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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Interplanetary program to optimize simulated trajectories (IPOST). Volume 4: Sample cases

The Interplanetary Program to Optimize Simulated Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization are performed using the Standard NPSOL algorithm. The IPOST structure allows sub-problems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Hong, P. E.↗
NASA NTRS1992

Interplanetary Program to Optimize Simulated Trajectories (IPOST). Volume 1: User's guide

IPOST is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence fo trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the coat function. Targeting and optimization is performed using the Stanford NPSOL algorithm. IPOST structure allows sub-problems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Hong, P. E.↗
NASA NTRS1992

Interplanetary Program to Optimize Simulated Trajectories (IPOST). Volume 2: Analytic manual

The Interplanetary Program to Optimize Space Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization is performed using the Stanford NPSOL algorithm. IPOST structure allows subproblems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Hong, P. E.↗
DOE OSTI2026

Marginal Soils Index Analysis & Geospatial Data

This data package contains output files associated with Mongird et al. (in prep) organized into four dataset directories. Each dataset is described in more detail below. 1. Marginal Soils Index Analysis Description: This folder contains a csv file with land needs and availability by state, power generating technology type, and scenario in 2050 when suitable siting areas are additionally constrained to areas with increasing levels of soil marginality. Files: msi_constrained_siting_availability_2050.csv Variables: Scenario - Projected 2050 scenario name State - US state abbreviation Technology - Generating technology type solar = solar photovoltaic gas_cc_re = natural gas combined cycle (recirculating cooling) wind = onshore wind gas_cc_ccs_re = natural gas combined cycle with carbon capture sequestration (recirculating cooling) gas_cc_dry = natural gas combined cycle with (dry cooling) gas_cc_pond = natural gas combined cycle with (pond cooling) coal_conv_ccs_re = conventional coal with carbon capture sequestration (recirculating cooling) Req_Capacity_MW - The amount of rated capacity required in 2050 of the given technology type in the given state and under the given scenario from the capacity expansion plan Req_Capacity_Factor - The assumed capacity factor (fraction between 0 and 1) for the given technology type in the given state and under the given scenario by the capacity expansion plan Req_Land_km2 - The amount of land required (in km-squared) to host the required generating capacity that is capable of meeting the specified capacity factor for the given technology type in the given state and under the given scenario Req_Energy_TWh - Product of Req_Capacity_MW, Req_Capacity_Factor, and 8760/1e6 for the given technology type in the given state and under the given scenario MSI_Case - The level of MSI that siting the given technology is additionally constrained to, where >0 means siting is additionally constrained to suitable land areas that have an MSI value greater than 0 >=1 means siting is additionally constrained to suitable land areas that have an MSI value greater than or equal to 1 >=2 means siting is additionally constrained to suitable land areas that have an MSI value greater than or equal to 2 >=3 means siting is additionally constrained to suitable land areas that have an MSI value greater than or equal to 3 Soil Attribute Rasters Description: This folder contains geospatial raster files for individual soil parameters upscaled to the listed grid resolution (30m or 1 km). 1 km resolution files are a spatial average of non-missing 30m resolution values. All raster files use the USA Contiguous Albers Equal Area Conic (ESRI:102003) projection. Files: avg_cond_raster_ .tif - Average conductivity of the saturation extract across all soil horizons within a depth of 40 inches, measured in mmhos/cm max_cond_raster_ .tif - Maximum conductivity of the saturation extract across all soil horizons within a depth of 40 inches, measured in mmhos/cm min_ph_raster_ .tif- Min pH values across all soil horizons within a depth of 40 inches. avg_ph_raster_ .tif - Average pH value across all soil horizons within a depth of 40 inches. max_ph_raster_ .tif- Max pH value across all soil horizons within a depth of 40 inches. erosion_factor_raster_ .tif - Product of k-factor and percent slope flood_freq_raster_ .tif - Number of months of the year during which the area is commonly, frequently, or very frequently flooded. max_sar_raster_ .tif - Maximum sodium adsorption ratio across all horizons within a depth of 40 inches rock_frac_raster_ .tif - Fraction of the upper 6 inches of soil composed of rock fragments larger than 3 inches. temp_regime_raster_ .tif - Soil temperature regime with the following key: 0 = pergelic 1 = gelic 2 = cryic 3 = frigid 4 = isofrigid 5 = mesic 6 = isomesic 7 = thermic 8 = isothermic 9 = hyperthermic 10 =isohyperthermic Marginal Soils Index Rasters Description: This folder contains geospatial raster files of the Marginal Soils Index at the listed grid resolution (30m or 1 km). 1 km resolution files are a spatial average of 30m resolution. Both raster files use the USA Contiguous Albers Equal Area Conic (ESRI:102003) projection. A value of 0 indicates that there were no soil attributes present that indicate marginal soil. NA values indicate that data was unavailable or bodies of water. Files: marginal_soils_index_30m_raster.tif marginal_soils_index_1km_raster.tif Marginal Soils Index Resource Potential Rasters Description: This folder contains geospatial raster files of the Marginal Soils Index + Resource Potential (MSI+RP) score at 1km resolution for geothermal, solar, and wind technologies. Raster files use the USA Contiguous Albers Equal Area Conic (ESRI:102003) projection. NA values indicate that the location is not suitable for siting the given technology due to policy, environmental, socioeconomic, topological, and other constraints regardless of soil marginality level. Areas with values greater than or equal to zero represent the product of the normalized MSI value and the normalized resource potential value. Files: geothermal_msi_ep_score_raster.tif solar_msi_ep_score_raster.tif wind_msi_ep_score_raster.tif Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Agriculture↗
DOE OSTI2026

Marginal Soils Index Analysis & Geospatial Data

This data package contains output files associated with the Mongird et al. paper entitled "Can US power grid expansion avoid prime agricultural lands?" and is organized into four dataset directories. Each dataset is described in more detail below. 1. Marginal Soils Index Analysis Description: This folder contains a csv file with land needs and availability by state, power generating technology type, and scenario in 2050 when suitable siting areas are additionally constrained to areas with increasing levels of soil marginality. Files: msi_constrained_siting_availability_2050.csv Variables: Scenario - Projected 2050 scenario name State - US state abbreviation Technology - Generating technology type solar = solar photovoltaic gas_cc_re = natural gas combined cycle (recirculating cooling) wind = onshore wind gas_cc_ccs_re = natural gas combined cycle with carbon capture sequestration (recirculating cooling) gas_cc_dry = natural gas combined cycle with (dry cooling) gas_cc_pond = natural gas combined cycle with (pond cooling) coal_conv_ccs_re = conventional coal with carbon capture sequestration (recirculating cooling) Req_Capacity_MW - The amount of rated capacity required in 2050 of the given technology type in the given state and under the given scenario from the capacity expansion plan Req_Capacity_Factor - The assumed capacity factor (fraction between 0 and 1) for the given technology type in the given state and under the given scenario by the capacity expansion plan Req_Land_km2 - The amount of land required (in km-squared) to host the required generating capacity that is capable of meeting the specified capacity factor for the given technology type in the given state and under the given scenario Req_Energy_TWh - Product of Req_Capacity_MW, Req_Capacity_Factor, and 8760/1e6 for the given technology type in the given state and under the given scenario MSI_Case - The level of MSI that siting the given technology is additionally constrained to, where >0 means siting is additionally constrained to suitable land areas that have an MSI value greater than 0 >=1 means siting is additionally constrained to suitable land areas that have an MSI value greater than or equal to 1 >=2 means siting is additionally constrained to suitable land areas that have an MSI value greater than or equal to 2 >=3 means siting is additionally constrained to suitable land areas that have an MSI value greater than or equal to 3 Soil Attribute Rasters Description: This folder contains geospatial raster files for individual soil parameters upscaled to the listed grid resolution (30m or 1 km). 1 km resolution files are a spatial average of non-missing 30m resolution values. All raster files use the USA Contiguous Albers Equal Area Conic (ESRI:102003) projection. Files: avg_cond_raster_ .tif - Average conductivity of the saturation extract across all soil horizons within a depth of 40 inches, measured in mmhos/cm max_cond_raster_ .tif - Maximum conductivity of the saturation extract across all soil horizons within a depth of 40 inches, measured in mmhos/cm min_ph_raster_ .tif- Min pH values across all soil horizons within a depth of 40 inches. avg_ph_raster_ .tif - Average pH value across all soil horizons within a depth of 40 inches. max_ph_raster_ .tif- Max pH value across all soil horizons within a depth of 40 inches. erosion_factor_raster_ .tif - Product of k-factor and percent slope flood_freq_raster_ .tif - Number of months of the year during which the area is commonly, frequently, or very frequently flooded. max_sar_raster_ .tif - Maximum sodium adsorption ratio across all horizons within a depth of 40 inches rock_frac_raster_ .tif - Fraction of the upper 6 inches of soil composed of rock fragments larger than 3 inches. temp_regime_raster_ .tif - Soil temperature regime with the following key: 0 = pergelic 1 = gelic 2 = cryic 3 = frigid 4 = isofrigid 5 = mesic 6 = isomesic 7 = thermic 8 = isothermic 9 = hyperthermic 10 =isohyperthermic Marginal Soils Index Rasters Description: This folder contains geospatial raster files of the Marginal Soils Index at the listed grid resolution (30m or 1 km). 1 km resolution files are a spatial average of 30m resolution. Both raster files use the USA Contiguous Albers Equal Area Conic (ESRI:102003) projection. A value of 0 indicates that there were no soil attributes present that indicate marginal soil. NA values indicate that data was unavailable or bodies of water. Files: marginal_soils_index_30m_raster.tif marginal_soils_index_1km_raster.tif Marginal Soils Index Resource Potential Rasters Description: This folder contains geospatial raster files of the Marginal Soils Index + Resource Potential (MSIxRP) score at 1km resolution for geothermal, solar, and wind technologies. Raster files use the USA Contiguous Albers Equal Area Conic (ESRI:102003) projection. NA values indicate that the location is not suitable for siting the given technology due to policy, environmental, socioeconomic, topological, and other constraints regardless of soil marginality level. Areas with values greater than or equal to zero represent the product of the normalized MSI value and the normalized resource potential value. Files: geothermal_msi_rp_score_raster.tif solar_msi_rp_score_raster.tif wind_msi_rp_score_raster.tif Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Agriculture↗
NASA NTRS1976

Design of efficient stiffened shells of revolution

A method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self-adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.

Majumder, D. K.↗
DOE OSTI2022

Building Load Control Using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we use the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve tradeoff between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions. Summary of Contribution: The problem studied in this paper is motivated by a building load control problem that uses the aggregation of heating, ventilation, and air conditioning (HVAC) loads as flexible reserves to absorb uncertain solar photovoltaic (PV) generation. The problem is formulated as distributionally robust chance-constrained (DRCC) programs with right-hand side (RHS) uncertainty. In addition, we propose a risk-adjustable variant of the DRCC programs, where the risk level, instead of being predetermined, is treated as a decision variable. The paper aims to provide tractable reformulations and solution algorithms for both the (general) DRCC and the (general) adjustable DRCC models with RHS uncertainty.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2025

Tutorial: MATLAB Implementation of a Successive Convexification Algorithm for 3 DoF Rocket Landings

The primary objective of this work is to fill in gaps and explore an alternate way of solving the 3 DoF rocket-powered landing problem presented in the 2016 AIAA paper by Szmuk, Ackimese, and Berning using successive convexification (SCvx). In the original paper, CVX, an automatic parsing package, was used to transcribe the high-level trajectory optimization problem into a format that could be read by a conic solver. The parsing step, generally computationally intensive, is hidden from the user. The use of CVX is sufficient for the generation of trajectories off-line due to the lack of runtime and flight software implementation constraints. For on-line applications, it is necessary to parse the problem for flight software implementation. References on hand-parsing powered descent guidance (PDG) problems are sparse. In this Tech Memo, the process of transcribing the 3 DoF PDG problem into the format required by MATLAB’s built-in second-order cone solver, coneprog.m, is presented in detail. Due to the abridged 3 DoF dynamics and the relatively simple nonlinearities, this reference is the natural starting point for anyone interested in grasping the concepts behind SCvx pertaining to PDG and the parsing step. Simulation results shown in this report were independently created by solving the problem using coneprog.m. The intent of this memo is to serve as a supplemental material to the original paper by breaking down the concept behind successive convexification and shed light into the parsing process. Readers are encouraged to first familiarize themselves with the material laid out in the original reference.

Alex Hayes↗
NASA NTRS2012

Polarimetric Signatures of Initiating Convection During MC3E

One of the goals of the Mid-latitude Continental Convective Clouds Experiment (MC3E) field campaign was to provide constraints for space-based rainfall retrieval algorithms over land. This study used datasets collected during the 2011 field campaign to combine radiometer and ground-based radar polarimetric retrievals in order to better understand hydrometeor type, habit and distribution for initiating continental convection. Cross-track and conically scanning nadir views from the Conical Scanning Millimeter-wave Imaging Radiometer (CoSMIR) were compared with ground-based polarimetric radar retrievals along the ER-2 flight track. Polarimetric signatures for both airborne radiometers and ground-based radars were well co-located with deep convection to relate radiometric signatures with low-level polarimetric radar data for hydrometeor identification and diameter estimation. For the time period of study, Z(sub DR) values indicated no presence of hail at the surface. However, the Z(sub DR) column extended well above the melting level into the mixed phase region, suggesting a possible source of frozen drop embryos for the future formation of hail. The results shown from this study contribute ground truth datasets for GPM PR algorithm development for convective events, which is an improvement upon previous stratiform precipitation centered framework.

Emory, Amber↗
NASA NTRS2012

On Heatshield Shapes for Mars Entry Capsules

The 70deg sphere-cone - the standard geometry for all US Mars entry missions - is thoroughly examined via flow field simulations at a select few peak heating points along candidate flight trajectories. Emphasis is placed on turbulent heating based on the Baldwin- Lomax turbulence model. It is shown that increased leeward turbulent heating for a 70 sphere-cone flying at angle of attack is primarily due to the discontinuity in curvature between the spherical nose cap and the conical frustum - the attachment of the sonic line at this sphere-cone junction leads to a supersonic edge Mach number over the leeward acreage. In an attempt to mitigate this problem of elevated turbulent heating, alternate geometries, without any curvature discontinuities in the acreage, are developed. Two approaches, one based on nonlinear optimization with constraints, and one based on the use of non-uniform rational B-splines, are considered. All configurations examined remain axisymmetric. The aerothermal performance of alternate geometries is shown to be superior to that of the 70 sphere-cone.

Prabhu, DInesh K.↗
NASA NTRS2015

Trajectories for a Near Term Mission to the Interstellar Medium

Trajectories for rapid access to the interstellar medium (ISM) with a Kuiper Belt Object (KBO) flyby, launching between 2022 and 2030, are described. An impulsive-patched-conic broad search algorithm combined with a local optimizer is used for the trajectory computations. Two classes of trajectories, (1) with a powered Jupiter flyby and (2) with a perihelion maneuver, are studied and compared. Planetary flybys combined with leveraging maneuvers reduce launch C3 requirements (by factor of 2 or more) and help satisfy mission-phasing constraints. Low launch C3 combined with leveraging and a perihelion maneuver is found to be enabling for a near-term potential mission to the ISM.

ISM↗
DOE OSTI2021

Concentrated radiative cooling and its constraint from reciprocity

Concentrated radiative cooling, an analogous concept of the concentrated solar power technology, has the potential of amplifying both the cooling power and the temperature reduction. However, concentrators have not yet been systematically optimized. Moreover, a widely used theoretical approach to analyze such systems has neglected a fundamental constraint from reciprocity, which can lead to an overestimate of cooling performance and unclarified limits of amplification factors. Here we develop a theoretical framework addressing these shortcomings. Modeling suggests the optimized shape and geometric dimensions of concentrators, as well as the limiting cooling power and temperature reduction. Using an electroplated Al 2 O 3 emitter and an optimized conical concentrator, we experimentally amplify the nighttime radiative cooling by 26%.

Dong, Minghao↗
NASA NTRS1986

Supersonic airfoil optimization

A procedure for the optimization of supersonic airfoils is presented. A nonlinear, full-potential solver (NCOREL) is coupled with a numerical optimizer (CONMIN). The NCOREL code is a three-dimensional supersonic marching method, however, only two-dimensional (conical) results are used for the airfoil problem. Each airfoil evaluated in the NCOREL aerodynamic code is composed of a linear combination of user-specified basis airfoils. The weighting factors of the basis airfoils plus the angle of attack form the design variable vector. The inviscid drag coefficient is minimized subject to lift and crossflow Mach number gradient constraints. The optimization strategy is found to be extremely important for the efficient determination of an optimum airfoil.

Pittman, J. L.↗
NASA NTRS1980

A new method for optimizing multiple flyby trajectories

A new procedure has been developed which minimizes total impulsive Delta V for multiple flyby trajectories with constraints on flyby parameters and maneuver times. The method involves solving a bounds-constrained parameter optimization problem with a Newton algorithm utilizing analytic first and second derivatives. Each trajectory segment connecting consecutive maneuver points is found by first targeting from the preceding maneuver point to the parameters of the upcoming flyby and then propagating the resulting trajectory to the next maneuver point. Multi-conic techniques are used for trajectory propagation and for computation of the state transition matrix. This procedure has successfully optimized Galileo satellite tours containing up to 11 flybys.

Damario, L. A.↗
NASA NTRS1988

Strategy and calculations for the design of baffles for Wolter Type II telescopes

Spaceflight, stellar pointing telescopes require baffle systems to define the field of view and protect this observational area from stray and scattered light. In the case of near normal incidence telescope systems, the problem consists in controlling the stray/scattered radiation reaching the image plane when circular plates, the primary and secondary mirrors, are the imaging elements. The case addressed in this paper is quite different in that it involves baffling two conical surfaces, i.e., the primary and secondary mirrors of a Wolter Type II telescope. A strategy is described for systematically moving through the telescope system and establishing criteria for placement of baffles. Calculations are given which determine the size and number of permitted baffles as a function of practical physical parameters. Clear options are given for the design of minimum baffle lengths to meet packaging constraints.

Mangus, John D.↗
NASA NTRS1982

Starprobe thermal shield system design concepts

The mission goals, flight trajectory, and material durability requirements for the NASA Starprobe spacecraft are reviewed. The spacecraft will use a Jovian gravity assist to pass within four solar radii of the sun to study fields and particles near the sun, perform experiments dealing with relativity and gravity, and observe the structure of the solar atmosphere from the photosphere to the corona. Constraints on the system size and mass design are given, and the system is noted to be required to withstand 2500 K at perihelion, thermally insulate the instrument payload, have a tube for optical measurements, and provide protection from meteorite damage. A secondary shield is also required to dispense thermal radiation that passes the primary shield and could endanger the payload. Design options are discussed, along with temperature control requirements and a conical carbon-carbon primary shield with mass-loss rate characteristics sufficient to meet a 2.5 mg/sec criterion.

Maag, C. R.↗
NASA NTRS1991

Hypersonic waverider analysis - A comparison of numerical and experimental results

In this study two waverider configurations are analyzed numerically and experimentally. The geometries are designed using an inverse design and optimization code with the optimization procedure driven by maximized L/D and limited by geometric constraints. Euler and Navier-Stokes numerical simulations are performed with a partially flux-split finite-difference code developed at NASA Ames, F3D. Experimental data is obtained at NASA Langley in the Unitary Plan Wind Tunnel (UPWT) and the 20-Inch Mach 6 wind tunnel for flow visualization, force/moment, and surface pressure measurements at both on- and off-design conditions. Euler simulations are compared with analytic results obtained from conical flow theory, and Navier-Stokes simulations are compared with experimental results both qualitatively and quantitatively for on- and off-design conditions.

Jones, K. D.↗
NASA NTRS1995

Analytical investigations in aircraft and spacecraft trajectory optimization and optimal guidance

A collection of analytical studies is presented related to unconstrained and constrained aircraft (a/c) energy-state modeling and to spacecraft (s/c) motion under continuous thrust. With regard to a/c unconstrained energy-state modeling, the physical origin of the singular perturbation parameter that accounts for the observed 2-time-scale behavior of a/c during energy climbs is identified and explained. With regard to the constrained energy-state modeling, optimal control problems are studied involving active state-variable inequality constraints. Departing from the practical deficiencies of the control programs for such problems that result from the traditional formulations, a complete reformulation is proposed for these problems which, in contrast to the old formulation, will presumably lead to practically useful controllers that can track an inequality constraint boundary asymptotically, and even in the presence of 2-sided perturbations about it. Finally, with regard to s/c motion under continuous thrust, a thrust program is proposed for which the equations of 2-dimensional motion of a space vehicle in orbit, viewed as a point mass, afford an exact analytic solution. The thrust program arises under the assumption of tangential thrust from the costate system corresponding to minimum-fuel, power-limited, coplanar transfers between two arbitrary conics. The thrust program can be used not only with power-limited propulsion systems, but also with any propulsion system capable of generating continuous thrust of controllable magnitude, and, for propulsion types and classes of transfers for which it is sufficiently optimal the results of this report suggest a method of maneuvering during planetocentric or heliocentric orbital operations, requiring a minimum amount of computation; thus uniquely suitable for real-time feedback guidance implementations.

Markopoulos, Nikos↗