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At least 991 records · Page 55

The Predicted Growth of the Low Earth Orbit Space Debris Environment: An Assessment of Future Risk for Spacecraft

Space debris is a worldwide-recognized issue concerning the safety of commercial, military, and exploration spacecraft. The space debris environment includes both naturally occuring meteoroids and objects in Earth orbit that are generated by human activity, termed orbital debris. Space agencies around the world are addressing the dangers of debris collisions to both crewed and robotic spacecraft. In the United States, the Orbital Debris Program Office at the NASA Johnson Space Center leads the effort to categorize debris, predict its growth, and formulate mitigation policy for the environment from low Earth orbit (LEO) through geosynchronous orbit (GEO). This paper presents recent results derived from the NASA long-term debris environment model, LEGEND. It includes the revised NASA sodium potassium droplet model, newly corrected for a factor of two over-estimation of the droplet population. The study indicates a LEO environment that is already highly collisionally active among orbital debris larger than 1 cm in size. Most of the modeled collision events are non-catastrophic (i.e., They lead to a cratering of the target, but no large scale fragmentation.). But they are potentially mission-ending, and take place between impactors smaller than 10 cm and targets larger than 10 cm. Given the small size of the impactor these events would likely be undetectable by present-day measurement means. The activity continues into the future as would be expected. Impact rates of about four per year are predicted by the current study within the next 30 years, with the majority of targets being abandoned intacts (spent upper stages and spacecraft). Still, operational spacecraft do show a small collisional activity, one that increases over time as the small fragment population increases.

Krisko, Paula H.↗

Unstable Resonant Orbits near Earth and Their Applications in Planetary Missions

This paper explores the uses of planar, simple-periodic symmetrical families of orbits in mission designs in the Earth-Moon system. This classification is defined as the planar periodic orbits that pierce the x-axis in the rotating frame exactly twice per orbit where each piercing is orthogonal to the x-axis. A continuation method has been used to explore several families of this class of orbit in the Earth-Moon restricted three-body system. The invariant manifolds of the unstable orbits in each of these families are then produced and several mission designs are discussed that take advantage of these manifolds. Focus is given to mission designs that implement resonant orbits that periodically fly by the moon.

invariant manifolds↗

Coronas-F Orbit Monitoring and Re-Entry Prediction

Russian scientific satellite CORONAS-F was launched on July, 31, 2001. The object was inserted in near-circular orbit with the inclination 82.5deg and a mean altitude approx. 520 km. Due to the upper atmosphere drag CORONAS-F was permanently descended and as a result on December, 6, 2005 it has finished the earth-orbital flight, having lifetime in space approx. 4.5 years. The satellite structural features and its flight attitude control led to the significant variations of its ballistic coefficient during the flight. It was a cause of some specific difficulties in the fulfillment of the ballistic and navigation support of this space vehicle flight. Besides the main mission objective CORONAS-F also has been selected by the Inter-Agency Space Debris Coordination Committee (IADC) as a target object for the next regular international re-entry test campaign on a program of surveillance and re-entry prediction for the hazard space objects within their de-orbiting phases. Spacecraft (S/C) CORONAS-F kept its working state right up to the end of the flight - down to the atmosphere entry. This fact enabled to realization of the additional research experiments, concerning with an estimation of the atmospheric density within the low earth orbits (LEO) of the artificial satellites, and made possible to continue track the S/C during final phase of its flight by means of Russian regular command & tracking system, used for it control. Thus there appeared a unique possibility of using for tracking S/C at its de-orbiting phase not only passive radar facilities, belonging to the space surveillance systems and traditionally used for support of the IADC re-entry test campaigns, but also more precise active trajectory radio-tracking facilities from the ground control complex (GCC) applied for this object. Under the corresponding decision of the Russian side such capability of additional high-precise tracking control of the CORONAS-F flight in this period of time has been implemented. The organizing of the CORONAS-F ballistic and navigational support (BNS) and solving its main tasks (such as S/C orbit determination (OD) and its motion prediction and connected with them) both for regular mission stage and for additional flight program were realized by the group of specialists from the Mission Control Center (MCC). MCC was also assigned as a principal organization from the Russian side for participation in the 7th IADC re-entry test campaign on CORONAS-F. The CORONAS-F flight features and space environments circumstances during its flight as well as a methodology and technology of spacecraft ballistic and navigational support are given below. The BNS results for different phases of S/C flight, including the results of its re-entry predictions, obtained during the realization of the 7th IADC test campaign are submitted. The accuracy of space vehicle re-entry prediction and its dependence on various factors are analyzed in more details.

Ivanov, N. M.↗

Precise Orbit Determination for ALOS

The Advanced Land Observing Satellite (ALOS) has been developed to contribute to the fields of mapping, precise regional land coverage observation, disaster monitoring, and resource surveying. Because the mounted sensors need high geometrical accuracy, precise orbit determination for ALOS is essential for satisfying the mission objectives. So ALOS mounts a GPS receiver and a Laser Reflector (LR) for Satellite Laser Ranging (SLR). This paper deals with the precise orbit determination experiments for ALOS using Global and High Accuracy Trajectory determination System (GUTS) and the evaluation of the orbit determination accuracy by SLR data. The results show that, even though the GPS receiver loses lock of GPS signals more frequently than expected, GPS-based orbit is consistent with SLR-based orbit. And considering the 1 sigma error, orbit determination accuracy of a few decimeters (peak-to-peak) was achieved.

Nakamura, Ryo↗

Mars Reconnaissance Orbiter Aerobraking Daily Operations and Collision Avoidance

The Mars Reconnaissance Orbiter reached Mars on March 10, 2006 and performed a Mars orbit insertion maneuver of 1 km/s to enter into a large elliptical orbit. Three weeks later, aerobraking operations began and lasted about five months. Aerobraking utilized the atmospheric drag to reduce the large elliptical orbit into a smaller, near circular orbit. At the time of MRO aerobraking, there were three other operational spacecraft orbiting Mars and the navigation team had to minimize the possibility of a collision. This paper describes the daily operations of the MRO navigation team during this time as well as the collision avoidance strategy development and implementation.

Long, Stacia M.↗

Analysis of Envisat Orbit Maintenance Strategies to Improve/Increase Envisat ASAR Interferometry Opportunities

The biggest and most advanced Earth Observation Satellite in-orbit, developed by the European Space Agency (ESA) and its member states, is Envisat. It was launched on March 1, 2002 by an Ariane V from French Guyana and holds a total of 10 multi-disciplinary Earth observation instruments, among which an Advanced Synthetic Aperture Radar (ASAR). The ASAR user community requested the Flight Dynamics division of the European Space Operations Centre (ESOC) to investigate how the orbit control maintenance strategy for Envisat could be changed to optimize ASAR interferometry opportunities overall and in addition support the International Polar Year 2007/2008 initiative. The Polar Regions play a pivotal role in understanding our planet and our impact on it as they are recognized as sensitive barometers of environmental change. One of the main themes of the International Polar Year 2007/2008 is therefore the study of Earth s changing ice and snow, and its impact on our planet and our lives. Naturally, ESA would like to support this very important initiative. This paper presents the investigations that have been conducted to support these requests in the best possible way. It discusses the orbit maintenance strategy that has been in place since its launch, ensuring the actual orbit to be within 1 km of a so-called reference orbit, and presents the new orbit maintenance strategy that is aimed at improving/increasing the opportunities for Envisat ASAR interferometry, while preserving the fuel on board the spacecraft. The hydrazine on-board Envisat happens to be a precious resource as only approximately 300 kg of it was available at launch, like ERS-2. The difference being however that the mass of Envisat is approximately 3.2 times that of ERS-2.

Kuijper, D.↗

Improving the Near-Earth Micrometeoroid and Orbital Debris Environment Definition with LADC

The Large Area Debris Collector (LADC) is a 10 m(sup 2) aerogel and acoustic sensor system designed to characterize and collect submillimeter micrometeoroids and orbital debris on the International Space Station (ISS). The project is led by the U.S. Naval Research Laboratory (NRL) with major collaboration by the NASA Orbital Debris Program Office at Johnson Space Center. The U.S. Department of Defense Space Test Program (STP) is responsible for the integration, deployment, and retrieval of the system. The deployment is scheduled for August 2007 with an orbital collection period of one to two years. The combined area time product of LADC will provide a much needed orbital debris population update in the size regime that is important to the safety community - 100 mm and larger. Another key element for LADC is the source identification of the collected samples. Impact features such as track length and track volume can be used to estimate the impact speed and direction of any selected residual embedded in aerogel. Acoustic sensors can provide impact timing and impact location information. The combined dynamical signatures make it possible to reconstruct the orbits of some of the collected samples and lead to their source identification. Compositional analysis on the residuals can also separate debris from meteoroids and provide additional population breakdown for orbital debris (e.g., Al, paint, steel, Al2O3). To maximize the science return and minimize potential contamination from other ISS modules, a careful selection of the location and orientation of LADC on the ISS is needed. Key issues and engineering constraints encountered during mission preparation, and the expected science return based on the mission configuration, are summarized in this paper.

Liou, J.-C.↗

An Overview of the Mars Reconnaissance Orbiter (MRO) Science Mission

The Mars Reconnaissance Orbiter (MRO) is the latest addition to the suite of missions on or orbiting Mars as part of the NASA Mars Exploration Program. Launched on 12 August 2005, the orbiter successfully entered Mars orbit on 10 March 2006 and finished aerobraking on 30 August 2006. Now in its near-polar, near-circular, low-altitude (approximately 300 km), 3 p.m. orbit, the spacecraft is operating its payload of six scientific instruments throughout a one-Mars-year Primary Science Phase (PSP) of global mapping, regional survey, and targeted observations. Eight scientific investigations were chosen for MRO, two of which use either the spacecraft accelerometers or tracking of the spacecraft telecom signal to acquire data needed for analysis. Six instruments, including three imaging systems, a visible-near infrared spectrometer, a shallow-probing subsurface radar, and a thermal-infrared profiler, were selected to complement and extend the capabilities of current working spacecraft at Mars. Whether observing the atmosphere, surface, or subsurface, the MRO instruments are designed to achieve significantly higher resolution while maintaining coverage comparable to the current best observations. The requirements to return higher-resolution data, to target routinely from a low-altitude orbit, and to operate a complex suite of instruments were major challenges successfully met in the design and build of the spacecraft, as well as by the mission design. Calibration activities during the seven-month cruise to Mars and limited payload operations during a three-day checkout prior to the start of aerobraking demonstrated, where possible, that the spacecraft and payload still had the functions critical to the science mission. Two critical events, the deployment of the SHARAD radar antenna and the opening of the CRISM telescope cover, were successfully accomplished in September 2006. Normal data collection began 7 November 2006 after solar conjunction. As part of its science mission, MRO will also aid identification and characterization of the most promising sites for future landed missions, both in terms of safety and in terms of the scientific potential for future discovery. Ultimately, MRO data will advance our understanding of how Mars has evolved and by which processes that change occurs, all within a framework of identifying the presence, extent, and role of water in shaping the planet s climate over time.

astronomical instruments↗

MODIS Solar Diffuser On-orbit Performance

MODIS is a key instrument for the NASA Earth Observing System (EOS), currently operated on both the Terra and Aqua missions. Each MODIS instrument has 20 reflective solar bands (RSBs) and 16 thermal emissive bands (TEBs). MODIS RSB on-orbit calibration is reflectance based using an on-board solar diffuser (SD). The SD bi-directional reflectance factors (BRFs) were characterized pre-launch using reference diffuser samples, which are traceable to NIST reflectance standards. The SD BRF on-orbit degradation (or change) is tracked by another onboard device, called the solar diffuser stability monitor (SDSM). The SDSM is operated during each scheduled SD calibration event, making alternate observations of direct sunlight and the diffusely reflected sunlight from the SD. The time series of the ratios of SDSM's SD view to its Sun view provide SD degradation information. This paper presents and compares the Terra and Aqua MODIS SD on-orbit performance. Results show that the SD on-orbit degradation depends on the amount of solar exposure of the SD plate. In addition, it is strongly wavelengthdependent, with a larger degradation rate at shorter wavelengths. For Terra MODIS, an SD door anomaly occurred in May 2003 that led to a decision to fix the door permanently at an "open" position. Since then, the SD degradation rate has significantly increased due to more frequent solar exposure. As expected, the SD on-orbit performance directly impacts the RSB calibration performance. The lessons learned from MODIS on-orbit calibration will provide useful insights into the development and operation of future SD calibration systems.

Xiong, Xiaoxiong↗

Lunar Frozen Orbits

Based upon the derivation of the equations of frozen orbits about the Earth, an analytical formulation is presented for lunar frozen orbits (LFO) in a wide altitude range. Global examination is made of combinations of inclination, semimajor axis, and eccentricity to zero out the mean eccentricity and argument of periapsis drift. Included in this development are the effects of both the lunar gravity potential and third body perturbations. Unlike the Earth frozen orbits, with the major perturbation due to the uniform 52 through J5 gravity terms, lunar frozen orbits are restricted by the distribution of the lunar mascons. With accurate modeling, they exhibit a predictive pattern that drives the overall mission design. In addition to a derivation for analytical expressions, a fill1 numerical simulation is used for verification and examination of secular drift from all third body effects. This presentation addresses a selection of usable lunar orbits that reduce or eliminate the need for stationkeeping while maintaining usable science or communication/navigation orbit parameters.

Folta, David↗

MODIS Pre-launch and On-orbit Calibration

Two nearly identical MODIS instruments are currently operated on-orbit: one on-board the EOS Terra spacecraft launched in December 1999 and the other on-board the Aqua spacecraft launched in May 2002. Both sensors went through extensive pre-launch calibration and characterization activities that had provided many critically important parameters and sensor characteristics in support of their on-orbit operation and calibration. On-orbit each MODIS instrument is calibrated and characterized via a set of on-board calibrators (OBC) that include a solar diffuser (SD), a solar diffuser stability monitor (SDSM), a blackbody (BB), and a spectroradiometric calibration assembly (SRCA). This paper provides an overview of MODIS calibration and characterization methodologies and measurements performed, pre-launch and on-orbit, for both the reflective solar bands (RSB) and thermal emissive bands (TEB). It discusses issues on the calibration transfer from ground to on-board and from pre-launch to on-orbit, and illustrates the calibration consistency between Terra and Aqua MODIS. Examples in three key areas, radiometric, spatial, and spectral, are presented. Also addressed in the paper are the challenges and lessons learned during MODIS pre-launch and on-orbit calibration and performance.

Xiong, X.↗

Stochastic Analysis of Orbital Lifetimes of Spacecraft

A document discusses (1) a Monte-Carlo-based methodology for probabilistic prediction and analysis of orbital lifetimes of spacecraft and (2) Orbital Lifetime Monte Carlo (OLMC)--a Fortran computer program, consisting of a previously developed long-term orbit-propagator integrated with a Monte Carlo engine. OLMC enables modeling of variances of key physical parameters that affect orbital lifetimes through the use of probability distributions. These parameters include altitude, speed, and flight-path angle at insertion into orbit; solar flux; and launch delays. The products of OLMC are predicted lifetimes (durations above specified minimum altitudes) for the number of user-specified cases. Histograms generated from such predictions can be used to determine the probabilities that spacecraft will satisfy lifetime requirements. The document discusses uncertainties that affect modeling of orbital lifetimes. Issues of repeatability, smoothness of distributions, and code run time are considered for the purpose of establishing values of code-specific parameters and number of Monte Carlo runs. Results from test cases are interpreted as demonstrating that solar-flux predictions are primary sources of variations in predicted lifetimes. Therefore, it is concluded, multiple sets of predictions should be utilized to fully characterize the lifetime range of a spacecraft.

Sasamoto, Washito↗

Orbital Express Advanced Video Guidance Sensor

In May 2007 the first US fully autonomous rendezvous and capture was successfully performed by DARPA's Orbital Express (OE) mission. Since then, the Boeing ASTRO spacecraft and the Ball Aerospace NEXTSat have performed multiple rendezvous and docking maneuvers to demonstrate the technologies needed for satellite servicing. MSFC's Advanced Video Guidance Sensor (AVGS) is a primary near-field proximity operations sensor integrated into ASTRO's Autonomous Rendezvous and Capture Sensor System (ARCSS), which provides relative state knowledge to the ASTRO GN&C system. This paper provides an overview of the AVGS sensor flying on Orbital Express, and a summary of the ground testing and on-orbit performance of the AVGS for OE. The AVGS is a laser-based system that is capable of providing range and bearing at midrange distances and full six degree-of-freedom (6DOF) knowledge at near fields. The sensor fires lasers at two different frequencies to illuminate the Long Range Targets (LRTs) and the Short Range Targets (SRTs) on NEXTSat. Subtraction of one image from the other image removes extraneous light sources and reflections from anything other than the corner cubes on the LRTs and SRTs. This feature has played a significant role for Orbital Express in poor lighting conditions. The very bright spots that remain in the subtracted image are processed by the target recognition algorithms and the inverse-perspective algorithms, to provide 3DOF or 6DOF relative state information. Although Orbital Express has configured the ASTRO ARCSS system to only use AVGS at ranges of 120 m or less, some OE scenarios have provided opportunities for AVGS to acquire and track NEXTSat at greater distances. Orbital Express scenarios to date that have utilized AVGS include a berthing operation performed by the ASTRO robotic arm, sensor checkout maneuvers performed by the ASTRO robotic arm, 10-m unmated operations, 30-m unmated operations, and Scenario 3-1 anomaly recovery. The AVGS performed very well during the pre-unmated operations, effectively tracking beyond its 10-degree Pitch and Yaw limit-specifications, and did not require I-LOAD adjustments before unmated operations. AVGS provided excellent performance in the 10-m unmated operations, effectively tracking and maintaining lock for the duration of this scenario, and showing good agreement between the short and long range targets. During the 30-m unmated operations, the AVGS continuously tracked the SRT to 31.6 m, exceeding expectations, and continuously tracked the LRT from 8.8 m out to 31.6 m, with good agreement between these two target solutions. After this scenario was aborted at a 10-m separation during remate operations, the AVGS tracked the LRT out 54.3 m, until the relative attitude between the vehicles was too large. The vehicles remained apart for eight days, at ranges from 1 km to 6 km. During the approach to remate in this recovery operation, the AVGS began tracking the LRT at 150 m, well beyond the OE planned limits for AVGS ranges, and functioned as the primary sensor for the autonomous rendezvous and docking.

Howard, Ricky↗

A Preliminary Formation Flying Orbit Dynamics Analysis for Leonardo-BRDF

Leonardo-BRDF is a new NASA mission concept proposed to allow the investigation of radiative transfer and its effect on the Earth's climate and atmospheric phenomenon. Enabled by the recent developments in small-satellite and formation flying technology, the mission is envisioned to be composed of an array of spacecraft in carefully designed orbits. The different perspectives provided by a distributed array of spacecraft offer a unique advantage to study the Earth's albedo. This paper presents the flight dynamics analysis performed in the context of the Leonardo-BRDF science requirements. First, the albedo integral is investigated and the effect of viewing geometry on science return is studied. The method used in this paper, based on Gauss quadrature, provides the optimal formation geometry to ensure that the value of the integral is accurately approximated. An orbit design approach is presented to achieve specific relative orbit geometries while simultaneously satisfying orbit dynamics constraints to reduce formation-keeping fuel expenditure. The relative geometry afforded by the design is discussed in terms of mission requirements. An optimal Lambert initialization scheme is presented with the required DeltaV to distribute all spacecraft from a common parking orbit into their appropriate orbits in the formation. Finally, formation-keeping strategies are developed and the associated DeltaV's are calculated to maintain the formation in the presence of perturbations.

Hughes, Steven P.↗

Orbital Debris Quarterly News, Vol. 13, No. 2

Topics include: debris clouds left by satellite collision; debris flyby near the International Space Station; and break-up of an ullage motor from a Russian Proton launch vehicle. Findings from the analysis of the STS-126 Shuttle Endeavour window impact damage are provided. Abstracts from the NASA Orbital Debris program office are presented and address a variety of topics including: Reflectance Spectra Comparison of Orbital Debris, Intact Spacecraft, and Intact Rocket Bodies in the GEO Regime; Shape Distribution of Fragments From Microsatellite Impact Tests; Micrometeoroid and Orbital Debris Threat Mitigation Techniques for the Space Shuttle Orbiter; Space Debris Environment Remediation Concepts; and, In Situ Measurement Activities at the NASA Orbital Debris Program Office. Additionally, a Meeting Report is provided for the 12 meeting of the NASA/DoD Orbital Debris Working Group.

Liou, J.-C.↗

Forward Technology Solar Cell Experiment First On-Orbit Data

This paper presents first on orbit measured data from the Forward Technology Solar Cell Experiment (FTSCE). FTSCE is a space experiment housed within the 5th Materials on the International Space Station Experiment (MISSE-5). MISSE-5 was launched aboard the Shuttle return to flight mission (STS-114) on July 26, 2005 and deployed on the exterior of the International Space Station (ISS). The experiment will remain in orbit for nominally one year, after which it will be returned to Earth for post-flight testing and analysis. While on orbit, the experiment is designed to measure a 36 point current vs. voltage (IV) curve on each of the experimental solar cells, and the data is continuously telemetered to Earth. The experiment also measures the solar cell temperature and the orientation of the solar cells to the sun. A range of solar cell technologies are included in the experiment including state-of-the-art triple junction InGaP/GaAs/Ge solar cells from several vendors, thin film amorphous Si and CuIn(Ga)Se2 cells, and next-generation technologies like single-junction GaAs cells grown on Si wafers and metamorphic InGaP/InGaAs/Ge triple-junction cells. In addition to FTSCE, MISSE-5 also contains a Thin-Film Materials experiment. This is a passive experiment that will provide data on the effect of the space environment on more than 200 different materials. FTSCE was initially conceived in response to various on-orbit and ground test anomalies associated with space power systems. The Department of Defense (DoD) required a method of rapidly obtaining on orbit validation data for new space solar cell technologies, and NRL was tasked to devise an experiment to meet this requirement. Rapid access to space was provided by the MISSE Program which is a NASA Langley Research Center program. MISSE-5 is a completely self-contained experiment system with its own power generation and storage system and communications system. The communications system, referred to as PCSat, transmits and receives in the Amateur Radio band providing a node on the Amateur Radio Satellite Service. This paper presents an overview of the various aspects of MISSE-5 and a sample of the first measured on orbit data.

Walters, R. J.↗

Spiral Orbit Tribometer

The spiral orbit tribometer (SOT) bridges the gap between full-scale life testing and typically unrealistic accelerated life testing of ball-bearing lubricants in conjunction with bearing ball and race materials. The SOT operates under realistic conditions and quickly produces results, thereby providing information that can guide the selection of lubricant, ball, and race materials early in a design process. The SOT is based upon a simplified, retainerless thrust bearing comprising one ball between flat races (see figure). The SOT measures lubricant consumption and degradation rates and friction coefficients in boundary lubricated rolling and pivoting contacts. The ball is pressed between the lower and upper races with a controlled force and the lower plate is rotated. The combination of load and rotation causes the ball to move in a nearly circular orbit that is, more precisely, an opening spiral. The spiral s pitch is directly related to the friction coefficient. At the end of the orbit, the ball contacts the guide plate, restoring the orbit to its original radius. The orbit is repeatable throughout the entire test. A force transducer, mounted in-line with the guide plate, measures the force between the ball and the guide plate, which directly relates to the friction coefficient. The SOT, shown in the figure, can operate in under ultra-high vacuum (10(exp -9) Torr) or in a variety of gases at atmospheric pressure. The load force can be adjusted between 45 and 450 N. By varying the load force and ball diameter, mean Hertzian stresses between 0.5 and 5.0 GPa can be obtained. The ball s orbital speed range is between 1 and 100 rpm.

Pepper, Stephen V.↗

Turbulent Wing-Leading-Edge Correlation Assessment for the Shuttle Orbiter

This study was conducted in support of the Orbiter damage assessment activity that takes place for each Shuttle mission since STS-107 (STS - Space Transportation System). As part of the damage assessment activity, the state of boundary layer (laminar or turbulent) during reentry needs to be estimated in order to define the aerothermal environment on the Orbiter. Premature turbulence on the wing leading edge (WLE) is possible if a surface irregularity promotes early transition and the resulting turbulent wedge flow contaminates the WLE flow. The objective of this analysis is to develop a criterion to determine if and when the flow along the WLE experiences turbulent heating given an incoming turbulent boundary layer that contaminates the attachment line. The data to be analyzed were all obtained as part of the MH-13 Space Shuttle Orbiter Aerothermodynamic Test conducted on a 1.8%-scale Orbiter model at Calspan/University of Buffalo Research Center in the Large Energy National Shock Tunnels facility. A rational framework was used to develop a means to assess the state of the WLE flow on the Orbiter during reentry given a contaminated attachment-line flow. Evidence of turbulent flow on the WLE has been recently documented for a few STS missions during the Orbiter s flight history, albeit late in the reentry trajectory. The criterion developed herein will be compared to these flight results.

King, Rudolph A.↗