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Decision Aid for Conjunction Risk Mitigation by Differential Drag

In the previous five years, the rate of conjunctions that the NASA Conjunction Assessment Risk Analysis (CARA) team processed and analyzed has more than tripled. (NASA CARA, 2024) New missions in the early development phases are now required to plan for dealing with conjunctions under the present space environment, and also projecting forward into a future likely with even further increased utilization of the space environment. Some missions are investigating the possibility of using differential drag to remediate conjunctions without expending limited fuel or for missions without propulsive capabilities. The NASA CARA team studied the historical record of conjunctions to evaluate the circumstances under which differential drag may be successfully applied and have developed a series of tables to use as a decision aid for missions considering differential drag. Currently, if a CARA-protected mission with maneuvering capabilities is predicted to have a conjunction with probability of collision (Pc) greater than 7E-5 (the default value of the ‘yellow threshold’, which may have some other value agreed by CARA and the mission during the Orbital Collison Avoidance Planning (OCAP) process), CARA will use its Maneuver Trade Space (MTS) tool to evaluate and recommend options for the timing and magnitude of a risk mitigation maneuver (RMM), based on the mission’s capabilities. If the conjunction’s Pc is greater than 1E-4, the ‘red threshold’, then an RMM must be executed per NASA Procedural Requirements (NPR) 8079.1 (NASA, 2023), although missions may execute an RMM even if the Pc is lower. The magnitude of the maneuver is typically a few cm/s, and CARA estimates how many will be required for the mission’s nominal lifetime – typically a few per year – during the OCAP process, to inform the mission’s delta-V requirement. For traditional satellites, this is usually smaller than other requirements for orbit insertion, maintenance, and disposal, but for CubeSats or other small satellite missions, a propulsion system may not provide much more than a few cm/s of delta-V or may not fit at all within the available budget of money, time, size, weight, and/or power (SWaP). Conversely, CubeSats often have deployable solar panels, which offer the capacity to have much higher areas facing some directions than others. Such a mission can instead use ‘differential drag’ to remediate a conjunction -- in other words, change its drag area (usually increasing) to deviate from the predicted collision course. This is how Planet’s Dove spacecraft maintain their formations and remediate conjunction risks without having on-board propulsion (Foster, et al., 2017) (Griffith, et al., 2021). CARA has been developing improvements to MTS to support differential-drag for NASA's missions -- where it is effective. CARA records all conjunctions of their protected payloads, with historical records starting in 2005 (with significant conjunction events starting to occur on or after 2013). From this record, approximately 7,300 had a Pc greater than 1E-4 at 3 days prior to the time of closest approach, the time analyzed for differential drag efficacy. Of those, approximately 4,300 had fully-defined covariance matrices stored for both the primary and secondary objects; this set of conjunctions is the basis for the analysis of this work. CARA’s MTS tool was used to propagate the primary satellite forward from that decision point with varying degrees of increase to ballistic coefficient (BC). Because these conjunctions came from multiple missions, the nondimensional ‘delta-BC’ factor was used to quantify and normalize the increase in ballistic coefficient, defined as follows: Delta-BC = BC_new / BC_old - 1 Positive delta-BC factors represent an increase in drag compared to the nominal attitude, while negative delta-BC factors (to a minimum of -1) represent a decrease in drag. At the conclusion of the differential-drag ‘maneuver’, the Pc was recalculated to evaluate whether or not the conjunction was mitigated (Pc < 3E-6). These results were then binned and sorted along several axes, including altitude, amount of delta-BC, and (pre-maneuver) rate of energy dissipation (EDR), to identify underlying patterns. The altitude plot is shown in Figure 1. To validate this analysis, we consulted the record of a NASA mission which uses differential drag to maintain its orbit and remediate conjunction risk. CARA’s empirical record of the mission’s orbit history suggests it achieves a delta-BC of 2.2. Of the twenty-one RMM plans that were submitted by this mission, eighteen were matched with conjunctions in the historical record; of those, twelve were successfully remediated (final measured Pc < 3E-6), and six were not. This is consistent with the expected efficacy for missions orbiting at that altitude. We are presently simulating this mission’s RMMs with MTS; this work is ongoing, but so far, the MTS results are qualitatively in agreement with the empirical results -- correctly predicting that a maneuver would or would not remediate a conjunction, if not exactly matching the final post-remediation Pc value. We found that differential drag was most successful for satellites with perigees below 560 km, and which could adopt an average delta-BC of 2 or greater (that is, increasing their ballistic coefficient by a factor of 3). However, this is a difficult threshold for a mission to clear; very few spacecraft are capable of adopting a high-drag configuration for 72 hours continuously. Planet’s Dove spacecraft use differential drag to remediate conjunctions (Griffith, et al., 2021), and they have a maximum delta-BC factor of 9, but in practice (with mission and charging constraints) they achieve a time-averaged delta-BC that is closer to 2 (Foster, et al., 2017). A mission’s differential drag utility strongly depends on the operational constraints that has the capacity to limit the time-averaged delta-BC. A mission with a high maximum delta-BC of 5 or more can have an effective delta-BC of less than 1 due to operational constraints such as instrument and solar panel pointing, especially if this constraint results in holding an intermediate drag value for most of its orbit. CARA has developed tables that can be used as decision aids to advise missions-in-development about the best way to utilize their differential drag capabilities. For missions below 560 km with the operational flexibility to devote multiple days to holding a high-drag configuration (or a sufficiently high drag ratio to compensate for limitations on that time), they are -- more likely than not -- able to successfully remediate high-risk conjunctions. Conversely, missions that do not meet these exacting criteria -- most missions -- can instead be advised to use on-board propulsion systems to perform RMMs, or to turn their minimum-area face towards the approach vector, thereby reducing Pc at the moment of conjunction due to the decreased Hard-Body Radius (HBR), that is a strongly correlated variable in the Pc calculations. (NASA, 2023)

conjunction assessment↗
NASA NTRS2010

QBO Influence on Polar Stratospheric Variability in the GEOS Chemistry-Climate Model

The quasi-biennial oscillation modulates the strength of both the Arctic and Antarctic stratospheric vortices. Model and observational studies have found that the phase and characteristics of the quasi-biennial oscillation (QBO) contribute to the high degree of variability in the Arctic stratosphere in winter. While the Antarctic stratosphere is less variable, recent work has shown that Southern Hemisphere planetary wave driving increases in response to "warm pool" El Nino events that are coincident with the easterly phase of the QBO. These events hasten the breakup of the Antarctic polar vortex. The Goddard Earth Observing System (GEOS) chemistry-climate model (CCM) is now capable of generating a realistic QBO, due a new parameterization of gravity wave drag. In this presentation, we will use this new model capability to assess the influence of the QBO on polar stratospheric variability. Using simulations of the recent past, we will compare the modeled relationship between QBO phase and mid-winter vortex strength with the observed Holton-Tan relation, in both hemispheres. We will use simulations of the 21 St century to estimate future trends in the relationship between QBO phase and vortex strength. In addition, we will evaluate the combined influence of the QBO and El Nino/Southern Oscillation (ENSO) on the timing of the breakup of the polar stratospheric vortices in the GEOS CCM. We will compare the influence of these two natural phenomena with trends in the vortex breakup associated with ozone recovery and increasing greenhouse gas concentrations.

Hurwitz, M. M.↗
NASA NTRS2012

NASA's Gravitational - Wave Mission Concept Study

With the conclusion of the NASA/ESA partnership on the Laser Interferometer Space Antenna (LISA) Project, NASA initiated a study to explore mission concepts that will accomplish some or all of the LISA science objectives at lower cost. The Gravitational-Wave Mission Concept Study consisted of a public Request for Information (RFI), a Core Team of NASA engineers and scientists, a Community Science Team, a Science Task Force, and an open workshop. The RFI yielded were 12 mission concepts, 3 instrument concepts and 2 technologies. The responses ranged from concepts that eliminated the drag-free test mass of LISA to concepts that replace the test mass with an atom interferometer. The Core Team reviewed the noise budgets and sensitivity curves, the payload and spacecraft designs and requirements, orbits and trajectories and technical readiness and risk. The Science Task Force assessed the science performance by calculating the horizons. the detection rates and the accuracy of astrophysical parameter estimation for massive black hole mergers, stellar-mass compact objects inspiraling into central engines. and close compact binary systems. Three mission concepts have been studied by Team-X, JPL's concurrent design facility. to define a conceptual design evaluate kt,y performance parameters. assess risk and estimate cost and schedule. The Study results are summarized.

Stebbins, Robin↗
NASA NTRS1961

A Method for Longitudinal and Lateral Range Control for a High-Drag Low-Lift Vehicle Entering the Atmosphere of a Rotating Earth

A study has been made of a method for controlling the trajectory of a high-drag low-lift entry vehicle to a desired longitude and latitude on the surface of a rotating earth. By use of this control technique the vehicle can be guided to the desired point when the present position and heading of the vehicle are known and the desired longitude and latitude are specified. The present study makes use of a single reference trajectory and an estimate of the lift and side-force capabilities of the vehicle. This information is stored in a control-logic system and used with linear control equations to guide the vehicle to the desired destination. Results are presented of a number of trajectory studies which describe the operation of the control system and illustrate its ability to control the vehicle trajectory to the desired landing area.

Young, John W.↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗
NASA NTRS2020

Modeling Heatshield Erosion due to Dust Particle Impacts for Martian Entries

Heatshield design for spacecraft entering the atmosphere of Mars may be affected by the presence of atmospheric dust. Particle impacts with sufficient kinetic energy can cause spallation damage to the heatshield that must be estimated. The dust environment in terms of particle size distribution and number density can be inferred from ground-based or atmospheric observations at Mars. Using a Lagrangian approach, the particle trajectories through the shock layer can be computed using a set of coupled ordinary differential equations. The dust particles are small enough that non-continuum effects must be accounted for when computing the drag coefficient and heat transfer to the particle surface. Surface damage correlations for impact crater diameter and penetration depth are presented for fused-silica, AVCOAT, Shuttle tiles, cork, and Norcoat Liège. The cork and Norcoat Liège correlations are new and were developed in this study. The modeling equations presented in this paper are applied to compute the heatshield erosion due to dust particle impacts on the ExoMars Schiaparelli entry capsule during dust storm conditions.

Palmer, Grant↗
NASA NTRS2020

Modeling Heatshield Erosion Due to Dust Particle Impacts for Martian Entries

Heatshield design for spacecraft entering the atmosphere of Mars may be affected by the presence of atmospheric dust. Particle impacts with sufficient kinetic energy can cause spallation damage to the heatshield that must be estimated. The dust environment in terms of particle size distribution and number density can be inferred from ground-based or atmospheric observations at Mars. Using a Lagrangian approach, the particle trajectories through the shock layer can be computed using a set of coupled ordinary differential equations. The dust particles are small enough that non-continuum effects must be accounted for when computing the drag coefficient and heat transfer to the particle surface. Surface damage correlations for impact crater diameter and penetration depth are presented for fused-silica, AVCOAT, Shuttle tiles, cork, and Norcoat Liège. The cork and Norcoat Liège correlations are new and were developed in this study. The modeling equations presented in this paper are applied to compute the heatshield erosion due to dust particle impacts on the ExoMars Schiaparelli entry capsule during dust storm conditions.

Palmer, Grant↗
NASA NTRS1998

Global Warming Estimation from MSU

Microwave Sounding Unit (MSU) radiometer observations in Ch 2 (53.74 GHz) from sequential, sun-synchronous, polar-orbiting NOAA satellites contain small systematic errors. Some of these errors are time-dependent and some are time-independent. Small errors in Ch 2 data of successive satellites arise from calibration differences. Also, successive NOAA satellites tend to have different Local Equatorial Crossing Times (LECT), which introduce differences in Ch 2 data due to the diurnal cycle. These two sources of systematic error are largely time independent. However, because of atmospheric drag, there can be a drift in the LECT of a given satellite, which introduces time-dependent systematic errors. One of these errors is due to the progressive chance in the diurnal cycle and the other is due to associated chances in instrument heating by the sun. In order to infer global temperature trend from the these MSU data, we have eliminated explicitly the time-independent systematic errors. Both of the time-dependent errors cannot be assessed from each satellite. For this reason, their cumulative effect on the global temperature trend is evaluated implicitly. Christy et al. (1998) (CSL). based on their method of analysis of the MSU Ch 2 data, infer a global temperature cooling trend (-0.046 K per decade) from 1979 to 1997, although their near nadir measurements yield near zero trend (0.003 K/decade). Utilising an independent method of analysis, we infer global temperature warmed by 0.12 +/- 0.06 C per decade from the observations of the MSU Ch 2 during the period 1980 to 1997.

Prabhakara, C.↗
NASA NTRS1984

Comparison of various drag coefficient expansions using polynomials and splines

The longitudinal differential equation of motion has been used to investigate various aerodynamic expansion techniques. The total drag coefficient was expanded using conventional polynomials and splines with and without floating knot locations. This paper discusses the various techniques and approaches, compares results obtained from simultaneously fitting four separate flights (time vs distance measurements) and outlines the potential advantages and/or disadvantages of the various aerodynamic expansion techniques. It is believed that this is the first time splines have been used in the aerodynamic coefficient estimation process and that these results and techniques are germane to other applications.

Sabot, S. M.↗
NASA NTRS1955

Full-scale-wind-tunnel Tests of a 35 Degree Sweptback Wing Airplane with High-velocity Blowing over the Training-edge Flaps

A wind-tunnel investigation was made to determine the effects of ejecting high-velocity air near the leading edge of plain trailing-edge flaps on a 35 degree sweptback wing. The tests were made with flap deflections from 45 degrees to 85 degrees and with pressure ratios across the flap nozzles from sub-critical up to 2.9. A limited study of the effects of nozzle location and configuration on the efficiency of the flap was made. Measurements of the lift, drag, and pitching moment were made for Reynolds numbers from 5.8 to 10.1x10(6). Measurements were also made of the weight rate of flow, pressure, and temperature of the air supplied to the flap nozzles.The results show that blowing on the deflected flap produced large flap lift increments. The amount of air required to prevent flow separation on the flap was significantly less than that estimated from published two-dimensional data. When the amount of air ejected over the flap was just sufficient to prevent flow separation, the lift increment obtained agreed well with linear inviscid fluid theory up to flap deflections of 60 degrees. The flap lift increment at 85 degrees flap deflection was about 80 percent of that predicted theoretically.With larger amounts of air blown over the flap, these lift increments could be significantly increased. It was found that the performance of the flap was relatively insensitive to the location of the flap nozzle, to spacers in the nozzle, and to flow disturbances such as those caused by leading-edge slats or discontinuities on the wing or flap surfaces. Analysis of the results indicated that installation of this system on an F-86 airplane is feasible.

Kelley, Mark W↗
NASA NTRS2005

Forecasting the Impact of an 1859-calibre Superstorm on Satellite Resources

We have assembled a database of operational satellites in orbit as of 2004, and have developed a series of simple models to assess the economic impacts to this resource caused by various scenarios of superstorm events possible during the next sunspot cycle between 2010 and 2014. Despite the apparent robustness of our satellite assets against the kinds of storms we have encountered during the satellite era, our models suggest a potential economic loss exceeding $10(exp 11) for satellite replacement and lost profitability caused by a once a century single storm similar to the 1859 superstorm. From a combination of power system and attitude control system (the most vulnerable) failures, we estimate that 80 satellites (LEO, MEO, GEO) may be disabled as a consequence of a superstorm event. Additional consequences may include the failure of many of the GPS, GLONASS and Galileo satellite systems in MEO. Approximately 98 LEO satellites that normally would not have re-entered for many decades, may prematurely de-orbit in ca 2021 as a result of the temporarily increased atmospheric drag caused by the superstorm event occurring in 2012. The $10(exp 11) International Space Station may lose at least 15 kilometers of altitude, placing it in critical need for re-boosting by an amount that is potentially outside the range of typical Space Shuttle operations during the previous solar maximum in ca 2000, and at a time when NASA plans to decommission the Space Shuttle. Several LEO satellites will unexpectedly be placed on orbits that enter the ISS zone of avoidance, requiring some action by ground personnel and ISS astronauts to avoid close encounters. Radiation effects on astronauts have also been considered and could include a range of possibilities from acute radiation sickness for astronauts inside spacecraft, to near-lethal doses during EVAs. The specifics depends very sensitively on the spectral hardness of the accompanying SPE event. Currently, the ability to forecast extreme particle events and coronal mass ejections, or predict their fluences and geo-severity in the 24-hrs prior to the event, appears to be no better than 50/50. If the events of the 1859 superstorm serve as a guide, the scope of a contemporary superstorm will most certainly be an awesome event, but one that the vast majority of our other satellite resources may reasonably be expected to survive.

Odenwald, Sten↗
NASA NTRS1972

Ice crystal terminal velocities

Terminal velocities of different ice crystal forms were calculated using the most recent ice crystal drag coefficients, aspect ratios, and densities. The equations derived were primarily for use in calculating precipitation rates by sampling particles with an aircraft in cirrus clouds, and determining particle size in cirrus clouds by Doppler radar. However, the equations are sufficiently general for determining particle terminal velocity at any altitude, and most any crystal type. Two sets of equations were derived. The general equations provide a good estimate of terminal velocities at any altitude. The specific equations are a set of equations for ice crystal terminal velocities at 1000 mb. The calculations are in good agreement with terminal velocity measurements. The results from the present study were also compared to prior calculations by others and seem to give more reasonable results, particularly at higher altitudes.

Heymsfield, A.↗
NASA NTRS1972

Ice crystal terminal velocities.

Terminal velocities of different ice crystal forms were calculated, using the most recent ice crystal drag coefficients, aspect ratios, and densities. The equations derived were primarily for use in calculating precipitation rates by sampling particles with an aircraft in cirrus clouds, and determining particle size in cirrus clouds by Doppler radar. However, the equations are sufficiently general for determining particle terminal velocity at any altitude, and almost any crystal type. Two sets of equations were derived. The 'general' equations provide a good estimate of terminal velocities at any altitude. The 'specific' equations are a set of equations for ice crystal terminal velocities at 1000 mb. The calculations are in good agreement with terminal velocity measurements. The results from the present study were also compared to prior calculations by others and seem to give more reasonable results, particularly at higher altitudes.

Heymsfield, A.↗
NASA NTRS1994

The mass of Mars, Phobos, and Deimos, from the analysis of the Mariner 9 and Viking Orbiter tracking data

We have estimated the mass of Phobos, Deimos, and Mars using the Viking Orbiter and Mariner 9 tracking data. We divided the data into 282 arcs and sorted the data by periapse height, by inclination, and by satellite. The data were processed with the GEODYN/SOLVE orbit determination programs, which have previously been used to analyze planetary tracking data. The a priori Mars gravity field applied in this study was the 50th degree and order GMM-1 (Goddard Mars Model-1) model. The subsets of data were carefully edited to remove any arcs with close encounters of less than 500 km with either Phobos or Deimos. Whereas previous investigators have used close flybys (less than 500 km) to estimate the satellite masses, we have attempted to estimate the masses of Phobos and Deimos from multiday arcs which only included more distant encounters. The subsets of data were further edited to eliminate spurious data near solar conjunction (Nov.-Dec. 1976 and January 1979). In addition, the Viking-1 data from Oct. through Dec. 1978 were also excluded because of the low periapse altitude (as low as 232 km) and thus high sensitivity to atmospheric drag.

Smith, D. E.↗
NASA NTRS1999

Boom Softening and Nacelle Integration on an Arrow-Wing High-Speed Civil Transport Concept

During the last cycle of concept design and wind-tunnel testing, the goal of the low-boom- shaped HSCT concepts (the B-935, the LB-16, and the LB- 1 8) was to meet mission requirements and generate shaped, ground-level pressure signatures with nose shock strengths of 1.0 psf or less. The wind-tunnel tests of these concepts produced results that were partially successful and encouraging although not fully up to expectations. In spite of this, however, these conceptual designs were overly optimistic and not acceptable because: the wing planforms had excessive area; the wing structural aspect ratio was too high; one concept had aft-fuselage rather than under-the-wing engines; and the gross takeoff weights were unrealistically low because of engines that were early, high-tech versions of later, revised, more-realistic engines. The need for reducing the ground-level overpressure shock strengths still existed; a need to be met within more restrictive guidelines of mission performance and gross takeoff weight limitations. Therefore, it was decided that the next conceptual design cycle would focus on decreased nose shock strengths, "boom softening," in the signatures of the Boeing and the McDonnell Douglas baseline concepts rather than low-boom concepts with shaped-signature designs. Overly-optimistic results were not the only problem with these low-sonic-boom concepts. Papers given at the 1994 Sonic-Boom Workshop had demonstrated that the problem of successful nacelle integration on HSCT concepts had only been partially solved. Wind-tunnel pressure signature data, from the HSCT-11B (a.k.a. the LB-18) wind-tunnel model, showed that the Langley HSCT design and analysis method had been successful in reducing the nacelle-volume disturbances in the flow field. This was due.to the engine nacelles mounted behind the wing trailing-edge on the aft fuselage so that no nacelle-wing interference-lift flow-field disturbances were generated. While acceptable from a sonic-boom research point of view, this concept was unacceptable from several practical and structural considerations. Preliminary wind-tunnel pressure signature data from the LB-16 wind-tunnel model, which had the engine nacelles mounted under the wings (the usual location), indicated that the application of the Langley nacelle-integration method had been only partially successful in the reduction of the nacelle-volume with nacelle-wing interference-lift pressure disturbances. So, "boom softening" had to also address the task of successful integration of the engine nacelles, with the engines in the required under-the-wing location. Unless this problem was solved, low-sonic-boom and low-drag modifications to the wing planform, the airfoil shape, and the fuselage longitudinal area distribution could be nullified if the nacelle disturbances added increments to the nose-shock strengths that were removed through component tailoring. In this paper, an arrow-wing boom-softened HSC7 concept which incorporated modifications to a baseline McDonnell Douglas concept is discussed. The analysis of the concept's characteristics will include estimates of weight, center of gravity, takeoff field length, mission range, and predictions of its ground-level sonic-boom pressure signature. Additional modifications which enhanced the softened-boom performance of this concept are also described as well as estimates of the performance penalties induced by these modifications.

Mack, Robert J.↗
NASA NTRS2003

Computational Aeroheating Predictions for Mars Lander Configurations

The proposed Mars Science Laboratory (MSL) mission is intended to deliver a large rover to the Martian surface within 10 km of the target site. This paper presents computational fluid dynamics (CFD) predictions of forebody heating rates for two MSL entry configurations with fixed aerodynamic trim tabs. Results are compared to heating on a 70-deg sphere-cone reference geometry. All three heatshield geometries are designed to trim hypersonically at a 16 deg angle of attack in order to generate the lift-to-drag ratio (L/D) required for precision landing. Comparisons between CFD and tunnel data are generally in good agreement for each configuration, but the computations predict more flow separation and higher heating on a trim tab inclined 10 deg relative to the surface. CFD solutions at flight conditions were obtained using an 8-species Mars gas in chemical and thermal nonequilibrium. Laminar and Baldwin-Lomax solutions were used to estimate the effects of the trim tabs and turbulence on heating. A tab extending smoothly from the heatshield flank is not predicted to increase laminar or turbulent heating rates above the reference levels. Laminar heating on a tab deflected 10 deg from the conical heatshield is influenced by flow separation and is up to 35% above the baseline heating rate. The turbulent solution on the inclined tab configuration predicts attached flow and a 43% heating increase above the reference level.

Edquist, Karl T.↗
NASA NTRS1977

New contributions to the problem of capture

Libration-point capture is analyzed in the framework of the restricted three-body problem in order to obtain general results capable of predicting the major features of an arbitrary postcapture orbit, with specific reference to capture as the presumed mode of origin of Jupiter's outer satellites. Some examples of libration-point capture are computed, the time a body remains captured is estimated, and a long-term numerical integration of orbits is carried out which shows that the equation used to estimate capture lifetimes is quite conservative. An extended capture criterion is proposed and used to demonstrate that direct postcapture orbits lie outside retrograde ones. Mass change involving one or both primaries is evaluated as a means of producing permanent capture, it is found that mass-change effects can produce 'pull-down capture', and consideration is given to the orbital evolution of Jupiter's outer satellites. The effect of drag in the solar nebula or in a nebula around proto-Jupiter on the capture process is briefly investigated. It is concluded that a capture origin for the outer satellites is improbable within the last 4.6 billion years but that either mass change or nebula drag could have been effective in producing capture.

Heppenheimer, T. A.↗
NASA NTRSDate not supplied

Distribution of SLS Integrated Load Uncertainty to Surface Pressures and Sectional Loads

Aerodynamic loads that are important to launch vehicle programs such as NASA’s Space Launch System (SLS) include both integrated loads such as the force & moment on the entire vehicle and distributed loads. In this work two examples of distributed loads are considered: the pressure field on the surface of the vehicle and sectional loads, which are one-dimensional distributions along the axis of the launch vehicle. In some modern flight programs, the integrated loads, such as lift and drag, used to design the guidance and control laws for the vehicle come from wind tunnel testing, while distributed loads are produced using Computational Fluid Dynamics(CFD). The first task that is addressed in this paper, then, is to provide a formal method to adjust the distributed loads so that integrating them matches the prescribed integrated load. In addition, the integrated loads in a launch vehicle typically include an uncertainty estimate. The second task is to distribute this prescribed integrated uncertainty to each point in a distributed load. Both tasks are addressed using the same technique, which is to create distributed load profiles that isolate adjustments to one integrated load while leaving the others unaffected. These adjustments are informed by Proper Orthogonal Decomposition (POD) of the entire CFD-based distributed load database. Once applied, the adjusted distributed loads can be used to evaluate any scalar quantity of interest that might be needed by downstream users such as structural analysis or trajectory modelers.

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