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NASA NTRS2021

Adaptive Aerostructures for Revolutionary Civil Supersonic Transportation

To enable commercially viable civil supersonic transport (SST) aircraft, innovative solutions must be developed to meet noise and efficiency requirements for overland flight. This research effort consists of a multidisciplinary team of academic and industrial experts exploring for the first time the potential of small real-time geometric outer mold line (OML) reconfigurations to minimize sonic boom signatures and aircraft drag in response to changing ambient conditions, thereby enabling noise-compliant overland supersonic flight. The team utilizes recent advances in supersonic computational fluid dynamic (CFD) methods, new noise prediction tools, and new design approaches to consider embedded highly energy-dense shape memory alloy (SMA) actuators for local shape modifications to an SST aircraft leading to optimal low boom signature and low drag in different environments. This university-led program will provide strategic leadership toward technology convergence that advances NASA's Aerospace Research Mission Directorate's (ARMD) research objectives with regard to Thrust 2: “Innovation in Commercial Supersonic Aircraft” by exploring for the first time enabling low-boom operation across a range of flight conditions via structural adaptivity, and will promote education of the next generation of engineers. The overall research strategy is to pursue three critical areas: the design of configurations for reducing boom, SMA material development and modeling, and technology feasibility demonstration in a relevant environment. Initially, the team will identify potential applications where structure or geometry adaptivity provides a benefit in noise or drag across the entire flight envelope. For selected applications/structural locations, required OML geometry changes will be determined based on analysis of sonic boom ground signature and drag reduction using new design tools, trade studies, and atmospheric sensing techniques. Designs will be developed and evaluated against requirements on loading, stroke length, and operational temperature. New alloy formulations will be developed tailored for both autonomous and controlled actuation modes. As the SMA material development matures, integrated system-level factors will be investigated. Optimized designs for small-scale distributed adaptivity applications of maximum benefit will then be matured and tested, moving toward demonstration of the innovative technology approaches at a TRL 4-5 and showing that sonic booms can be reduced by reconfiguration on demand.

Koushik Datta↗

NASA NTRS2013

FE Simulation of SMA Seal for Mars Sample Return

Several NASA rovers and landers have been on Mars and performed successful in-situ exploration. Returning Martian samples to Earth for extensive analysis is of great interest to the planetary science community. Current Mars sample return architecture would require leaving the acquired samples on Mars for years before being retrieved by subsequent mission. Each sample would be sealed securely to keep its integrity. A reliable seal technique that does not affect the integrity of the samples and uses a simple low-mass tool is required. The shape memory alloy (SMA) seal technique is a promising candidate. A study of the thermal performances of several primary designs of a SMA seal for sample tubes by finite element (FE) simulation are presented in this paper. The results show sealing the sample tube by SMA plugs and controlling the sample temperature below the allowed temperature level are feasible.

seal↗

NASA NTRS2026

Mechanical Design and Operation of a Novel Lunar Environment Structural Test Rig (LESTR)

The Lunar Environment Structural Test Rig (LESTR) was developed to address a critical gap in mechanical property data for metal alloy wire materials under lunar-relevant conditions down to 40 K. Conventional aerospace material databases provide thermophysical properties for bulk metals over a wide temperature range, but validated mechanical and physical property data below 77 K, particularly for small-diameter wires, remain limited and are generally the exception rather than the rule. These conditions are essential for Artemis mission hardware such as shape memory alloy (SMA) rover tires. LESTR’s design requirements were to combine a high-stiffness electrodynamic load frame with closed- cycle cryogenic cooling, high-vacuum capability (10–6 torr), and noncontact optical strain measurement to enable tensile, four-point bend, and fatigue testing of wires or other materials and geometries at temperatures from 40 to 125 K. These considerable requirements were merged with the need to lower the barrier of testing for the end user as measured in terms of cost-per-test cycle, safety improvement, and reduction in upkeep costs associated with state-of-the-art solutions associated with cryomechanical material characterization. The system incorporates modular gripping and alignment fixtures; precision thermal management using cryocoolers and embedded heaters; and integrated instrumentation for displacement, load, temperature, and vacuum control. Calibration procedures establish correlations between tooling and specimen temperature, ensuring accurate thermal conditions across the design envelope unbound by cryofluid conditions in heritage immersion-based test systems. Initial validation tests using Inconel (Special Metals Corp.) wire demonstrated accurate ultimate strength and post-yield behavior. The load frame operation was also verified under representative service conditions, including thermal cycling and prolonged fatigue loading. By generating mechanical property data at ultralow temperatures, LESTR fills a critical gap in existing materials databases and provides a scalable platform for iterative alloy development and durability assessment for planetary hardware. This capability supports NASA’s long-term objectives for surface exploration by enabling design confidence for components operating in extreme cryogenic environments.

LESTR↗

NASA NTRSDate not supplied

Designing Non-Pneumatic, Structural Tires for Space: Challenges and Solutions for a Difficult Application

Design and development of Shape Memory Alloy (SMA) Tires is a difficult and challenging problem. A “build and test” approach isn’t practical due to both the expense and time associated with taking such an approach. The multiple iterations that would be required to close requirements space for a space flight hardware program makes this approach infeasible. Hence, details regarding GRC’s SMA modeling approach to solving this challenging problem will be highlighted and used to showcase the power associated with leveraging an SMA modeling framework during design.

Shape Memory Alloys (SMA)↗

NASA NTRS2005

Properties and Potential of Two (ni,pt)ti Alloys for Use as High-temperature Actuator Materials

The microstructure, transformation temperatures, basic tensile properties, shape memory behavior, and work output for two (Ni,Ti)Pt high-temperature shape memory alloys have been characterized. One was a Ni30Pt20Ti50 alloy (referred to as 20Pt) with transformation temperatures above 230 C and the other was a Ni20Pt30Ti50 alloy (30Pt) with transformation temperatures about 530 C. Both materials displayed shape memory behavior and were capable of 100% (no-load) strain recovery for strain levels up to their fracture limit (3-4%) when deformed at room temperature. For the 20Pt alloy, the tensile strength, modulus, and ductility dramatically increased when the material was tested just about the austenite finish (A(sub f)) temperature. For the 30Pt alloy, a similar change in yield behavior at temperatures above the A(sub f) was not observed. In this case the strength of the austentite phase was at best comparable and generally much weaker than the martensite phase. A ductility minimum was also observed just below the A(sub s) temperature in this alloy. As a result of these differences in tensile behavior, the two alloys performed completely different when thermally cycled under constant load. The 20Pt alloy behaved similar to conventional binary NiTi alloys with work output due to the martensite-to-austenite transformation initially increasing with applied stress. The maximum work output measured in the 20Pt alloy was nearly 9 J/cu cm and was limited by the tensile ductility of the material. In contrast, the martensite-to-austenite transformation in the 30Pt alloy was not capable of performing work against any bias load. The reason for this behavior was traced back to its basic mechanical properties, where the yield strength of the austenite phase was similar to or lower than that of the martensite phase, depending on temperature. Hence, the recovery or transformation strain for the 30Pt alloy under load was essentially zero, resulting in zero work output.

Noebe, Ronald↗

NASA NTRS2024

Development and Implementation of Large-Scale Numerical Models for Shape Memory Mars Spring Tires

The current work focuses on implementation of the user-defined shape memory alloy (SMA) model in the finite element analysis program ABAQUS for large-scale simulations of the Spring Tires made of SMA developed at the NASA Glenn Research Center. The main objective of this study was to improve and optimize the structural design of the SMA tires through in-depth numerical analysis and sensitivity studies. Various design variables (wire diam., coil diam., pitch, spring length, and bead angle) were varied to study their influence on the global load-displacement response of the tire construct. A detailed investigation of the three-dimensional stress states was also carried out to enhance understanding of the local changes as the tire goes through global deformation. It was concluded that a robust numerical model with a good predictive capability, together with a thoughtfully crafted sensitivity study, can result in reduced design iterations required to reach a desired tire performance. This will, in turn, lead to significantly reduced manufacturing time, required labor, and testing expense.

shape memory alloys↗

NASA NTRS2020

Dynamic Countermeasure Fabrics for Post-Spaceflight Orthostatic Intolerance

Aerospace orthostatic intolerance garments (OIG) have historically been pneumatic (e.g., NASA’s antigravity suit), an approach that inhibits mobility and requires connection to an air supply. Elastic compression garments, an alternative technology, are difficult to don/doff and cannot be worn in a noncompressive state, resulting in discomfort and usability challenges. This research evaluates a novel technology—contractile shape memory alloy (SMA) knitted actuators—that can enable low-profile, dynamic compression for an aerospace OIG. To characterize the functional capabilities of SMA knitted actuators, displacement control testing was conducted on 10 actuator samples with a range of geometric design parameters. Inactive (FI) and actuated forces (FA) were observed by repeatedly thermally cycling each sample at 0%, 15%, 30%, and 45% structural strain. Compression capabilities were approximated using medical compression hosiery standards and anthropometric data from a representative aerospace population (ANSUR 2012). Dynamic compression predictions reached 52 mmHg (single layer fabric) and 105 mmHg (double layer fabric) at the ankle. Low, inactive pressures (p, 20 mmHg) demonstrate that compression is controllable and can be dynamically increased upon actuation up to 33 mmHg in a single layer system and up to 67 mmHg in a double layer system. The results highlight the potential of SMA knitted actuators to enable low-profile, dynamic compression garments that can reach medically therapeutic pressures on an aerospace population to counteract OI symptoms. In addition to astronautic applications, this technology demonstrates widespread terrestrial medical and high-performance aircraft applicability.

Orthostatic intolerance↗

NASA NTRSDate not supplied

Capturing, Analyzing, Maintaining, and Disseminating Shape Memory Material Data Between Information Management Systems

With an increased demand on reducing the time, cost, and effort to develop new materials, Integrated Computational Materials Engineering (ICME) has received widespread attention in various engineering disciplines as a catalyst for significantly reducing experimental testing during the material design process. An ICME approach to design can enable ‘fit-for-purpose’ materials to be realized in engineering applications by incorporating well-understood process-property-performance relationships between the various length and time scales in a material’s structure, enabling material optimization. However, such an approach requires validated multiscale models at the various length scales for a material, which in turn requires a large amount of data, a robust means of storing the data, and the ability to link data to developed material models. The NASA Vision 2040 [1] has identified nine key elements to enabling ICME approaches in system level design, with one being “Data, Information, and Visualization”, thus outlining the importance of a robust information management system for ICME. As the relationship between microstructure, properties, and material performance become better understood and incorporated into multiscale models that can be leveraged in application design, the emergence of new materials with application-driven properties can be realized. One such new material class that has seen growing attention are shape memory materials (SMM), in which a material can transition between a deformed and undeformed state via a reversible phase transformation when subject to a thermal, mechanical, or magnetic load [2]. SMMs have been used widely in aerospace and biomedical industries, including applications such as actuators, low-shock mechanisms, medical staples, braces, and stents [3, 4]. These materials exhibit unique behavior due to their ability to transition between phases, and thus the mechanisms that enable this transition must be captured in a data information management system and incorporated into SMM material models. At NASA Glenn Research Center, the Shape Memory Materials Database (SMMD) Tool has been developed to capture the necessary information that governs SMM material behavior and provide users the ability to select and visualize various SMMs for a specific application [5]. The database contains point-wise data for published SMM materials, along with the pedigree metadata for traceability necessary for a robust information management system. The database is also capable of storing in-house test data performed at NASA GRC by interacting with the developed Shape Memory Alloy (SMA) Analytics tool to extract the necessary point-wise values and populate the database. Although the SMMD Tool offers its users a single, authoritative source for SMM material data that is critical for model development and material design, the full material pedigree of the in-house test data for SMMs is not currently captured and is out of the scope for the SMMD tool. In this work, the schema for capturing SMM test data within the larger NASA GRC ICME Schema [6, 7, 8, 9] will be developed and implemented for thermomechanical tests conducted at NASA GRC. The developed schema will not only store the relevant data needed for the SMMD tool, but also the material pedigree (i.e., production of the bulk material, bulk material analysis, sample cut-out diagrams, sample fabrication procedure, etc.), test pedigree (i.e., test equipment used, measurement systems used, raw test data), and analysis pedigree (i.e., how the data in the SMMD tool is calculated). Furthermore, a Python-based framework will be developed to seamlessly interact between the SMA Analytics and SMMD tools, which will write the full dataset and associated metadata to the GRC Information Management System before passing the required point-wise data to the SMMD tool. Data informatics is a key element of the NASA Vision 2040, which requires not only that data is stored and maintained throughout the material lifecycle, but that the data is also accessible and reusable such that material development efforts can be minimized. Therefore, for an ICME design approach to be realized, a centralized information management system that drives the ICME process must be able to communicate with other databases. The work that will be presented in this presentation will therefore not only demonstrate the ability of NASA GRC’s information management system to capture SMM data, but also its ability to interact with pre-existing tools specialized for such materials.

Data management↗

NASA NTRS2008

Novel Ice Mitigation Methods

After the loss of Columbia, there was great concern in the Space Shuttle program for the impact of debris against the leading edges of the Orbiter wings. It was quickly recognized that, in addition to impacts by foam, ice that formed on the liquid-oxygen bellows running down the outside of the External Tank could break free during launch and hit this sensitive area. A Center Director s Discretionary Fund (CDDF) project would concentrate on novel ideas that were potentially applicable. The most successful of the new concepts for ice mitigation involved shape memory alloy materials. These materials can be bent into a given shape and, when heated, will return to their original shape.

Source record↗

NASA NTRS2014

Modeling Materials: Design for Planetary Entry, Electric Aircraft, and Beyond

NASA missions push the limits of what is possible. The development of high-performance materials must keep pace with the agency's demanding, cutting-edge applications. Researchers at NASA's Ames Research Center are performing multiscale computational modeling to accelerate development times and further the design of next-generation aerospace materials. Multiscale modeling combines several computationally intensive techniques ranging from the atomic level to the macroscale, passing output from one level as input to the next level. These methods are applicable to a wide variety of materials systems. For example: (a) Ultra-high-temperature ceramics for hypersonic aircraft-we utilized the full range of multiscale modeling to characterize thermal protection materials for faster, safer air- and spacecraft, (b) Planetary entry heat shields for space vehicles-we computed thermal and mechanical properties of ablative composites by combining several methods, from atomistic simulations to macroscale computations, (c) Advanced batteries for electric aircraft-we performed large-scale molecular dynamics simulations of advanced electrolytes for ultra-high-energy capacity batteries to enable long-distance electric aircraft service; and (d) Shape-memory alloys for high-efficiency aircraft-we used high-fidelity electronic structure calculations to determine phase diagrams in shape-memory transformations. Advances in high-performance computing have been critical to the development of multiscale materials modeling. We used nearly one million processor hours on NASA's Pleiades supercomputer to characterize electrolytes with a fidelity that would be otherwise impossible. For this and other projects, Pleiades enables us to push the physics and accuracy of our calculations to new levels.

Supercomputing↗

NASA NTRS2016

Autonomous Slat-Cove-Filler Device for Reduction of Aeroacoustic Noise Associated with Aircraft Systems

A slat cove filler is utilized to reduce airframe noise resulting from deployment of a leading edge slat of an aircraft wing. The slat cove filler is preferably made of a super elastic shape memory alloy, and the slat cove filler shifts between stowed and deployed shapes as the slat is deployed. The slat cove filler may be configured such that a separate powered actuator is not required to change the shape of the slat cove filler from its deployed shape to its stowed shape and vice-versa. The outer contour of the slat cove filler preferably follows a profile designed to maintain accelerating flow in the gap between the slat cove filler and wing leading edge to provide for noise reduction.

Turner, Travis L.↗

NASA NTRS2004

Site preference of ternary alloying additions to NiTi: Fe, Pt, Pd, Au, Al, Cu, Zr and Hf

Atomistic modeling of the site substitution behavior of Pd in NiTi (J. Alloys and Comp. (2004), in press) has been extended to examine the behavior of several other alloying additions, namely, Fe, Pt, Au, Al, Cu, Zr and Hf in this important shape memory alloy. It was found that all elements, to a varying degree, displayed absolute preference for available sites in the deficient sublattice. How- ever, the energetics of the different substitutional schemes, coupled with large scale simulations indicate that the general trend in all cases is for the ternary addition to want to form stronger ordered structures with Ti.

Bozzolo, Guillermo↗

NASA NTRS2005

Two SMA-Actuated Miniature Mechanisms

The figures depict two miniature mechanisms actuated by strips made of shape-memory alloy (SMA). A typical SMA is a nickel-titanium alloy known by the trade name "Flexinol" or "Nitinol." In preparation for a typical application, a suitably sized and shaped piece of an SMA is deformed by a predetermined amount at the lower of two operating temperatures, then mounted in a mechanism. When stroking of the mechanism in one direction is desired, the piece of SMA is heated above a transition temperature to make it return to the "remembered" undeformed state. When stroking of the mechanism in the opposite direction is desired, the SMA is cooled below the transition temperature to make it return to the deformed state. Also, the SMA alloy chosen for a specific application is one that has a transition temperature somewhat above the ambient temperature, so that stroking in one direction or the opposite direction can be achieved by heating the SMA, or refraining from heating the SMA, respectively, above the transition temperature. In the present mechanisms as in typical other SMA mechanisms, the heating is effected by electric currents applied via electrical contacts at the ends of the SMA strips. The purpose served by the mechanism of Figure 1 is to lock or release a flexible latch attachment. In preparation for use in this mechanism, two initially straight SMA strips are deformed into curved springs that, when mounted in the mechanism at ambient temperature, clamp the knob at the lower end of the flexible latch attachment. When heated above their transition temperature by an electric current, the SMA strips return to their original straight configuration, thereby releasing the knob. This mechanism is redundant in the sense that as long as at least one of the two SMA strips straightens when commanded to do so, the knob is released. The mechanism of Figure 2 is suited to any of a variety of applications in which there are requirements for a small mechanism that affords lowtorque rotary actuation through a finite angular range. As shown here, the mechanism is used to rotate a coverlatch pin to a release position. In this case, a straight and flat SMA strip is torsionally deformed to a twist angle of about 90deg by use of a torsion bias spring. When the SMA strip is heated, it rotates to its original straight and flat condition.

Willey, Cliff E.↗

NASA NTRS2014

A Morphing Radiator for High-Turndown Thermal Control of Crewed Space Exploration Vehicles

Spacecraft designed for missions beyond low earth orbit (LEO) face a difficult thermal control challenge, particularly in the case of crewed vehicles where the thermal control system (TCS) must maintain a relatively constant internal environment temperature despite a vastly varying external thermal environment and despite heat rejection needs that are contrary to the potential of the environment. A thermal control system may be required to reject a higher heat load to warm environments and a lower heat load to cold environments, necessitating a relatively high turndown ratio. A modern thermal control system is capable of a turndown ratio of on the order of 12:1, but crew safety and environment compatibility have constrained these solutions to massive multi-loop fluid systems. This paper discusses the analysis of a unique radiator design that employs the behavior of shape memory alloys (SMAs) to vary the turndown of, and thus enable, a single-loop vehicle thermal control system for space exploration vehicles. This design, a morphing radiator, varies its shape in response to facesheet temperature to control view of space and primary surface emissivity. Because temperature dependence is inherent to SMA behavior, the design requires no accommodation for control, instrumentation, or power supply in order to operate. Thermal and radiation modeling of the morphing radiator predict a turndown ranging from 11.9:1 to 35:1 independent of TCS configuration. Coupled thermal-stress analyses predict that the desired morphing behavior of the concept is attainable. A system level mass analysis shows that by enabling a single loop architecture this design could reduce the TCS mass by between 139 kg and 225 kg. The concept has been demonstrated in proof-of-concept benchtop tests.

Cognata, Thomas J.↗

NASA NTRS2015

A Morphing Radiator for High-Turndown Thermal Control of Crewed Space Exploration Vehicles

Spacecraft designed for missions beyond low earth orbit (LEO) face a difficult thermal control challenge, particularly in the case of crewed vehicles where the thermal control system (TCS) must maintain a relatively constant internal environment temperature despite a vastly varying external thermal environment and despite heat rejection needs that are contrary to the potential of the environment. A thermal control system is in other words required to reject a higher heat load to warm environments and a lower heat load to cold environments, necessitating a quite high turndown ratio. A modern thermal control system is capable of a turndown ratio of on the order of 12:1, but for crew safety and environment compatibility these are massive multi-loop fluid systems. This paper discusses the analysis of a unique radiator design which employs the behavior of shape memory alloys (SMA) to vary the turndown of, and thus enable, a single-loop vehicle thermal control system for space exploration vehicles. This design, a morphing radiator, varies its shape in response to facesheet temperature to control view of space and primary surface emissivity. Because temperature dependence is inherent to SMA behavior, the design requires no accommodation for control, instrumentation, nor power supply in order to operate. Thermal and radiation modeling of the morphing radiator predict a turndown ranging from 11.9:1 to 35:1 independent of TCS configuration. Stress and deformation analyses predict the desired morphing behavior of the concept. A system level mass analysis shows that by enabling a single loop architecture this design could reduce the TCS mass by between 139 kg and 225 kg. The concept is demonstrated in proof-of-concept benchtop tests.

Cognata, Thomas J.↗

NASA NTRS2003

Rollable Thin-Shell Nanolaminate Mirrors

A class of lightweight, deployable, thin-shell, curved mirrors with built-in precise-shape-control actuators is being developed for high-resolution scientific imaging. This technology incorporates a combination of advanced design concepts in actuation and membrane optics that, heretofore, have been considered as separate innovations. These mirrors are conceived to be stowed compactly in a launch shroud and transported aboard spacecraft, then deployed in outer space to required precise shapes at much larger dimensions (diameters of the order of meters or tens of meters). A typical shell rollable mirror structure would include: (1) a flexible single- or multiple-layer face sheet that would include an integrated reflective surface layer that would constitute the mirror; (2) structural supports in the form of stiffeners made of a shape-memory alloy (SMA); and (3) piezoelectric actuators. The actuators, together with an electronic control subsystem, would implement a concept of hierarchical distributed control, in which (1) the SMA actuators would be used for global shape control and would generate the large deformations needed for the deployment process and (2) the piezoelectric actuators would generate smaller deformations and would be used primarily to effect fine local control of the shape of the mirror.

Hickey, Gregory↗

NASA NTRS2017

Shape Morphing Adaptive Radiator Technology (SMART) Updates to Techport Entry

The Shape-Morphing Adaptive Radiator Technology (SMART) project builds off the FY16 research effort that developed a flexible composite radiator panel and demonstrated its ability to actuate from SMA's attached to it. The proposed FY17 Shape-Morphing Adaptive Radiator Technology (SMART) project's goal is to 1) develop a practical radiator design with shape memory alloys (SMAs) bonded to the radiator's panel, and 2) build a multi-panel radiator prototype for subsequent system level thermal vacuum tests. The morphing radiator employs SMA materials to passively change its shape to adapt its rate of heat rejection to vehicle requirements. Conceptually, the radiator panel has a naturally closed position (like a cylinder) in a cold environment. Whenever the radiator's temperature gradually rises, SMA's affixed to the face sheet will pull the face sheet open a commensurate amount - increasing the radiators view to space and causing it to reject more heat. In a vehicle, the radiator's variable heat rejection capabilities would reduce the number of additional heat rejection devices in a vehicle's thermal control system. This technology aims to help achieve the required maximum to minimum heat rejection ratio required for manned space vehicles to adopt a lighter, simpler, single loop thermal control architecture (ATCS). Single loop architectures are viewed as an attractive means to reduce mass and complexity over traditional dual-loop solutions. However, fluids generally considered safe enough to flow within crewed cabins (e.g. propylene glycol-water mixtures) have much higher freezing points and viscosities than those used in the external sides of dual loop ATCSs (e.g. Ammonia and HFE7000).

Erickson, Lisa↗

NASA NTRS2000

Flight Control Using Distributed Shape-Change Effector Arrays

Recent discoveries in material science and fluidics have been used to create a variety of novel effector devices that offer great potential to enable new approaches to aerospace vehicle flight control. Examples include small inflatable blisters, shape-memory alloy diaphragms, and piezoelectric patches that may be used to produce distortions or bumps on the surface of an airfoil to generate control moments. Small jets have also been used to produce a virtual shape-change through fluidic means by creating a recirculation bubble on the surface of an airfoil. An advanced aerospace vehicle might use distributed arrays of hundreds of such devices to generate moments for stabilization and maneuver control, either augmenting or replacing conventional ailerons, flaps or rudders. This research demonstrates the design and use of shape-change device arrays for a tailless aircraft in a low-rate maneuvering application. A methodology for assessing the control authority of the device arrays is described, and a suite of arrays is used in a dynamic simulation to illustrate allocation and deployment methodologies. Although the authority of the preliminary shape-change array designs studied in this paper appeared quite low, the simulation results indicate that the effector suite possessed sufficient authority to stabilize and maneuver the vehicle in mild turbulence.

Raney, David L.↗