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NASA NTRS2019

Calibration and Data Analysis Recommendations for Three-Component Moment Balances

Fundamental characteristics of design, calibration, and application of three-component moment balances are investigated in great detail. These balances are typically used to determine loads on control surfaces, canards, or other parts that are attached to a wind tunnel model. First, three different descriptions of the load state of a moment balance are reviewed. Then, load transformations between different load formats and the combined load diagram for two of the three load components are discussed. An error analysis showed that it is critical to maximize the product of the distance between the bending moment gages and their sensitivities in order to minimize the overall error in the normal force prediction. In addition, it is important to apply a sufficient number of calibration loadings near the first bending moment gage. Then, unwanted near-linear dependencies between the two bending moment gage outputs can be avoided. The error in the bending moment prediction is also investigated that results from the elastic deformation of the metric part of the balance under load. Finally, the application of the Non-Iterative Method to three-component moment balance calibration data is described in order to obtain regression models that can be used to predict loads from measured outputs during a wind tunnel test.

Strain-Gage Balance↗

NASA NTRS2023

Three Eruptions Observed by Remote Sensing Instruments Onboard Solar Orbiter

On February 21 and March 21 – 22, 2021, the Extreme Ultraviolet Imager (EUI) onboard Solar Orbiter observed three prominence eruptions. The eruptions were associated with coronal mass ejections (CMEs) observed by Metis, Solar Orbiter’s coronagraph. All three eruptions were also observed by instruments onboard the Solar–TErrestrial RElations Observatory (Ahead; STEREO-A), the Solar Dynamics Observatory (SDO), and the Solar and Heliospheric Observatory (SOHO). Here we present an analysis of these eruptions. We investigate their morphology, direction of propagation, and 3D properties. We demonstrate the success of applying two 3D reconstruction methods to three CMEs and their corresponding prominences observed from three perspectives and different distances from the Sun. This allows us to analyze the evolution of the events, from the erupting prominences low in the corona to the corresponding CMEs high in the corona. We also study the changes in the global magnetic field before and after the eruptions and the magnetic field configuration at the site of the eruptions using magnetic field extrapolation methods. This work highlights the importance of multi-perspective observations in studying the morphology of the erupting prominences, their source regions, and associated CMEs. The upcoming Solar Orbiter observations from higher latitudes will help to constrain this kind of study better.

Coronal mass ejections↗

NASA NTRS1962

The Restricted Three-Body-Problem as a Perturbation of Euler's Problem of Two Fixed Centers and Its Application to Lunar Trajectories

The restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.

Euler equation↗

NASA NTRS2001

Three-dimensional ballistocardiography and respiratory motion in sustained microgravity

BACKGROUND: We measured the three-dimensional ballistocardiogram (BCG) in a free-floating subject in sustained microgravity during spaceflight to test the usefulness of such measurements for future non-invasive monitoring of cardiac function, and to examine the effects of respiratory movement on the BCG in three axes. METHODS: Acceleration was measured using a three-axis accelerometer fastened to the lumbar region of the subject while simultaneous recordings of ECG, and respiratory motion via impedance plethysmography were also made. Data were recorded during a 146-s period of inactivity on the part of the subject during which time there was no contact with the spacecraft. RESULTS: Total body motion due to respiratory activity was consistent with that calculated from the known action of the diaphragm and conservation of momentum. The accelerations due to cardiac activity, ensemble averaged over the R-R interval, were greatest along the head-to-foot axis. Maximum amplitude of the HIJK complex of the BCG generated by ventricular ejection was greatest in the head to foot axis (approximately 70 x 10(-3) m x s(-2)), but there were also substantial accelerations along the dorsoventral axis of up to 43 10(-3) m x s(-2), that are not measured interrestrial two-dimensional studies. The amplitude of the BCG was strongly affected by lung volume, with accelerations being reduced 50 to 70% between end-inspiration and end-expiration. CONCLUSIONS: These data suggest a greatly reduced transmission of the cardiac motion to the body at end-expiration (FRC) than at higher lung volumes. The BCG might be further developed as a non-invasive means of monitoring parameters such as stroke volume in microgravity.

Flight Experiment↗

NASA NTRS2001

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold 'tubes' associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.

three body problem↗

NASA NTRS2014

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle/Multi-Pixel Polarimetric Measurements

This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth's atmosphere.

linearization↗

NASA NTRS2014

An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.

Cebeci, T.↗

NASA NTRS1973

An experimental investigation of three oblique-wing and body combinations at Mach numbers between 0.60 and 1.40

An experimental investigation was conducted in an 11- by 11-foot transonic wind tunnel to determine the aerodynamic characteristics of three oblique high aspect ratio wings in combination with a high fineness-ratio Sears-Haack body. The three wings had the same elliptical planform and base line curvature but had different airfoil sections. One wing had an airfoil section designed to have a lift coefficient of 1.0 at a Mach number of 0.7, another to have shock-free supersonic flow over the upper surface, and the other to have a lift coefficient of 1.3 at a Mach number of 0.6. Longitudinal and lateral-directional stability data were obtained at wing yaw angles of 0 deg, 45 deg, 50 deg, and 60 deg over a test Mach number range from 0.6 to 1.4 for angles of attack between minus 7 deg and 9 deg. Reynolds numbers for the study were 4 and 6 million per foot. Flow-visualization studies were made to examine the nature of the flow on the wing surfaces. Notable differences were found in the aerodynamic characteristics of the three wing-body combinations, particularly in the lateral-directional characteristics.

Graham, L. A.↗