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At least 433 records · Page 24

Unstructured Grid Development for the Space Launch System Liftoff and Transition Lineloads Computational Analysis

Production of aerodynamic lineloads databases for the Space Launch System (SLS) vehicle at Liftoff and Transition (LOT) conditions has required the development of a Computational Fluid Dynamics (CFD) workflow capable of producing high-quality solutions for this unique phase of flight. Aerodynamic considerations included a wide range of flow angles (from 0°up to 90°total angle of attack), resulting leeside separation, and interaction effects between the three bodies of the integrated SLS vehicle, as well as the nearby launch tower. Computational mesh development for similar problems at the NASA Langley Research Center (such as for the Constellation/Ares launch vehicles) has primarily relied on in-house tools such as VGRID/POSTGRID, with grids designed for NASA-developed and maintained flow solvers such as USM3D and FUN3D. The workflow for such problems has evolved over the development of the various SLS configurations to incorporate new tools such as the Heldenpatch/Heldenmesh grid generator (Helden Aerospace) and CREATE-AV Kestrel (US Department of Defense) flow solver. This paper describes efforts to benchmark a grid generation approach for LOT problems using Heldenpatch/Heldenmesh and Kestrel, verified against prior best practices from VGRID/POSTGRID. Parameters studied include surface grid density, first-layer viscous cell height, and volume grid growth rate parameters. Resulting solutions are compared based on total force and moment values, sectional line loads, and surface pressures, all validated against existing wind tunnel aerodynamic databases where available for the SLS Block 1B Cargo configuration.

Space launch systems↗

Types of Public Engagement for a Multi-Year Mission: The Interstellar Probe

How do we engage the public with a 50+ year mission? Scientists face challenges in effectively interacting with the public [1-4], along with the ever-changing nature of such a long-duration mission and updating of results. The Interstellar Probe initiative may benefit from an education and public engagement team for the purpose of professional development for scientists, exploring different tools for engagement, and outreach opportunities for a wide swath of communication. Some examples of such public engagement can follow the resources and engagement as that from the Lunar and Planetary Institute (LPI), Impact Earth, the Toolbox for Research and Exploration (TREX), and even previous mission initiatives and engagement with the public, such as the Cassini mission [4-7]. This abstract simply outlines the different types of public engagement that the Interstellar Probe could potentially develop and eventually undertake. Specifically, there are 4 main themes to explore: Public, Visual, Audio, and Research. Inclusivity should also be a factor on how to better engage the public through a multi-year mission

C Ahrens↗

LA-8 Computational Analysis and Validation Studies Using FlightStream

With the emerging market of Urban Air Mobility and the associated unique new flight vehicles with the capability of vertical takeoff and landing, design tools need to be calibrated to assist in the development of these new flight vehicle concepts. Distributed electric propulsion (DEP) covers these vehicles with high-energy flow from the array of motors, which leads to extensive propulsion/airframe interaction effects. With limited experimental data of vehicles using DEP and vehicle operation across a large range of angles of attack, including post-stall conditions, there is a lack of validated design tools to advance new vehicle concepts that have blown wings and operate in multiple flight modes. Although some CFD tools can handle the integration of multiple propulsors and unique geometries, the computational time with a full vehicle is extraordinary. FlightStream, a surface vorticity flow solver that can run in a fraction of the time of other CFD methods, has been evaluated using the Langley Aerodrome No. 8 (LA-8) vehicle as a test case. The LA-8 vehicle is a DEP tandem tilt-wing research vehicle that was designed, built, and tested at NASA Langley Research Center. The LA-8 design features both high-performance and high-technical risks aspects. The vehicle has gone through extensive design of experiments wind tunnel testing in the NASA Langley 12-Foot Low-Speed Wind Tunnel in order to capture all modes of operation. In addition, the LA-8 vehicle has undergone wind tunnel testing with and without propellers, which contributes to the validation of FlightStream for aerodynamic performance in blown and unblown wing cases. This study shows that FlightStream can produce trends and magnitudes of the lift and drag coefficients similar to the data collected from the wind tunnel testing of LA-8. The test cases were both blown and unblown wing cases and with and without high lift control surface deflections.

Steven Curtis Geuther↗

Irrigation Water Demand Sensitivity to Climate Variability across the Contiguous United States

Climate variability is an important driver of irrigation water use in many regions. Efforts to anticipate climate change impacts on future water availability can benefit from understanding how irrigation water demand has responded to these drivers to date. Here we apply satellite derived data, meteorological reanalysis, an advanced land surface model, and available state level reports to quantify irrigation demand sensitivities to temperature and precipitation across the Contiguous United States, for the period of 2002-2017. As expected, strong negative correlations are found between precipitation and irrigation withdrawals, both simulated and reported. Temperature sensitivities, however, vary by region and season, as do the interactive effects of temperature and precipitation on irrigation. Climate-induced irrigation variability is largest in transitional climate zones. These transitional zones are generally separate from the regions where rates of irrigation withdrawals are greatest, such that climate-induced variability in irrigation demand represents a water resource consideration that is distinct from chronic over pumping.

Wanshu Nie↗

Modeling of the Tau and Muon Neutrino-induced Optical Cherenkov Signals from Upward-moving Extensive Air Showers

We present a detailed modeling and computation methodology to determine the optical Cherenkovsignals produced by upward-moving extensive air showers (EASs) induced byτ-leptons and muons,sourced from the interaction of high-energy astrophysical neutrinos interacting in the Earth. Fol-lowing and extending the physics modeling and Cherenkov signal simulations performed in [1], thisscheme encompasses a new, state-of-the-art computation of the muon neutrino propagation insidethe Earth and the contribution to theτ-lepton muon decay channel. The modeling takes into ac-count all possibleτ-lepton decay and muon energy loss channels that feed the optical Cherenkovemission, produced by both tau and muon initiated EASs. The EAS modeling uses the electronenergy, angular, and lateral distributions in the EAS and their evolution as well as the wavelengthdependence of the Cherenkov emission and its atmospheric attenuation. The results presented hereare focused on the detection capabilities of sub-orbital (balloon-borne) and orbital (satellite) basedinstruments. The latter case was calculated for POEMMAato compare to that presented in [1],specifically including the muon-decay channel ofτ-leptons and the muonic EAS Cherenkov signalfrom muon neutrino interactions in the Earth. By detailing all these individual contributions tothe optical Cherenkov emission and detection, we show how the ensemble that includes muonicchannels provides a large detection capability for space-based, high-energy cosmic neutrino detec-tion. Specifically, we show that for neutrino energies∼<10 PeV, the upward-EAS sensitivity due tomuon neutrino interactions in the Earth begin to dominate over that for tau neutrino interactions,effectively extending the neutrino sensitivity to lower energies.

A L Cummings↗

Improving the transient sensitivity of AMEGO-X using single-site events

AMEGO-X is a proposed Compton/pair telescope which will image and survey the medium-energy gamma-ray sky between 100 keV and 1 GeV. It is designed to detect and characterize gamma-ray emission from multi-messenger sources. On short time scales (<100s), including information from single-site events (photoelectric effect interactions)significantly increases AMEGO-X's sensitivity and lowers its energy threshold down to 25 keV. In this presentation, we will present AMEGO-X's sensitivity to transient events such as gamma-ray bursts and magnetar giant flares, and discuss the improvements due to the inclusion of single-site events. We will also discuss AMEGO-X's ability to localize transient sources and alert the community for follow-up observations.

Henrike Fleischhack↗

Improving the Transient Sensitivity of AMEGO-X Using Single-site Events

AMEGO-X is a Compton/pair gamma-ray telescope, submitted to NASA's 2021 MIDEX AO, which will image and survey the medium-energy gamma-ray sky between 100 keV and 1 GeV. It is designed to detect and characterize gamma-ray emission from multi-messenger sources. On short time scales (<100s), including information from single-site events (photoelectric effect interactions) significantly increases AMEGO-X's sensitivity and lowers its energy threshold down to 25 keV. In this presentation, we will present AMEGO-X's sensitivity to transient events such as gamma-ray bursts and magnetar giant flares, and discuss the improvements due to the inclusion of single-site events. We will also discuss AMEGO-X's ability to localize transient sources and alert the community for follow-up observations.

Henrike Fleischhack↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗

Performance Modeling of Urban Air Mobility Vehicles to Support Air Traffic Management Research

The recent emergence of Urban Air Mobility (UAM) vehicles has resulted in a need for flight performance models that enable comprehensive simulation-based research on air traffic management topics such as route structure, scheduling, and separation standards. Successful performance modeling methods exist for a wide range of traditional aircraft designs. However, comparable modeling methods appropriate for UAM vehicles that combine fixed-wing and rotorcraft performance have not yet been established. One challenge to progress has been the lack of available data capturing the performance characteristics and unique flight profiles of these aircraft. This paper describes methods used to generate the required performance data and the development of performance models for UAM vehicles. Included is a review of the energy and power equations often used in developing performance models for traditional aircraft as well as a discussion of their applicability to UAM vehicles. The challenge of generating realistic performance data in over-actuated vehicles transitioning from hover to cruise flight is also addressed through an approach based on objective function optimization. A table-based performance model format adapted to UAM configurations is described, as well as parametric models intended to accompany the performance table to allow detailed modeling of power and fuel consumption during accelerated flight, turning flight, or flight at an arbitrary climb or descent rate. A discussion of future work is also provided, including the need for refinement of UAM performance modeling methods and formats, especially in conjunction with improvements to aerodynamic modeling of vehicles with complex designs where strong interaction effects may dominate important regions of the flight envelope.

Performance Modeling↗

Performance Modeling of Urban Air Mobility Vehicles to Support Air Traffic Management Research

The recent emergence of Urban Air Mobility (UAM) vehicles has resulted in a need for flight performance models that enable comprehensive simulation-based research on air traffic management topics such as route structure, scheduling, and separation standards. Successful performance modeling methods exist for a wide range of traditional aircraft designs. However, comparable modeling methods appropriate for UAM vehicles that combine fixed-wing and rotorcraft performance have not yet been established. One challenge to progress has been the lack of available data capturing the performance characteristics and unique flight profiles of these aircraft. This paper describes methods used to generate the required performance data and the development of performance models for UAM vehicles. Included is a review of the energy and power equations often used in developing performance models for traditional aircraft as well as a discussion of their applicability to UAM vehicles. The challenge of generating realistic performance data in over-actuated vehicles transitioning from hover to cruise flight is also addressed through an approach based on objective function optimization. A table-based performance model format adapted to UAM configurations is described, as well as parametric models intended to accompany the performance table to allow detailed modeling of power and fuel consumption during accelerated flight, turning flight, or flight at an arbitrary climb or descent rate. A discussion of future work is also provided, including the need for refinement of UAM performance modeling methods and formats, especially in conjunction with improvements to aerodynamic modeling of vehicles with complex designs where strong interaction effects may dominate important regions of the flight envelope.

Performance Modeling↗

Transition Modeling Based on the Dual N-factor Method for the CRM-NLF Wind Tunnel Configuration

The dual N-factor method is used to model the boundary-layer transition over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. The paper presents a systematic methodology for transition prediction in the presence of a dual shock system and extends the prior capability for iteratively coupled computational fluid dynamics (CFD) predictions to incorporate three-dimensional, transonic wings. The method employs stability computations based on the linear parabolized stability equations (PSE), along with a dual N-factor criterion. The iterative process begins with the fully turbulent Reynolds-averaged-Navier-Stokes (RANS) mean flow solution. For the first iteration, a mean flow solution is calculated with an imposed transition front that aligns with the shock front from the fully turbulent solution. Subsequently, stability computations are performed along a set of streamlines across the wing to calculate the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) modes. The transition criterion based on the dual N-factor method is used to infer the updated transition front and the process is successively repeated until convergence of the solution. Within three iterations, the predicted fronts for angles of attack of 1.45, 1.98, 2.46 and 2.94 degrees and a mean-aerodynamic-chord Reynolds number equal to 15 million, approach visual convergence in most regions of the studied cases, and the resulting predictions are in good agreement with the transition fronts deduced from measurements of temperature-sensitive paint. Even though surface pressure measurements based on fully-turbulent flow agree well with the measured pressure coefficient distributions, strong viscous-inviscid interaction effects cause significant shifts in the shock locations based on the imposed transition front, underscoring the intrusive nature of static pressure measurements using surface mounted ports on the CRM-NLF configuration.

Boundary Layer Transition↗

Ab-Initio Study of Stacking Fault Segregation Behavior in Ni-based Superalloys at High Temperatures

Ni-based superalloys demonstrate extraordinary creep properties compared to traditional metallic systems due to the formation of L12 (γ’) precipitates. Despite experimental evidence of alloying element segregation to the stacking faults, prior ab-initio efforts indicated repulsion of Nb from superlattice intrinsic stacking faults (SISFs) . Due to the importance of this element in key strengthening mechanisms, we developed a new technique to account for multi-component segregation behavior at temperature combining ab-initio molecular dynamics (AIMD) and Monte-Carlo (MC) simulations. Using this technique, we replicated experimentally observed segregation behavior of Nb, Co, and Ti to the SISF in L12 (Figure 1). Furthermore, we investigated the co-segregation behaviors of individual pairs of alloying elements to determine the interaction effects which lead to this segregation behavior in the full alloy system. By simulating the reduced-chemistry models using our approach, we reconciled previous ab-initio calculations demonstrating repulsion of Nb from the SISF and the experimentally observed segregation behavior.

Molecular Dynamics↗

Development of the Dust Ejecta Radar Technology (DERT) to Determine Plume-Surface Interaction Ejecta Velocities on Planetary Surfaces

Here we present a novel use of millimeter wave doppler radar to measure the velocity of ejecta generated by the impingement of rocket plumes on a planetary surface. The Dust Ejecta Radar Technology (DERT) provides a unique dataset based on direct measurements of ejecta particle velocities during plume-surface interactions. DERT is a continuous wave (CW) 94 GHz radar unit that is being developed at Kennedy Space Center. DERT has measured velocities of a pendulum (~ 1 m/s), a rotating strip (60 m/s), projected regolith simulant BP-1 (~ 250 m/s) and rifle rounds (~ 820 m/s). Signal-to-Noise Ratios of up to 60 dB have been demonstrated. Data collected from DERT will inform the development of high-fidelity computational models of plume-surface interaction effects and will help address NASA Strategic Knowledge Gaps related to characterizing entry, descent and landing effects, and the risks associated with high-speed ejecta on the lander and lunar surface assets.

PSI↗

Dust Ejecta RADAR Technology (DERT): A Millimeter Wave Doppler Radar to Measure Plume Surface Interaction Ejecta Velocities

A novel method to measure the velocity of ejecta generated by the impingement of rocket plumes on a lunar or planetary surface is presented. Dust Ejecta RADAR Technology (DERT), is a Millimeter Wave Doppler Radar sensor that provides a unique dataset based on direct measurements of ejecta particle velocities during plume-surface interactions, which will help inform risk assessments associated with impacts by high-speed ejecta particles. DERT has measured velocities of a pendulum (~1 m/s), a rotating strip (60 m/s), projected regolith simulant BP-1 (~250 m/s) and rifle rounds (~820 m/s). Signal-to-noise ratios of up to 60 dB with regolith simulant BP-1 have been demonstrated with a CW 94 GHz unit. Data collected from DERT will inform the development of high-fidelity computational models of plume-surface interaction effects and will help address NASA Strategic Knowledge Gaps related to characterizing entry, descent and landing effects, and the risks associated with high-speed ejecta on the lander and lunar surface assets. Recent efforts to develop DERT as a flight instrument are presented as well as the development of a Lunar Regolith Ejecta Simulator (LuRES) system to calibrate DERT.

PSI↗

Development of the Dust Ejecta Radar Technology (DERT) to Determine Plume-Surface Interaction Ejecta Velocities on Planetary Surfaces

Here we present a novel use of millimeter wave doppler radar to measure the velocity of ejecta generated by the impingement of rocket plumes on a planetary surface. The Dust Ejecta Radar Technology (DERT) provides a unique dataset based on direct measurements of ejecta particle velocities during plume-surface interactions. DERT is a continuous wave (CW) 94 GHz radar unit that is being developed at Kennedy Space Center. DERT has measured velocities of a pendulum (~ 1 m/s), a rotating strip (60 m/s), projected regolith simulant BP-1 (~ 250 m/s) and rifle rounds (~ 820 m/s). Signal-to-Noise Ratios of up to 60 dB have been demonstrated. Data collected from DERT will inform the development of high-fidelity computational models of plume-surface interaction effects and will help address NASA Strategic Knowledge Gaps related to characterizing entry, descent and landing effects, and the risks associated with high-speed ejecta on the lander and lunar surface assets.

PSI↗

Space shuttle orbiter rear mounted reaction control system jet interaction study

The effect of interaction between the reaction control system (RCS) jets and the flow over the space shuttle orbiter in the atmosphere was investigated in the NASA Langley 31-inch continuous flow hypersonic tunnel at a nominal Mach number of 10.3 and in the AEDC continuous flow hypersonic tunnel B at a nominal Mach number of 6, using 0.01 and .0125 scale force models with aft RCS nozzles mounted both on the model and on the sting of the force model balance. The data show that RCS nozzle exit momentum ratio is the primary correlating parameter for effects where the plume impinges on an adjacent surface and mass flow ratio is the parameter when the plume interaction is primarily with the external stream. An analytic model of aft mounted RCS units was developed in which the total reaction control moments are the sum of thrust, impingement, interaction, and cross-coupling terms.

Rausch, J. R.↗

The effects of canard-wing flow-field interactions on longitudinal stability, effective dihedral and potential deep-stall trim

The literature available on high aspect ratio canard configurations shows them to have some unique stability characteristics. Using a generic canard-wing model, the effects of canard-wing flow-field interactions on stability were investigated in the NASA Langley Twelve-Foot Low-Speed Wind Tunnel. Results for the attached flow regime indicate linear interactions shift the neutral point of a canard configuration forward, but the effect of a canard on a wing can change significantly when the flow over the surface begins to separate, even several degrees below stall. The asymmetry of the canard downwash in a sideslip condition can result in an increment in effective dihedral roughly proportional to canard lift coefficient. At very high angles of attack the presence of a wing can cause an incremental normal force on a canard, contributing to the possibility of a deep-stall trim point. This effect is greater for a high canard and less for a low one.

Muchmore, C. B., Jr.↗