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At least 19 records

Performance Risk Model (PRisM) Proof-of-Concept: An Operational Decision Support Tool to Predict Crew Performance in Space from Available Performance Tests

The Crew Health and Performance-Probabilistic Risk Assessment (CHP-PRA) team at NASA Glenn Research Center has developed a range of tools to evaluate astronaut health during spaceflight and to optimize the medical set required for missions. Among these, the Performance Risk Model (PRisM) represents a novel advancement, extending CHP-PRA’s focus beyond medical systems into the domain of human performance. Such tool could be pivotal in optimizing astronaut capabilities during space travel, thereby enhancing overall mission success. PRisM leverages data from well-established performance assessments conducted during previous crewed space missions and Earth analogs to strategically predict outcomes for planned tasks, even when direct performance testing has not been conducted for those specific tasks. To evaluate performance, PRisM references the various metrics outlined in NASA-STD-3001 and employs a methodology to integrate different performance scales. This framework analyzes the contribution of various human system task categories (HSTCs) to task execution and compares these contributions to the HSTCs’ involvement in other known tests. The model further employs a Monte Carlo simulation to sample performance scores from their distribution in operationally relevant tests such as those in Mulavara et al. (2018) and, by leveraging similarities in HSTC involvement, transfers this knowledge to actual mission tasks, such as those outlined in the "Human Exploration of Mars: Preliminary List of Crew Tasks”. The current PRisM proof-of-concept includes analyses of the impact of exercise and specific medications on astronauts’ performance, with provisions to incorporate additional countermeasures as data becomes available. Furthermore, the tool is customizable to include any system necessary to fully encompass the domain of human systems and can be adapted to evaluate performance for any spaceflight activities as requested by operational stakeholders. PRisM has the potential to assist the Human Research Program in exploring the capabilities trade space for optimized crew performance.

performance modeling

Investigation of Performance of Axial-Flow Compressor of XT-46 Turbine-Propeller Engine. II - Performance of Revised Compressor at Design Equivalent Speed: Performance of Revised Compressor at Design Equivalent Speed - II

The compressor from the XT-46 turbine-propeller engine was revised by removing the last two rows of stator blades and by eliminating the interstage leakage paths described in a previous report. With the revised compressor, the flow choking point shifted upstream into the last rotor-blade row but the maximum weight flow was not increased over that of the original compressor. The flow range of the revised compressor was reduced to about two-thirds that obtained with the original compressor. The later stages of the compressor did not produce the design static-pressure increase probably because of excessive boundary-layer build-up in this region. Measurements obtained in the ninth-stage stator showed that the performance up to this station was promising but that the last three stages of the compressor were limiting the useful operating range of the preceding stages. Some modifications in flow-passage geometry and blade settings are believed to be necessary, however, before any major improvements in over-all compressor performance can be obtained.

Creagh, John W. R.

Preliminary Results of British Nene II Engine Altitude-Chamber Performance Investigation. I - Altitude Performance Using Standard 18.75-Inch-Diameter Jet Nozzle: Altitude Performance Using Standard 18.75-Inch-Diameter Jet Nozzle - 1

An investigation is being conducted to determine the altitude performance characteristics of the British Nene II engine and its components. The present paper presents the preliminary results obtained using a standard jet nozzle. The test results presented are for conditions simulating altitudes from sea level to 60,000 feet and ram pressure ratios from 1.0 to 2.3. These ram pressure ratios correspond to flight Mach numbers between zero and 1.16 assuming a 100 percent ram recovery.

Barson, Zelmar

Performance of Axial-Flow Supersonic Compressor on XJ-55-FF-1 Turbojet Engine. I - Preliminary Performance of Compressor: Preliminary Performance of Compressor - 1

An investigation was conducted to determine the performance characteristics of the axial-flow supersonic compressor of the XJ-55-FF-1 turbo Jet engine. The test unit consisted of a row of inlet guide vanes and a supersonic rotor; the stator vanes after the rotor were omitted. The maximum pressure ratio produced in the single stage was 2.28 at an equivalent tip speed or 1814 feet per second with an adiabatic efficiency of approximately 0.61, equivalent weight flow of 13.4 pounds per second. The maximum efficiency of 0.79 was obtained at an equivalent tip speed of 801 feet per second.

Hartmann, Melvin J.

Simulated Altitude Performance of Combustors for the 24C Turbojet Engine. III - Performance of Rectangular-Slot Baskets: Performance of Rectangular-Slot Baskets - 3

The performance of an annular combustion chamber from a 24C turbojet engine was investigated over a range of simulated altitudes from 20,000 to 55,000 feet and corrected engine rotor speeds from 6000 to 13,000 rpm at a simulated ram-pressure ratio of 1.04. The purpose of the investigation was to determine the effects on the altitude operational limits, combustor-outlet gas temperature distribution, combustion efficiencies, and combustor inlet-to-outlet total-pressure drops of two changes in the 24C-4B basket air-passage arrangements that were designed to improve combustor-outlet temperature distribution. These changes were: (a) replacement of the downstream secondary air holes with large rectangular slots further upstream (rectangular-slot basket), and (b) enlargement of anticoking holes in the rectangular-slot basket (modified rectangular-slot basket). The results indicate that improved outlet-gas temperature distribution of each succeeding combustor basket investigated was attained at a sacrifice in the altitude limit of operation. The altitude limits of operation of the combustor with the original basket ranged from 34,000 feet at a corrected engine speed of 6000 rpm to a maximum of 52,000 feet at 12 ' 500 rpm. The altitude limits of the rectangular-slot basket were about 2000 feet lower throughout the engine speed range than those of the original basket. The altitude limits of the combustor with the modified rectangular-slot basket were about equivalent to those of the other baskets in the corrected-engine-speed range from 12,000 to 12,500 rpm but were about 10,000 feet lower than those of the original basket in the corrected-engine-speed range from 6000 to 9000 rpm. For the same inlet-air conditions, the combustion efficiencies were highest for the original basket and progressively lower for each of the other two baskets. The combustor inlet-to-outlet pressure drops of all three combustor baskets at the same operating conditions were within +/- 10 percent of the pressure drop of the original basket.

Tischler, Adelbert O.

Evaluation of the Trade Space Between UAS Maneuver Performance and SAA System Performance Requirements

A need exists to safely integrate Unmanned Aircraft Systems (UAS) into the National Airspace System. Replacing manned aircraft's see-and-avoid capability in the absence of an onboard pilot is one of the key challenges associated with safe integration. Sense-and-avoid (SAA) systems will have to achieve yet-to-be-determined required separation distances for a wide range of encounters. They will also need to account for the maneuver performance of the UAS they are paired with. The work described in this paper is aimed at developing an understanding of the trade space between UAS maneuver performance and SAA system performance requirements. An assessment of current manned and unmanned aircraft performance was used to establish potential UAS performance test matrix bounds. Then, nearterm UAS integration work was used to narrow down the scope. A simulator was developed with sufficient fidelity to assess SAA system performance requirements for a wide range of encounters. The simulator generates closest-point-of-approach (CPA) data from the wide range of UAS performance models maneuvering against a single intruder with various encounter geometries. The simulator is described herein and has both a graphical user interface and batch interface to support detailed analysis of individual UAS encounters and macro analysis of a very large set of UAS and encounter models, respectively. Results from the simulator using approximate performance data from a well-known manned aircraft is presented to provide insight into the problem and as verification and validation of the simulator. Analysis of climb, descent, and level turn maneuvers to avoid a collision is presented. Noting the diversity of backgrounds in the UAS community, a description of the UAS aerodynamic and propulsive design and performance parameters is included. Initial attempts to model the results made it clear that developing maneuver performance groups is required. Discussion of the performance groups developed and how to know in which group an aircraft belongs for a given flight condition and encounter is included. The groups are specific to airplane, flight condition, and encounter, rather than airplane-only specific. Results and methodology for developing UAS maneuver performance requirements are presented for each maneuver as well. Results for the vertical maneuver indicate that a minimum specific excess power value can assure a minimum CPA for a given time-to-go prediction. However, smaller values of specific excess power may achieve or exceed the same CPA if the UAS has sufficient speed to trade for altitude. Level turn results are less impacted by specific excess power and are presented as a function of turn rate. The effect of altitude is also discussed for the turns. Next steps and future work are discussed. Future studies will lead to better quantification of the preliminary results and cover the remainder of the proposed test matrix. It is anticipated that this will be done in conjunction with RTCA SC-228 over the next few months.

Jack, Devin P.

Exploration of the Trade Space Between Unmanned Aircraft Systems Descent Maneuver Performance and Sense-and-Avoid System Performance Requirements

A need exists to safely integrate Unmanned Aircraft Systems (UAS) into the United States' National Airspace System. Replacing manned aircraft's see-and-avoid capability in the absence of an onboard pilot is one of the key challenges associated with safe integration. Sense-and-avoid (SAA) systems will have to achieve yet-to-be-determined required separation distances for a wide range of encounters. They will also need to account for the maneuver performance of the UAS they are paired with. The work described in this paper is aimed at developing an understanding of the trade space between UAS maneuver performance and SAA system performance requirements, focusing on a descent avoidance maneuver. An assessment of current manned and unmanned aircraft performance was used to establish potential UAS performance test matrix bounds. Then, near-term UAS integration work was used to narrow down the scope. A simulator was developed with sufficient fidelity to assess SAA system performance requirements. The simulator generates closest-point-of-approach (CPA) data from the wide range of UAS performance models maneuvering against a single intruder with various encounter geometries. Initial attempts to model the results made it clear that developing maneuver performance groups is required. Discussion of the performance groups developed and how to know in which group an aircraft belongs for a given flight condition and encounter is included. The groups are airplane, flight condition, and encounter specific, rather than airplane-only specific. Results and methodology for developing UAS maneuver performance requirements are presented for a descent avoidance maneuver. Results for the descent maneuver indicate that a minimum specific excess power magnitude can assure a minimum CPA for a given time-to-go prediction. However, smaller amounts of specific excess power may achieve or exceed the same CPA if the UAS has sufficient speed to trade for altitude. The results of this study will support UAS maneuver performance requirements development for integrating UAS in the NAS. The methods described are being used to help RTCA Special Committee 228 develop requirements.

Jack, Devin P.

Study of the Correlation between the Performances of Lunar Vehicle Wheels Predicted by the Nepean Wheeled Vehicle Performance Model and Test Data

This paper describes the results of a study of the correlation between the performances of wheels for lunar vehicles predicted using the Nepean wheeled vehicle performance model (NWVPM), developed under the auspices of Vehicle Systems Development Corporation, Ottawa, Canada, and the corresponding test data presented in Performance evaluation of wheels for lunar vehicles , Technical Report M-70-2, prepared for George C. Marshall Space Flight Center, National Aeronautics and Space Administration (NASA), USA, by the US Army Engineer Waterways Experiment Station (WES). The NWVPM was originally developed for design and performance evaluation of terrestrial off-road wheeled vehicles. The purpose of this study is to assess the potential of the NWVPM for evaluating wheel candidates for the new generation of extra-terrestrial vehicles. Two versions of a wire-mesh wheel and a hoop-spring wheel, which were considered as candidates for lunar roving vehicles for the NASA Apollo program in the late 1960s, together with a pneumatic wheel were examined in this study. The tractive performances of these wheels and of a 464 test vehicle with the pneumatic wheels on air-dry sand were predicted using the NWVPM and compared with the corresponding test data obtained under Earth s gravity and previously documented in the above-named report. While test data on wheel or vehicle performances obtained under Earth s gravity may not necessarily be representative of those on extra-terrestrial bodies, because of the differences in gravity and in environmental conditions, such as atmospheric pressure, it is still a valid approach to use test data obtained under Earth s gravity to evaluate the predictive capability of the NWVPM and its potential applications to predicting wheel or wheeled rover performances on extra-terrestrial bodies. Results of this study show that, using the ratio (P20/W) of the drawbar pull to normal load at 20 per cent slip as a performance indicator, there is a reasonable correlation between the predictions and experimental data. This indicates that the NWVPM has the potential as an engineering tool for evaluating wheel candidates for a future generation of extra-terrestrial vehicles, provided that appropriate input data are available.

Wong, J. Y.

Performance Data Report: Space Medicine Division, Human Research Program, Behavioural Health and Performance Research Element

This report is the result of a collaborative effort between NASA?s Behavioral Health & Performance (BHP) Research and Operations Group to investigate and determine the availability of data pertaining to behavioral performance (and other pertinent variables) that have been collected by the laboratories at NASA?s Johnson Space Center. BHP?s Operations and Research groups collaborated to systematically identify what types of performance data are needed in relevant BHP performance domains and also to conduct structured interviews with NASA personnel to identify which data do or do not exist currently (and for instances where such data exist, to evaluate the type, quality, accessibility, and confidentiality of those data). The authors defined outcome categories of performance that encapsulate BHP performance domains, mapped BHP Research Risks and Gaps onto those performance outcome categories, and identified and prioritized indicators for each outcome category. The team identified key points of contact (subject matter experts [SMEs]) as potential interviewees, created a template for structured interview questions about sources and accessibility of performance data, and coordinated and conducted structured interviews with the SMEs. The methodology, results, and implications of this effort, as well as forward work needed, are discussed in this report.

Shea, Camille

Strategies for Quantifying Human Space Flight Performance in the Crew Health and Performance System

The Crew Health and Performance-Probabilistic Risk Assessment (CHP-PRA) team at NASA Glenn Research Center is planning a customized approach to quantify human spaceflight performance changes with respect to changes to the CHP system functions and capabilities. Using the Directed Acyclic Graphs (DAG) initiated by NASA’s Human Systems Risk Board (HSRB) [1], the team is surveying potential candidate models and novel strategies that generate metrics suitable for supporting decision making related to how the CHP system may influence human system performance risk. One such investigation includes classic Human Reliability Analysis (HRA) models. Traditionally, HRA methods estimate the occurrence of human errors and their impact on the success of an activity when designing and operating a system. While humans perceive, interpret, decide on, and carry out a course of action, the factors affecting performance and error likelihood are commonly referred to as performance shaping factors (PSFs). Originally developed to alleviate safety concerns related to nuclear power plant operations, HRA methods such as THERP [2] and CREAM [3] dismantle an activity into tasks, requiring elemental steps to be executed, and assess their failure due to predefined PSFs. In this study, we compare generic HRA methods and those that incorporate some human spaceflight aspects, such as sleep conditions (SCREAM [4]), with respect to how they may be adopted to capture performance with an intention to mitigate detrimental outcomes elucidated by the HSRB DAGs. We suggest strategies to quantify astronaut performance specific to spaceflight activities and illustrate how such concepts may help in optimizing the CHP system capabilities with respect to Artemis missions.

dag

Flat-Plate Solar-Collector Performance Evaluation with a Solar Simulator as a Basis for Collector Selection and Performance Prediction

The use of a solar simulator for performance determination permits collector testing under standard conditions of wind, ambient temperature, flow rate and sun. The performance results determined with the simulator have been found to be in good agreement with outdoor performance results. The measured thermal efficiency and evaluation of 23 collectors are reported which differ according to absorber material (copper, aluminum, steel), absorber coating (nonselective black paint, selective copper oxide, selective black nickel, selective black chrome), type of glazing material (glass, Tedlar, Lexan, antireflection glass), the use of honeycomb material and the use of vacuum to prevent thermal convection losses. The collectors were given performance rankings based on noon-hour solar conditions and all-day solar conditions. The determination with the simulator of an all-day collector performance was made possible by tests at different incident angles. The solar performance rankings were made based on whether the collector is to be used for pool heating, hot water, absorption air conditioning, heating, or for a solar Rankine machine.

Simon, F. F.

Charts for estimating performance of high-performance helicopters

Theoretically derived charts showing the profile-drag-thrust ratio are presented for helicopter rotors operating in forward flight and having hinged rectangular blades with a linear twist of 0 degree, 8 degrees, and 16 degrees. The charts, showing the profile-drag characteristics of the rotor for various combinations of pitch angle, ratio of thrust coefficient to solidity, and a parameter representing shaft power input, are presented for tip-speed ratios ranging from 0.05 to 0.50. Also presented in chart form are the ratio of thrust coefficient to solidity as a function of angles of attack, as a function of inflow ratio and collective pitch, and as a function of power and thrust coefficients. The charts in this report are considered more accurate than previous ones for flight conditions involving high inflow velocities and large regions of reversed velocity that may be encountered by high-performance helicopters. The charts may be used to study the effects of design changes on rotor performance and to indicate optimum performance conditions, as well as to estimate quickly rotor performance in forward flight. They are also useful in obtaining inflow-ratio and pitch-angle values for use in calculating flapping coefficients and spanwise loadings. The method of applying the charts to performance estimation is illustrated through sample calculation of a typical rotor-performance problem.

Gessow, Alfred

Effects of Gas Turbine Component Performance on Engine and Rotary Wing Vehicle Size and Performance

In support of the Fundamental Aeronautics Program, Subsonic Rotary Wing Project, further gas turbine engine studies have been performed to quantify the effects of advanced gas turbine technologies on engine weight and fuel efficiency and the subsequent effects on a civilian rotary wing vehicle size and mission fuel. The Large Civil Tiltrotor (LCTR) vehicle and mission and a previous gas turbine engine study will be discussed as a starting point for this effort. Methodology used to assess effects of different compressor and turbine component performance on engine size, weight and fuel efficiency will be presented. A process to relate engine performance to overall LCTR vehicle size and fuel use will also be given. Technology assumptions and levels of performance used in this analysis for the compressor and turbine components performances will be discussed. Optimum cycles (in terms of power specific fuel consumption) will be determined with subsequent engine weight analysis. The combination of engine weight and specific fuel consumption will be used to estimate their effect on the overall LCTR vehicle size and mission fuel usage. All results will be summarized to help suggest which component performance areas have the most effect on the overall mission.

Snyder, Christopher A.

Risk of Impaired Performance Due to Reduced Muscle Mass, Strength &, Endurance (Short Title: Muscle) and Risk of Reduced Physical Performance Capabilities Due to Reduced Aerobic Capacity (Short Title: Aerobic)

This report reviews the scientific literature regarding the human system risks to the microgravity environment of space flight in relation to human performance. The primary human performance-related risks involve deconditioning of the cardiovascular and skeletal muscles systems due to prolonged exposure to the reduced gravitational input. The chronological history of U.S. space flight is reviewed as a starting point to inform and understand the gaps in the knowledge to these risks. Maintenance of physical performance capabilities involves understanding the health of many organ systems (peripheral [vascular, heart, blood volume, skeletal muscle] and central [brain]) that ultimately contribute to the submaximal and maximal capacity of the aerobic (VO2peak), skeletal muscle (strength and endurance) systems. Maintaining astronaut VO2peak, muscle mass, strength, and endurance before, during, and after space flight is a significant priority to NASA for the current International Space Station (ISS) era, as well as for future exploration missions. A growing research database from both space flight and ground-based analog studies finds that the cardiorespiratory system is compromised and skeletal muscles (predominantly postural muscles of the lower limbs) undergo atrophy. These structural and metabolic responses to living in microgravity conditions contribute to physiological deconditioning during space flight that potentially increase the risks to astronauts returning to surface operations (i.e., Moon, Mars, or Earth). The time course changes from short to long-duration space flight and the relationships between in-flight performance deconditioning levels are not well characterized. Moreover, there are large interindividual variabilities that may be dependent on genetics, age, sex, preflight fitness levels, and individual exercise prescriptions that need further careful evaluations. Efforts should be made to understand the current status of preflight, in-flight, and postflight exercise performance capability and to define the operational goals and target areas for protection with the in-flight exercise program. There is a bi-directional relationship between exercise prescription and hardware countermeasures that need further understanding in-flight. For example, hardware with limited capabilities/modalities may be counterbalanced by changes in exercise prescription (i.e., frequency, time, intensity, volume) for providing effective responses to maintain fitness. Importantly, the minimal requirements for exercise prescription on ISS hardware may not translate to lower capability hardware on exploration missions. Due to limited volume on exploration vehicles, future Artemis missions to the Lunar surface will not have similar exercise hardware capabilities as ISS. This may alter the effectiveness of hardware to provide adequate physiological stress on bodily systems allowing for adaptations to maintain aerobic capacity, strength, and bone density. Thus, it will be important to understand the exercise responses of current ISS countermeasures to develop individualized exercise prescriptions that minimize aerobic and muscular risks, accounting for the large variability of responses among crewmembers. Newer exploration exercise hardware is currently being evaluated that is more compact (i.e., E4D and Orion Flywheel) and will require careful evaluation of the hardware on the stressor (i.e., metabolic rate, oxygen uptake, and heart rate work relationships, and force plate load profiles) needed the human body to protect and maintain crew health and performance. Moreover, exercise responses on the hardware need careful evaluation on the chronic adaptations. Lastly, in-flight evaluation of hardware exercise response may differ in 0-g or partial-g compared to 1-g. Therefore, it cannot be assumed that the stress on the body will be the same in each environment. Understanding this has a direct impact on exercise prescriptions. This document provides an overview of key scientific investigations that have been conducted before, during, and after human space flight missions, as well as from human ground-based analog studies that contribute to the evidence base on changes in aerobic capacity and muscle mass, strength, and endurance. Additional data from rodent and nonhuman primate experiments of skeletal muscle unloading completed during space flight or ground-based flight-simulations provide supportive information about this risk topic. Most importantly, a recent, large dataset from long-duration ISS crew has been added to give improved insight into the variability of exercise response of crew, demonstrating that a large portion of the crew population return to Earth with greater than 10-20% loss of aerobic capacity and muscle strength and endurance. Data from human space flight and ground-based studies are narrowing in on the required exercise paradigms but thus far still provide an incomplete answer to an effective approach for maintaining skeletal muscle function and aerobic fitness of all human space travelers. Finally, the relationship of this risk topic to various space flight operational scenarios is examined and discussed.

Eric Rivas

The Future of Integrated Performance Modeling in the Crew Health and Performance – Probabilistic Risk Assessment Project

The NASA engineering community utilizes event-driven and fault-tree probabilistic techniques to classify risks in the space environment by taking advantage of the inherent knowledge of complex spaceflight system design and testing to quantify failure risk. In harmonizing the risk of human space flight, answering the question of ‘How do we balance health, performance and resource risks with other engineering risks on long duration space missions?’ remains a deeply challenging and largely qualitative practice. The Human Research Program’s Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT) was a significant step forward in efforts to robustly quantify the risk to crew health for exploration missions. However, there remains a significant gap in the ability to comprehensively assess and characterize risk across the disparate functionalities and capabilities which comprise the Crew Health and Performance (CHP) system. The Crew Health and Performance – Probabilistic Risk Assessment (CHP-PRA) project seeks to characterize CHP risks by expanding beyond the foundation established by its PRA predecessors like IMM and MEDPRAT, that simulate medical risk metrics like loss of crew life and evacuations. One of the new risk measures in the CHP-PRA system is embodied in our Performance Risk Model (PRisM). PRisM provides a novel way of assessing crew performance on mission tasks, using a generalized framework which relates back to NASA-STD-3001. This approach allows PRisM to capture and integrate data from a variety of different domains into a single, unified, reproducible representation of astronaut performance. In this presentation, we discuss the motivation for the CHP-PRA work and give a high level overview of the goals of the project, outline the forward work for PRisM, and discuss collaboration opportunities for the community who might explore if their domain knowledge and data could be represented, integrated, and quantified with these tools, whose outcomes are metrics useful for supporting operational mission planning and decision making.

Lauren McIntyre

Measurement-based performance evaluation technique for high-performance computers

A measurement-based performance evaluation technique has been used to characterize the OS performance of Cedar, a hierarchical shared-memory multiprocessor system. Thirteen OS performance meters were used to capture the operating system activities for compute-bound workloads. Three representative applications from the Perfect Benchmark Suite were used to measure the OS performance in a dedicated system and in multiprogrammed workloads. It was found that 13-23 percent of the total execution time on a dedicated system was spent in executing OS-related activities. Under multiprogramming, 12-14 percent of the total execution time was used by the OS. The impact of multiprogramming on the operating system performance meters was also measured.

Sharma, S.

Preliminary Results of Altitude-Wind-Tunnel Investigation of X24C-4B Turbojet Engine. II - Engine Performance: Engine Performance - II

An investigation was conducted in the NACA Cleveland altitude wind tunnel to evaluate the performance characteristics of the X24C-4B turbojet engine over a range of simulated altitudes from 5000 to 45,000 feet,simulated flight Mach numbers from 0 to 1.08, and engine speeds from 4000 to 12,500 rpm. Performance data are presented to show graphically the effects of altitude at a flight Mach number of 0.25 and of flight Mach number at an altitude of 25,000 feet. The performance data are generalized to show the applicability of methods used to determine performance at any altitude from data obtained at a given altitude. A complete tabulation of performance data, as well as lubrication- and fuel- system data, is presented.

Meyer, Carl L.