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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRSDate not supplied

Flight Mechanics Analysis of Low-Earth Orbit Flight Test of an Inflatable Decelerator

The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) successfully demonstrated the capability of an inflatable aeroshell. Prior to launch, flight mechanics analysis was conducted to better understand the predicted splashdown point of the re-entry vehicle and ejectable data recorder. Best estimated trajectory separation states were utilized to understand the LOFTID trajectory over the entire 36 minute launch window. Weather forecasting model were integrated into the simulation to improve trajectory prediction accuracy. Automation tools were developed to facilitate the rapid generation of trajectory predictions during operations. The resulting improvements to the flight mechanics modeling and simulation allowed for pre-launch splashdown point to be within 3 nautical miles of the actual splashdown point.

Rohan G Deshmukh↗
NASA NTRSDate not supplied

Flight Mechanics Analysis of Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID)

The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) successfully demonstrated the capability of an inflatable aeroshell. Prior to launch, flight mechanics analysis was conducted to better understand the predicted splashdown point of the re-entry vehicle and ejectable data recorder. Best estimated trajectory separation states were utilized to understand the LOFTID trajectory over the entire 36 minute launch window. Weather forecasting model were integrated into the simulation to improve trajectory prediction accuracy. Automation tools were developed to facilitate the rapid generation of trajectory predictions during operations. The resulting improvements to the flight mechanics modeling and simulation allowed for pre-launch splashdown point to be within 3 nautical miles of the actual splashdown point.

Rohan Deshmukh↗
NASA NTRS2000

In Space Nuclear Power as an Enabling Technology for Deep Space Exploration

Deep Space Exploration missions, both for scientific and Human Exploration and Development (HEDS), appear to be as weight limited today as they would have been 35 years ago. Right behind the weight constraints is the nearly equally important mission limitation of cost. Launch vehicles, upper stages and in-space propulsion systems also cost about the same today with the same efficiency as they have had for many years (excluding impact of inflation). Both these dual mission constraints combine to force either very expensive, mega systems missions or very light weight, but high risk/low margin planetary spacecraft designs, such as the recent unsuccessful attempts for an extremely low cost mission to Mars during the 1998-99 opportunity (i.e., Mars Climate Orbiter and the Mars Polar Lander). When one considers spacecraft missions to the outer heliopause or even the outer planets, the enormous weight and cost constraints will impose even more daunting concerns for mission cost, risk and the ability to establish adequate mission margins for success. This paper will discuss the benefits of using a safe in-space nuclear reactor as the basis for providing both sufficient electric power and high performance space propulsion that will greatly reduce mission risk and significantly increase weight (IMLEO) and cost margins. Weight and cost margins are increased by enabling much higher payload fractions and redundant design features for a given launch vehicle (higher payload fraction of IMLEO). The paper will also discuss and summarize the recent advances in nuclear reactor technology and safety of modern reactor designs and operating practice and experience, as well as advances in reactor coupled power generation and high performance nuclear thermal and electric propulsion technologies. It will be shown that these nuclear power and propulsion technologies are major enabling capabilities for higher reliability, higher margin and lower cost deep space missions design to reliably reach the outer planets for scientific exploration.

Sackheim, Robert L.↗
NASA NTRSDate not supplied

Small Satellite-sized Hypersonic Inflatable Decelerators for Interplanetary Science Missions

To take full advantage of our increased access to space, through reduced launch costs that ridesharing opportunities present, innovative and lower cost options for interplanetary exploration are needed. Capitalizing on the technology miniaturization trends and the SmallSat class of vehicles could provide advancements for interplanetary space exploration. Presented here, are the results of a feasibility study conducted during an internship at NASA Langley Research Center that explored the use of a SmallSat-sized Hypersonic Inflatable Aerodynamic Decelerator (HIAD) to enable interplanetary orbital science missions via aerocapture.

Shelly C. Mann↗
NASA NTRSDate not supplied

Small Satellite-sized Hypersonic Inflatable Decelerators for Interplanetary Science Missions

To take full advantage of our increased access to space, through reduced launch costs that ridesharing opportunities present, innovative and lower cost options for interplanetary exploration are needed. Capitalizing on the technology miniaturization trends and the SmallSat class of vehicles could provide advancements for interplanetary space exploration. Presented here, are the results of a feasibility study conducted during an internship at NASA Langley Research Center that explored the use of a SmallSat-sized Hypersonic Inflatable Aerodynamic Decelerator (HIAD) to enable interplanetary orbital science missions via aerocapture.

Shelly C. Mann↗
NASA NTRS2006

Advanced Radioisotope Power System Enabled Titan Rover Concept with Inflatable Wheels

This viewgraph presentation reviews study into exploration of Titan. Including a possible Titan Rover that would use the advanced radioisotope power system (RPS). The goal of the study is to demonstrate a simple, credible and affordable rover mission concept for Titan in-situ exploration, enabled by an Advanced RPS. The presentation reviews the possible launch vehicle, and trajectory options; desired instrumentation that would be aboard the rover; and considerations for the design of the rover.

rovers↗
NASA NTRS2004

Static Testing of an Inflatable/Rigidizable Hexapod Structure

Scientific application of large space antennas and telescopes is fostering the study of ultralightweight and inflatable structures. These so-called gossamer structures are tightly packaged for launch and subsequent deployment. Of particular interest is a hexapod configuration often found in vehicle ride simulators, ground-based telescopes, and antennas. One such configuration was modeled and tested at NASA Langley. Discrepancies between dynamic test data and predictions from a finite element model prompted additional static testing. This paper discusses static tests that were conducted to update stiffness parameters in the finite element model.

Berger, K. T.↗
NASA NTRS2015

Overview of the 2nd Gen 3.7m HIAD Static Load Test

To support NASAs long term goal of landing humans on Mars, technologies which enable the landing of heavy payloads are being developed. Current entry, decent, and landing technologies are not practical for human class payloads due to geometric constraints dictated by current launch vehicle fairing limitations. Therefore, past and present technologies are now being explored to provide a mass and volume efficient solution to atmospheric entry, including Hypersonic Inflatable Aerodynamic Decelerators (HIADs). In October of 2014, a 3.7m HIAD inflatable structure with an integrated flexible thermal protection sys-tem (F-TPS) was subjected to a static load test series to verify the designs structural performance. The 3.7m HIAD structure was constructed in a 70 deg sphere-cone stacked-toroid configuration using eight inflatable tori, which were joined together using adhesives and high strength textile webbing to help distribute the loads throughout the inflatable structure. The inflatable structure was fabricated using 2nd generation structural materials that permit an increase in use temperature to 400 C+ as compared to the 250 C limitation of the 1st generation materials. In addition to the temperature benefit, these materials also offer a 40 reduction in structure mass. The 3.7m F-TPS was fabricated using high performance materials to protect the inflatable structure from heat loads that would be seen during atmospheric entry. The F-TPS was constructed of 2nd generation TPS materials increasing its heating capability from 35W sq cm to over 100W sq cm. This test article is the first stacked-torus HIAD to be fabricated and tested with a 70 deg sphere-cone. All previous stacked-torus HIADs have employed a 60o sphere-cone. To perform the static load test series, a custom test fixture was constructed. The fixture consisted of a structural tub rim with enough height to allow for dis-placement of the inflatable structure as loads were applied. The tub rim was attached to the floor to provide an airtight seal. The center body of the inflatable structure was attached to a pedestal mount as seen in Figure 1. Using an impermeable membrane seal draped over the test article, partial vacuum was pulled beneath the HIAD, resulting in a uniform static pressure load applied to the outer surface. During the test series an extensive amount of instrumentation was used to characterize deformed shape, shoulder deflection, strap loads, and cord loads as a function of structural configuration and applied static load. In this overview, the 3.7m HIAD static load test series will be discussed in detail, including the 3.7m HIAD inflatable structure and flexible TPS design, test setup and execution, and finally results and conclusions from the test series.

HIAD↗
NASA NTRS2018

The HIAD Orbital Flight Demonstration Instrumentation Suite

NASA's Hypersonic Inflatable Aerodynamic Decelerator (HIAD) technology has been selected for a Technology Demonstration Mission under the Science and Technology Mission Directorate. HIADs are an enabling technology that can facilitate atmospheric entry of heavy payloads to planets such as Earth and Mars using a deployable aeroshell. The deployable nature of the HIAD technology allows it to overcome the size constraints imposed on current rigid aeroshell entry systems. This permits use of larger aeroshells resulting in increased entry system performance (e.g. higher payload mass and/or volume, higher landing altitude at Mars). The Low Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) is currently scheduled for mid-2021. LOFTID will be launched out of Vandenberg Air Force Base as a secondary payload on an expendable launch vehicle. The flight test will employ a 6m diameter, 70 degree sphere-cone aeroshell and will provide invaluable high-energy orbital re-entry flight data. This data will be essential in supporting the HIAD team to mature the technology to diameters of 10m and greater. Aeroshells of this scale will address near-term commercial applications and potential future NASA missions. LOFTID will incorporate an extensive instrumentation suite totaling over 150 science measurements. This will include thermocouples, heat flux sensors, IR cameras, and a radiometer to characterize the aeroheating environment and aeroshell thermal response. An inertial measurement unit (IMU), GPS, and flush air data system will be included in order to reconstruct the flown trajectory and aerodynamic characteristics. Loadcells will be used to measure the HIAD structural loading, and HD cameras will be mounted on the aft segment looking at the aeroshell to monitor structural response. In addition to the primary instrumentation suite, a new fiber optic sensing system will be used to measure nose temperatures as a technology demonstration. The LOFTID instrumentation suites leverages Agency-wide expertise, with hardware development occurring at Ames Research Center, Langley Research Center, Marshall Space Flight Center and Armstrong Flight Research Center. This presentation will discuss the measurement objectives for the LOFTID mission, and the extensive instrumentation suite that has been selected to capture the HIAD's performance during the high-energy orbital re-entry flight test.

Swanson, G. T.↗
NASA NTRS2018

The HIAD Orbital Flight Demonstration Instrumentation Suite

NASA's Hypersonic Inflatable Aerodynamic Decelerator (HIAD) technology has been selected for a Technology Demonstration Mission under the Science and Technology Mission Directorate. HIADs are an enabling technology that can facilitate atmospheric entry of heavy payloads to planets such as Earth and Mars using a deployable aeroshell. The deployable nature of the HIAD technology allows it to overcome the size constraints imposed on current rigid aeroshell entry systems. This permits use of larger aeroshells resulting in increased entry system performance (e.g. higher payload mass and/or volume, higher landing altitude at Mars). The Low Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) is currently scheduled for mid-2021. LOFTID will be launched out of Vandenberg Air Force Base as a secondary payload on an expendable launch vehicle. The flight test will employ a 6m diameter, 70-deg sphere-cone aeroshell and will provide invaluable high-energy orbital re-entry flight data. This data will be essential in supporting the HIAD team to mature the technology to diameters of 10m and greater. Aeroshells of this scale will address near-term commercial applications and potential future NASA missions.LOFTID will incorporate an extensive instrumentation suite totaling over 150 science measurements. This will include thermocouples, heat flux sensors, IR cameras, and a radiometer to characterize the aeroheating environment and aeroshell thermal response. An inertial measurement unit (IMU), GPS, and flush air data system will be included in order to reconstruct the flown trajectory and aerodynamic characteristics. Loadcells will be used to measure the HIAD structural loading, and HD cameras will be mounted on the aft segment looking at the aeroshell to monitor structural response. In addition to the primary instrumentation suite, a new fiber optic sensing system will be used to measure nose temperatures as a technology demonstration. The LOFTID instrumentation suites leverages Agency-wide expertise, with hardware development occurring at Ames Research Center, Langley Research Center, Marshall Space Flight Center and Armstrong Flight Research Center.This presentation will discuss the measurement objectives for the LOFTID mission, and the extensive instrumentation suite that has been selected to capture the HIAD's performance during the high-energy orbital re-entry flight test.

Swanson, Greg↗
NASA NTRS1992

Inflatable habitation for the lunar base

Inflatable structures have a number of advantages over rigid modules in providing habitation at a lunar base. Some of these advantages are packaging efficiency, convenience of expansion, flexibility, and psychological benefit to the inhabitants. The relatively small, rigid cylinders fitted to the payload compartment of a launch vehicle are not as efficient volumetrically as a collapsible structure that fits into the same space when packaged, but when deployed is much larger. Pressurized volume is a valuable resource. By providing that resource efficiently, in large units, labor intensive external expansion (such as adding additional modules to the existing base) can be minimized. The expansive interior in an inflatable would facilitate rearrangement of the interior to suite the evolving needs of the base. This large, continuous volume would also relieve claustrophobia, enhancing habitability and improving morale. The purpose of this paper is to explore some of the aspects of inflatable habitat design, including structural, architectural, and environmental considerations. As a specific case, the conceptual design of an inflatable lunar habitat, developed for the Lunar Base Systems Study at the Johnson Space Center, is described.

Roberts, M.↗
NASA NTRS2016

Performance Efficient Launch Vehicle Recovery and Reuse

For decades, economic reuse of launch vehicles has been an elusive goal. Recent attempts at demonstrating elements of launch vehicle recovery for reuse have invigorated a debate over the merits of different approaches. The parameter most often used to assess the cost of access to space is dollars-per-kilogram to orbit. When comparing reusable vs. expendable launch vehicles, that ratio has been shown to be most sensitive to the performance lost as a result of enabling the reusability. This paper will briefly review the historical background and results of recent attempts to recover launch vehicle assets for reuse. The business case for reuse will be reviewed, with emphasis on the performance expended to recover those assets, and the practicality of the most ambitious reuse concept, namely propulsive return to the launch site. In 2015, United Launch Alliance (ULA) announced its Sensible, Modular, Autonomous Return Technology (SMART) reuse plan for recovery of the booster module for its new Vulcan launch vehicle. That plan employs a non-propulsive approach where atmospheric entry, descent and landing (EDL) technologies are utilized. Elements of such a system have a wide variety of applications, from recovery of launch vehicle elements in suborbital trajectories all the way to human space exploration. This paper will include an update on ULA's booster module recovery approach, which relies on Hypersonic Inflatable Aerodynamic Decelerator (HIAD) and Mid-Air Retrieval (MAR) technologies, including its concept of operations (ConOps). The HIAD design, as well as parafoil staging and MAR concepts, will be discussed. Recent HIAD development activities and near term plans including scalability, next generation materials for the inflatable structure and heat shield, and gas generator inflation systems will be provided. MAR topics will include the ConOps for recovery, helicopter selection and staging, and the state of the art of parachute recovery systems using large parafoils for space asset recovery and high altitude deployment. The next proposed HIAD flight demonstration is called HULA (for HIAD on ULA), and will feature a 6m diameter HIAD. An update for the HULA concept will be provided in this paper. As proposed, this demonstration will fly as a secondary payload on an Atlas mission. The Centaur upper stage provides the reentry pointing, deorbit burn, and entry vehicle spin up. The flight test will culminate with a recovery of the HIAD using MAR. HULA will provide data from a Low Earth Orbit (LEO) return aeroheating environment that enables predictive model correlation and refinement. The resultant reduction in performance uncertainties should lead to design efficiencies that are increasingly significant at larger scales. Relevance to human scale Mars EDL using a HIAD will also be presented, and the applicability of the data generated from both HULA and SMART Vulcan flights, and its value for NASA's human exploration efforts will be discussed. A summary and conclusion will follow.

Reed, John G.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-27111-DND

Rigid aeroshell systems are rapidly approaching the payload limit that current technology can deliver while fitting within the payload envelope of existing launch vehicles. The need for higher entry mass, landing elevation, and more controllability has pushed NASA to improve existing atmospheric entry technologies to further its scientific and exploration capabilities. Hypersonic Inflatable Aerodynamic Decelerators (HIADs) are an emerging technology that allows entry vehicles to deliver larger payloads to higher landing elevations by providing a larger aeroshell diameter than rigid aeroshells. HIADs offer new methods of entry vehicle trajectory control through shape morphing of the inflatable aeroshell. This dissertation explores different concepts of morphing a HIAD by assessing its structural integrity, aerodynamic performance, and systems integration. Analytical models are developed to predict the amount of force required to achieve a desired morphed shape, an actuator and sensor are selected based on performance requirements, and a controller is designed to morph the HIAD through Lift-to-Drag modulation. The actuator and sensor system and controller are then integrated into a small-scale development unit of a HIAD and experimental results are compared to numerical simulations. Conclusions and contributions of this research are presented along with a discussion on further research opportunities of Morphing HIADs.

Adam Milne Slagle↗
NASA NTRSDate not supplied

Design and Qualification or the Low-Earth Orbit Flight Test of an Inflatable Decelerator(LOFTID) Payload Adapter Separation System (PASS)

On November 10, 2022, NASA and United Launch Alliance (ULA) launched Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) as a secondary payload on an Atlas V Centaur from Vandenburg Space Force Base (VSFB). After deploying the primary payload, JPSS-2, to a sun-synchronous orbit, the Centaur reoriented LOFTID for reentry, ejecting the Payload Adaptor to expose the stowed LOFTID reentry vehicle (RV). The Hypersonic Inflatable Aerodynamic Decelerator (HIAD) was then deployed and inflated, and the Centaur reoriented the RV to the desired entry attitude, spun the vehicle to roughly three rpm, and separated the reentry vehicle. After nearly half an orbit of free flight, LOFTID reentered the atmosphere at >8 km/sec, demonstrating stable flight from hypersonic entry through subsonic parachute deployment. A mission-unique Payload Adapter Separation System (PASS) enabled the successful LOFTID flight demonstration, allowing the launch vehicle to accommodate a superstack of two independent, similarly sized payloads. This paper discusses the design, development, and qualification of the LOFTID PASS along with lessons learned.

HIAD↗
NASA NTRS2006

Structural Analysis and Testing of the Inflatable Re-entry Vehicle Experiment (IRVE)

The Inflatable Re-entry Vehicle Experiment (IRVE) is a 3.0 meter, 60 degree half-angle sphere cone, inflatable aeroshell experiment designed to demonstrate various aspects of inflatable technology during Earth re-entry. IRVE will be launched on a Terrier-Improved Orion sounding rocket from NASA s Wallops Flight Facility in the fall of 2006 to an altitude of approximately 164 kilometers and re-enter the Earth s atmosphere. The experiment will demonstrate exo-atmospheric inflation, inflatable structure leak performance throughout the flight regime, structural integrity under aerodynamic pressure and associated deceleration loads, thermal protection system performance, and aerodynamic stability. Structural integrity and dynamic response of the inflatable will be monitored with photogrammetric measurements of the leeward side of the aeroshell during flight. Aerodynamic stability and drag performance will be verified with on-board inertial measurements and radar tracking from multiple ground radar stations. In addition to demonstrating inflatable technology, IRVE will help validate structural, aerothermal, and trajectory modeling and analysis techniques for the inflatable aeroshell system. This paper discusses the structural analysis and testing of the IRVE inflatable structure. Equations are presented for calculating fabric loads in sphere cone aeroshells, and finite element results are presented which validate the equations. Fabric material properties and testing are discussed along with aeroshell fabrication techniques. Stiffness and dynamics tests conducted on a small-scale development unit and a full-scale prototype unit are presented along with correlated finite element models to predict the in-flight fundamental mod

Lindell, Michael C.↗
NASA NTRS2002

Analytical Modal Analysis for Thin-Film Flat Lenses

Due to strong potential applications and more demanding requirements imposed upon thin-film structures for space deployable, there has been increasing research and development activities during recent years in the field of vibration analysis of these types of structures. Moreover, interests in employing these structural components have received renewed emphasis in recent years within NASA and the Air Force. This is due to their inherent lightweight, low packaging and launch volume, and relative simplicity of deployment. Among the potential mission concepts for which these structural elements are included, one can mention solar sails, space solar power generation systems, solar thermal propulsion vehicles, large space telescopes, and inflatable communication antennas. This paper presents analytical procedures to determine vibration and physical characteristics of thin film lenses with circular and elliptical shapes membranes considered in design of a solar concentrator. In general, three methods are used to obtain approximate solutions of Helmholtz boundary value problems. One method requires that solution satisfy the differential equation exactly and the boundary condition approximately. Another method demands a solution that satisfies the boundary conditions exactly and the governing equations approximately. The third method sees a solution that satisfies both the governing equation and boundary conditions approximately. Extensive reviews of vibrations of membrane and plates are provided by Leissa and Mazumdar.

Hamid R. Hamidzadeh↗
NASA NTRS1999

The Mars Pathfinder Mission and Science Results

Mars Pathfinder, the first low-cost, quick Discovery class mission to be completed, successfully landed on the surface of Mars on July 4, 1997, deployed and navigated a small rover, and collected data from 3 science instruments and 10 technology experiments. The mission operated on Mars for 3 months and returned 2.3 Gbits of new data, including over 16,500 lander and 550 rover images, 16 chemical analyses of rocks and soil, and 8.5 million individual temperature, pressure and wind measurements. The rover traversed 100 m clockwise around the lander, exploring about 200 square meters of the surface. The mission captured the imagination of the public, and garnered front page headlines during the first week. A total of about 566 million internet "hits" were registered during the first month of the mission, with 47 million "hits" on July 8th alone, making the Pathfinder landing by far the largest internet event in history at the time. Pathfinder was the first mission to deploy a rover on Mars. It carried a chemical analysis instrument, to characterize the rocks and soils in a landing area over hundreds of square meters on Mars, which provided a calibration point or "ground truth" for orbital remote sensing observations. The combination of spectral imaging of the landing area by the lander camera, chemical analyses aboard the rover, and close-up imaging of colors, textures and fabrics with the rover cameras offered the potential of identifying rocks (petrology and mineralogy). With this payload, a landing site in Ares Vallis was selected because it appeared acceptably safe and offered the prospect of analyzing a variety of rock types expected to be deposited by catastrophic floods, which enabled addressing first-order scientific questions such as differentiation of the crust, the development of weathering products, and the nature of the early Martian environment and its subsequent evolution. The 3 instruments and rover allowed seven areas of scientific investigation: the geology and geomorphology of the surface, mineralogy and geochemistry of rocks and soils, physical properties of surface materials, magnetic properties of airborne dust, atmospheric science including aerosols, and rotational and orbital dynamics of Mars. Scientists were assembled into 7 Science Operations Groups that were responsible for requesting measurements by the 3 instruments, rover and engineering subsystems for carrying out their scientific investigations and for analyzing the data and reporting on their findings. The spacecraft was launched on December 4, 1996 and had a 7 month cruise to Mars, with four trajectory correction maneuvers. The vehicle entered the atmosphere directly following cruise stage separation. Parachute deployment, heatshield and lander separation, radar ground acquisition, airbag inflation and rocket ignition all occurred before landing at 2:58 AM true local solar time (9:56:55 AM PDT). The lander bounced at least 15 times up to 12 in high without airbag rupture, demonstrating the robustness of this landing system. Reconstruction of the final landing sequence indicates that the parachute/backshel1/1ander was tilted due to a northwest directed wind and wind shear, which resulted in the lander bouncing about I km to the northwest and initially downhill about 20 m from where the solid rockets fired. Two anomalously bright spots located in the lander scene are likely the heatshield, which continued in a ballistic trajectory about 2 km downrange (west southwest), and the backshell/parachute, which stayed nearer to where the rockets fired. Unconnected disturbed soil patches in the scene indicate that the final few bounces of the lander were from the east-southeast and were followed by a gentle roll to the west before coming to rest on the base petal. The location of the lander away from where the solid rockets fired and considerations of the exhaust products used to inflate the airbags and their fate, indicate that the Pathfinder landing system is one of the cleanest designed leaving the local area essentially contaminant free. The radio signal from the low-=gain antenna was received at 11:34 AM PDT indicating a successful landing.

Golombek, M. P.↗
NASA NTRS1976

SEATSAT programs option analysis

A preliminary analysis of the costs of SEASAT follow-on options is presented. All the options assume the existence of SEASAT-A as currently defined in the SEASAT Economic Assessment. It is assumed that each option will continue through the year 2000 and approach operational system status in the 1983-1986 period, depending upon the sensor package selected. The launch vehicle assumed through 1983 is the Atlas Agena. After 1983, it is assumed SEASAT-A will switch to the use of the Space Shuttle. All cost estimates are 1976 dollars for fiscal year cost accounting, with no inflation rate included.

Luckl, L.↗