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At least 271 records · Page 15

Cooling of Electric Motors Used for Propulsion on SCEPTOR

NASA is developing a suite of hybrid-electric propulsion technologies for aircraft. These technologies have the benefit of lower emissions, diminished noise, increased efficiency, and reduced fuel burn. These will provide lower operating costs for aircraft operators. Replacing internal combustion engines with distributed electric propulsion is a keystone of this technology suite, but presents many new problems to aircraft system designers. One of the problems is how to cool these electric motors without adding significant aerodynamic drag, cooling system weight or fan power. This paper discusses the options evaluated for cooling the motors on SCEPTOR (Scalable Convergent Electric Propulsion Technology and Operations Research): a project that will demonstrate Distributed Electric Propulsion technology in flight. Options for external and internal cooling, inlet and exhaust locations, ducting and adjustable cowling, and axial and centrifugal fans were evaluated. The final design was based on a trade between effectiveness, simplicity, robustness, mass and performance over a range of ground and flight operation environments.

Propulsion↗

A Conventional Liner Acoustic/Drag Interaction Benchmark Database

The aerodynamic drag of acoustic liners has become a significant topic in the design of such for aircraft noise applications. In order to evaluate the benefits of concepts designed to reduce liner drag, it is necessary to establish the baseline performance of liners employing the typical design features of conventional configurations. This paper details a set of experiments in the NASA Langley Grazing Flow Impedance Tube to quantify the relative drag of a number of perforate-over-honeycomb liner configurations at flow speeds of M=0.3 and 0.5. These conventional liners are investigated to determine their resistance factors using a static pressure drop approach. Comparison of the resistance factors gives a relative measurement of liner drag. For these same flow conditions, acoustic measurements are performed with tonal excitation from 400 to 3000 Hz at source sound pressure levels of 140 and 150 dB. Educed impedance and attenuation spectra are used to determine the interaction between acoustic performance and drag.

Howerton, Brian M.↗

Asteroid Fragmentation Approaches for Modeling Atmospheric Energy Deposition

During asteroid entry, energy is deposited in the atmosphere through thermal ablation and momentum-loss due to aerodynamic drag. Analytic models of asteroid entry and breakup physics are used to compute the energy deposition, which can then be compared against measured light curves and used to estimate ground damage due to airburst events. This work assesses and compares energy deposition results from four existing approaches to asteroid breakup modeling, and presents a new model that combines key elements of those approaches. The existing approaches considered include a liquid drop or "pancake" model where the object is treated as a single deforming body, and a set of discrete fragment models where the object breaks progressively into individual fragments. The new model incorporates both independent fragments and aggregate debris clouds to represent a broader range of fragmentation behaviors and reproduce more detailed light curve features. All five models are used to estimate the energy deposition rate versus altitude for the Chelyabinsk meteor impact, and results are compared with an observationally derived energy deposition curve. Comparisons show that four of the five approaches are able to match the overall observed energy deposition profile, but the features of the combined model are needed to better replicate both the primary and secondary peaks of the Chelyabinsk curve.

Modeling↗

Estimation, Navigation and Control of Multi-Rotor Drones in an Urban Wind Field

The paper presents an on-board estimation, navigation and control architecture for multi-rotor drones flying in urban environment. It consists of adaptive algorithms to estimate vehicle's aerodynamic drag coefficients with respect to still air and the urban wind components along the flight trajectory, with guaranteed fast and reliable convergence to the true values; navigation algorithms to generate feasible trajectories between given way-points that take into account the estimated wind; and of control algorithms to track the generated trajectories as long as the vehicle retains sufficient number of functioning rotors capable of compensating for the estimated wind. All components of this on-board system are computationally effective and are intended for a real time implementation. The algorithms were tested in simulations.

Stepanyan, Vahram↗

A Plasma Aerocapture and Entry System for Manned Missions and Planetary Deep Space Orbiters

A rapid mission to Mars requires a large change in vehicle velocity upon arrival to establish a stable orbit. This demand is even greater for a Neptune science, requiring many kilometers per second of V. It is clear from past mission studies that a manned Mars mission and deep space planetary orbiters require aerobraking and aerocapture which use aerodynamic drag forces to slow the spacecraft. Aerocapture would enable long term studies of the outer planets and moons that would not be possible with existing braking methodologies. While the ability to utilize these atmospheres to slow down and capture spacecraft would dramatically reduce the cost, launch mass, and travel time, currently planned approaches require significant additional spacecraft mass and risk as the spacecraft must descend deep into the planetary atmosphere in order to produce significant drag on a relatively small aeroshell. The plasma based Magnetoshell being developed in this program holds the potential to perform the desired braking with significantly increased drag and control while dramatically reducing mass. Most importantly, this technology significantly lowers the risk involved with aerocapture thereby making manned planetary missions possible. The fundamental physics of the Magnetoshell is based on demonstrated experimental results. Successful implementation will dramatically decrease radiation exposures, mission risk, launch cost, and launch mass. Implementation of aerobraking by employing a solid deflector or aeroshell as a method for orbit insertion and circularization has been successfully demonstrated in the past, resulting in launch mass savings greater than 50%. In order to reduce the effect of frictional heating and dynamic pressure on the typically fragile aeroshell, or worse solar panels, the braking must be distributed over many orbital passes at a high altitude in the less dense regions of the atmosphere. It can thus take several months for a meter-scale, 1000 kg, aeroshell to execute the many elliptic orbital passes through the atmosphere to achieve the required V. This rather slow method of braking not only reduces frictional heating and dynamic forces, but also avoids unpredictable dynamic behavior due to turbulence, as well as unknown and seasonally variable atmospheric composition and temperature which has led to dangerous, mission-critical events. For exploration class missions such as DRA 5.0 aerocapture and Thermal Protection Systems (TPS) are proposed for breaking at Mars for cargo missions. Traditional aerocapture is considered too risky for manned missions. Even with the enormous mass savings that aerocapture allows, it still requires 80 tons of aeroshell and significantly increased launch mass and propellant. As will be shown, by using Magnetoshells for aerobraking, the DRA 5.0 mission will save 224 metric tons (MT) and greater than $2 B in launch costs. Beyond the dramatic savings for existing mission architectures, a low-mass, risk-free aerocapture system would allow much more rapid missions to Mars and deep space orbiters by allowing direct, faster trajectories. As will be shown, the plasma Magnetoshell Aerobraking, Aerocapture, and Entry System (AAES) not only reduces mass and cost while enabling significant new mission architectures, but also significantly reduces radiation exposures by decreasing trip times.

Manned Missions↗

Adaptive Deployable Entry Placement Technology (ADEPT) Development for Small Sat Class Venus Missions

The Adaptable, Deployable Entry and Placement Technology (ADEPT) is a novel approach for entry vehicle design. Similar to an umbrella, it is stowed during launch and deployed prior to entry. ADEPT employs a high performance, 3-D woven, carbon fabric to serve as the primary surface of the mechanically deployed system. The successful ADEPT sounding rocket flight test matured the 1-meter Class ADEPT in the areas of deployment and structural integrity, and provided aerodynamic flight characteristics of the ADEPT open-back configuration from Mach 3 to Mach 0.3. Aerocapture uses the aerodynamic drag from a single hyperbolic atmospheric pass to provide the delta-V needed for orbit insertion. Studies suggest that, compared to propulsive orbit insertion, aerocapture could increase delivered payload by 70 percent at Venus. Drag modulation aerocapture, which shows promise of being simpler and more cost-effective than the more-often studied lift modulation methods, uses in-flight transformations of an entry vehicle's drag area to control the amount of deceleration produced during an atmospheric pass. In single-event drag modulation, a drag device is jettisoned after the appropriate deceleration. ADEPT, due to its unique ability to fold and unfold, is being considered for this SmallSat class payload mission applications.

Cassell, Alan M.↗

Space-Based Sentinels for Measurement of Infrared Cooling in the Thermosphere for Space Weather Nowcasting

Infrared radiative cooling by nitric oxide (NO) and carbon dioxide (CO2) modulates the thermosphere’s density and thermal response to geomagnetic storms. Satellite tracking and collision avoidance planning require accurate density forecasts during these events. Over the past several years, failed density forecasts have been tied to the onset of rapid and significant cooling due to production of NO and its associated radiative cooling via emission of infrared radiation at 5.3 μm. These results have been diagnosed, after the fact, through analyses of measurements of infrared cooling made by the Sounding of the Atmosphere using Broadband Emission Radiometry instrument now in orbit over 16 years on the National Aeronautics and Space Administration Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics satellite. Radiative cooling rates for NO and CO2 have been further shown to be directly correlated with composition and exospheric temperature changes during geomagnetic storms. These results strongly suggest that a network of smallsats observing the infrared radiative cooling of the thermosphere could serve as space weather sentinels. These sentinels would observe and provide radiative cooling rate data in real time to generate nowcasts of density and aerodynamic drag on space vehicles. Currently, radiative cooling is not directly considered in operational space weather forecast models. In addition, recent research has shown that different geomagnetic storm types generate substantially different infrared radiative response, and hence, substantially different thermospheric density response. The ability to identify these storms, and to measure and predict the Earth’s response to them, should enable substantial improvement in thermospheric density forecasts.

Mlynczak, Martin G.↗

Structural Analysis and Performance-Based Validation of a Composite Wing Spar

Electric-motor powered aircraft possess the ability to operate with efficient energy delivery, but lack the operational range of internal combustion engine powered aircraft. This range limitation requires the use of high aspect ratio, thin-chord wings to minimize aerodynamic drag losses, which results in highly loaded composite spar structures. High aspect ratio wings are required to increase mission durations for a NASA-developed experimental multi-rotor electric powered aircraft denoted as the Scalable Convergent Electric Propulsion Technology and Operations Research (SCEPTOR) or “X-57”. This paper examines the structural performance of the composite main wing spars to validate spar strength using ply-based laminate finite element methods. Geometric scaling of a main spar test-section was initially proposed for proof-testing but sacrificed stability. Ply-based structures modeling with local structural features was implemented as a risk-reduction methodology. Ply-based modeling was selected to augment the conventional “building block” approach to reduce risk, and leverage a “performance-based” approval processes encouraged in Federal Aviation Administration (FAA) design guidance. Therefore, ply-based laminate modeling of the full-scale main spar and forward spar shear-web attachments were subsequently undertaken to determine load path complexity with predicted flight loads. Ply-based modeling included stress concentrations and interlaminate behavior at interface locations that can be obscured in traditional finite element sizing models. Analysis of the wing spar laminate ply-based models compared with bearing test coupon performance was used to reduce future wing assembly proof-testing burden and facilitate performance-based flight hardware safety for the X-57 experimental aircraft.

Moore, James B.↗

Design and Optimization of Steering Laws for Geocentric Solar Sailing

Solar sail technology has the potential to be a practical method of propulsion for future deep space Cubesats and small satellites. Although in general, deep space, heliocentric flight is the optimal regime for solar sailing, many near-term solar sail flight demonstrations have, or will occur in Earth-centered orbits. This is particularly true for low-cost, smallsat-based solar sail technology demonstration flights, such as the Planetary Society LightSail 1 and 2, and the upcoming NASA Advanced Composite Solar Sail System (ACS3). ACS3 will be the first spaceflight application of NASA’s newest smallsat deployable composite boom technology, and NASA’s first practical solar sail. Launch of ACS3 is currently anticipated for late 2021 or early 2022. In this paper, we will describe the challenges of operating solar sailing spacecraft in low Earth orbits, where, depending on initial orbital altitude and inclination, disturbances due to aerodynamic drag, eclipsing can be of the same order or greater than forces caused by solar radiation pressure. A notional smallsat-class solar sailing vehicle based on the ACS3 solar sail will be used as a reference for trajectory design and optimization studies. As a starting point we will assume initially circular orbits, and a locally optimal steering law designed to maximize the rate of change in semi major axis, similar to that described by McInnes. This will be generalized to orbits with arbitrary initial inclinations and non-zero eccentricities, and to account for atmospheric drag and eclipsing effects. Optimal steering laws for maximizing rate-of-change in orbit inclination and eccentricity will also be explored. Finally, we will examine potential for Earth-centered solar sailing mission applications beyond technology demonstrations, including: continuous observations from inside the Earth’s magnetotail; augmented geostationary capabilities from displaced geostationary orbits; and continuous polar observation for climate science investigations from pole-sitter orbits.

W. Keats Wilkie↗

Analysis of Launch Vehicle Liftoff Debris: Historical Perspective from Space Shuttle and Application to Artemis I

Human exploration-class launch vehicles are inherently prone to debris due to the extreme environments generated during pre-launch operations, liftoff, and flight. The use of cryogenic propellants often requires thermal protection system (TPS) coatings, typically foam, to maintain the propellant conditions in the tank and prevent an accumulation ice on the external surface of the vehicle. Some ice growth is to be expected at umbilical interfaces, vents, flanges, or brackets where it is difficult to apply TPS. This ice may come loose at any time due to wind on the launch pad, structural vibration and acoustics after rocket ignition, or aerodynamic forces during flight. This phenomena is especially apparent on vehicles with no TPS, such as the Saturn V rockets used in the Apollo Program, see Figure 1. During propellant tanking, the thermal contraction of the underlying substrate may generate cracks in the TPS (Figure 1). Chunks of TPS can release due to the expansion of ingested gas from cryopumping or from aerodynamic forces if the crack creates an offset surface. Most foams will also have a certain amount of “popcorning” where small pieces of foam will pop off during flight because of the differential between the static surface pressure and the pressure of the gas trapped in the foam cell structure. There are a number of other coating or closeout materials that may be shed from the vehicle and become debris. During pre-launch operations and liftoff, the vehicle may also be exposed to debris originating from the launch pad or ground support equipment. This debris is separate from foreign object debris, or FOD, which is not intended to be present and is strictly controlled through operations and maintenance procedures. In this case, debris is generated from hardware and materials that are necessary for launch and are subject to the intense vibration, acoustics, and direct plume impingement of the launch environment. Examples include ice from umbilicals, tape and tie wraps that protect cables, and rust or corrosion from the launch platform. While NASA has historically been aware of debris as a potential issue that could cause a failure resulting in loss of mission, loss of vehicle, or loss of crew, the likelihood and severity of that risk was not always well understood or given sufficient weight in program and flight decisions. After the Space Shuttle Columbia accident (STS-107), the investigation found that foam TPS debris shed from the external tank was the proximate cause of the damage to the orbiter wing. Six previous observations of debris released from the foam ramp that covered the bipod connecting the forward end of the orbiter to the external tank resulted in minor changes or were determined to be accepted flight risks. Two occurrences of bipod ramp foam loss were not identified until the STS-107 investigation. Despite the damage inflicted by these debris strikes, the Shuttle Program Requirements Control Board deemed the vehicle safe to fly. During the Return to Flight effort following the Columbia disaster, NASA Engineering developed a process for the assessment of debris transport, impact, and damage tolerance to support independent assessments of risk by NASA Safety and Mission Assurance (S&MA). Under this system, each element (vehicle or ground system) defines a catalog of all expected debris based on launch history, component testing, or analysis. Debris transport analysis (DTA) is conducted using the debris catalog characteristics and potential flow transport mechanisms (e.g., vehicle aerodynamics, gravity, wind, plume-driven). The predicted debris impact locations and velocities are provided to the hardware owners, who use available test data and analysis to determine whether each component can withstand the impacts. In cases where the element hardware may be severely damaged or fail, the options are to mitigate the debris source through some change in design or operation, or to work with S&MA to try to characterize the probability of the impact and damage for program risk acceptance. Because of the differences in debris characteristics and transport, the DTA has been divided between the Liftoff and Ascent regimes. The development and application of Liftoff DTA methodology from the Shuttle Program to the current Artemis Program is the subject of this paper. Liftoff DTA covers the time from the start of pre-launch operations at the launch pad, up until the vehicle clears the launch tower and there is no longer any interaction with ground systems. Debris transport during this period is broadly classified as either gravity, wind, and plume-entrained (GWPE) or plume driven (PD). GWPE debris is generally lower speed, travelling in a forward-to-aft direction. PD transport includes flow features from the rocket ignition transient, as well as plume impingement and recirculation that occur as the vehicle lifts off the launch platform. In these cases, the debris typically moves in an aft-to-forward direction at higher speeds. The applicable transport mechanisms must be considered for each piece of debris depending on the material, and release location and time. For example, rust or metallic debris from the tower could fall (GWPE) and impact the vehicle before landing on the launch platform deck where it could be also be transported by plume impingement (PD). However, falling ice (GWPE) from an umbilical is unlikely to survive impact with the vehicle or launch platform and be available for PD transport. Modeling of debris transport is accomplished using a set of DTA tools which simulate debris trajectories subject to a reference frame acceleration (i.e., gravity) and aerodynamic drag. Where the trajectory encounters a solid surface, the debris is allowed to rebound with a specified coefficient of restitution. The drag is calculated by interpolating the fluid state at each point in the debris trajectory from high-fidelity computational fluid dynamics (CFD) simulations of the launch vehicle and pad. The CFD data may either be static (steady state or time averaged), typically for GWPE transport, or dynamic (time-accurate) for PD flow features like the ignition transient. Examples of the CFD flow field solutions for the Space Launch System (SLS) rocket and launch pad are shown in Figure 2. Typical SLS debris trajectory predictions from DTA are illustrated in Figure 3. The final version of this paper will include a more detailed examination of the Liftoff DTA process developed during the Shuttle Program, and how it has been augmented and applied to the SLS rocket under the Artemis Program. Comparisons with debris observations from the Artemis I launch will demonstrate validation of the tools and methodology.

Debris↗

NASA’s Efficient Quiet Integrated Propulsors (Equip) Technical Challenge

Advances in aircraft propulsor technology - ducted and unducted - are key elements to developing a sustainable aviation future. Increasing propulsive efficiency comes with significant challenges. The long-term trend in aircraft engine design has been towards higher bypass ratios to increase efficiency and decrease noise. Current designs are pushing against limits on engine size; the engine must fit under the wing and overcome the nacelle weight, aerodynamic drag, and airframe integration penalties associated with an ultra-high bypass ratio. The next-generation ducted engines will have shorter inlets and smaller rotor-stator spacing to minimize nacelle area. This increases the potential for non-uniform flow at the fan face and less area for acoustic liners. Unducted engines eliminate the nacelle penalty while presenting challenges to noise and operability in distorted flow environments. The overall diameter in both cases raises questions about engine-airframe integration to maximize efficiency gains and minimize installation penalties. The National Aeronautics and Space Administration (NASA) Advanced Air Vehicles Program (AAVP) approved the Efficient Quiet Integrated Propulsor (EQuIP) Technical Challenge (TC) under the Advanced Air Transport Technology (AATT) Project to work on next-generation propulsor technologies in collaboration with NASA’s government and industry partners in the Sustainable Flight National Partnership. The EQuIP TC leverages NASA resources with Federal Aviation Administration (FAA) and industry investments under the FAA’s Continuous Lower Energy Emissions and Noise (CLEEN) program to address technical challenges on the propulsor subject to the flow field imposed by the engine-airframe-flight environment. The EQuIP TC complements NASA Aeronautics Research Mission Directorate’s (ARMD) existing investments in sustainable aviation for the next-generation of commercial aircraft and contributes to meeting the noise and efficiency goals set by the Sustainable Flight National Partnership and U.S. Aviation Climate Action Plan. This paper introduces the EQuIP TC, describes key parts of its development, and presents the background research used to scope its impact.

Propulsion↗

Developing a Pyrolysis Gas Thermal Blocking Model for Reentry Demise

In NASA’s Object Reentry Survival Analysis Tool (ORSAT), aerodynamic drag and aerothermal heating coefficients are computed for each of the free-molecular, continuum, and transitional flow regimes using analytical and semi-analytical methods. These heating coefficients were derived for typical metallic materials that melt and do not have a strong gas-phase contribution to the flow in the boundary layer. Modern satellites typically feature fiber-reinforced polymer (FRP) components, such as solar array booms, facesheets of sandwich panels, or overwraps for composite-overwrapped pressure vessels (COPV). These FRP materials do not behave the same as metals in the reentry environment, but instead will pyrolyze and develop significant volumes of gas into the boundary layer. Accurately predicting the reentry demise of FRP components is critical to assessing the reentry casualty risk for modern spacecraft. Research in recent years has shown that this demisability can depend heavily on how the expulsion of gaseous pyrolysis products through the outer surface of the material affects the heat flux at the surface. The ODPO has been developing a reduced-order model of the effect of pyrolysis gas blowing on the heat flux based on correlations between a blowing factor and a non-dimensional heat flux to be incorporated in the upcoming version 7.3 of the Object Reentry Survivability Analysis Tool (ORSAT). This presentation discusses the progress of this development project and the challenges remaining for generalizing the model across families of FRP materials.

Benton Greene↗

Iterative optimal subcritical aerodynamic design code including profile drag

A subcritical aerodynamic design computer code has been developed, which uses linearized aerodynamics along with sweep theory and airfoil data to obtain minimum total drag preliminary designs for multiple planform configurations. These optimum designs consist of incidence distributions yielding minimum total drag at design values of Mach number and lift and pitching moment coefficients. Linear lofting is used between airfoil stations. Solutions for isolated transport wings have shown that the solution is unique, and that including profile drag effects decreases tip loading and incidence relative to values obtained for minimum induced drag solutions. Further, including effects of variation of profile drag with Reynolds number can cause appreciable changes in the optimal design for tapered wings. Example solutions are also discussed for multiple planform configurations.

Kuhlman, J. M.↗

Determination of aerodynamic stability and drag of the Titan 3 C SRM during entry

An experimental aerodynamic investigation was conducted in the NASA/MSFC 14-inch Trisonic Wind Tunnel on a 0.00736 scale model of Titan 3 C Solid Rocket Motor (SRM). Static stability and drag data were obtained for Mach numbers of 0.6 to 4.96, angles of attack of minus 10 deg to 190 deg, and roll angles of 0 to 360 deg. The resulting data will be used to predict the dynamic motions of the SRM during entry which will then be compared to flight data. This comparison will improve and lend credibility to methods for predicting the entry dynamics of the space shuttle Solid Rocket Booster (SRB), which is needed for recovery studies and design of the parachute recovery system.

Ramsey, P. E.↗

Aerodynamic stability and drag characteristics of a parallel burn/SRM ascent configuration (M equals 0.6 to 4.96)

Experimental aerodynamic investigations were conducted in the NASA/MSFC 14-inch trisonic wind tunnel during April 1972 on a 0.004-scale model of a solid rocket motor version of the space shuttle ascent configuration. The configuration consisted of a parallel burn solid rocket motor booster on an external HO centerline tank orbiter. Six component aerodynamic force and moment data were recorded over an angle of attack range from -10 deg to +10 deg at zero degrees sideslip and over a sideslip range from -10 deg to +10 deg at zero degrees angle of attack. Mach numbers ranged from 0.6 to 4.96. The purpose of the test was to determine the performance and stability characteristics of the complete ascent configuration and buildup, and to determine the effects of variations in HO tank and SRM nose shaping, orbiter incidence and position, and position of the solid rocket motors.

Sims, F.↗

Aerodynamic stability and drag characteristics of a parallel burn/SRM ascent configuration at Mach numbers from 0.6 to 4.96

Experimental aerodynamic investigations were conducted in the NASA/MSFC 14-inch trisonic wind tunnel during March 1972 on a .003366 scale model of a solid rocket motor version of the space shuttle ascent configuration. The configuration consisted of a parallel burn solid rocket motor booster on an external H-O centerline tank orbiter. Six component aerodynamic force and moment date were recorded over an angle of attack range from -10 to 10 deg at zero degrees sideslip and over a sideslip range from -10 to 10 deg at 0, +6, and -6 deg angle of attack. Mach number ranged from 0.6 to 4.96. The performance and stability characteristics of the complete ascent configuration and build-up, and the effects of variations in tank diameter, orbiter incidence, fairings and positioning of the solid rocket motors and tank fins were determined.

Sims, J. F.↗

Aerodynamic stability and drag characteristics of the MSFC pressure fed booster configurations at Mach numbers from 0.9 to5.0

Experimental aerodynamic investigations were conducted in the NASA/MSFC 14 x 14 Inch Trisonic Wind Tunnel during January 1972 on 0.003366 and 0.00419 scale models of the MSFC space shuttle pressure fed booster configurations. The configurations tested were a 40 deg cone/cylinder/13 deg flare with and without fins, a 40 deg cone/cylinder/13 deg flare/9 deg flare with and without fins, a 35 deg cone/cylinder with and without fins, a 35 deg cone/cylinder/7 deg flare and a 35 deg cone/cylinder with straight extension. Six component aerodynamic force and moment data were recorded over a Mach number range of 0.9 to 5.0. Model angle of attack range was -10 to +10 deg and +20 to 80 at 0 deg sideslip. Model sideslip range was -10 to +10 deg at nominal angles of attack of 0, 30 and 51 deg

Baker, J.↗