near Engine Temperatures, Christopher J. Vorgert

Theses and Dissertations

This thesis explores multiple topics, including the relative importance of nondimensional parameters that relate film cooling performance within different temperature regimes and the effects of internal coolant flow and coolant temperature on overall film cooling effectiveness. A Hastelloy model representative of a turbine blade was utilized for IR tests. Near engine temperatures were produced via premixed propane and air combustion in a Well-Stirred Reactor (WSR) with air supplied as the film coolant gas. Near ambient conditions used heated air for freestream flow and carbon dioxide, argon, or air as film coolant gases. It was found that even with multiple matched …


Computational Optimization Under Uncertainty Of An Active Flow Control Jet, Luke A. Welch Mar 2017

Computational Optimization Under Uncertainty Of An Active Flow Control Jet, Luke A. Welch

Theses and Dissertations

Optimization under uncertainty is performed to determine the optimal parameters of an active flow control jet to impart robust control during transonic cruise. A steady blowing jet is optimized on an airfoil to impart a change in lift greater than or equal to that generated by traditional control surfaces. The design candidates are computationally evaluated using the NASA flow solver, FUN3D, under 20 unique combinations of angle of attack, Reynolds number, and Mach number in order to propagate model input uncertainty. The mean change in lift and the associated standard deviation are included in the optimization framework to help ensure …


Military Space Mission Design And Analysis In A Multi-Body Environment: An Investigation Of High-Altitude Orbits As Alternative Transfer Paths, Parking Orbits For Reconstitution, And Unconventional Mission Orbits, John N. Brick Mar 2017

Military Space Mission Design And Analysis In A Multi-Body Environment: An Investigation Of High-Altitude Orbits As Alternative Transfer Paths, Parking Orbits For Reconstitution, And Unconventional Mission Orbits, John N. Brick

Theses and Dissertations

High-altitude satellite trajectories are analyzed in the Earth-Moon circular restricted three-body problem. The equations of motion for this dynamical model possess no known closed-form analytical solution; therefore, numerical methods are employed. To gain insight into the dynamics of high-altitude trajectories in this multi-body dynamical environment, periapsis Poincare' maps are generated at particular values of the Jacobi Constant. These maps are employed as visual aids to generate initial guesses for orbital transfers and to determine the predictability of the long term behavior of a spacecraft's trajectory. Results of the current investigation demonstrate that high-altitude transfers may be performed for comparable, and …


Optimal Design Of A Hexakis Icosahedron Vacuum Based Lighter Than Air Vehicle, Joseph R. Schwemmer Mar 2017

Optimal Design Of A Hexakis Icosahedron Vacuum Based Lighter Than Air Vehicle, Joseph R. Schwemmer

Theses and Dissertations

Due to the rising cost and scarcity of helium, new methods to ensure buoyancy for lighter-than-air vehicles (LTAVs) are being sought. One alternative under study uses an internal vacuum to reduce the weight to buoyancy ratio. It's a novel approach; however, the vacuum presents challenges for the vehicle's structure. The structure must have minimum mass while preventing buckling and excess stress throughout the frame and membrane. The structure under analysis is a hexakis icosahedron with a membrane covering. Achieving minimum mass involves optimizing the structure under the loading conditions. Finite-element analysis (FEA) and direct-search methods are employed, providing an optimal …


Optimal Configurations For Aerosol Monitoring With Multi-Rotor Small Unmanned Aerial Systems, Inna D. Chavez Mar 2017

Optimal Configurations For Aerosol Monitoring With Multi-Rotor Small Unmanned Aerial Systems, Inna D. Chavez

Theses and Dissertations

Applicability of aerosol sampling on multi-rotor unmanned aerial systems (UAS) platform was investigated. Multi-rotor UAS have impacts of wind speed, turbulence, and orientation possibly contributing to sampling bias. The SKC IMPACT sampler, Tecora C.A.Th.I.A., and modified three-dimensionally printed Universal Inlet for Airborne-Particle Size-Selective Sampling were selected based on particle size-selectivity and operational independence to wind. Airflow visualizations concluded that below UAS fuselage was optimal sampler placement. Tests were conducted with Arizona Road Dust in a still-air chamber, and aerosolized sugar in a wind tunnel. Inlet mounting was evaluated in, upright, upside-down, and horizontal orientations. Horizontal orientations of all inlets resulted …


An Analysis Of Radio-Frequency Geolocation Techniques For Satellite Systems Design, Daniel R. Barnes Mar 2017

An Analysis Of Radio-Frequency Geolocation Techniques For Satellite Systems Design, Daniel R. Barnes

Theses and Dissertations

This research 1) evaluates the effectiveness of CubeSat radio-frequency geolocation and 2) analyzes the sensitivity of different RF algorithms to system parameters. A MATLAB simulation is developed to assess geolocation accuracy for variable system designs and techniques (AOA, TDOA, T/FDOA). An unconstrained maximum likelihood estimator (MLE) and three different digital elevation models (DEM) are utilized as the surface of the Earth constraint to improve geolocation accuracy. The results presented show the effectiveness of the MLE and DEM techniques, the sensitivity of AOA, TDOA, and T/FDOA algorithms, and the system level performance of a CubeSat geolocation cluster in a 500km circular …


Fatigue Behavior Of An Advanced Melt-Infiltrated Sic/Sic Composite At 1200°C In Air And In Steam, Nicholas J. Boucher Mar 2017

Fatigue Behavior Of An Advanced Melt-Infiltrated Sic/Sic Composite At 1200°C In Air And In Steam, Nicholas J. Boucher

Theses and Dissertations

The tension-tension fatigue behavior of an advanced melt-infiltrated (MI) silicon carbide/silicon carbide (SiC/SiC) ceramic matrix composite (CMC) was investigated at 1200 degrees Celsius in air and in steam. The MI composite consisted of ten 0/90 plies of Hi-Nicalon-S SiC fibers woven in a five harness satin weave (5HSW), a CVI BN interphase to provide a weak fiber-matrix interphase, and a CVI SiC matrix layer followed by infiltration with SiC particulate slurry and molten silicon. Nine tensile specimens of the material were used in a pilot investigation of mechanical performance at elevated temperature. One specimen was used in a monotonic tensile …


Analysis Of Additively Manufactured Lattice Structures Using Finite Element Methods, Christopher A. Box Mar 2017

Analysis Of Additively Manufactured Lattice Structures Using Finite Element Methods, Christopher A. Box

Theses and Dissertations

Additive Manufacturing (AM) processes are well known for their ability to fabricate parts with complex geometries. Lattice structures leverage this ability to create parts with high strength-to-weight ratio and other desirable structural qualities. This research presents a parameterized modeling tool using common Finite Element Analysis (FEA) and scripting software with which aggregated lattice structures can be analyzed, given different geometric properties and loading conditions. A full factorial Design of Experiments is run to explore the effects of various parameters on the strength of lattice structures. Experimental compressive strength results from three FDM-produced PLA lattices are discussed and compared to predictions …


Stressed Oxidation Of Hafnium Diboride In Air At 1500°C, Thomas A. Bowen Mar 2017

Stressed Oxidation Of Hafnium Diboride In Air At 1500°C, Thomas A. Bowen

Theses and Dissertations

Hypersonic vehicles with narrow airfoils produce thin boundary layers and shock temperatures in excess of 2000°C, exceeding the operating limits of traditional aerospace materials. The use of ultra-high temperature ceramics (UHTCs) allows for operating temperatures far exceeding those of metallic alloys. One such UHTC is hafnium diboride (HfB2). Transition metal diborides generally experience significant oxidation degradation at elevated temperatures. The use of additives, such as silicon carbide (SiC) has been shown to reduce the oxidation of transition metal diborides. This research focused on the compressive creep of HfB2 with varying amounts of SiC in air at 1500°C. …


Investigation Of Dynamic Store Separation Out Of A Weapons Bay Cavity Utilizing A Low Speed Wind Tunnel, Andrew D. Bower Mar 2017

Investigation Of Dynamic Store Separation Out Of A Weapons Bay Cavity Utilizing A Low Speed Wind Tunnel, Andrew D. Bower

Theses and Dissertations

Characterizing mission store trajectories as they separate from a weapons bay cavity is highly relevant to the Air Force mission. The flow around a weapons bay is unsteady. The unsteady flow can cause a mission store separation trajectory to be unpredictable, and such is the case for what some have termed a pitch bifurcation. Traditional wind tunnel testing is incapable of detecting a bifurcation because traditional wind tunnel testing records time-averaged data. In this study, an experimental testing system was developed and refined in order to support the time-accurate characterization of dynamic mission store separation events. A Motion Test Apparatus …


Evaluating The Autonomous Flying Qualities Of A Simulated Variable Stability Aircraft, Ali M. Hamidani Mar 2017

Evaluating The Autonomous Flying Qualities Of A Simulated Variable Stability Aircraft, Ali M. Hamidani

Theses and Dissertations

Delivering communications from high altitudes, at airspeeds of just 30 knots, gathering data from active volcanoes and forming hurricanes, and collecting ISR over hostile territories, UAVs are at the ready to perform those missions that are too dull, dirty, or dangerous for manned aircraft. However, the proliferation of this new technology has its fair share of challenges. Over 460 DoD UAV mishaps have occurred since 2001, with almost half resulting in damages of $2M or more. One incident almost ended in fatalities, when a UAV, suffering from loss of control, collided with a C-130. That loss of control is what …


The Impact Of Atmospheric Fluctuations On Optimal Boost Glide Hypersonic Vehicle Dynamics, Melissa A. Dunkel Mar 2017

The Impact Of Atmospheric Fluctuations On Optimal Boost Glide Hypersonic Vehicle Dynamics, Melissa A. Dunkel

Theses and Dissertations

A project under the management of Air Force Research Laboratory has begun development of a six degree of freedom model for use in hypersonic vehicle development and application. One area of interest is the perturbation of vehicle behavior based on atmospheric fluctuations – how the performance of the vehicle changes with respect to “hot”, “cold” and standard day conditions. The method developed to fill this need uses real-world data from the Global Forecast System to create a “hot” and “cold” day dataset to compare with the standard day model. The key parameter is atmospheric density, a value calculated over a …


Time-Dependent Validation Of Finite Element Strain Distribution Of A Plastically-Deformed Plate Via Digital Image Correlation, Kevin R. Knapp Mar 2017

Time-Dependent Validation Of Finite Element Strain Distribution Of A Plastically-Deformed Plate Via Digital Image Correlation, Kevin R. Knapp

Theses and Dissertations

Generation of residual stress is an essential step in the generation of Goodman data via Air Force Research Laboratory's vibration-based fatigue test. Conventional Goodman data is constructed through uniaxial fatigue testing at a rate of 40 Hz, while the vibration-based testing excites stresses at 1,600 Hz in a stress state that is similar to those seen in gas turbine engine airfoils. A pre-strain procedure is conducted to form residual tensile stress, which serves as a steady stress when the specimen is subjected to fully-reversed vibration-based fatigue loads. This steady tensile stress is desired at the fatigue zone of the test …


Investigating Analytical And Numerical Methods To Predict Satellite Orbits Using Two-Line Element Sets, Adam T. Rich Mar 2017

Investigating Analytical And Numerical Methods To Predict Satellite Orbits Using Two-Line Element Sets, Adam T. Rich

Theses and Dissertations

As Low Earth Orbit (LEO) contains an ever-increasing number of objects, the prediction of future object positions must be precise in order to avoid collisions. Object positions are distributed in two-line element (TLE) sets and are generated using the analytical propagator known as Simplified General Perturbations 4 (SGP4). However, a numerical integrator called Special Perturbations (SP) provides an alternative approach to TLE generation and propagation. In this thesis, TLE accuracy was determined with both models, and the length of time that a single element set can provide valid information was also established. With two-line element sets as data, comparisons were …


Combined Stereo Vision And Inertial Navigation For Automated Aerial Refueling, Daniel T. Johnson Mar 2017

Combined Stereo Vision And Inertial Navigation For Automated Aerial Refueling, Daniel T. Johnson

Theses and Dissertations

This paper describes the design of an EKF to obtain the precise relative position of two aircraft in a refueling maneuver while operating in GPS denied environments. The EKF uses the INS already present in both aircraft as well as the stereo camera system organic to new tanker systems. The aircraft trajectories are generated according to authentic refueling profiles with flight dynamics software and executed in a 3D virtual environment to enable deterministic simulation of the stereo camera system and to demonstrate the effectiveness of the combined system in a refueling scenario. Results show the system can achieve sufficient accuracy …


Small Fixed-Wing Aerial Positioning Using Inter-Vehicle Ranging Combined With Visual Odometry, Benjamin M. Fain Mar 2017

Small Fixed-Wing Aerial Positioning Using Inter-Vehicle Ranging Combined With Visual Odometry, Benjamin M. Fain

Theses and Dissertations

There has been increasing interest in developing the ability for small unmanned aerial systems (SUAS) to be able to operate in environments where GPS is not available. This research considers the case of a larger aircraft loitering above a smaller GPS-denied SUAS. This larger aircraft is assumed to have greater resources which can overcome the GPS jamming and provide range information to the SUAS flying a mission below. This research demonstrates that using a ranging update combined with an aircraft motion model and visual odometry can greatly improve the accuracy of a SUASs estimated position in a GPS-denied environment.


Formation Flight Of Earth Satellites On Kam Torus Using Classical Orbital Elements, Marissa C. Reabe Mar 2017

Formation Flight Of Earth Satellites On Kam Torus Using Classical Orbital Elements, Marissa C. Reabe

Theses and Dissertations

This research uses the KAM theory that has been refined by Wiesel to show that Earth-satellites dynamics can be represented by an integrable Hamiltonian system with a small perturbation, like Earths geopotential. The satellite will follow a torus in phase space and remain on that KAM torus for all time unless acted on by a non-conservative force. A torus frequency was calculated, in this research, using a truth model in System Tool Kit (STK) and the High Precision Orbit Propagator (HPOP) to develop an accurate ephemeris file listing the Classical Orbital Elements (COEs). The frequencies found from the truth model …