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NASA NTRSDate not supplied

Design Development of a Stable, Lightweight, Tall and Self-Deploying Lunar Tower

Deployable composite booms with spaceflight heritage are being investigated at the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) and the Massachusetts Institute of Technology (MIT) Space Resources Workshop for their potential to be vertically deployed in the lunar gravity field, in support of the NASA Artemis campaign. This paper reports new design development results—after the original presentation at the NASA 2020 BIG Idea Challenge—for a 16.5-meter-tall, compact, self-deploying composite tower intended to support the exploration of lunar permanently shadowed regions by nearby robotic assets or humans. Possible applications include vertical solar arrays and the provision of elevated lines-of-sight to science or engineering payloads, in support of nearby targets operating in areas of interest that may be hard to reach. Useful elevated payloads include radio repeaters, remote sensing and imaging, navigation and power beaming systems. However, while these lightweight rollable booms have an excellent height to mass ratio, they typically exhibit axial curvature upon deployment resulting in appreciable lateral dead-load deflection of the tip mass relative to the tower base. This static deflection increases with tower height and tip mass, not only constraining the value delivered by the tower but also endangering its integrity. To develop a competitive, lightweight deployable composite boom tower, a capability to correct static deflections during and after deployment will be required. In this paper, a deployable guy wire stability system will be presented for the MIT / LaRC self-erecting composite boom lunar tower that provides real time measurements, maintains tension both actively (during deployment) and passively (post-deployment), and can serve as a reconfigurable platform to test and trade alternative stability system configurations, such as with added spreaders inspired by sailing boat masts. Using a calibrated photogrammetry system, the natural lateral deflection of the boom tip relative to the boom base at different deployed heights was recorded for different configurations. With real-time force measurements it was found that tensioned guy wires can significantly reduce the static tip deflection of a deployable composite boom under dead load and can dampen a dynamic oscillation in under a minute. It was also found that control authority is greatest where it is needed most, i.e., for the lever arm closest to being opposite the direction of deflection. For a tower height of at least 11 m and spreader length of at least 60 cm, a solution of differential tension in all three arms exists and, in principle, provides sufficient control authority to correct or significantly reduce boom tip deflections. Notably, natural deflections occur almost entirely normal to the seams of the boom cross-section, but the natural boom tip lateral deflection under dead load upon deployment was approximately 5% of boom deployed length, exceeding the manufacturing acceptance specification of 1%. Ongoing and future work includes the further investigation towards mitigating manufacture-caused lateral deflection, trading of alternative guy wire system designs, as well as the design development of a second-generation tower incorporating a more capable boom design with the learnings from the proof-of-concept system presented here.

deployable composite boom↗

NASA NTRS1994

Kinematic functions for redundancy resolution using configuration control

The invention fulfills new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals are accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix of the end-effector mass matrix that affect the inertial torques or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical-advantage and velocity-ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy resolution criteria. The new goals for redundancy resolution allow a more efficient utilization of the redundant joints based on the desired task requirements.

Seraji, Homayoun↗

NASA NTRS1996

Augmentation of Rocket Propulsion: Physical Limits

Rocket propulsion is not ideal when the propellant is not ejected at a unique velocity in an inertial frame. An ideal velocity distribution requires that the exhaust velocity vary linearly with the velocity of the vehicle in an inertial frame. It also requires that the velocity distribution variance as a thermodynamic quantity be minimized. A rocket vehicle with an inert propellant is not optimal, because it does not take advantage of the propellant mass for energy storage. Nor is it logical to provide another energy storage device in order to realize variable exhaust velocity, because it would have to be partly unfilled at the beginning of the mission. Performance is enhanced by pushing on the surrounding because it increases the reaction mass and decreases the reaction jet velocity. This decreases the fraction of the energy taken away by the propellant and increases the share taken by the payload. For an optimal model with the propellant used as fuel, the augmentation realized by pushing on air is greatest for vehicles with a low initial/final mass ratio. For a typical vehicle in the Earth's atmosphere, the augmentation is seen mainly at altitudes below about 80 km. When drag is taken into account, there is a well-defined optimum size for the air intake. Pushing on air has the potential to increase the performance of rockets which pass through the atmosphere. This is apart from benefits derived from "air breathing", or using the oxygen in the atmosphere to reduce the mass of an on-board oxidizer. Because of the potential of these measures, it is vital to model these effects more carefully and explore technology that may realize their advantages.

Taylor, Charles R.↗

NASA NTRS2019

Mid-Lift-to-Drag Ratio Rigid Vehicle 6-DOF EDL Performance Using Tunable Apollo Powered Guidance

The Mid-Lift-to-Drag ratio Rigid Vehicle (MRV) is a candidate in the NASA multi-center effort to determine the most cost effective vehicle to deliver a large-mass payload to the surface of Mars for a human mission. Products of this effort include six-degree-of-freedom (6DoF) entry-to-descent trajectory performance studies for each candidate vehicle. These high fidelity analyses help determine the best guidance and control (G&C) strategies for a feasible, robust trajectory. This paper presents an analysis of the MRV's G&C design by applying common entry and descent associated uncertainties using a Fully Numerical Predictor-corrector Entry Guidance (FNPEG) and tunable Apollo powered descent guidance.

human↗

NASA NTRS2019

Mid-Lift-To-Drag Ratio Rigid Vehicle 6-DOF EDL Performance Using Tunable Apollo Powered Guidance

The Mid-Lift-to-Drag ratio Rigid Vehicle (MRV) is a candidate in the NASA multi-center effort to determine the most cost effective vehicle to deliver a large-mass payload to the surface of Mars for a human mission. Products of this effort include six-degree-of-freedom (6DoF) entry-to-landing trajectory performance studies for each candidate vehicle. These high fidelity analyses help determine the best guidance and control (G&C) strategies for a feasible, robust trajectory. This paper presents an analysis of the MRV's G&C design by applying common entry and descent associated uncertainties using a Fully Numerical Predictor-corrector Entry Guidance (FNPEG) and tunable Apollo powered descent guidance.

Johnson, Breanna J.↗

NASA NTRS1985

Launching rockets and small satellites from the lunar surface

Scientific payloads and their propulsion systems optimized for launch from the lunar surface differ considerably from their counterparts for use on earth. For spin-stabilized payloads, the preferred shape is a large diameter-to-length ratio to provide stability during the thrust phase. The rocket motor required for a 50-kg payload to reach an altitude of one lunar radius would have a mass of about 41 kg. To place spin-stabilized vehicles into low altitude circular orbits, they are first launched into an elliptical orbit with altitude about 840 km at aposelene. When the spacecraft crosses the desired circular orbit, small retro-rockets are fired to attain the appropriate direction and speed. Values of the launch angle, velocity increments, and other parameters for circular orbits of several altitudes are tabulated. To boost a 50-kg payload into a 100-km altitude circular orbit requires a total rocket motor mass of about 90 kg.

Anderson, K. A.↗

NASA NTRS2017

Extrapolating the Trends of Test Drop Data with Opening Shock Factor Calculations: the Case of the Orion Main and Drogue Parachutes Inflating to 1st Reefed Stage

We describe a new calculation of the opening shock factor C (sub k) characterizing the inflation performance of NASA's Orion spacecraft main and drogue parachutes opening under a reefing constraint (1st stage reefing), as currently tested in the Capsule Parachute Assembly System (CPAS) program. This calculation is based on an application of the Momentum-Impulse Theorem at low mass ratio (R (sub m) is less than 10 (sup -1)) and on an earlier analysis of the opening performance of drogues decelerating point masses and inflating along horizontal trajectories. Herein we extend the reach of the Theorem to include the effects of payload drag and gravitational impulse during near-vertical motion - both important pre-requisites for CPAS parachute analysis. The result is a family of C (sub k) versus R (sub m) curves which can be used for extrapolating beyond the drop-tested envelope. The paper proves this claim in the case of the CPAS Mains and Drogues opening while trailing either a Parachute Compartment Drop Test Vehicle or a Parachute Test Vehicle (an Orion capsule boiler plate). It is seen that in all cases the values of the opening shock factor can be extrapolated over a range in mass ratio that is at least twice that of the test drop data.

Potvin, Jean↗

NASA NTRS2000

Human Mars Transportation Applications Using Solar Electric Propulsion

Advanced solar electric power systems and electric propulsion technology constitute viable elements for conducting human Mars transfer missions that are roughly comparable in performance to similar missions utilizing alternative high thrust systems, with the one exception being their inability to achieve short Earth-Mars trip times. A modest solar electric propulsion human Mars scenario is presented that features the use of conjunction class trajectories in concert with pre-emplacement of surface assets that can be used in a series of visits to Mars. Major elements of the Mars solar electric transfer vehicle can be direct derivatives of present state-of-the-art Solar array and electric thruster systems. During the study, several elements affecting system performance were evaluated, including varying Earth orbit altitude for departure, recapturing the transfer stage at Earth for reuse, varying power system mass-to-power ratio, and assessing solar array degradation on performance induced by Van Allen belt passage. Comparisons are made to chemical propulsion and nuclear thermal propulsion Mars vehicles carrying similar payloads.

Donahue, Benjamin B.↗

NASA NTRS2001

Sampling of Trace Atmospheric Constituents Above the Surface of Mars from a Montgolfiere Balloon

We suggest that use of an aerially deployed, solar-heated balloon, or Montgolfiere, during a Martian polar summer could provide an optimal platform for atmospheric measurements near the surface. Solar Montgolfieres are empty balloons with a hole in the bottom that fill with ambient atmosphere while failing and are rapidly heated in by the sun, thus providing buoyancy. Such a balloon would be driven by the Martian winds in the constant sunlight of a high latitude entry and could provide a traverse of thousands of kilometers. It would encircle the Martian north polar region over a period,likely lasting over one earth month, and its altitude could be controlled as low as 100 meters to as high as 4000 meters above the surface. The significant payload of tens of kilograms allowed by this technology could readily accommodate the mass of instrumentation and the power source needed for a sensitive search for disequilibrium species that might provide the atmospheric signature of localized subsurface biological or geological activity. A mass spectrometer used in combination with gas enrichment techniques can provide sensitivities to sub parts per billion for several species of interest. Additional highly specific and sensitive detectors can search for other species or measurements of their mixing ratio variation along the path of the balloon. It would be useful to combine these atmospheric measurements with electromagnetic sounding to search for variations in subsurface conductivity that might indicate the presence of subsurface water. After a month of operation, the balloon could also soft land the DBMS to provide additional data on soil samples from a 1-2 meter subsurface drill. In order to float a 30-kg payload at altitudes between 100 m and 4000 m above the Martian north polar surface, an aluminized polyethylene Montgolfiere would be approximately 29 meters in diameter and have a mass of 27 kg. Altitude variations could be accomplished by means of an upper vent to release hot gas, as has been tested at JPL, or be means of a simple, internal winch mechanism to decrease the volume of the balloon. JPL has successfully deployed three polyethylene Montgolfieres at 4-6 mbar pressure in the Earth's stratosphere and will be deploying a 20-m diameter polyethylene Montgolfiere later in 2001.

Jones, Jack A.↗

NASA NTRS2015

Multiplying Mars Lander Opportunities with Marsdrop Microlanders

From canyons to glaciers, from geology to astrobiology, the amount of exciting surface science awaiting us at Mars greatly outstrips available mission opportunities. Based on the thrice -flown Aerospace Corporation Earth Reentry Breakup Recorder (REBR), we present a method for accurate landing of small instrument payloads on Mars, utilizing excess cruise -stage mass on larger missions. One to a few such microlanders might add 1-5% to the cost of a primary mission with inconsequential risk. Using the REBR and JPL Deep Space 2 starting points for a passively stable entry vehicle provides a low mass and low ballistic coefficient, enabling subsonic d employment of a steerable parawing glider, capable of 10+ km of guided flight at a 3:1 glide ratio. Originally developed for the Gemini human space program, the parawing is attractive for a volume -limited microprobe, minimizing descent velocity, and providing sufficient remaining volume for a useful scientific payload. The ability to steer the parawing during descent opens unique opportunities, including terrain- relative navigation for landing within tens of meters of one of several specified targets within a given uncertainty ellipse. In addition to scientific value, some Mars human exploration Strategic Knowledge Gaps could be addressed with deployment of focused instruments at multiple locations.

Staehle, Robert L.↗

NASA NTRS2005

Realizing "2001: A Space Odyssey": Piloted Spherical Torus Nuclear Fusion Propulsion

A conceptual vehicle design enabling fast, piloted outer solar system travel was created predicated on a small aspect ratio spherical torus nuclear fusion reactor. The initial requirements were satisfied by the vehicle concept, which could deliver a 172 mt crew payload from Earth to Jupiter rendezvous in 118 days, with an initial mass in low Earth orbit of 1,690 mt. Engineering conceptual design, analysis, and assessment was performed on all major systems including artificial gravity payload, central truss, nuclear fusion reactor, power conversion, magnetic nozzle, fast wave plasma heating, tankage, fuel pellet injector, startup/re-start fission reactor and battery bank, refrigeration, reaction control, communications, mission design, and space operations. Detailed fusion reactor design included analysis of plasma characteristics, power balance/utilization, first wall, toroidal field coils, heat transfer, and neutron/x-ray radiation. Technical comparisons are made between the vehicle concept and the interplanetary spacecraft depicted in the motion picture 2001: A Space Odyssey.

Williams, Craig H.↗

NASA NTRS1987

Transport vehicle for manned Mars missions powered by inertial confinement fusion

Inertial confinement fusion (ICF) is an ideal engine power source for manned spacecraft to Mars because of its inherently high power-to-mass ratios and high specific impulses. In this paper a concept is produced for a vehicle powered by ICF and utilizing a magnetic thrust chamber to avoid plasma thermalization with wall structures and the resultant degradation of specific impulse, that are unavoidable with the use of mechanical thrust chambers. This vehicle is capable of 100-day manned Mars missions with a 100-metric-ton payload and a total vehicle launch mass near 6000 metric tons, based on advanced technology assumed to be available by A.D. 2020.

Orth, Charles D.↗

NASA NTRS1981

Integrated propulsion for near-Earth space missions. Volume 2: Technical

The calculation approach is described for parametric analysis of candidate electric propulsion systems employed in LEO to GEO missions. Occultation relations, atmospheric density effects, and natural radiation effects are presented. A solar cell cover glass tradeoff is performed to determine optimum glass thickness. Solar array and spacecraft pointing strategies are described for low altitude flight and for optimum array illumination during ascent. Mass ratio tradeoffs versus transfer time provide direction for thruster technology improvements. Integrated electric propulsion analysis is performed for orbit boosting, inclination change, attitude control, stationkeeping, repositioning, and disposal functions as well as power sharing with payload on orbit. Comparison with chemical auxiliary propulsion is made to quantify the advantages of integrated propulsion in terms of weight savings and concomittant launch cost savings.

Dailey, C. L.↗

NASA NTRS2007

Mars Science Laboratory: Entry, Descent, and Landing System Performance

In 2010, the Mars Science Laboratory (MSL) mission will pioneer the next generation of robotic Entry, Descent, and Landing (EDL) systems, by delivering the largest and most capable rover to date to the surface of Mars. To do so, MSL will fly a guided lifting entry at a lift-to-drag ratio in excess of that ever flown at Mars, deploy the largest parachute ever at Mars, and perform a novel Sky Crane maneuver. Through improved altitude capability, increased latitude coverage, and more accurate payload delivery, MSL is allowing the science community to consider the exploration of previously inaccessible regions of the planet. The MSL EDL system is a new EDL architecture based on Viking heritage technologies and designed to meet the challenges of landing increasing massive payloads on Mars. In accordance with level-1 requirements, the MSL EDL system is being designed to land an 850 kg rover to altitudes as high as 1 km above the Mars Orbiter Laser Altimeter defined areoid within 10 km of the desired landing site. Accordingly, MSL will enter the largest entry mass, fly the largest 70 degree sphere-cone aeroshell, generate the largest hypersonic lift-to-drag ratio, and deploy the largest Disk-Gap-Band supersonic parachute of any previous mission to Mars. Major EDL events include a hypersonic guided entry, supersonic parachute deploy and inflation, subsonic heatshield jettison, terminal descent sensor acquisition, powered descent initiation, sky crane terminal descent, rover touchdown detection, and descent stage flyaway. Key performance metrics, derived from level-1 requirements and tracked by the EDL design team to indicate performance capability and timeline margins, include altitude and range at parachute deploy, time on radar, and propellant use. The MSL EDL system, which will continue to develop over the next three years, will enable a notable extension in the advancement of Mars surface science by delivering more science capability than ever before to the surface of Mars. This paper describes the current MSL EDL system performance as predicted by end-to-end EDL simulations, highlights the sensitivity of this baseline performance to several key environmental assumptions, and discusses some of the challenges faced in delivering such an unprecedented rover payload to the surface of Mars.

Way, David W.↗

NASA NTRS2006

Mars Science Laboratory: Entry, Descent, and Landing System Performance

Way, David W.↗

NASA NTRS2001

Impact of Energy Gain and Subsystem Characteristics on Fusion Propulsion Performance

Rapid transport of large payloads and human crews throughout the solar system requires propulsion systems having very high specific impulse (I(sub sp) > 10(exp 4) to 10(exp 5) s). It also calls for systems with extremely low mass-power ratios (alpha < 10(exp -1) kg/kW). Such low alpha are beyond the reach of conventional power-limited propulsion, but may be attainable with fusion and other nuclear concepts that produce energy within the propellant. The magnitude of energy gain must be large enough to sustain the nuclear process while still providing a high jet power relative to the massive energy-intensive subsystems associated with these concepts. This paper evaluates the impact of energy gain and subsystem characteristics on alpha. Central to the analysis are general parameters that embody the essential features of any 'gain-limited' propulsion power balance. Results show that the gains required to achieve alpha = 10(exp -1) kg/kW with foreseeable technology range from approximately 100 to over 2000, which is three to five orders of magnitude greater than current fusion state of the arL Sensitivity analyses point to the parameters exerting the most influence for either: (1) lowering a and improving mission performance or (2) relaxing gain requirements and reducing demands on the fusion process. The greatest impact comes from reducing mass and increasing efficiency of the thruster and subsystems downstream of the fusion process. High relative gain, through enhanced fusion processes or more efficient drivers and processors, is also desirable. There is a benefit in improving driver and subsystem characteristics upstream of the fusion process, but it diminishes at relative gains > 100.

Chakrabarti, S.↗

NASA NTRS2016

Analysis of a Radioisotope Thermal Rocket Engine

The Triton Hopper is a concept for a global hopper vehicle which uses a radioisotope rocket engine and In-situ propellant acquisition to explore the surface of Neptune's moon, Triton. The current Triton Hopper concept stores heated Nitrogen in a spherical tank to be used as the propellant. The aim of the research was to investigate the benefits of storing propellant at ambient temperature and heating it through the use of a thermal block during engine operation, as opposed to storing gas at a high temperature. Lithium, Lithium Fluoride and Beryllium were considered as possible materials for the thermal block. A heat energy analysis indicated that a lithium thermal mass would provide the highest heat energy for a temperature change from 900 Celsius to -100 Celsius. A heat transfer analysis was performed for Nitrogen at -100 Celsius flowing through 1000 passages inside a 1kg lithium thermal block at a temperature of 900 Celsius. The system was analyzed as turbulent flow through a tube with constant surface temperature. The analysis indicated that the propellant reached a maximum temperature of 877 Celsius before entering the nozzle. At this exit temperature, the average specific impulse [I(sub sp)] of the engine was determined to be 157s. Previous studies for the stored heated gas concept suggest that the engine would have an average I(sub sp) of approximately 52s. Thus, the use of a thermal block concept results in a 200 percent engine performance increase. In addition, a tank sizing study was performed to determine if the concept is feasible in terms of mass requirements. The mass for a spherical carbon fiber COPV storing 35kg of nitrogen at an initial temperature of -100 Celsius and a pressure of 1000psia, was determined to be 7.2kg. The specific impulse analysis indicated that the maximum engine performance is obtained for a mass ratio of 5kg of Nitrogen per every 1kg of lithium thermal mass. Thus for 35kg of Nitrogen the total thermal mass would be 7kg. This brings the total mass of the system to 49.2.kg which is less than the 56kg landing payload capacity of the Triton Hopper. Finally, an insulation analysis using 10mm of MLI insulation indicated that a total of 22 watts of heat are lost to the environment. With the heat loss known, the power required to heat the thermal mass to 900 Celsius in 24 days was determined to be 2.15 watts. The study's results allowed us to conclude that the thermal mass concept is the better option due to the performance increase provided, the low power requirement and its compliance with the landing mass requirement of the Triton Hopper.

Radioisotope↗

NASA NTRS2019

Design of a Nozzle for the Spyder 2nd Stage Solid Rocket Motor

During the 2019 summer term, the author worked with a group of four interns to complete the preliminary design of a 2nd stage solid rocket motor for Up Aerospace’s Spyder Launch Vehicle. The Spyder vehicle is a four stage, solid fuel rocket designed as part of collaboration between NASA and Up Aerospace to develop a vehicle capable of delivering a 10 kg, 6U CubeSat into a 350 km, circular, low Earth orbit. As part of the agreement, NASA is tasked with designing high performance 2nd, 3rd, and 4th stages while Up Aerospace will provide the 1st stage, derived from the first stage of the company’s sub-orbital Spaceloft XL vehicle. Previous intern teams have designed the 3rd and 4th stages, which left the preliminary design of the 2nd stage motor to be completed this summer. The purpose of this report is to highlight a trade study which the author conducted to determine the nozzle geometry which would most benefit the performance of the 2nd stage motor. In this study, various nozzle parameters such as throat radius (RSI), expansion ratio, mass and their effects on the Isp and Delta V of the 2nd Stage were investigated. From this study, a nozzle geometry providing the necessary performance was chosen and implemented as part of the preliminary design of the 2nd stage motor. To mature the 2nd stage motor design, a trade space was needed to determine the nozzle configuration which would most benefit the performance of the 2nd stage. The trade space established did not only evaluate different expansion ratios for the same throat radius, but also investigated the possible performance gained from decreasing the throat radius to increase the expansion ratio and Isp capable of being delivered by the nozzle. Decreasing the throat radius would cause the chamber pressure to increase, consequently increasing the case and insulation mass required to safely operate a motor at higher pressures. To account for this factor, accurate estimates of inert mass first needed to be established. After doing so, the effects of varying nozzle expansion ratios, exit half angles, and subsequently length and mass were evaluated against motor and nozzle performance factors such as delta V and Isp. For this study, four throat radii ranging from 1.75” to 2.375” and consequently four different chamber pressures ranging 550 psia to 1200 psia were investigated. BACKGROUND To launch into Low Earth Orbit, a payload needs to be accelerated to the orbital velocity necessary to keep it from falling back to Earth. The change in velocity required between launch and orbital insertion is known as Delta V. The Delta V which a rocket or stage can deliver can be calculated using the Ideal Rocket equation, 𝛥𝑉=−𝑔0∗𝐼𝑠𝑝∗ln(𝑀𝑓𝑀𝑖) (3) Where 𝑔0 is the acceleration due to gravity at the earth’s surface, 𝐼𝑠𝑝 is the specific impulse of the rocket, 𝑀𝑖 is the initial mass of the rocket, and 𝑀𝑓 is the final mass of the rocket after burnout. From preliminary calculations beyond the scope of this paper, it was determined that 30500 ft/s of delta V would be required for a payload to be inserted into a 350 km circular orbit around the Earth. Using the known masses and Isp values of the 1st, 3rd, and 4th stages and equation 3, the delta V of each stage was calculated. The delta V required by the 2nd stage could then be found by taking the difference between the total delta V required and the delta V of the 1st, 3rd, and 4th stages. From this, the required delta V of the 2nd Stage was calculated to be 7340 ft/s. Specific impulse is an efficiency factor of the nozzle which defines the impulse delivered by the motor per unit of propellant weight. The main variables of a nozzle’s specific impulse investigated in this trade were exit cone half angle, throat radius, and expansion ratio which is affected by the throat radius. The expansion ratio, ε, of a nozzle is defined as the ratio between the nozzle exit area and throat area, and can be calculated using the equation, ε=𝑅𝑒𝑥𝑖𝑡2𝑅𝑠𝑖2 (2) Where 𝑅𝑒𝑥𝑖𝑡 is the radius of the nozzle’s exit and 𝑅𝑠𝑖 is the radius of the nozzle’s throat. A larger expansion ratio and smaller exit half angle will increase the Isp of a nozzle by allowing the gas to expand more and by allowing more of the exhaust gas to produce thrust in the direction of the motor’s central axis. A cross section view of the 2nd Stage motor with the major components annotated is provided in figure 1.

Bennett, Daniel↗