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A simple analytical aerodynamic model of Langley Winged-Cone Aerospace Plane concept

A simple three DOF analytical aerodynamic model of the Langley Winged-Coned Aerospace Plane concept is presented in a form suitable for simulation, trajectory optimization, and guidance and control studies. The analytical model is especially suitable for methods based on variational calculus. Analytical expressions are presented for lift, drag, and pitching moment coefficients from subsonic to hypersonic Mach numbers and angles of attack up to +/- 20 deg. This analytical model has break points at Mach numbers of 1.0, 1.4, 4.0, and 6.0. Across these Mach number break points, the lift, drag, and pitching moment coefficients are made continuous but their derivatives are not. There are no break points in angle of attack. The effect of control surface deflection is not considered. The present analytical model compares well with the APAS calculations and wind tunnel test data for most angles of attack and Mach numbers.

Pamadi, Bandu N.

Theoretical investigation of wave-vector-dependent analytical and numerical formulations of the interband impact-ionization transition rate for electrons in bulk silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E. Scholl, and M. Rudan (1993), and a more exact, numerical method of Y. Wang and K. F. Brennan (1994). Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formular, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with the completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to the overlap intergrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such the transition rate may be overestimated at those points for which 'near vertical,' small change in k, transitions occur.

Kolnik, Jan

Theoretical Investigation of Wave-Vector-Dependent Analytical and Numerical Formulations of the Interband Impact-Ionization Transition Rate for Electron in Bulk Silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E Scholl, and M. Rudan, and a more exact, numerical method of Y. Wang and K. F. Brennan. Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formula, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with (he completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to (he overlap integrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such [he transition rate may be overestimated at those points for which "near vertical," small change in k, transitions occur.

Kolnik, Jan

Sensor arrays for detecting analytes in fluids

A sensor array for detecting an analyte in a fluid, comprising at least first and second chemically sensitive resistors electrically connected to an electrical measuring apparatus, wherein each of the chemically sensitive resistors comprises a mixture of nonconductive material and a conductive material. Each resistor provides an electrical path through the mixture of nonconductive material and the conductive material. The resistors also provide a difference in resistance between the conductive elements when contacted with a fluid comprising an analyte at a first concentration, than when contacted with an analyte at a second different concentration. A broad range of analytes can be detected using the sensors of the present invention. Examples of such analytes include, but are not limited to, alkanes, alkenes, alkynes, dienes, alicyclic hydrocarbons, arenes, alcohols, ethers, ketones, aldehydes, carbonyls, carbanions, polynuclear aromatics, organic derivatives, biomolecules, sugars, isoprenes, isoprenoids and fatty acids. Moreover, applications for the sensors of the present invention include, but are not limited to, environmental toxicology, remediation, biomedicine, material quality control, food monitoring and agricultural monitoring.

Lewis, Nathan S.

Trace level detection of analytes using artificial olfactometry

The present invention provides a device for detecting the presence of an analyte, such as for example, a lightweight device, including: a sample chamber having a fluid inlet port for the influx of the analyte; a fluid concentrator in flow communication with the sample chamber wherein the fluid concentrator has an absorbent material capable of absorbing the analyte and capable of desorbing a concentrated analyte; and an array of sensors in fluid communication with the concentrated analyte to be released from the fluid concentrator.

Lewis, Nathan S.

Sample Acquisition and Analytical Chemistry Challenges to Verifying Compliance to Aviators Breathing Oxygen (ABO) Purity Specification

NASA has been developing and testing two different types of oxygen separation systems. One type of oxygen separation system uses pressure swing technology, the other type uses a solid electrolyte electrochemical oxygen separation cell. Both development systems have been subjected to long term testing, and performance testing under a variety of environmental and operational conditions. Testing these two systems revealed that measuring the product purity of oxygen, and determining if an oxygen separation device meets Aviator's Breathing Oxygen (ABO) specifications is a subtle and sometimes difficult analytical chemistry job. Verifying product purity of cryogenically produced oxygen presents a different set of analytical chemistry challenges. This presentation will describe some of the sample acquisition and analytical chemistry challenges presented by verifying oxygen produced by an oxygen separator - and verifying oxygen produced by cryogenic separation processes. The primary contaminant that causes gas samples to fail to meet ABO requirements is water. The maximum amount of water vapor allowed is 7 ppmv. The principal challenge of verifying oxygen produced by an oxygen separator is that it is produced relatively slowly, and at comparatively low temperatures. A short term failure that occurs for just a few minutes in the course of a 1 week run could cause an entire tank to be rejected. Continuous monitoring of oxygen purity and water vapor could identify problems as soon as they occur. Long term oxygen separator tests were instrumented with an oxygen analyzer and with an hygrometer: a GE Moisture Monitor Series 35. This hygrometer uses an aluminum oxide sensor. The user's manual does not report this, but long term exposure to pure oxygen causes the aluminum oxide sensor head to bias dry. Oxygen product that exceeded the 7 ppm specification was improperly accepted, because the sensor had biased. The bias is permanent - exposure to air does not cause the sensor to return to its original response - but the bias can be accounted for by recalibrating the sensor. After this issue was found, continuous measurements of water vapor in the oxygen product were made using an FTIR. The FTIR cell is relatively large, so response time is slow - but moisture measurements were repeatable and accurate. Verifying ABO compliance for oxygen produced by commercial cryogenic processes has a different set of sample acquisition and analytical chemistry challenges. Customers want analytical chemists to conserve as much as possible. Hygrometers are not exposed to hours of continuous flow of oxygen, so they don't bias, but small amounts of contamination in valves can cause a "fail". K bottles are periodically cleaned and recertified - after cleaning residual moisture can cause a "fail". Operators let bottle pressure drop to room pressure, introduce outside air into the bottle, and the subsequent fill will "fail". Outside storage of K‐bottles has allowed enough in‐leakage, so contents will "fail".

Graf, John

System and Method for Providing a Climate Data Analytic Services Application Programming Interface

A system, method and computer-readable storage devices for providing a climate data analytic services application programming interface. The system includes a programming library that enables client device software to invoke the capabilities of a climate data analytics system through requests to various services supported by the climate data analytics system, and also includes a client-side communications interface that enables the programming library's methods to interact with a climate data analytics system's server interface to obtain access to the capabilities of the system. In one implementation, the programming library is implemented in the Python programming language. The programming library can include basic utilities that call a single, server-side method implemented by one of the various services supported by the climate data analytics system, and extended utilities that call a series of basic utilities and/or other extended utilities that have been placed under programmatic control in order to create client-side convenience methods and workflows.

Schnase, John L.

Analytic Spacecraft Attitude and Rate Estimation Performance During Attitude Sensor Outages

Analytic expressions for spacecraft attitude and rate estimation performance of an attitude estimation filter in terms of sensor specifications are useful tools for spacecraft design. Farrenkopf (1978) famously found analytic expressions for steady-state pre-update and post-update attitude and gyro bias estimate error variances for an attitude estimation filter for a single-axis spacecraft with a Rate Output Gyro (ROG). Markley and Reynolds (2000) extended the analysis for a Rate-Integrating Gyro (RIG) with angle white noise. These expressions allow for the rapid evaluation of system performance during preliminary mission design phases. One contribution of this paper is the analytic calculation of the steady-state pre-update and post-update angular rate estimate uncertainty for both the ROG and RIG cases. The primary contribution of this paper is the extension of the results for both the ROG and the RIG cases to the situation of an attitude sensor outage. This situation arises frequently in practice; for example when a star sensor’s field of view is occluded, when a star sensor’s readings are unreliable during a thruster burn that vibrates the spacecraft, or during star sensor outages due to radiation upsets. Analytic expressions for the attitude estimate uncertainty, gyro bias estimate uncertainty, and angular rate estimate uncertainty are given in terms of the attitude sensor outage interval, the star tracker measurement noise, and gyro noise parameters. Validity of the analytic results is demonstrated via Monte Carlo simulation.

Galante, Joseph M.

Analytic Spacecraft Attitude and Rate Estimation Performance During Attitude Sensor Outages

Analytic expressions for spacecraft attitude and rate estimation performance of an attitude estimation filter in terms of sensor specifications are useful tools for spacecraft design. Farrenkopf (1978) famously found analytic expressions for steady-state pre-update and post-update attitude and gyro bias estimate error variances for an attitude estimation filter for a single-axis spacecraft with a Rate Output Gyro (ROG). Markley and Reynolds (2000) extended the analysis for a Rate-Integrating Gyro (RIG) with angle white noise. These expressions allow for the rapid evaluation of system performance during preliminary mission design phases. One contribution of this paper is the analytic calculation of the steady-state pre-update and post-update angular rate estimate uncertainty for both the ROG and RIG cases. The primary contribution of this paper is the extension of the results for both the ROG and the RIG cases to the situation of an attitude sensor outage. This situation arises frequently in practice; for example when a star sensor’s field of view is occluded, when a star sensor’s readings are unreliable during a thruster burn that vibrates the spacecraft, or during star sensor outages due to radiation upsets. Analytic expressions for the attitude estimate uncertainty, gyro bias estimate uncertainty, and angular rate estimate uncertainty are given in terms of the attitude sensor outage interval, the star tracker measurement noise, and gyro noise parameters. Validity of the analytic results is demonstrated via Monte Carlo simulation.

Galante, Joseph M.

Machine Learning-Based Predictive Analytics for Aircraft Engine Conceptual Design

Big data and artificial intelligence/machine learning are transforming the global business environment. Data is now the most valuable asset for enterprises in every industry. Companies are using data-driven insights for competitive advantage. With that, the adoption of machine learning-based data analytics is rapidly taking hold across various industries, producing autonomous systems that support human decision-making. This work explored the application of machine learning to aircraft engine conceptual design. Supervised machine-learning algorithms for regression and classification were employed to study patterns in an existing, open-source database of production and research turbofan engines, and resulting in predictive analytics for use in predicting performance of new turbofan designs. Specifically, the author developed machine learning-based analytics to predict cruise thrust specific fuel consumption (TSFC) and core sizes of high-efficiency turbofan engines, using engine design parameters as the input. The predictive analytics were trained and deployed in Keras, an open-source neural networks application program interface (API) written in Python, with Google’s TensorFlow (an open source library for numerical computation) serving as the backend engine. The promising results of the predictive analytics show that machine-learning techniques merit further exploration for application in aircraft engine conceptual design.

deep-learning

A Web of Data Analytics Services

Cloud Computing has become the ubiquitous approach to our Big Data challenge. However, one will quickly discover that moving (a.k.a. forklifting) existing on-premise data analytics solutions to the Cloud doesn’t always translate to costing saving and performance boost. The Cloud’s elasticity, its availability, and its wide selection of computing options and selections of costing models making Cloud an attractive environment to tackle our Big Data challenge. The fact is Cloud, on its own, is not the silver bullet to our daunting challenge need for analyze and derive scientific inferences through vast collections of multi-sensor measurements. We would like to have all scientific data in one easy to access environment, but getting the world of scientific data in one analytic system is immensely difficult to achieve. This paper describes the data analytics web architecture NASA is developing by infusing instances of Integrated Data Analytics systems next to the data. The goal is to minimize unnecessary data movement through collection of data access and analytics webservices for researchers to interact with and analyze measurements without have to download data to their local computer. These services are RESTful and provisioned by the data centers with the help from subject matter and science experts. These services encapsulate the physical computing infrastructure, which could local computing cluster, on-premise or public Cloud environment.

Huang, Thomas

Analytical Needs in a Sample Receiving Facility: Input from the MSR Operation Definition Team

The return of scientifically selected samples from Mars would provide a rare opportunity forinvestigation with the full range of the latest technology available, but to take full advantageof this opportunity, it is important to plan ahead to ensure the pristine nature of the samplesupon arrival within the Earth environment until scientific investigations can begin.The NASA/ESA science community-driven MSR Science Planning Group – Phase 2 (MSPG2)delivered recommendations and guidance regarding curation (1) and science (2, 3) activities tobe performed on the samples under containment. High-level requirements for the infrastruc-ture were also developed by MSPG2 (4). In order to prepare infrastructure-targeted input forthe ESA and NASA facility studies planned in the 2022-2023 timeframe, the agency-led MSROperational Scenarios Definition Team (MOSDT) was assembled to conceptualize the sampleoperations that will inform future architecture teams. Emphasis was placed on the respon-sibility of MOSDT to use community-defined requirements and to represent the view of the international scientific community.All necessary and sufficient instruments and analytical needs described in MSPG2 were inte-grated in MOSDT main deliverable, the operational workflow (see Hays et al, this conference).In MSPG2, notional instruments were split between curation analytical needs, and objective-driven (time-sensitive and sterilization-sensitive) science analytical needs. In MOSDT, whilethe first phases of curation, “pre-Basic Characterization” and “Basic Characterization” wererather streamlined and separate from other analytical needs, “Preliminary Examination” and“Science” instruments were not always physically segregated. In addition to the necessary andsufficient instruments described by MSPG2, the MOSDT recommended additional supportequipment for sterilization, cleanliness and contamination monitoring.It was sometimes necessary for the MOSDT to rely on assumptions to integrate instruments inthe activity workflow. In general, the assumptions were very conservative to limit contaminationand cross-contamination risks. It is expected that future work to refine limits of contaminationwill enable optimization of instrumentation.The community was consulted during the course of the MOSDT work. This abstract’s aimis two-fold: on one hand, inform the scientific community and overall MSR stakeholders, tobring their attention on the analytical needs currently considered as necessary and sufficient;on the other hand, to solicit feedback from a larger community audience to optimize and refineanalytical needs during the next phases of MSR ground-segment preparation.Disclaimer: The decision to implement Mars Sample Return will not be finalized until NASA’scompletion of the program’s National Environmental Policy Act (NEPA) process. This docu-ment is being made available for informational purposes only.[1] Tait et al. (2021) Preliminary planning for Mars Sample Return (MSR) curation activities ina Sample Receiving Facility (SRF). Astrobiology in press, doi:10.1089/ast.2021.0105. [2] Toscaet al. (2021) Time-sensitive aspects of Mars Sample Return (MSR) science. Astrobiologyin press, doi:10.1089/ast.2021.0115. [3] Velbel et al. (2021) Planning implications relatedto sterilization-sensitive science investigations associated with Mars Sample Return (MSR).Astrobiology in press, doi:10.1089/ast.2021.0113. [4] Carrier et al. (2021) Science and curationconsiderations for the design of a Mars Sample Return (MSR) Sample Receiving Facility (SRF).Astrobiology in press, doi:10.1089/ast.2021.0110.

Mars Sample Return

In-Lab Rapid Analytical Detection of Lunar Volatiles By Universal Gas Analyzer With Comparison to GC-MS System

Introduction: The curation of permanently shadowed regions (PSRs) [1] on the lunar surface is centered around studies based upon the observed volatiles from the LCROSS mission [2]. The rapid detection of important volatile gases and vapors present in planetary bodies and Astromaterials by a standalone analytical device is an area of intense research interest in our group and Planetary Exploration & Astromaterials Research Laboratory (PEARL) facility and this work is relevant to the future preparation of viable lunar simulants for testing curation efforts down the road. The groundbreaking results obtained from the LCROSS Mission [2] open the requirements for the direct detection of volatiles present in regolith materials collected from the lunar surface. The mass spectrometry of volatile chemicals is a general technique that utilizes a set of instruments that creates charged ions from a gaseous chemical species and measures the intensities vs. mass-to-charge ratio (m/z) [3]. In this context, we discuss in-lab experimental results and procedures for rapid qualitative analysis of main LCROSS volatiles (water, H2S, NH3, CO2, and CH3OH) by a Universal Gas Analyzer (UGA) instrument. Additionally, the instrument performance was evaluated by measuring the isotopic abundance ratio of atmospheric Ar-40 to Ar-36 present in room air since, argon is a relevant gas in planetary studies as it can provide an insight and reference point to isotope studies [4]. Additional, cross comparisons were attempted and made between the two instruments to develop a robust analytical technique by comparing mass spectral data for H2S headspace samples with a Trace-1310/ ISQ 7000 (ThermoFisher Scientific.) GC-MS system. Background: The benchtop UGA System is equipped with an SRS UGA 300 quadrupole mass spectrometer designed and built by Stanford Research Systems [5]. This system can be configured for several types of gaseous chemical analysis. The inlet line continuously samples gases at low flow rates (several milliliters per minute) through a capillary limiting the intake pressure making the instrument ideal for online analysis of select gases and/or room atmosphere. Moreover, in our current UGA system, a change in composition at the inlet can be detected in about 200 milliseconds and a complete spectrum is acquired (for a range of 1-100 amu) in under 45 sec with masses measured at rates up to 25 msec per point [5]. This system provides a quick upstream analytical data that we can then compare to results obtained by our GC-MS system. Sample Preparation: Small volume (2-4 mL) of analyte sample was taken in a 10 mL glass vial and sealed with a crimped cap and purged with pure Ar or N2 gas to displace air from the top. The headspace sample was scanned by the UGA instrument at analog, histogram, and pressure vs. time modes. The isotopic abundance ratio for 40Ar-to-36Ar was estimated by measuring partial pressure vs. time scans and setting the mass at 40 and 36 respectively. Results and Discussions: In this work, we have investigated the applicability of the UGA system by qualitative analysis of a series of LCROSS volatiles measured individually. Fig. 1 demonstrates a set of vertically offset spectra for the partial pressures measured as a function of mass-to-charge (m/z) ratios. The average acquisition time for each spectrum was less than a minute suggesting that the UGA system is ideal for quick analysis of geochemical volatiles. For the cross-comparison, we analyzed an H2S headspace sample by a Trace-1310/ISQ-7000 system and compared mass spectral data with previously measured UGA histogram scan data (Fig. 2). In both cases, major peak positions are the same, however, the intensities of fragment ions ([1H132S]+ and [32S]+) are higher for UGA suggesting that the fragment ionization process is stronger in UGA compared to that of GC-MS. To investigate how the integrated area under each chromatogram varies with the headspace sample volume, a set of five H2S headspace samples with increasing volumes was analyzed by the GC-MS system (Fig. 3, inset). A small volume (e.g., 200 to 1000 µL) of H2S/H2O vapor was withdrawn from a 20 mL stock sample vial containing ~5 mL of 0.4% H2S in water by a gas-tight syringe and added to another 20 mL vial filled with argon and analyzed by the GC-MS system. Finally, the UGA detector sensitivity was evaluated by calculating the atmospheric 40Ar-to-36Ar isotopic abundance ratio in room air by running a partial pressure vs. time scan with setting the atomic mass at 40, and 36. Fig. 4(a) shows a ~25 min duration “P vs. time” scan for 40Ar (plot for 36Ar is not shown). The partial pressure values (~100 points) were corrected by subtracting the corresponding background pressure value for 37Ar and utilized to calculate 40Ar-to-36Ar isotopic abundance ratios as shown by Fig. 4b. The average isotopic abundance ratio is ~306 with a 2*STDEV ~13. This abundance ratio is significantly close to the previously reported value of 298.56 [6] and the ratio obtained by our GC-MS system (303 for a UHP grade Ar sample). Conclusions: Our study strongly evidenced that the benchtop UGA system is a valuable analytical tool for the detection of major LCROSS volatiles. The rapid scanning capability, the inexpensiveness of the whole system, and impressive detection sensitivity prove its worthiness as an essential device for advanced geochemical applications. Moreover, cross comparisons with the GC-MS provide important bridges into advanced curatorial efforts into the future. References: [1] Bickel, V.T., et al. (2021) Nat Commun 12, 5607. [2] Colaprete, A., et al. (2010) Science, 330, 463-468. [3] Glavin, D. P. et al. (2012) 2012 IEEE Aerospace Conference, 1-11. [4] Willett, C. D., et al. (2022) Geochimica et Cosmochimica Acta 329, 119-134. [5] Operation Manual and Programming Reference. (2018) Universal gas Analyzers, Stanford Research Systems. [6] Lee, J. Y., et al. (2006) Geochimica et Cosmochimica Acta 70, 4507–4512. Notes: (4 figures are attached with text as shown by the attached file)

Curation

An Analysis of Earth Science Data Analytics Use Cases

The increase in the number and volume, and sources, of globally available Earth science data measurements and datasets have afforded Earth scientists and applications researchers unprecedented opportunities to study our Earth in ever more sophisticated ways. In fact, the NASA Earth Observing System Data Information System (EOSDIS) archives have doubled from 2007 to 2014, to 9.1 PB (Ramapriyan, 2009; and https:earthdata.nasa.govaboutsystem-- performance). In addition, other US agency, international programs, field experiments, ground stations, and citizen scientists provide a plethora of additional sources for studying Earth. Co--analyzing huge amounts of heterogeneous data to glean out unobvious information is a daunting task. Earth science data analytics (ESDA) is the process of examining large amounts of data of a variety of types to uncover hidden patterns, unknown correlations and other useful information. It can include Data Preparation, Data Reduction, and Data Analysis. Through work associated with the Earth Science Information Partners (ESIP) Federation, a collection of Earth science data analytics use cases have been collected and analyzed for the purpose of extracting the types of Earth science data analytics employed, and requirements for data analytics tools and techniques yet to be implemented, based on use case needs. ESIP generated use case template, ESDA use cases, use case types, and preliminary use case analysis (this is a work in progress) will be presented.

data analytics

Earthdata Cloud Analytics Project

This presentation describes a nascent project in NASA to develop a framework to support end-user analytics of NASA's Earth science data in the cloud. The chief benefit of migrating EOSDIS (Earth Observation System Data and Information Systems) data to the cloud is to position the data next to enormous computing capacity to allow end users to process data at scale. The Earthdata Cloud Analytics project will user a service-based approach to facilitate the infusion of evolving analytics technology and the integration with non-NASA analytics or other complementary functionality at other agencies and in other nations.

data services

An analytic guidance technique for planetary and lunar approach trajectories.

An explicit, analytic guidance technique is developed for the hyperbolic approach phases of interplanetary and lunar spacecraft trajectories. The guidance technique is based upon a first-order analytic solution for the perturbed planet-centered (or moon-centered) trajectory. This trajectory is represented as the sum of two components: (1) the unperturbed osculating hyperbola at pericenter, and (2) first-order position and velocity perturbations due to gravitational effects of the sun and other planets. A closed-form analytic approximation for these perturbations valid for the entire approach trajectory is derived, thereby eliminating the need for numerical integration of the equations of motion. By means of this analytic trajectory model, the approach guidance problem is reduced to an equivalent two-body problem. The guidance objectives are specified in terms of actual, attainable conditions at pericenter, and the required corrective velocity is determined explicitly for both fixed and variable times of arrival.

Carlson, N. A.

Cold air study of the effect on turbine stator blade aerodynamic performance of coolant ejection from various trailing edge slot geometries. 2: Comparison of experimental and analytical results

Experimentally determined efficiencies of turbine stator blades having trailing-edge coolant ejection are compared with efficiencies predicted from two previously published approximate analytical methods. The experimental results were obtained from two-dimensional data with the temperature of the primary and coolant flows both being nearly ambient. Data from five stator blade configurations having different slotted trailing-edge geometries were included in the comparison. The two analytical methods gave results which agreed reasonably well with experimental results. An average of the absolute values of differences between experimental and predicted efficiencies for all five blade configurations showed that one method gave average efficiency differences which were about 1.3 percent different than experimental efficiencies, while the other method gave average efficiency differences that were about 0.7 percent different than experimental. However, in some instances, maximum differences of as much as 4 percent occurred. A comparison between experimental and analytical results indicated that the ratio of trailing-edge slot width to trailing-edge thickness influences the measured efficiencies to a greater extent than is accounted for by either analytical model.

Prust, H. W., Jr.

Analysis of structural dynamic data from Skylab. Volume 2: Skylab analytical and test model data

The orbital configuration test modal data, analytical test correlation modal data, and analytical flight configuration modal data are presented. Tables showing the generalized mass contributions (GMCs) for each of the thirty tests modes are given along with the two dimensional mode shape plots and tables of GMCs for the test correlated analytical modes. The two dimensional mode shape plots for the analytical modes and uncoupled and coupled modes of the orbital flight configuration at three development phases of the model are included.

Demchak, L.