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NASA NTRS1990

Staggered solution procedures for multibody dynamics simulation

The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.

Park, K. C.↗

NASA NTRS1995

Artificial neural network application for space station power system fault diagnosis

This study presents a methodology for fault diagnosis using a Two-Stage Artificial Neural Network Clustering Algorithm. Previously, SPICE models of a 5-bus DC power distribution system with assumed constant output power during contingencies from the DDCU were used to evaluate the ANN's fault diagnosis capabilities. This on-going study uses EMTP models of the components (distribution lines, SPDU, TPDU, loads) and power sources (DDCU) of Space Station Alpha's electrical Power Distribution System as a basis for the ANN fault diagnostic tool. The results from the two studies are contrasted. In the event of a major fault, ground controllers need the ability to identify the type of fault, isolate the fault to the orbital replaceable unit level and provide the necessary information for the power management expert system to optimally determine a degraded-mode load schedule. To accomplish these goals, the electrical power distribution system's architecture can be subdivided into three major classes: DC-DC converter to loads, DC Switching Unit (DCSU) to Main bus Switching Unit (MBSU), and Power Sources to DCSU. Each class which has its own electrical characteristics and operations, requires a unique fault analysis philosophy. This study identifies these philosophies as Riddles 1, 2 and 3 respectively. The results of the on-going study addresses Riddle-1. It is concluded in this study that the combination of the EMTP models of the DDCU, distribution cables and electrical loads yields a more accurate model of the behavior and in addition yielded more accurate fault diagnosis using ANN versus the results obtained with the SPICE models.

Momoh, James A.↗

NASA NTRS1994

Liquid Flyback Booster Pre-Phase A Study Assessment

Mw concept of a flyback booster has been around since early in the Shuttle program. The original two-stage Shuttle concepts used a manned flyback booster. These boosters were eliminated from the program for funding and size reasons. The current Shuttle uses two Redesigned Solid Rocket Motors (RSRMs), which are recovered and refurbished after each flight; this is one of the major cost factors of the program. Replacement options have been studied over the past ten years. The conclusion reached by the most recent study is that the liquid flyback booster (LFBB) is the only competitive option from a life-cycle cost perspective. The purpose of this study was to assess the feasibility and practicality of LFBBs. The study provides an expansion of the recommendations made during the during the aforementioned study. The primary benefits are the potential for enhanced reusability and a reuction of recurring costs. The potential savings in vehicle turnaround could offset the up-front costs. Development of LFBBs requires a commitment to the Shuttle program for 20 to 30 years. LFBBs also offer enhanced safety and abort capabilities. Currently, any failure of an RSRM can be considered catastrophic since them we no intact abort capabilities during the burn of the RSRMS. The performance goal of the LFBBs was to lift a fully loaded Orbiter under optimal conditions, so as not to be the limiting factor of the performance capability of the Shuttle. In addition, a final benefit is the availability of growth paths for applications other than the Shuttle.

Peterson, W.↗

NASA NTRS2001

Development and Validation of High Performance Unshrouded Centrifugal Impeller

The feasibility of using a two-stage unshrouded impeller turbopump to replace the current three-stage reusable launch vehicle engine shrouded impeller hydrogen pump has been evaluated from the standpoint of turbopump weight reduction and overall payload improvement. These advantages are a by-product of the higher tip speeds that an unshrouded impeller can sustain. The issues associated with the effect of unshrouded impeller tip clearance on pump efficiency and head have been evaluated with one-dimensional tools and full three-dimensional rotordynamic fluid reaction forces and coefficients have been established through time dependent computational fluid dynamics (CFD) simulation of the whole 360 degree impeller with different rotor eccentricities and whirling ratios. Unlike the shrouded impeller, the unshrouded impeller forces are evaluated as the sum of the pressure forces on the blade and the pressure forces on the hub using the CFD results. The turbopump axial thrust control has been optimized by adjusting the first stage impeller backend wear ring seal diameter and diverting the second stage backend balance piston flow to the proper location. The structural integrity associated with the high tip speed has been checked by analyzing a 3D-Finite Element Model at maximum design conditions (6% higher than the design speed). This impeller was fabricated and tested in the NASA Marshall Space Flight Center water-test rig. The experimental data will be compared with the analytical predictions and presented in another paper. The experimental data provides validation data for the numerical design and analysis methodology. The validated numerical methodology can be used to help design different unshrouded impeller configurations.

Chen, Wei-Chung↗

NASA NTRS2003

High-Energy Two-Stage Pulsed Plasma Thruster

A high-energy (28 kJ per pulse) two-stage pulsed plasma thruster (MSFC PPT-1) has been constructed and tested. The motivation of this project is to develop a high power (approximately 500 kW), high specific impulse (approximately 10000 s), highly efficient (greater than 50%) thruster for use as primary propulsion in a high power nuclear electric propulsion system. PPT-1 was designed to overcome four negative characteristics which have detracted from the utility of pulsed plasma thrusters: poor electrical efficiency, poor propellant utilization efficiency, electrode erosion, and reliability issues associated with the use of high speed gas valves and high current switches. Traditional PPTs have been plagued with poor efficiency because they have not been operated in a plasma regime that fully exploits the potential benefits of pulsed plasma acceleration by electromagnetic forces. PPTs have generally been used to accelerate low-density plasmas with long current pulses. Operation of thrusters in this plasma regime allows for the development of certain undesirable particle-kinetic effects, such as Hall effect-induced current sheet canting. PPT-1 was designed to propel a highly collisional, dense plasma that has more fluid-like properties and, hence, is more effectively pushed by a magnetic field. The high-density plasma loading into the second stage of the accelerator is achieved through the use of a dense plasma injector (first stage). The injector produces a thermal plasma, derived from a molten lithium propellant feed system, which is subsequently accelerated by the second stage using mega-amp level currents, which eject the plasma at a speed on the order of 100 kilometers per second. Traditional PPTs also suffer from dynamic efficiency losses associated with snowplow loading of distributed neutral propellant. The twostage scheme used in PPT-I allows the propellant to be loaded in a manner which more closely approximates the optimal slug loading. Lithium propellant was chosen to test whether or not the reduced electrode erosion found in the Lithium Lorentz Force Accelerator (LiLFA) could also be realized in a pulsed plasma thruster. The use of the molten lithium dense plasma injector also eliminates the need for a gas valve and electrical switch; the injector design fulfills both roles, and uses no moving parts to provide, in principle, a highly reliable propellant feed and electrical switching system. Experimental results reported in this paper include: second-stage current traces, high-speed photographic and holographic imaging of the thruster exit plume, and internal mapping of the discharge chamber magnetic field from B-dot probe data. The magnetic field data is used to create a two-dimensional description of the evolution of the current sheet inside the thruster.

Markusic, Tom↗

NASA NTRS2008

Using LDPC Code Constraints to Aid Recovery of Symbol Timing

A method of utilizing information available in the constraints imposed by a low-density parity-check (LDPC) code has been proposed as a means of aiding the recovery of symbol timing in the reception of a binary-phase-shift-keying (BPSK) signal representing such a code in the presence of noise, timing error, and/or Doppler shift between the transmitter and the receiver. This method and the receiver architecture in which it would be implemented belong to a class of timing-recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. Acquisition and tracking of a signal of the type described above have traditionally been performed upstream of, and independently of, decoding and have typically involved utilization of a phase-locked loop (PLL). However, the LDPC decoding process, which is iterative, provides information that can be fed back to the timing-recovery receiver circuits to improve performance significantly over that attainable in the absence of such feedback. Prior methods of coupling LDPC decoding with timing recovery had focused on the use of output code words produced as the iterations progress. In contrast, in the present method, one exploits the information available from the metrics computed for the constraint nodes of an LDPC code during the decoding process. In addition, the method involves the use of a waveform model that captures, better than do the waveform models of the prior methods, distortions introduced by receiver timing errors and transmitter/ receiver motions. An LDPC code is commonly represented by use of a bipartite graph containing two sets of nodes. In the graph corresponding to an (n,k) code, the n variable nodes correspond to the code word symbols and the n-k constraint nodes represent the constraints that the code places on the variable nodes in order for them to form a valid code word. The decoding procedure involves iterative computation of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.

Jones, Christopher↗

NASA NTRS1954

Analysis of Rocket, Ram-Jet, and Turbojet Engines for Supersonic Propulsion of Long-Range Missles. II - Rocket Missile Performance

The theoretical performance of a two-stage ballistic rocket mis having a centerbody and two parallel boosters was investigated for J oxygen and ammonia-fluorine propellants. Both power-plant and missi parameters were optimized to give minimum cost on-the basis of the analysis for a range of 5500 nautical miles. After optimum values were found, each parameter was varied independently to determine its effect on performance of the missile. The missile using the ammonia-fluorine propellant weighs about one half as much as a missile using JP4-oxygen. Based on an expected unit cost of fluorine in quantity production, the ammonia-fluorine missile has a substantially lower relative cost than a JP4-oxygen missile. Optimum chamber pressures for both propellant systems and for both the centerbody and boosters were between 450 and 600 pounds per square inch. High design altitudes for the exhaust nozzle are desirable for both the centerbody and boosters. For the centerbody, the design altitude should be between 45,000 and 60,000 feet, with the value for ammonia-fluorine lower than that for JP4-oxygen. For the boosters, the design altitude should be 20,000 to 30,000 feet, with the value for the ammonia-fluorine. missile higher.

Huff, Vearl N.↗

NASA NTRS2011

Orbiter Trajectory Analysis for a Two-Stage Reusable Launch Vehicle

Trajectory analysis performed on NASA's reference two-stage-to-orbit launch vehicle upper stage will be presented. The work was completed in support of the Hypersonics Multidisciplinary Analysis and Optimization effort for the NASA-Air Force Joint System Study. Three degree-of-freedom (3-DOF) untrimmed trajectory analysis was performed for the orbiter ascent, closure and re-entry. An iterative closure process resulted in a 333,000 lb initial mass for the orbiter. The re-entry trajectory satisfied heating constraints for all payload out cases and met the constraints with reduced margins for payload in cases. Abort trajectories for engine out at staging, engine out during ascent, and failure to circularize in orbit, gave insight to the robustness of the orbiter. A trimmed ascent trajectory defined an engine gimbal location and the body flap angle best suited for maximizing injected mass. A trimmed re-entry trajectory revealed a need to update the trim routine to accommodate full flap aerodynamic data.

Cowling, Adam L.↗

NASA NTRS2011

A Technology Pathway for Airbreathing, Combined-Cycle, Horizontal Space Launch Through SR-71 Based Trajectory Modeling

Access to space is in the early stages of commercialization. Private enterprises, mainly under direct or indirect subsidy by the government, have been making headway into the LEO launch systems infrastructure, of small-weight-class payloads of approximately 1000 lbs. These moderate gains have emboldened the launch industry and they are poised to move into the middle-weight class (roughly 5000 lbs). These commercially successful systems are based on relatively straightforward LOX-RP, two-stage, bi-propellant rocket technology developed by the government 40 years ago, accompanied by many technology improvements. In this paper we examine a known generic LOX-RP system with the focus on the booster stage (1st stage). The booster stage is then compared to modeled Rocket-Based and Turbine-Based Combined Cycle booster stages. The air-breathing propulsion stages are based on/or extrapolated from known performance parameters of ground tested RBCC (the Marquardt Ejector Ramjet) and TBCC (the SR-71/J-58 engine) data. Validated engine models using GECAT and SCCREAM are coupled with trajectory optimization and analysis in POST-II to explore viable launch scenarios using hypothetical aerospaceplane platform obeying the aerodynamic model of the SR-71. Finally, and assessment is made of the requisite research technology advances necessary for successful commercial and government adoption of combined-cycle engine systems for space access.

Kloesel, Kurt J.↗

NASA NTRS2011

Evaluation of Bosch-Based Systems Using Non-Traditional Catalysts at Reduced Temperatures

Oxygen and water resupply make open loop atmosphere revitalization (AR) systems unfavorable for long-term missions beyond low Earth orbit. Crucial to closing the AR loop are carbon dioxide reduction systems with low mass and volume, minimal power requirements, and minimal consumables. For this purpose, NASA is exploring using Bosch-based systems. The Bosch process is favorable over state-of-the-art Sabatier-based processes due to complete loop closure. However, traditional operation of the Bosch required high reaction temperatures, high recycle rates, and significant consumables in the form of catalyst resupply due to carbon fouling. A number of configurations have been proposed for next-generation Bosch systems. First, alternative catalysts (catalysts other than steel wool) can be used in a traditional single-stage Bosch reactor to improve reaction kinetics and increase carbon packing density. Second, the Bosch reactor may be split into separate stages wherein the first reactor stage is dedicated to carbon monoxide and water formation via the reverse water-gas shift reaction and the second reactor stage is dedicated to carbon formation. A series system will enable maximum efficiency of both steps of the Bosch reaction, resulting in optimized operation and maximum carbon formation rate. This paper details the results of testing of both single-stage and two-stage Bosch systems with alternative catalysts at reduced temperatures. These results are compared to a traditional Bosch system operated with a steel wool catalyst.

Abney, Morgan B.↗

NASA NTRS2013

An Efficient, Highly Flexible Multi-Channel Digital Downconverter Architecture

In this innovation, a digital downconverter has been created that produces a large (16 or greater) number of output channels of smaller bandwidths. Additionally, this design has the flexibility to tune each channel independently to anywhere in the input bandwidth to cover a wide range of output bandwidths (from 32 MHz down to 1 kHz). Both the flexibility in channel frequency selection and the more than four orders of magnitude range in output bandwidths (decimation rates from 32 to 640,000) presented significant challenges to be solved. The solution involved breaking the digital downconversion process into a two-stage process. The first stage is a 2 oversampled filter bank that divides the whole input bandwidth as a real input signal into seven overlapping, contiguous channels represented with complex samples. Using the symmetry of the sine and cosine functions in a similar way to that of an FFT (fast Fourier transform), this downconversion is very efficient and gives seven channels fixed in frequency. An arbitrary number of smaller bandwidth channels can be formed from second-stage downconverters placed after the first stage of downconversion. Because of the overlapping of the first stage, there is no gap in coverage of the entire input bandwidth. The input to any of the second-stage downconverting channels has a multiplexer that chooses one of the seven wideband channels from the first stage. These second-stage downconverters take up fewer resources because they operate at lower bandwidths than doing the entire downconversion process from the input bandwidth for each independent channel. These second-stage downconverters are each independent with fine frequency control tuning, providing extreme flexibility in positioning the center frequency of a downconverted channel. Finally, these second-stage downconverters have flexible decimation factors over four orders of magnitude The algorithm was developed to run in an FPGA (field programmable gate array) at input data sampling rates of up to 1,280 MHz. The current implementation takes a 1,280-MHz real input, and first breaks it up into seven 160-MHz complex channels, each spaced 80 MHz apart. The eighth channel at baseband was not required for this implementation, and led to more optimization. Afterwards, 16 second stage narrow band channels with independently tunable center frequencies and bandwidth settings are implemented A future implementation in a larger Xilinx FPGA will hold up to 32 independent second-stage channels.

Goodhart, Charles E.↗

NASA NTRS2014

A Compact Two-Stage 120 W GaN High Power Amplifier for SweepSAR Radar Systems

This work presents the design and measured results of a fully integrated switched power two-stage GaN HEMT high-power amplifier (HPA) achieving 60% power-added efficiency at over 120Woutput power. This high-efficiency GaN HEMT HPA is an enabling technology for L-band SweepSAR interferometric instruments that enable frequent repeat intervals and high-resolution imagery. The L-band HPA was designed using space-qualified state-of-the-art GaN HEMT technology. The amplifier exhibits over 34 dB of power gain at 51 dBm of output power across an 80 MHz bandwidth. The HPA is divided into two stages, an 8 W driver stage and 120 W output stage. The amplifier is designed for pulsed operation, with a high-speed DC drain switch operating at the pulsed-repetition interval and settles within 200 ns. In addition to the electrical design, a thermally optimized package was designed, that allows for direct thermal radiation to maintain low-junction temperatures for the GaN parts maximizing long-term reliability. Lastly, real radar waveforms are characterized and analysis of amplitude and phase stability over temperature demonstrate ultra-stable operation over temperature using integrated bias compensation circuitry allowing less than 0.2 dB amplitude variation and 2 deg phase variation over a 70 C range.

Thrivikraman, Tushar↗

NASA NTRS2015

Mars Ascent Vehicle-First Stage Motor

This project is development effort of a first stage solid motor based on a two-stage solid motor Mars Ascent Vehicle (MAV) design for the robotic Mars Sample Return (MSR) mission (fig. 1). The MSR MAV has been studied for decades and multiple concepts have been shown to meet the mission objectives as posed.1 However, there remains significant uncertainty with the MAV requirements. The sample container and sample cache itself is immature. Additionally, MAV-specific requirements ranging from full three-axis controlled and strict communication requirements to minimal capability concepts are still under consideration. Given the maturity of the overall mission requirements, the MAV has been limited to a large number of parametric analyses and paper studies. Recently, a Jet Propulsion Laboratory study highlighted the flexibility of a two-stage solid motor concept. The MAV itself is driven by the constraints of the Entry, Decent, and Landing (EDL) system. Within the EDL constraints, there is a range of MAV options ranging in complexity from simple spun upper stage options to higher capability three-axis controlled solutions. There are also options to trade the ratio of mission (Delta)V between the first and second stage. Finally, sensitivity studies also indicated that solid motors with a high percentage of off-load flexability only had minor impact on the total system mass over a single point design optimized motor. This flexibility in the first stage motor has allowed NASA to mature the design of the motor beyond parametric analyses and start to address known design challenges of the motor.

Dankanich, John↗

NASA NTRS2014

A Simple Analytic Model for Estimating Mars Ascent Vehicle Mass and Performance

The Mars Ascent Vehicle (MAV) is a crucial component in any sample return campaign. In this paper we present a universal model for a two-stage MAV along with the analytic equations and simple parametric relationships necessary to quickly estimate MAV mass and performance. Ascent trajectories can be modeled as two-burn transfers from the surface with appropriate loss estimations for finite burns, steering, and drag. Minimizing lift-off mass is achieved by balancing optimized staging and an optimized path-to-orbit. This model allows designers to quickly find optimized solutions and to see the effects of design choices.

Woolley, Ryan C.↗

NASA NTRS2016

Design of a Two-Stage Light Gas Gun for Muzzle Velocities of 10 - 11 kms

Space debris poses a major risk to spacecraft. In low earth orbit, impact velocities can be 10 11 kms and as high as 15 kms. For debris shield design, it would be desirable to be able to launch controlled shape projectiles to these velocities. The design of the proposed 10 11 kmsec gun uses, as a starting point, the Ames 1.280.22 two stage gun, which has achieved muzzle velocities of 10 11.3 kmsec. That gun is scaled up to a 0.3125 launch tube diameter. The gun is then optimized with respect to maximum pressures by varying the pump tube length to diameter ratio (LD), the piston mass and the hydrogen pressure. A pump tube LD of 36.4 is selected giving the best overall performance. Piezometric ratios for the optimized guns are found to be 2.3, much more favorable than for more traditional two stage light gas guns, which range from 4 to 6. The maximum powder chamber pressures are 20 to 30 ksi. To reduce maximum pressures, the desirable range of the included angle of the cone of the high pressure coupling is found to be 7.3 to 14.6 degrees. Lowering the break valve rupture pressure is found to lower the maximum projectile base pressure, but to raise the maximum gun pressure. For the optimized gun with a pump tube LD of 36.4, increasing the muzzle velocity by decreasing the projectile mass and increasing the powder loads is studied. It appears that saboted spheres could be launched to 10.25 and possibly as high as 10.7 10.8 kmsec, and that disc-like plastic models could be launched to 11.05 kms. The use of a tantalum liner to greatly reduce bore erosion and increase muzzle velocity is discussed. With a tantalum liner, CFD code calculations predict muzzle velocities as high as 12 to 13 kms.

Gun Design↗

NASA NTRS2016

Design of a Two-Stage Light Gas Gun for Muzzle Velocities of 10 - 11 km/s

Space debris poses a major risk to spacecraft. In low earth orbit, impact velocities can be 10 - 11 km/s and as high as 15 km/s. For debris shield design, it would be desirable to be able to launch projectiles of known shape and mass to these velocities. The design of the proposed 10 - 11 km/sec gun uses, as a starting point, the Ames 1.28”/0.22” two stage gun, which has achieved muzzle velocities of 10 - 11.3 km/sec. That gun is scaled up to a 0.3125” launch tube diameter. The gun is then optimized with respect to maximum pressures by varying the pump tube length to diameter ratio (L/D), the piston mass and the hydrogen pressure. A pump tube L/D of 36.4 is selected giving the best overall performance. Piezometric ratios for the optimized guns are found to be ~2.3, much more favorable than for more traditional two stage light gas guns, which range from 4 to 6. (The piezometric ratio for a gun is defined as the maximum projectile base pressure divided by the constant projectile base pressure which, acting over the entire barrel length, would produce the same muzzle velocity.) The maximum powder chamber pressures are 20 to 30 ksi. To reduce maximum pressures, the desirable range of the included angle of the cone of the high pressure coupling is found to be 7.3 to 14.6 degrees. Lowering the break valve rupture pressure is found to lower the maximum projectile base pressure, but to raise the maximum gun pressure. For the optimized gun with a pump tube L/D of 36.4, increasing the muzzle velocity by decreasing the projectile mass and increasing the powder loads is studied. It appears that saboted spheres could be launched to 10.25 and possibly as high as 10.8 km/sec, and that disc-like plastic models could be launched to 11.05 km/s. The use of a tantalum liner to greatly reduce bore erosion and increase muzzle velocity is discussed. With a tantalum liner, CFD code calculations predict muzzle velocities as high as 12 to 13 km/s.

Bogdanoff, David W.↗

NASA NTRS2019

Small Launch Vehicle Sizing Analysis with Solid Rocket Examples

Small launch vehicles are governed by the same physics as large launch vehicles of course, but due to their small size, some aspects and sensitivities become more important and others less. This paper shows semi-empirical correlations to quantify dry mass fraction for both stage and whole vehicle optimization: mass fraction due to density, mass fraction due to thrust-to-weight, and mass fraction due to size reduction. For single-stage optimizations, a stage performance requirement can be met by a locus of mass fraction vs. specific impulse. Based on the above correlations, this alone can recommend a solid or liquid rocket for a stage. Rocket designs of similar technology levels are compared, focusing on where stages become less mass-efficient as they get smaller. The Mars Ascent Vehicle is shown to exemplify a trade between a two-stage solids vehicle and a one- or two-stage liquids vehicle.

Kibbey, Tim↗

NASA NTRS2019

Small Launch Vehicle Sizing Analysis With Solid Rocket Examples

Kibbey, Tim↗