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NASA NTRS2005

Evaluation of radioisotope electric propulsion for selected interplanetary science missions

This study assessed the benefits and applicability of REP to missions relevant to the In-Space Propulsion Program (ISPP) using first and second generation RPS with specific powers of 4 We/kg and 8 We/kg, respectively. Three missions representing small body targets, medium outer planet class, and main belt asteroids and comets were evaluated. Those missions were a Trojan Asteroid Orbiter, Comet Surface Sample Return (CSSR), and Jupiter Polar Orbiter with Probes (JPOP). For each mission, REP cost and performance was compared with solar electric propulsion system (SEPS) and SOA chemical propulsion system (SCPS) cost and performance. The outcome of the analysis would be a determinant for potential inclusion in the ISPP investment portfolio.

trojan asteroid↗

NASA NTRS2007

A Comprehensive Characterization of Microorganisms and Allergens in Spacecraft Environment

The determination of risk from infectious disease during long-duration missions is composed of several factors including (1) the host#s susceptibility, (2) the host#s exposure to the infectious disease agent, and (3) the concentration of the infectious agent, and (4) the characteristics of the infectious agent. While stringent steps are taken to minimize the transfer of potential pathogens to spacecraft, several medically significant organisms have been isolated from both the Mir and International Space Station (ISS). Historically, the method for isolation and identification of microorganisms from spacecraft environmental samples depended upon their growth on culture media. Unfortunately, only a fraction of the organisms may grow on a culture medium, potentially omitting those microorganisms whose nutritional and physical requirements for growth are not met. Thus, several pathogens may not have been detected, such as Legionella pneumophila, the etiological agent of Legionnaire#s disease. We hypothesize that environmental analysis using non-culture-based technologies will reveal microorganisms, allergens, and microbial toxins not previously reported in spacecraft, allowing for a more complete health assessment. The development of techniques for this flight experiment, operationally named SWAB, has already provided advances in NASA laboratory processes and beneficial information toward human health risk assessment. The first accomplishment of the SWAB experiment was the incorporation of 16S ribosomal DNA sequencing for the identification of bacteria. The use of this molecular technique has increased bacterial speciation of environmental isolates from previous flights three fold compared to conventional methodology. This increased efficiency in bacterial speciation provides a better understanding of the microbial ecology and the potential risk to the crew. Additional SWAB studies focused on the use of molecular-based DNA fingerprinting using repetitive sequencebased polymerase chain reaction (rep-PCR). This technology has allowed contamination tracking of microorganisms between crewmembers and their environment. This study not only demonstrated that ISS has a greater diversity of organisms than originally expected, but also provided insight into possible routes of infection to the crew. Additional ground-based studies used rep-PCR and protein based assays to determine the potential of methicillin resistant Staphylococcus aureus (MRSA) aboard ISS. MRSA has become increasingly common on Earth and pose a treatment problem for infections during flight. While no MRSA have been isolated from ISS to date, the mecA gene product that is responsible for methicillin resistance was isolated in other Staphylococcus species aboard ISS suggesting a potential of MRSA through gene transfer. Using improved sample collection technologies, flight sampling for SWAB was initiated in August 2006 and should continue through spring of 2007. The focus of these flight samples is the collection of DNA for evaluation by Denaturing Gradient Gel Electrophoresis (DGGE). Unlike other techniques, DGGE does not depend on any microbial growth on culture media allowing a more comprehensive assessment of the spacecraft interior. This study should provide insight into the true microbial ecology that is experienced by the crew during flight. This information will lead toward an accurate microbial risk assessment to help set flight requirements to protect the safety, health, and performance of the crew.

Ott, C. M.↗

NASA NTRS2008

An Overview of the Impact of Energetic Particle Precipitation on the Mesosphere and Stratosphere

Energetic precipitating particles (EPPs) can cause significant constituent changes in the polar mesosphere and stratosphere (middle atmosphere) during certain periods. Both protons and electrons can influence the polar middle atmosphere through ionization and dissociation processes. EPPs can enhance HOx (H, OH, HO2) through the formation of positive ions followed by complex ion chemistry and NOx (N, NO, NO2) through the dissociation of molecular nitrogen. The HO, increases can lead to ozone destruction in the mesosphere and upper stratosphere via several catalytic loss cycles. Such middle atmospheric HOx,-caused ozone loss is rather short-lived due to the relatively short lifetime (hours) of the HOx constituents. The HOx,-caused ozone depletion has been observed during several solar proton events (SPEs) in the past 40 years. HOx enhancements due to SPEs were confirmed by observations in the past solar cycle. A number of modeling studies have been undertaken over this time period that show predictions of enhanced HO, accompanied by decreased ozone due to energetic particles. The NO, family has a longer lifetime than the HOx family and can also lead to catalytic ozone destruction. EPP-caused enhancements of the NOx family can affect ozone promptly, if produced in the stratosphere, or subsequently, if produced in the 1ow.er thermosphere or mesosphere and transported to the stratosphere. NOx enhancements due to auroral electrons, medium and high energy electrons, relativistic electron precipitation (REP) events, and SPEs have been measured and/or modeled for decades Only a small number of SPEs (less than 10) in each solar cycle have sufficient flux of high energy protons (greater than 30 MeV) to produce a significant amount of NOx directly in the stratosphere to cause a measurable ozone destruction. Very high energy electrons (greater than 1500 keV) during REP events can also produce NOx directly in the stratosphere, however, the frequency and intensity of these electrons is uncertain. Indirect stratospheric EPP effects result when NO, is produced in the mesosphere and lower thermosphere and transported to the stratosphere during the late fall or winter. Such EPP-produced NOx may last up to months beyond its initial production. This EPP-produced mesospheric and lower thermospheric NOx primarily results from auroral electrons (approx. 1- 30 keV), medium- and high-energy electrons (approx. 30-1500 keV), and medium energy protons (approx. 1-30 MeV). The EPP-caused direct and indirect effects on the stratosphere are important in the polar regions during particular years, especially near solar maximum. This talk will attempt to provide an overview of several of the EPP-related important processes and their impact on the mesosphere and stratosphere. Much progress has been made in this field in the past several years and it is anticipated that other workshop participants will address aspects of this topic in their presentations.

Jackman, Charles H.↗

NASA NTRS2010

Squat Ground Reaction Force on a Horizontal Squat Device, Free Weights, and Smith Machine

Bed rest is an analog to spaceflight and advancement of exercise countermeasures is dependent on the development of exercise equipment that closely mimic actual upright exercise. The Horizontal Squat Device (HSD) was developed to allow a supine exerciser to perform squats that mimic upright squat exercise. PURPOSE: To compare vertical ground reaction force (GRFv) on the HSD with Free Weight (FW) or Smith Machine (SM) during squat exercise. METHODS: Subjects (3F, 3M) performed sets of squat exercise with increasing loads up to 1-repetition (rep) maximum. GRF data were collected and compared with previous GRF data for squat exercise performed with FW & SM. Loads on the HSD were adjusted to magnitudes comparable with FW & SM by subtracting the subject s body weight (BW). Peak GRFv for 45-, 55-, 64-, & 73-kg loads above BW were calculated. Percent (%) difference between HSD and the two upright conditions were computed. Effect size was calculated for the 45-kg load. RESULTS: Most subjects were unable to lift >45 kg on the HSD; however, 1 subject completed all loads. Anecdotal evidence suggested that most subjects shoulders or back failed before their legs. The mean % difference are shown. In the 45-kg condition, effect sizes were 0.37 & 0.83 (p>0.05) for HSD vs. FW and HSD vs. SM, respectively, indicating no differences between exercise modes. CONCLUSION: When BW was added to the target load, results indicated that vertical forces were similar to those in FW and SM exercise. The exercise prescription for the HSD should include a total external resistance equivalent to goal load plus subject BW. The HSD may be used as an analog to upright exercise in bed rest studies, but because most subjects were unable to lift >45 kg, it may be necessary to prescribe higher reps and lower loads to better target the leg musculature

Scott-Pandorf, Melissa M.↗

NASA NTRS2013

Modeling Relativistic Electron Precipitation Bremsstrahlung X-Ray Intensities at 10-100 km Manned Vehicle Altitudes

Relativisitic electron precipitation (REP) events occur when beams or bunches of relativistic electrons of magnetospheric origin enter the Earth's atmosphere, typically at auroral latitudes. REP events are associated with a variety of space weather effects, including production of transitional and bremsstrahlung radiation, catalytic depletion of stratospheric ozone, and scintillation of transionospheric radio waves. This study examines the intensities of x‐rays produced at airliner, manned balloon, and space reuseable launch vehicles (sRLVs). The monoenergetic beam is modeled in cylindrical symetry using the paraxial ray equation. Bremsstrahlung photon production is calculated using the traditional Sauter‐Elwert cross‐section, providing x‐ray emission spectra differential in energy and angle. Attenuation is computed for a plane‐stratified standard atmosphere, and the loss processes include photoionization, Rayleigh and Compton scattering, electron‐positron pair production, and photonuclear interaction. Peak altitudes of electron energy deposition and bremsstrahlung x‐ray production were calculated for beams of energies from 1 MeV through 100 MeV. The altitude peak of bremsstrahlung deposition was consistently and significantly lower that that of the electron deposition due to the longer mean free paths of x‐rays compared to electrons within the atmosphere. For example, for a nadir‐directed monoenergetic 5 MeV beam, the peak deposition altitude was calculated to be 42 km, but the resulting bremsstrahlung deposition peaked at 25 km. This has implications for crew and passenger safety, especially with the growth of the space tourism industry. A survey of results covering the 1‐100 MeV spectrum for the three altitude ranges of interest will be presented.

Krause, L. Habsh↗

NASA NTRS2015

Low-Mass, Low-Power Hall Thruster System

NASA is developing an electric propulsion system capable of producing 20 mN thrust with input power up to 1,000 W and specific impulse ranging from 1,600 to 3,500 seconds. The key technical challenge is the target mass of 1 kg for the thruster and 2 kg for the power processing unit (PPU). In Phase I, Busek Company, Inc., developed an overall subsystem design for the thruster/cathode, PPU, and xenon feed system. This project demonstrated the feasibility of a low-mass power processing architecture that replaces four of the DC-DC converters of a typical PPU with a single multifunctional converter and a low-mass Hall thruster design employing permanent magnets. In Phase II, the team developed an engineering prototype model of its low-mass BHT-600 Hall thruster system, with the primary focus on the low-mass PPU and thruster. The goal was to develop an electric propulsion thruster with the appropriate specific impulse and propellant throughput to enable radioisotope electric propulsion (REP). This is important because REP offers the benefits of nuclear electric propulsion without the need for an excessively large spacecraft and power system.

Pote, Bruce↗

NASA NTRS2017

Improvement of Automated POST Case Success Rate Using Support Vector Machines

During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal [1]. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases [2]. Additional work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points [3]. The conclusion of the previous work illustrated the utility of the graph theory approach for completing a DOE through POST. However, this approach was still dependent upon the use of random repetitions to generate seed points for the graph. As noted in [3], only 8% of these random repetitions resulted in converged trajectories. This ultimately affects the ability of the random reps method to confidently approach the global optima for a given vehicle case in a reasonable amount of time. With only an 8% pass rate, tens or hundreds of thousands of reps may be needed to be confident that the best repetition is at least close to the global optima. However, typical design study time constraints require that fewer repetitions be attempted, sometimes resulting in seed points that have only a handful of successful completions. If a small number of successful repetitions are used to generate a seed point, the graph method may inherit some inaccuracies as it chains DOE cases from the non-global-optimal seed points. This creates inherent noise in the graph data, which can limit the accuracy of the resulting surrogate models. For this reason, the goal of this work is to improve the seed point generation method and ultimately the accuracy of the resulting POST surrogate model. The work focuses on increasing the case pass rate for seed point generation.

Zwack, Matthew R.↗

NASA NTRS2019

WWAO-WSWC Workshop Report 2019 Final

EXECUTIVE SUMMARY The Western States Water Council (WSWC) and the NASA Western Water Applications Office (WWAO) hosted a joint workshop on technology transfer for water management in the Western U.S. The goals of the workshop were to understand how different agencies approach the technology transfer and research to operations (R2O) process, identify best practices, and discuss existing barriers to successful technology infusion into operational water resource management systems at the state and federal level. The workshop took place August 7-9, 2019 in Irvine, CA. Key outcomes of the meeting include the following:• U.S. Rep. Grace Napolitano provided opening remarks for the workshop, where she highlighted the critical value of water data and the importance of collaboration between state and federal agencies in working to advance the use of water data in water management, planning and policy. • A total of 33 participants (including remote participants) were part of the workshop. They included principal investigators and project teams supported by NASA (Cyanobacteria Assessment Network, Evapotranspiration for Western States, Evaporative Stress Index, the Airborne Snow Observatory, Satellite-based Snow Water Equivalent in the Sierra Nevadas, and Fallowed Area Mapping) as well as representatives from federal (USGS, NOAA, USBR, EPA) and state (CA, WY, OR, NE) agency partners. • One main outcome of the meeting was the consensus that successful transitions of new applications and new technologies into operations require careful planning, effective communication within and across institutions, resources and considerable time investments. In addition, there was broad agreement that significant lead time is often required to allow for identification of financial and technical resources to sustain operational use of new data, information and tools.• The meeting included remarks from U.S. Rep. Napolitano and discussions during presentations and breakout groups about key opportunities to develop best practices and streamline the technology transfer process. • For example, one key set of best practices that emerged revolved around the the importance of building trust and establishing clear lines of communication between the research and operational institutions. The conversations led to defining two key components of trust-building. The first aspect is purely technical. It requires effectively demonstrating that the proposed application meets the end user’s needs in terms of accuracy, format, resolution, latency, metadata and documentation. The second aspect of building trust involves developing sustained, productive and mutually-beneficial relationships with the partner operational agency. The best practices presented here span both the technical as well as the relational aspects of cultivating trust. • This workshop served as a first step in developing a broader community discussion around R2O in western water management. Many of the best practices and lessons learned described in this report represent starting places for action within the WWAO, WSWC and our colleagues’ institutions. • Effective implementation of the best practices that emerged from this workshop will require sustained investments of time, resources and transition planning. In recognition of this, the WSWC and the WWAO proposed continuation of discussions begun at the workshop through a series of semi-annual or annual workshops.

Wilardson, Tony↗

NASA NTRS2022

A Novel High-Performance Mission-Enabling Multi-Purpose Radioisotope Heat Source

Recent studies indicate science mission concepts targeting access to the sub-surface oceans of icy moons require ice-penetrating cryobots powered by advanced Radioisotope Power Systems (RPS). These systems would deliver waste heat for ice-melting in the range of 10 kW. Minimizing the transit time through the kilometers-thick ice shells to just a few years requires these RPS to utilize heat sources having a higher thermal energy volumetric density than the existing flight-qualified General-Purpose Heat Source (GPHS). A Compact Heat Source (CPHS)has been conceptualized in which the graphite impact shells(GIS) of the existing GPHS are rearranged in a hexagonal aeroshell containing seven GIS per module, as opposed to the standard two per module; offering a thermal energy density of 0.57 W/cm3versus 0.29 W/cm3 offered by the GPHS simply from the repackaging of Technology Readiness Level (TRL)9 subassemblies. Preliminary thermal modeling of the CPHS integrated into a notional radioisotope thermoelectric generator(RTG) structure further suggests that centerline temperatures are well within allowable limits during nominal operation. Given the need for the CPHS for a subset of missions, it is worth exploring the applicability of the CPHS for more general RTG purposes. We discuss herein how the CPHS may be implemented with either heritage or in-development thermoelectric converter technologies into a Next-Generation RTG concept. Due to a higher energy density, the legacy heat rejection fin arrangement must be modified to permit a sufficiently low cold-side temperature. Preliminary finite element analysis suggests fin-root temperatures can be kept as low as 520 K while allowing the generator to fit within the usable dimensions of currently available United States Department of Energy shipping containers. Such temperatures would certainly be compatible with the use of high temperature thermoelectric converter technologies.. A prime candidate is the heritage silicon-germanium (SiGe) unicouple, whose design could be adapted by approximately halving the leg-length, but without changes in hot and cold junction interfaces, which are features critical to the proven performance and reliability of these devices. The estimated Beginning of Life power for a SiGe-based CPHS-RTG using 12 CPHS for a thermal inventory of 10.5 kW is greater than 600 W under deep space operating conditions. Using higher performance segmented couples currently in development that are based on skutterudite,La3−xTe4and 14-1-11 Zintl thermoelectric materials in lieu of the SiGe unicouples would increase the power level to more than1 kW. The high specific power (We/kg) attribute of CPHS-RTGs found in this study could potentially enable Radioisotope Electric Propulsion (REP) mission concepts. Past NASA REP mission concept studies identified specific power needs in excess of 6to 8 We/kg. Based on a GPHS-RTG-like system configuration, we show that at fin root temperatures between 530 K and 570K (deep space environment), specific powers exceeding 10 We/kg are achievable using high performance segmented thermoelectric converters. The compact sizing and power density of the CPHS-RTG would constitute a significant step upgrade in specific power when compared to heritage GPHS-RTG (approximately5.1 We/kg) and off-the-shelf Multi-Mission RTG (approximately 2.6 We/kg).

Nesmith, Bill J.↗

NASA NTRS1973

Computer programs for predicting supersonic and hypersonic interference flow fields and heating

This report describes computer codes which calculate two-dimensional shock interference patterns. These codes compute the six types of interference flows as defined by Edney (Aeronaut. Res. Inst. of Sweden FAA Rep. 115). Results include properties of the inviscid flow field and the inviscid-viscous interaction at the surface along with peak pressure and peak heating at the impingement point.

Morris, D. J.↗

NASA NTRS1972

Energy spectra in relativistic electron precipitation events.

Two events in August 1967, categorized as relativistic electron precipitation (REP) events by their effect on VHF transmissions propagated via the forward-scatter mode, have been examined with regard to the energy spectra of trapped and precipitated electrons. These two substorm-associated events August 11 and August 25 differ with respect to the relativistic, trapped electron population at synchronous altitude; in the August 25 event there was a nonadiabatic enhancement of relativistic (greater than 400 keV) electrons, while in the August 11 event no relativistic electrons were produced. In both events electron spectra deduced from bremsstrahlung measurements (made on a field line close to that of the satellite) had approximately the same e-folding energies as the trapped electron enhancements. However, the spectrum of electrons in the August 25 event was significantly harder than the spectrum in the event of August 11.

Rosenberg, T. J.↗

NASA NTRS1981

Atmospheric nitrous oxide produced by solar protons and relativistic electrons

A mechanism by which solar proton (SP) events and relativistic electron precipitation (REP) events may lead to the production of stratospheric NO is described. The process comprises the production of N2O in the mesosphere, its downward migration, and conversion in the stratosphere to NO by the reaction N2O + O(D) yields 2NO. This process would amplify direct NO production by more than 10%.

Prasad, S. S.↗

NASA NTRS1981

Measurements of middle-atmosphere electric fields and associated electrical conductivities

A simple antenna for measuring the vertical electric field in the 'middle atmosphere' has been flown on a number of rocket-launched parachute-borne payloads. The data from the first nine such flights, launched under a variety of geophysical conditions, are presented, along with electrical conductivities measured simultaneously. The data include indications of layered peaks of several volts per meter in the mesospheric field at high and low latitudes in situations of relatively low conductivity. During an auroral 'REP' event the electric field reversed direction in the lower stratosphere, accompanied by a substantial enhancement in conductivity. The data generally do not confirm speculations based only on the extension of the thunderstorm circuit from below or the mapping of ionospheric and magnetospheric fields from above, but seem to require, in addition, internal generation processes in the middle atmosphere.

Hale, L. C.↗

NASA NTRS1983

DNA fusion product of phage P2 with plasmid pBR322 - A new phasmid

The chromosome of the temperate bacteriophage P2 and that of the plasmid pBR322 have been joined in vitro after treatment with restriction endonuclease EcoRI. The fusion product - a phasmid - can behave as a plasmid, as a phage and as a prophage. It can replicate its DNA under the control of either the specific replication mechanism of the parent phage in a polA mutant or that of the parent plasmid in a rep mutant. Several interesting interactions between the two replication modes are indicated. In particular, phage particles may be produced even when the phage mode of DNA replication is blocked, and this throws new light on the involvement of the early gene A in the regulation of late gene expression in phage P2.

Nicoletti, M.↗

NASA NTRS1991

Precipitating relativistic electrons - Their long-term effect on stratospheric odd nitrogen levels

Using electron count rate data at geostationary orbit, daily energy spectra, extending from 30 keV to 15 MeV, have been developed for trapped relativistic electrons at 6.6 earth radii. These spectra have been used to model the flux of these electrons into the atmosphere at 120 km. Energy deposition calculations permit daily sources of HO(x) and NO(y) to be calculated at auroral and subauroral latitudes due to relativistic electron precipitation (REP) for the period June 13, 1979, through June 4, 1988. Both short-term and long-term source variations are quite large over the period considered. The results suggest that a significant contribution to the anomalously large and unexplained global O3 declines between 1979 and 1985 has been made by the catalytic destruction of O3 by odd nitrogen in the lower stratosphere at mid to high latitudes. The results also provide evidence for a clear and strong linkage between solar variability, the state of the magnetosphere, and the chemical climatological state of the middle and lower atmosphere.

Callis, Linwood B.↗

NASA NTRS1958

Heat-Transfer Measurements in Free Flight at Mach Numbers up to 14.6 on a Flat-Faced Conical Nose with a Total Angle of 29 Degrees

Skin-temperature measurements have been made at several locations on a flat-faced cone-cylinder nose which was flight tested on a fivestage rocket-propeller model to a Mach number of 14.64 and a free-stream Reynolds number of 2.0 x 10(exp 6), based on flat-face diameter, at an altitude of 66,300 feet. The copper nose had a 29 deg total-angle conical section which was 1.6 flat-face diameters long. The aerodynamic-heating rates determined from the temperature measurements reached 1,440 Btu/( sec) (sq ft) on the flat face. The heating rates near the center of the flat face agreed well at Mach numbers up to 13.6 with those obtained by a theory for laminar stagnation-point heating in equilibrium dissociated air (Avco Res. Rep. 1). At Mach numbers above 13.6, the heating rates at locations near the center of the flat face became progressively lower than stagnation-point theory and. were 29 percent lower at Mach number 14.6 at the end. of the test. The reason for this behavior of the heating on the central part of the flat face was not determined. Excluding the relatively low heating rates that occurred on the central part of the nose at the highest Mach numbers, the distribution of experimental heating along the innermost 0.79 of the flat-face radius, expressed as a percentage of stagnation-point heating, was in fair agreement with the distribution predicted by laminar theory. At a location of 0.71 radii from the stagnation point, the experimental heating was very near 130 percent of the theoretical stagnation-point rate at Mach numbers from 11 to 14.5. The experimental beating rates on the conical section of the nose were in good agreement with laminar-cone theory using the assumption of theoretical sharp-cone static pressure on the conical section.

Rumsey, Charles B↗

NASA NTRS1951

Calculation of the lateral control of swept and unswept flexible wings of arbitrary stiffness

A method similar to that of NACA rep. 1000 is presented for calculating the effectiveness and the reversal speed of lateral-control devices on swept and unswept wings of arbitrary stiffness. Provision is made for using either stiffness curves and root-rotation constants or structural influence coefficients in the analysis. Computing forms and an illustrative example are included to facilitate calculations by means of the method. The effectiveness of conventional aileron configurations and the margin against aileron reversal are shown to be relatively low for swept wings at all speeds and for all wing plan forms at supersonic speeds.

Diederich, Franklin W↗

NASA NTRS1952

Method for calculating lift distributions for unswept wings with flaps or ailerons by use of nonlinear section lift data

A method is presented which allows the use of nonlinear section lift data in the calculation of the spanwise lift distribution of unswept wings with flaps or ailerons. This method is based upon lifting line theory and is an extension to the method described in NACA rep. 865. The mathematical treatment of the discontinuity in absolute angle of attack at the end of the flap or aileron involves the use of a correction factor which accounts for the inability of a limited trigonometric series to represent adequately the spanwise lift distribution. A treatment of the apparent discontinuity in maximum section lift coefficient is also described. Simplified computing forms containing detailed examples are given for both symmetrical and asymmetrical lift distributions. A few comparisons of calculated characteristics with those obtained experimentally are also presented.

Sivells, James C↗