Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Metric geometry”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Trajectory based, 3-dimensional heating and ablation calculations for the Apollo Lunar/Earth return capsule

Three dimensional (3-D) surface heating and ablation rate distributions have been obtained based on the geometry of the project Apollo Lunar/Earth return capsule and high Reynolds number inviscid/boundary layer methods. This application is based on the principles of the pseudo-three dimensional axisymmetric streamline analogy. Inviscid surface streamlines are determined for the forebody portion of the Apollo capsule using a CFD solver. Streamlines are obtained for the 20 deg angle-of-attack flight case, and the associated streamline metrics are determined. Boundary layer heating and ablation calculations are performed along selected Apollo forebody streamlines using the non-similar boundary layer code. Surface radiative heating estimates were obtained and the validity of the streamline tracing analogy is examined. These comparisons and the Apollo trajectory heating results are discussed.

Henline, W. D.↗
NASA NTRSDate not supplied

Exploring the Impact of Compliance With Maneuvering Guidelines for Space Traffic Management

If the current estimate of proposed large constellations is realized, the near-Earth space environment will see more than 50,000 new satellites added to the catalog of resident space objects (RSOs) in the coming decade. This is an order of magnitude increase from the current population and poses new policy challenges as global operators seek to leverage the benefits these new satellite systems provide while also ensuring a sustainable approach to collision avoidance. Various guidelines have been proposed to date to support this effort, including the development of right of way rules to guide how a collision avoidance maneuver should be performed, and how the maneuver burden should be shared between the two satellites involved. However, it is very difficult to evaluate and compare proposed guidelines due to the complex nature of space traffic and the rapidly changing space environment. This study seeks to address this issue by utilizing the Virtual Environment for Space Traffic Analysis (VESTA), a high-fidelity simulation tool that has been developed at Georgia Tech over the past few years with the explicit purpose of evaluating the future of space traffic environment. Using this tool, a sensitivity study is performed that incorporates a likely set of future large constellations and provides metrics on the impact that a select set of proposed maneuvering guidelines would have on operators given realistic variations in spacecraft capabilities (e.g. maneuverability and propulsion capabilities), and other factors (owner-country, public vs. private, etc.). Specifically, this study compares three potential right of way rules: 1) a rule based on maneuverability proposed by the Space Safety Coalition, 2) a rule based on the geometry of the spacecraft rendezvous, and 3) a rule that equally distributes the maneuver burden between two operators, The results highlight general observations on the effectiveness and limitations of each of the proposed maneuvering guidelines. In addition to the choice of right of way rule, success of space traffic management will be significantly impacted by compliance – which operators, or how many operators, comply with the space traffic rules. The findings of this analysis have important implications for future methods that could be pursued to put in place right of way rules. For example, non-binding right of way rules may have variable levels of compliance that differ across actors. The impact of compliance by just one nation, or non-compliance by just one nation, help to demonstrate the impact of ensuring all major space actors coordinate on this effort. Overall, this analysis provides insight into the relative gains in safety (decrease in collision risk) that would likely result from more politically intense efforts to increase the number of countries implementing space traffic management rules.

conjunction assessment↗
NASA NTRS1986

Titan Probe navigation analysis

In the proposed Cassini mission, a combined Saturn Orbiter/Titan Probe spacecraft will be launched from the Space Shuttle to arrive at Saturn around 2002, by means of a delta-VEGA trajectory. After Saturn-orbit insertion and a pericrone raise maneuver, the probe will be released to enter the Titan atmosphere and impact onto its surface. During its descent phase and impact onto Titan, the probe will maintain radio contact with the orbiter. Since the Titan-probe experimental phase lasts for only about four hours, probe-orbiter geometry and probe-delivery accuracy are critical to successful completion of this part of the mission. From a preliminary navigation analysis for probe delivery accuracy, it seems feasible to deliver the probe within 50 km (1-sigma value) of the desired aim-point in the Titan B-plane. The covariance study, however, clearly indicates the need for optical data, in addition to radio metric data. A Monte Carlo study indicates that a Delta-V capability of 98 m/sec for trajectory correction maneuvers will be sufficient to cover 99 percent of all contingencies during the segment from Saturn-orbit insertion to Titan-probe release.

Vijayaraghavan, A.↗
NASA NTRS2000

Solar Power System Evaluated for the Human Exploration of Mars

The electric power system is a crucial element of any mission for the human exploration of the Martian surface. The bulk of the power generated will be delivered to crew life support systems, extravehicular activity suits, robotic vehicles, and predeployed in situ resource utilization (ISRU) equipment. In one mission scenario, before the crew departs for Mars, the ISRU plant operates for 435 days producing liquefied methane and oxygen for ascent-stage propellants and water for crew life support. About 200 days after ISRU production is completed, the crew arrives for a 500-day surface stay. In this scenario, the power system must operate for a total of 1130 days (equivalent to 1100 Martian "sols"), providing 400 MW-hr of energy to the ISRU plant and up to 18 kW of daytime user power. A photovoltaic power-generation system with regenerative fuel cell (RFC) energy storage has been under study at the NASA Glenn Research Center at Lewis Field. The conceptual power system is dominated by the 4000- m2 class photovoltaic array that is deployed orthogonally as four tent structures, each approximately 5 m on a side and 100-m long. The structures are composed of composite members deployed by an articulating mast, an inflatable boom, or rover vehicles, and are subsequently anchored to the ground. Array panels consist of thin polymer membranes with thin-film solar cells. The array is divided into eight independent electrical sections with solar cell strings operating at 600 V. Energy storage is provided by regenerative fuel cells based on hydrogen-oxygen proton exchange membrane technology. Hydrogen and oxygen reactants are stored in gaseous form at 3000 psi, and the water produced is stored at 14.7 psi. The fuel cell operating temperature is maintained by a 40-m2 deployable pumped-fluid loop radiator that uses water as the working fluid. The power management and distribution (PMAD) architecture features eight independent, regulated 600-Vdc channels. Power management and distribution power cables use various gauges of copper conductors with ethylene tetrafluoroethylene insulation. To assess power system design options and sizing, we developed a dedicated Fortran code to predict detailed power system performance and estimate system mass. This code also modeled the requisite Mars surface environments: solar insolation, Sun angles, dust storms, dust deposition, and thermal and ultraviolet radiation. Using this code, trade studies were performed to assess performance and mass sensitivities to power system design parameters (photovoltaic array geometry and orientation) and mission parameters (landing date and landing site latitude, terrain slope, and dust storm activity). Mission analysis cases were also run. Power results are shown in this graph for an analysis case with a September 1, 2012, landing date; 18.95 North latitude landing site; two seasonal dusts storms; and tent arrays. To meet user load requirements and the ISRU energy requirement, an 8-metric ton (MT) power system and 4000-m2 photovoltaic array area were required for the assumed advanced CuInS2 thin-film solar cell technology. In this figure, the top curve is the average daytime photovoltaic array power, the middle curve is average daytime user load power, and the bottom curve is nighttime power. At mission day 1, daytime user power exceeds 120 kW before falling off to 80 kW at the end of the mission. Throughout the mission, nighttime user power is set to the nighttime power requirement. In this analysis, "nighttime" is defined as the 13- to 15-hr period when array power output is below the daytime power requirement. During dust storms, power system capability falls off dramatically so that by mission day 900, a daily energy balance cannot be maintained. Under these conditions, the ISRU plant is placed in standby mode, and the regenerative fuel cell energy storage is gradually discharged to meet user loads.

Kerslake, Thomas W.↗
NASA NTRS2013

Painleve-gullstrand-type Coordinates for the Five-dimensional Myers-Perry Black Hole

The Painleve-Gullstrand coordinates provide a convenient framework for presenting the Schwarzschild geometry because of their flat constant-time hypersurfaces, and the fact that they are free of coordinate singularities outside r=0. Generalizations of Painlev´e-Gullstrand coordinates suitable for the Kerr geometry have been presented by Doran and Nat´ario. These coordinate systems feature a time coordinate identical to the proper time of zero-angular-momentum observers that are dropped from infinity. Here, the methods of Doran and Nat´ario are extended to the five-dimensional rotating black hole found by Myers and Perry. The result is a new formulation of the Myers-Perry metric. The properties and physical significance of these new coordinates are discussed.

Generalizations↗
NASA NTRS2013

Characterizing Wheel-Soil Interaction Loads Using Meshfree Finite Element Methods: A Sensitivity Analysis for Design Trade Studies

A wheel experiencing sinkage and slippage events poses a high risk to planetary rover missions as evidenced by the mobility challenges endured by the Mars Exploration Rover (MER) project. Current wheel design practice utilizes loads derived from a series of events in the life cycle of the rover which do not include (1) failure metrics related to wheel sinkage and slippage and (2) performance trade-offs based on grouser placement/orientation. Wheel designs are rigorously tested experimentally through a variety of drive scenarios and simulated soil environments; however, a robust simulation capability is still in development due to myriad of complex interaction phenomena that contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree nite element approaches enable simulations that capture su cient detail of wheel-soil interaction while remaining computationally feasible. This study implements the JPL wheel-soil benchmark problem in the commercial code environment utilizing the large deformation modeling capability of Smooth Particle Hydrodynamics (SPH) meshfree methods. The nominal, benchmark wheel-soil interaction model that produces numerically stable and physically realistic results is presented and simulations are shown for both wheel traverse and wheel sinkage cases. A sensitivity analysis developing the capability and framework for future ight applications is conducted to illustrate the importance of perturbations to critical material properties and parameters. Implementation of the proposed soil-wheel interaction simulation capability and associated sensitivity framework has the potential to reduce experimentation cost and improve the early stage wheel design proce

terramechanics↗
DOE OSTI2020

The Simons Observatory: Modeling Optical Systematics in the Large Aperture Telescope

We present geometrical and physical optics simulation results for the Simons Observatory Large Aperture Telescope. This work was developed as part of the general design process for the telescope; allowing us to evaluate the impact of various design choices on performance metrics and potential systematic effects. The primary goal of the simulations was to evaluate the final design of the reflectors and the cold optics which are now being built. We describe non-sequential ray tracing used to inform the design of the cold optics, including absorbers internal to each optics tube. We discuss ray tracing simulations of the telescope structure that allow us to determine geometries that minimize detector loading and mitigate spurious near-field effects that have not been resolved by the internal baffling. We also describe physical optics simulations, performed over a range of frequencies and field locations, that produce estimates of monochromatic far field beam patterns which in turn are used to gauge general optical performance. Finally, we describe simulations that shed light on beam sidelobes from panel gap diffraction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Neutral leakage, power dissipation and pedestal fueling in open vs closed divertors

The effect of divertor closure on neutral leakage, power dissipation and pedestal fueling is explored using the SOLPS code for different densities including attached and detached divertor conditions for DIII-D open and closed divertors. Here, a metric for divertor closure in terms of the percentage of neutrals escaping the divertor is presented. At the detachment onset the population of neutrals escaping the divertor is 12% for the closed divertor and 35% for the open divertor. This results in a lower contribution of the convective term to the total heat flux and increased power losses in the closed divertor. The comparison between the two geometries reveals that for the same upstream density, the upstream temperature is 23% higher in the closed divertor. The physical mechanisms for detachment at lower upstream density in the closed divertor are also identified with the reduction of the convective term directly resulting in 40% decrease and the increased power losses contributing with a factor of 2. The baffling also lowers the neutral flux refueling the pedestal resulting in further reduction of the core density for achieving detachment. The results introduced here show that the divertor recycling is the primary fueling mechanism in DIII-D. It is shown that fueling occurring in the region between the X-point and the outer midplane is at least four times lower in the closed divertor due the baffling structure which enhances target neutral trapping and consequently reduced upstream leakage. Due to the openness of the inner leg to the common flux and HFS regions both open and closed divertor experience almost identical fueling at the HFS highlighting the need to also consider the inboard divertor for shape optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Network Uncertainty Quantification for Analysis of Multi-Component Systems

To impact physical mechanical system design decisions and realize the full promise of high-fidelity computational tools, simulation results must be integrated at the earliest stages of the design process. This is particularly challenging when dealing with uncertainty and optimizing for system-level performance metrics, as full-system models (often notoriously expensive and time-consuming to develop) are generally required to propagate uncertainties to system-level quantities of interest. Methods for propagating parameter and boundary condition uncertainty in networks of interconnected components hold promise for enabling design under uncertainty in real-world applications. These methods avoid the need for time consuming mesh generation of full-system geometries when changes are made to components or subassemblies. Additionally, they explicitly tie full-system model predictions to component/subassembly validation data which is valuable for qualification. These methods work by leveraging the fact that many engineered systems are inherently modular, being comprised of a hierarchy of components and subassemblies that are individually modified or replaced to define new system designs. By doing so, these methods enable rapid model development and the incorporation of uncertainty quantification earlier in the design process. The resulting formulation of the uncertainty propagation problem is iterative. We express the system model as a network of interconnected component models, which exchange solution information at component boundaries. We present a pair of approaches for propagating uncertainty in this type of decomposed system and provide implementations in the form of an open-source software library. We demonstrate these tools on a variety of applications and demonstrate the impact of problem-specific details on the performance and accuracy of the resulting UQ analysis. This work represents the most comprehensive investigation of these network uncertainty propagation methods to date.

42 ENGINEERING↗
NASA NTRS2018

Conceptual Aerodynamic Design of a Tail-Cone Thruster System Under Axi-Symmetric Inlet Distortion

This paper presents a conceptual design of a tail-cone thruster system which is operating under an axisymmetric inlet distortion. An effort to realize the targeted fuel burn saving that was proposed in NASA's STARC_ABL aircraft design is made through a CFD (Computational Fluid Dynamics)-based design approach. This method employs three iterative steps to exploit the CFD tools until the design requirements are met: a quasi-2D through-flow model to design the fan/EGV (Exit Guide Vane), a 3-D RANS (Reynolds Averaging Navier-Stokes) simulation of the single blade row to account for the inlet/fan and the EGV/nozzle interaction, and a 3-D RANS simulation of the airframe with a propulsor installed - propulsion airframe integration (PAI). The design requirements which include the thrust, and shaft power of the propulsor are matched throughout the evaluations coming from two CFD domains, i.e., the turbo-machinery and the PAI. During the switch between these different computational domains, the inlet and exit profiles are matched via the correction factors of the body-force model. The present tail-cone thruster (TCT) aerodynamic design leverages a low-pressure ratio fan (FPR=1.2 to approximately 1.25) of which the camber-line angles are predicted by a quasi-2D through-flow model. The quasi-2D model is derived to analyze the radially distorted flow resulting from the ingested boundary layer at the inlet. It also estimates the appropriate velocity vectors of the metal angles of the fan and EGV which is subjected to different types of vortex at the fan exit. The baseline geometry is revisited and its internal flow-path and exhaust cone are redesigned to illustrate the strong correlation among the components of the propulsor in the PAI domain. The peak efficiency point of the fan/EGV with respect to the blade counts, also known as solidity, and rotational speed is chosen for the cruise condition via parametric studies. The corresponding performance maps are presented. The resulting performance metrics of the new conceptual design of the BLI (Boundary Layer Ingestion) propulsor are analyzed and compared with these of the baseline in the PAI aspect. Finally, ideas of the CFD based design of a BLI propulsor are discussed based on the observations drawn from the numerical results.

Inlet↗
NASA NTRS2023

Anisotropic Mach Cone Aligned Mesh Adaptation for Low Boom Simulations

An automated off-body Mach cone aligned structured curvilinear grid generation procedure is presented for near-field computational fluid dynamics simulations. This procedure combines output-based indicators and mesh redistribution to perform anisotropic mesh adaptation while maintaining Mach cone alignment. Automation is achieved through a novel direction-based adaptation indicator formulation. The adaptation procedure is demonstrated on the JAXA Wing Body geometry and X-59 C608 demonstrator model from the Second and Third AIAA Sonic Boom Prediction Workshops, respectively. It is demonstrated that anisotropic mesh adaptation may result in a greater than fifty percent reduction in resource usage required to achieve the same level of accuracy as uniform and user constructed Mach cone aligned grids for near-field pressure signatures, ground-level overpressure signatures, and loudness metrics.

CST↗
NASA NTRS2023

Anisotropic Mach Cone Aligned Mesh Adaptation for Low Boom Simulations

An automated off-body Mach cone aligned structured curvilinear grid generation procedure is presented for near-field computational fluid dynamics simulations. This procedure combines output-based indicators and mesh redistribution to perform anisotropic mesh adaptation while maintaining Mach cone alignment. Automation is achieved through a novel direction-based adaptation indicator formulation. The adaptation procedure is demonstrated on the JAXA Wing Body geometry and X-59 C608 demonstrator model from the Second and Third AIAA Sonic Boom Prediction Workshops, respectively. It is demonstrated that anisotropic mesh adaptation may result in a greater than fifty percent reduction in resource usage required to achieve the same level of accuracy as uniform and user constructed Mach cone aligned grids for near-field pressure signatures, ground-level overpressure signatures, and loudness metrics.

CST↗
NASA NTRS2019

Overflow Simulations of Unmanned Aircraft Systems

National airspace, the management for access and operation of these vehicles is required. This management is being developed under the unmanned aircraft system traffic management system (UTM) program. To determine the aerodynamic characteristics of drones, wind tunnel experiments and computation fluid dynamic (CFD) analysis have been conducted. These experiments and analyses are undertaken to understand the flight capabilities of these vehicles in variable head and cross wind conditions. The results of these investigations will provide metrics for the safe operation of these vehicles in and around civil populations and in urban settings. The focus of this paper is to model a drone installed in a wind tunnel for varying pitch attitudes and rotor rpm settings. Specifically, the IRIS drone is modeled in the NASA-Ames 7x10 ft. W/T. The tunnel mounting hardware and the tunnel enclosure are modeled with the IRIS drone geometry. The rotors of the drone are modeled using two methodologies: a rotor disk model and individual blade representations. The results of the analysis are compared with available experimental data to validate the computational approach.

Stremel, Paul M.↗
DOE OSTI2026

Preliminary neutronic and thermal analysis of Inertial Fusion Energy systems with a focus on thick liquid wall concepts

This paper provides an assessment of the neutronic behavior of Inertial Fusion Energy systems using the Serpent 2 Monte Carlo code. The study explores different types of reactor concepts, including dry-wall and thick liquid wall systems. In particular, it characterizes the tritium breeding and energy multiplication performance, as well as the effect of long-term irradiation on structural materials. For this purpose, the displacement per atom (DPA) and the gas production rate in structural materials are calculated. A simplified geometry with varying geometrical parameters is used as a representation for the different kinds of devices. Additionally, the case of the HYLIFE-II concept is used to assess modeling inaccuracies arising from certain approximations. A comparison between the simplified geometry and a realistic one is performed, thanks to Serpent’s capability to run transport calculations on unstructured meshes. The study then addresses the impact of these discrepancies on the temperature distribution in the first wall using the GeN-Foam code for conjugate heat transfer analysis. The results highlight the necessity to consider the heterogeneous nature of the liquid wall, as simplified models tend to underestimate radiation damage metrics and heat loads.

Conjugate heat transfer↗
NASA NTRS2024

NASA HECC Geometry and Performance Review Part 1: Validation of a Computational Model for the Vaneless Diffuser Configuration with As-Manufactured Impeller Geometry

An investigation of the NASA High Efficiency Centrifugal Compressor (HECC) vaneless diffuser configuration was performed. This multipart investigation presents an extensive validation of the computational model against experimental data. The validated model was then used to explore the effects geometric differences between the as-manufactured and design-intent impellers. Lastly, the validated model was used for comparison against an experimental tip clearance study. Part I of the investigation focused on describing the HECC vaneless computational model and its validation against the experimental data published in GT2023-103128. To generate the model, a verification of the manufactured impeller was performed and was confirmed to match the impeller CAD. Section data from the impeller CAD, referred to as the As-Manufactured geometry, were used for development of the computational model. Steady RANS simulations utilizing the Wilcox K-Omega 98 turbulence model and a multiblock structured mesh were used to conduct a mesh convergence study. The resultant mesh was then used for simulations at both design-speed and off-design speed conditions. The simulations compared well to data in both 1D and 2D terms for the major performance metrics of efficiency, total pressure rise, and total temperature rise. Based on the observed results the model was deemed validated and was used in the latter two parts of the multipart investigation.

centrifugal compressor↗
NASA NTRS2019

Overflow Analysis of Unmanned Aircraft Systems

With the increasing presence of unmanned aircraft systems (UAS), or drones, in the national airspace, the management for access and operation of these vehicles is required. NASA’s management approach is being developed under the unmanned aircraft system traffic management (UTM) program. To determine the aerodynamic characteristics of drones, wind tunnel experiments and computation fluid dynamic (CFD) analysis have been conducted. These experiments and analyses are undertaken to understand the flight capabilities of these vehicles in variable head and cross wind conditions. The results of these investigations will provide metrics for the safe operation of these vehicles in and around civil populations and in urban settings. The focus of this paper is to model a drone installed in a wind tunnel for varying pitch attitudes and rotor rpm settings. Specifically, the IRIS drone is modeled in the NASA-Ames 7x10 ft wind tunnel. The tunnel mounting hardware and the tunnel enclosure are modeled along with the IRIS drone geometry. The rotors of the drone are modeled using two methodologies: a rotor disk model and full rotating rotors with moving grids. The results of the analysis are compared with available experimental data to validate the computational approach.

Stremel, Paul M.↗
DOE OSTI2020

Development and validation of the cavitation-induced erosion risk assessment tool

This work presents the development of a cavitation-induced erosion risk assessment (CIERA) tool that links multiphase flow simulation predictions with the progress towards material erosion. To develop a robust erosion modeling tool, the cavitation and erosion predictions for pressurized diesel fuel flow within a channel geometry were validated over a range of Reynolds and cavitation number conditions in two different aluminum channel geometries, one featuring a rounded inlet corner and the other with a sharp inlet corner. The multiphase flow development within the channel was modeled using a compressible mixture model, where phase change was represented with the homogeneous relaxation model and the turbulent flow evolution was modeled using a dynamic structure approach for Large Eddy Simulations. To improve representation of the incubation period before material rupture over existing approaches, a physics-based metric was derived based on the cumulative energy absorbed by the solid material from repeated hydrodynamic impacts. When the average peak pressure was related to the incubation period, the incubation period and its sensitivity to changes in flow conditions were found to be overpredicted. In contrast, predictions from CIERA provided a more accurate means to qualitatively and quantitatively predict the influence of flow conditions on the incubation period before material erosion. When the predicted stored energy was related to the solid material properties to estimate the incubation period, multiphase flow simulations demonstrated accurate representation of the sensitivity of erosion severity to changes in flow conditions. The use of CIERA led to quantitative agreement of the predicted incubation period within 5% of the experimentally measured incubation period.

42 ENGINEERING↗
NASA NTRS1999

Supersonic Aftbody Closure Wind-Tunnel Testing, Data Analysis, and Computational Results

This paper reports on the model, test, and results from the Langley Supersonic Aftbody Closure wind tunnel test. This project is an experimental evaluation of the 1.5% Technology Concept Aircraft (TCA) aftbody closure model (Model 23) in the Langley Unitary Plan Wind Tunnel. The baseline TCA design is the result of a multidisciplinary, multipoint optimization process and was developed using linear design and analysis methods, supplemented with Euler and Navier-Stokes numerical methods. After a thorough design review, it was decided to use an upswept blade attached to the forebody as the mounting system. Structural concerns dictated that a wingtip support system would not be feasible. Only the aftbody part of the model is metric. The metric break was chosen to be at the fuselage station where prior aft-sting supported models had been truncated. Model 23 is thus a modified version of Model 20. The wing strongback, flap parts, and nacelles from Model 20 were used, whereas new aftbodies, a common forebody, and some new tails were fabricated. In summary, significant differences in longitudinal and direction stability and control characteristics between the ABF and ABB aftbody geometries were measured. Correcting the experimental data obtained for the TCA configuration with the flared aftbody to the representative of the baseline TCA closed aftbody will result in a significant reduction in longitudinal stability, a moderate reduction in stabilizer effectiveness and directional stability, and a moderate to significant reduction in rudder effectiveness. These reductions in the stability and control effectiveness levels of the baseline TCA closed aftbody are attributed to the reduction in carry-over area.

Allen, Jerry↗