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Bistatic Radar Experiments with UAV: Qualification and Performance of a Miniaturized Instrument

Spacecraft-to-ground bistatic radar is an established technique that has enabled the study of the planetary surfaces and near sub-surfaces properties by using the telecommunication signals amplitude, phase, and polarization. The Planetary Radar and Radio Science group at the Jet Propulsion Laboratory (JPL) has been involved in many planetary bistatic radar experiments since the 1970’s using orbiters and Deep Space Network (DSN) antennas. The recent advances in Unmanned Aerial Vehicles (UAVs) technologies are making the UAVs more popular in scientific surveying applications. One such application is the use of UAVs in bistatic radar measurements to explore surfaces on Earth. Our analyses show that UAV-based bistatic radar measurements will improve our understanding of the finer-scale characteristic variations of the surface by acquiring the higher resolution data for a specific region of interest compared to data obtained from a spacecraft. The Mars helicopter, a technology demonstration to test the first powered flight on Mars, will be the beginning of a new era of exploration with UAVs on Mars. This leap in planetary UAV technology has renewed the importance of developing a miniaturized bistatic radar instrument (under 1 kg) compatible with a UAV platform able to meet the science requirements for studying surfaces on Earth, Mars, and other planetary bodies. As part of a task at JPL, we have been working on a technology demonstration using a compact bistatic radar instrument designed to be the payload of a UAV employing signals of opportunity from Earth’s orbiters, i.e. Global Positioning System (GPS). In this paper, we present our design and development of the instrument, our evaluation of different L-band antennas, the performance of compact open-loop receivers in support of Earth and planetary bistatic radar observations, and the instrument fit test on an UAV platform. As part of this publication, we also highlight the results of a field experiment dedicated to test the sensitivity of the miniaturized bistatic radar instrument to different electrical properties of the surface.

Brockers, Roland

Change Detection Experiments Using Low Cost UAVs

This paper presents the progress in the development of a low-cost change-detection system. This system is being developed to provide users with the ability to use a low-cost unmanned aerial vehicle (UAV) and image processing system that can detect changes in specific fixed ground locations using video provided by an autonomous UAV. The results of field experiments conducted with the US Army at Ft. A.P.Hill are presented.

Logan, Michael J.

In-Time UAV Flight-Trajectory Estimation and Tracking Using Bayesian Filters

Rapid increase of UAV operation in the next decade in areas of on-demand delivery, medical transportation services, law enforcement, traffic surveillance and several others pose potential risks to the low altitude airspace above densely populated areas. Safety assessment of airspace demands the need for a novel UAV traffic management (UTM) framework for regulation and tracking of the vehicles. Particularly for low-altitude UAV operations, quality of GPS measurements feeding into the UAV is often compromised by loss of communication link caused by presence of trees or tall buildings in proximity to the UAV flight path. Inaccurate GPS locations may yield to unreliable monitoring and inaccurate prognosis of remaining battery life and other safety metrics which rely on future expected trajectory of the UAV. This work therefore proposes a generalized monitoring and prediction methodology for autonomous UAVs using in-time GPS measurements. Firstly, a typical 4D smooth trajectory generation technique from a series of waypoint locations with associated expected times-of-arrival based on B-spline curves is presented. Initial uncertainty in the vehicle's expected cruise velocity is quantified to compute confidence intervals along the entire flight trajectory using error interval propagation approach. Further, the generated planned trajectory is considered as the prior knowledge which is updated during its flight with incoming GPS measurements in order to estimate its current location and corresponding kinematic profiles. Estimation of position is denoted in dicrete state-space representation such that position at a future time step is derived from position and velocity at current time step and expected velocity at the future time step. A linear Bayesian filtering algorithm is employed to efficiently refine position estimation from noisy GPS measurements and update the confidence intervals. Further, a dynamic re-planning strategy is implemented to incorporate unexpected detour or delay scenarios. Finally, critical challenges related to uncertainty quantification in trajectory prognosis for autonomous vehicles are identified, and potential solutions are discussed at the end of the paper. The entire monitoring framework is demonstrated on real UAV flight experiments conducted at the NASA Langley Research Center.

Banerjee, Portia

In-Time Safety Assessment & Risk Prediction for Unmanned Aerial Systems

One of the critical challenges in emerging autonomous systems is timely mitigation of hazards encountered during operation which may not be known or accounted for at the time of design. Efficient execution of unmanned systems therefore demands a paradigm shift from scheduled periodic maintenance to predictive risk analysis that includes condition-based-monitoring, real-time reliability assessment and hazard mitigation. Particularly, the state-of-health parameters needs to be computed at the component level, unit level as well as the integrated system level. While in the former two levels, the physics of health propagation may be based on underlying electro-mechanical properties, system level prognostics often relies on data-driven models. Further, uncertainty from model, measurements and input sources should be accurately quantified to generate meaningful prediction results that can be fed into reliable decision making processes. Finally, the expected risk and time to failure has to be computed based on the current state-of-health of the overall system. This talk presents a conceptual design of such an in-time safety assurance approach for unmanned aerial vehicles (UAV) operating at low altitudes near and over populated areas. Typical in-flight hazard incidents include unplanned detour, proximity to obstacles, mid-flight component faults, limited battery life and poor quality of GPS measurements. Safety assessment therefore comprises trajectory generation and re-plan, battery RUL computation, distributed fault diagnostics and uncertainty management of predicted trajectory based on GPS measurement noise. The entire monitoring framework will be demonstrated on simulated as well as real UAV flight experiments conducted at the NASA Langley Research Center. This tutorial will therefore guide the audience through a step-by-step tracking of an autonomous system with focus on in-time risk prediction in the presence of unforeseen hazards and uncertain environment.

diagnostics

Vibration Anomaly Detection by Clustering in Unmanned Aerial Vehicles.

One of the critical factors affecting flight safety of unmanned aerial vehicles (UAVs) is the amount of vibration they are exposed to during a flight. On one hand, external causes such as wind gusts and turbulences or internal vehicle-centric faults such as incorrect sensor mounting or propeller imbalances can cause high vibrations in UAVs. On the other hand, high vibration itself may induce noise in the onboard miniature sensors of the UAV such as its accelerometers, gyroscopes and GPS that can lead to uncertain state estimation causing the multi-rotor to drift from its desired position or even result in loss-of-control. Hence, it is important to monitor the vibration levels during a UAV flight. This paper specifically looks into vibrations recorded by the autopilot system of a multi-rotor in presence of varying magnitudes of wind. Using data from experimental flights conducted at two separate flight test regions under varying wind conditions, we aim to classify between a nominal and anomalous vibration level for small UAV systems. Further, we analyse other parameters of interest that affect vibrations in UAVs such as UAV air speed and any propeller imbalance signatures. Analysis results from experimental flights demonstrate the effect of wind on vibration magnitude in unmanned aircrafts.

unmanned aviation

Tensor Decomposition Analysis for UAV Anomaly Detection

Vibrational anomalies can provide valuable insights into the health status of an unmanned aerial vehicle, potentially indicating system degradation including propeller, motor, or sensor damage, as well as environmental anomalies such as strong wind gusts and turbulence. However, many causes for vibrational anomalies are not related to vehicle health, such as sharp shifts in velocity or direction of flight. Thus, depending strictly on vibration signals to detect anomalies can result in false positives for failures. Hence, it is important to include additional telemetries in detecting and diagnosing in-flight anomalies. This paper considers an approach to anomaly detection based on tensor decompositions that incorporates information from vibration signals, as well as additional flight data such as velocity, current draw, voltage drop, and attitude. Using experimental flight data collected by the University of Notre Dame, we construct third-order tensors then apply the CANDECOMP/PARAFAC decomposition to identify trends within each flight and classify flights as nominal or anomalous.

unmanned aviation

Use of the Aerosonde Unihabited Aerial Vehicle (UAV) in the Fourth Convection and Moisture Experiment (CAMEX 4)

The Fourth Convection and Moisture Experiment (CAMEX 4) was a scientific field experiment based in Florida in summer 2001 focused on the study of hurricanes off the east coast of the United States. Sponsored by the National Aeronautics and Space Administration's Office of Earth Science, and conducted in collaboration with the National Oceanic and Atmospheric Administration's annual hurricane research program, CAMEX 4 utilized aircraft, ground-based and satellite instrumentation to obtain unprecedented, three dimensional characterizations of these important storms. The Aerosonde UAV was selected by NASA to participate in CAMEX 4 because it provided a unique capability to obtain measurements in the atmospheric boundary layer in and around the storms, unattainable by other platforms or measurement capabilities. This talk focuses on the NASA review process that was followed to coordinate the UAV activity with the conventional aircraft operations, as well as with the other participating agencies and the FAA. We will discuss how Aerosonde addressed the issues of safety, coordination and communication and summarize the lessons learned.

Hipskind, R. Stephen

NASA Earth Science Research and Applications Using UAVs

The NASA Earth Science Enterprise sponsored the UAV Science Demonstration Project, which funded two projects: the Altus Cumulus Electrification Study (ACES) and the UAV Coffee Harvest Optimization experiment. These projects were intended to begin a process of integrating UAVs into the mainstream of NASA s airborne Earth Science Research and Applications programs. The Earth Science Enterprise is moving forward given the positive science results of these demonstration projects to incorporate more platforms with additional scientific utility into the program and to look toward a horizon where the current piloted aircraft may not be able to carry out the science objectives of a mission. Longer duration, extended range, slower aircraft speed, etc. all have scientific advantages in many of the disciplines within Earth Science. The challenge we now face are identifying those capabilities that exist and exploiting them while identifying the gaps. This challenge has two facets: the engineering aspects of redesigning or modifying sensors and a paradigm shift by the scientists.

Guillory, Anthony R.

X-Band Radar for Studies of Tropical Storms from High Altitude UAV Platform

The increased role of unmanned aerial vehicles (UAV) in NASA's suborbital program has created a strong interest in the development of instruments with new capabilities, more compact sizes and reduced weights than the instruments currently operated on manned aircrafts. There is a strong demand and tremendous potential for using high altitude UAV (HUAV) to carry weather radars for measurements of reflectivity and wind fields from tropical storms. Tropical storm genesis frequently occurs in ocean regions that are inaccessible to piloted aircraft due to the long off shore range and the required periods of time to gather significant data. Important factors of interest for the study of hurricane genesis include surface winds, profiled winds, sea surface temperatures, precipitation, and boundary layer conditions. Current satellite precipitation and surface wind sensors have resolutions that are too large and revisit times that are too infrequent to study this problem. Furthermore, none of the spaceborne sensors measure winds within the storm itself. A dual beam X-band Doppler radar, UAV Radar (URAD), is under development at the NASA Goddard Space Flight Center for the study of tropical storms from HUAV platforms, such as a Global Hawk. X-band is the most desirable frequency for airborne weather radars since these can be built in a relatively compact size using off-the-shelf components which cost significantly less than other higher frequency radars. Furthermore, X-band radars provide good sensitivity with tolerable attenuation in storms. The low-cost and light-weight URAD will provide new capabilities for studying hurricane genesis by analyzing the vertical structure of tropical cyclones as well as 3D reflectivity and wind fields in clouds. It will enable us to measure both the 3D precipitation structure and surface winds by using two antenna beams: fixed nadir and conical scanning each produced by its associated subsystem. The nadir subsystem is a magnetron based radar modified from a marine radar transceiver. It is capable of measuring vertical reflectivity and velocity profile while being a lower-cost, smaller size, and lighter weight version of the NASA ER-2 Doppler Radar (EDOP), which has flown during many NASA field campaigns and has provided valuable scientific information on hurricanes and weather phenomena. Unfortunately, EDOP is too large and heavy for most UAV platforms, but the experience gained with this instrument provided us with the heritage to build a new low-cost, light-weight, smaller system that will be capable of flying on UAVs. The scanning subsystem uses a TWT transmitter and provides measurements of 3D reflectivity/wind fields in-clouds. Conical scanning of the radar beam at a 35 deg. incidence angle will also provide information of surface wind speed and direction derived from the surface return over a single 360 deg. sweep. URAD data system will be Linux based with the capability of autonomous operation. It will utilize cutting edge digital receiver and FPGA technologies to carry out the data acquisition and processing tasks. High speed navigation data from the aircraft will also be captured and saved along with radar data for 3D measurement field reconstruction and aircraft motion correction. There is a tremendous potential for UAVs to carry down-looking weather radars for measurements of reflectivity, horizontal and vertical winds from tropical storms. With operation from HUAV platforms, the dual beam X-band radar under development promises to provide greatly needed information for tropical storm research.

Rodriquez, Shannon

Uncertainty Quantification of Expected Time-of-Arrival in UAV Flight Trajectory

One of the foremost requirements for accurate in-flight safety monitoring of autonomous unmanned aerial vehicles (UAVs) is tracking of their flight trajectory. Existing UAVs leverage autonomous flight functionalities based on trajectory generation algorithms developed in robotic applications such as polynomial or spline curves in order to facilitate kinematic smoothness, minimum vibrations and fuel efficiency. However in practice, the actual path may be subjected to unexpected local weather conditions, unexpected obstacles along the path or abrupt traffic changes in the low-altitude airspace resulting in large errors of the predicted time-of-arrival at way-points. In this study, an approach to quantify and propagate uncertainty in 4D trajectories is proposed. The paper presents a simple error interval propagation method based on the expected cruise speed of the UAV and its associated uncertainty. The uncertainty is then propagated in time to estimate reasonable confidence intervals on the times-of-arrival of the vehicle at each way-point as well as along the entire flight-path. The uncertainty propagation is demonstrated on a state-of-the-art trajectory generation algorithm based on non-uniform rational B-spline (NURBS) curves. Further, the effect of a stationary wind field is incorporated in the uncertainty propagation approach. The proposed method is implemented on synthetic and real data obtained from flight experiments with a small UAV.

Uncertainty Quantification

Preliminary Findings of the Photovoltaic Cell Calibration Experiment on Pathfinder Flight 95-3

The objective of the photovoltaic (PV) cell calibration experiment for Pathfinder was to develop an experiment compatible with an ultralight UAV to predict the performance of PV cells at AM0, the solar spectrum in space, using the Langley plot technique. The Langley plot is a valuable technique for this purpose and requires accurate measurements of air mass (pressure), cell temperature, solar irradiance, and current-voltage(IV) characteristics with the cells directed normal to the direct ray of the sun. Pathfinder's mission objective (95-3) of 65,000 ft. maximum altitude, is ideal for performing the Langley plot measurements. Miniaturization of electronic data acquisition equipment enabled the design and construction of an accurate and light weight measurement system that meets Pathfinder's low payload weight requirements.

Vargas-Aburto, Carlos

Improving Trust in Deep Neural Networks with Nearest Neighbors

Deep neural networks are used increasingly for perception and decision-making in UAVs. For example, they can be used to recognize objects from images and decide what actions the vehicle should take. While deep neural networks can perform very well at complex tasks, their decisions may be unintuitive to a human operator. When a human disagrees with a neural network prediction, due to the black box nature of deep neural networks, it can be unclear whether the system knows something the human does not or whether the system is malfunctioning. This uncertainty is problematic when it comes to ensuring safety. As a result, it is important to develop technologies for explaining neural network decisions for trust and safety. This paper explores a modification to the deep neural network classification layer to produce both a predicted label and an explanation to support its prediction. Specifically, at test time, we replace the final output layer of the neural network classifier by a k-nearest neighbor classifier. The nearest neighbor classifier produces 1) a predicted label through voting and 2) the nearest neighbors involved in the prediction, which represent the most similar examples from the training dataset. Because prediction and explanation are derived from the same underlying process, this approach guarantees that the explanations are always relevant to the predictions. We demonstrate the approach on a convolutional neural network for a UAV image classification task. We perform experiments using a forest trail image dataset and show empirically that the hybrid classifier can produce intuitive explanations without loss of predictive performance compared to the original neural network. We also show how the approach can be used to help identify potential issues in the network and training process.

Lee, Ritchie

UAV Inspection of Electrical Transmission Infrastructure with Path Conformance Autonomy and Lidar-Based Geofences NASA Report on UTM Reference Mission Flights at Southern Company Flights November 2016

Flights at low altitudes in close proximity to electrical transmission infrastructure present serious navigational challenges: GPS and radio communication quality is variable and yet tight position control is needed to measure defects while avoiding collisions with ground structures. To advance unmanned aerial vehicle (UAV) navigation technology while accomplishing a task with economic and societal benefit, a high voltage electrical infrastructure inspection reference mission was designed. An integrated air-ground platform was developed for this mission and tested in two days of experimental flights to determine whether navigational augmentation was needed to successfully conduct a controlled inspection experiment. The airborne component of the platform was a multirotor UAV built from commercial off-the-shelf hardware and software, and the ground component was a commercial laptop running open source software. A compact ultraviolet sensor mounted on the UAV can locate 'hot spots' (potential failure points in the electric grid), so long as the UAV flight path adequately samples the airspace near the power grid structures. To improve navigation, the platform was supplemented with two navigation technologies: lidar-to-polyhedron preflight processing for obstacle demarcation and inspection distance planning, and trajectory management software to enforce inspection standoff distance. Both navigation technologies were essential to obtaining useful results from the hot spot sensor in this obstacle-rich, low-altitude airspace. Because the electrical grid extends into crowded airspaces, the UAV position was tracked with NASA unmanned aerial system traffic management (UTM) technology. The following results were obtained: (1) Inspection of high-voltage electrical transmission infrastructure to locate 'hot spots' of ultraviolet emission requires navigation methods that are not broadly available and are not needed at higher altitude flights above ground structures. (2) The sensing capability of a novel airborne UV detector was verified with a standard ground-based instrument. Flights with this sensor showed that UAV measurement operations and recording methods are viable. With improved sensor range, UAVs equipped with compact UV sensors could serve as the detection elements in a self-diagnosing power grid. (3) Simplification of rich lidar maps to polyhedral obstacle maps reduces data volume by orders of magnitude, so that computation with the resultant maps in real time is possible. This enables real-time obstacle avoidance autonomy. Stable navigation may be feasible in the GPS-deprived environment near transmission lines by a UAV that senses ground structures and compares them to these simplified maps. (4) A new, formally verified path conformance software system that runs onboard a UAV was demonstrated in flight for the first time. It successfully maneuvered the aircraft after a sudden lateral perturbation that models a gust of wind, and processed lidar-derived polyhedral obstacle maps in real time. (5) Tracking of the UAV in the national airspace using the NASA UTM technology was a key safety component of this reference mission, since the flights were conducted beneath the landing approach to a heavily used runway. Comparison to autopilot tracking showed that UTM tracking accurately records the UAV position throughout the flight path.

Moore, Andrew J.

Satellite communications provisions on NASA Ames instrumented aircraft platforms for Earth science research/applications

Earth science activities at NASA Ames are research in atmospheric and ecosystem science, development of remote sensing and in situ sampling instruments, and their integration into scientific research platform aircraft. The use of satellite communications can greatly extend the capability of these agency research platform aircraft. Current projects and plans involve satellite links on the Perseus UAV and the ER-2 via TDRSS and a proposed experiment on the NASA Advanced Communications Technology Satellite. Provisions for data links on the Perseus research platform, via TDRSS S-band multiple access service, have been developed and are being tested. Test flights at Dryden are planned to demonstrate successful end-to-end data transfer. A Unisys Corp. airborne satcom STARLink system is being integrated into an Ames ER-2 aircraft. This equipment will support multiple data rates up to 43 Mb/s each via the TDRS S Ku-band single access service. The first flight mission for this high-rate link is planned for August 1995. Ames and JPL have proposed an ACTS experiment to use real-time satellite communications to improve wildfire research campaigns. Researchers and fire management teams making use of instrumented aircraft platforms at a prescribed burn site will be able to communicate with experts at Ames, the U.S. Forest Service, and emergency response agencies.

Shameson, L.

Old Journey, New Heights

If you could see the road ahead, you might pass up a fantastic opportunity because you're blinded by the potential pitfalls. In my case, I was testing the project management waters at the NASA Dryden Flight Research Center after ten years of being a research engineer. I was an eager (but ignorant) rookie project manager (PM) and I was willing to engage in just about any project without knowing what it would entail. The assignment I accepted was to help NASA's Environment Research Aircraft and Sensor Technology (ERAST) Project, a partnership with a fledgling Uninhabited Aerial Vehicle (UAV) industry, to tackle stratospheric flight. I remember one of our industrial partners querying me about whether or not I understood what 1 was getting into. Like one of those bobble-head toys that have become quite popular, I nodded. But in reality, I didn't have a clue. His response was, "Hang on, it's going to be a wild ride." He was right. In retrospect, if I had clearly understood the ten years of pitfalls that were coming, I might not have "hung on." Now I can look back and say that I would not trade the experience for anything. The lows included the destruction of a number of UAVs on my watch. Later someone told me that we should not be surprised if we lost one UAV for every ten flights. We wrote many chapters in the book on what can go wrong with UAVs-and we are still writing. As you can imagine, each mishap was accompanied by an investigation. What an education!

DelFrate, John

Demonstrating Acquisition of Real-Time Thermal Data over Fires Utilizing UAVs

NASA-Ames Research Center, in collaboration with General Atomics Aeronautical Systems, Inc. has been developing real-time data acquisition and information delivery systems employing uninhabited aerial vehicle (UAV) technology for disaster mitigation and assessment demonstrations. Working in conjunction with the US Forest Service, a disaster community agency responsible for wildfire management and mitigation, we developed a large-scale wildfire demonstration called the First Response Experiment (FIRE). During that experiment in late summer 2001, the participants demonstrated the melding of innovative technologies such as UAV platforms, real-time data processing, and data telemetry for quick analysis of a disaster event. The General Atomics ALTUS UAV, the Airborne Infrared Disaster Assessment System (AIRDAS) and Over-The-Horizon (OTH) satellite data telemetry equipment were employed over a controlled burn to test the feasibility of a disaster monitoring and mitigation platform for hazardous duty. The ALTUS UAV was employed to demonstrate the long duration, altitude, and payload capability of unmanned platforms for acquiring disaster related data. The ALTUS has an operational altitude to 45,000 feet (13,700 in), with a flight duration of twenty-four hours and a payload capacity of over 300 lbs. (148.5 kg). This allows the platform to operate under the conditions that would be necessary for monitoring and mitigating disaster events throughout the Unites States. The four channel AIRDAS data (calibrated thermal infrared digital imagery of the fire event) was sent from the ALTUS UAV via a satellite communications system (NERA transponder and INMARSAT satellite) to a data archive server and an image processing work station at NASA-Ames Research Center, 400 miles away.

Wegener, Steven S.

Demonstrating Acquisition of Real-Time Thermal Data Over Fires Utilizing UAVs

A disaster mitigation demonstration, designed to integrate remote-piloted aerial platforms, a thermal infrared imaging payload, over-the-horizon (OTH) data telemetry and advanced image geo-rectification technologies was initiated in 2001. Project FiRE incorporates the use of a remotely piloted Uninhabited Aerial Vehicle (UAV), thermal imagery, and over-the-horizon satellite data telemetry to provide geo-corrected data over a controlled burn, to a fire management community in near real-time. The experiment demonstrated the use of a thermal multi-spectral scanner, integrated on a large payload capacity UAV, distributing data over-the-horizon via satellite communication telemetry equipment, and precision geo-rectification of the resultant data on the ground for data distribution to the Internet. The use of the UAV allowed remote-piloted flight (thereby reducing the potential for loss of human life during hazardous missions), and the ability to "finger and stare" over the fire for extended periods of time (beyond the capabilities of human-pilot endurance). Improved bit-rate capacity telemetry capabilities increased the amount, structure, and information content of the image data relayed to the ground. The integration of precision navigation instrumentation allowed improved accuracies in geo-rectification of the resultant imagery, easing data ingestion and overlay in a GIS framework. We focus on these technological advances and demonstrate how these emerging technologies can be readily integrated to support disaster mitigation and monitoring strategies regionally and nationally.

Ambrosia, Vincent G.

Forced Oscillation Wind Tunnel Testing for FASER Flight Research Aircraft

As unmanned air vehicles (UAVs) continue to expand their flight envelopes into areas of high angular rate and high angle of attack, modeling the complex unsteady aerodynamics for simulation in these regimes has become more difficult using traditional methods. The goal of this experiment was to improve the current six degree-of-freedom aerodynamic model of a small UAV by replacing the analytically derived damping derivatives with experimentally derived values. The UAV is named the Free-flying Aircraft for Sub-scale Experimental Research, FASER, and was tested in the NASA Langley Research Center 12- Foot Low-Speed Tunnel. The forced oscillation wind tunnel test technique was used to measure damping in the roll and yaw axes. By imparting a variety of sinusoidal motions, the effects of non-dimensional angular rate and reduced frequency were examined over a large range of angle of attack and side-slip combinations. Tests were performed at angles of attack from -5 to 40 degrees, sideslip angles of -30 to 30 degrees, oscillation amplitudes from 5 to 30 degrees, and reduced frequencies from 0.010 to 0.133. Additionally, the effect of aileron or elevator deflection on the damping coefficients was examined. Comparisons are made of two different data reduction methods used to obtain the damping derivatives. The results show that the damping derivatives are mainly a function of angle of attack and have dependence on the non-dimensional rate and reduced frequency only in the stall/post-stall regime

Hoe, Garrison