Flight Simulation and Design

Drawing on decades of engineering experience with designs and simulations of spacecraft and flight vehicles, Triton Systems employs (as well as developed)  a suite of computer programs for modeling vehicles in flight or making engineering trades to establish the basis for their design.  While the developed programs are unique to Triton, others such as MATLAB Toolboxes and ALIBRE computer aided design (CAD) package are used industry wide.  As expected, in the analysis and design process, many of these computer programs interact with each other and the programs listed below is more of a sampling than a complete list.

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Internally Developed Trajectory Programs

 1.  LAUNCH5: Used as a basis to evaluate liquid rocket stage alternatives for Space Shuttle and other launchers, this program converges on ascent targets within several iterations based on a minimum Hamiltonian optimization and guidance algorithm.  For design studies, the program includes modules for propellant selections, tank volume estimates, engine performance calculations based on propellant selections, mixture ratios, combustion chamber pressures and nozzle expansion ratios. These models are derived from the NASA Lewis Chemical Equilibrium and Application program CEA described below, calibrated with existing rocket engines. As a result, for design studies, partial derivatives for a host of design parameters can be obtained and applied to a mission, a stage or an overall launch vehicle configuration.

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 2.  AEXTRAP: On orbit simulations of finite burns, relative motion, upper stage ascents or re-entries are provided by this program.  A low thrust maneuver targeting algorithm provides predictions of first and second burn cutoffs for milli-g maneuvers for precision orbit raising.  The method is based on forward and backward integration of the first and second burn to determine eccentricity matches for the coast condition.

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 3.  JETFJ2: Derived from LAUNCH5, this program addresses performance of horizontal takeoff launch vehicles with wings and air-breathing (jet) engines. The Stellar-J family of launch vehicles has been simulated with this program, creating an increasingly larger library of default property files for engine selections, upper stages, gross liftoff weights and other parameters.  The upper stage optimization and guidance subroutine employs the same min-H algorithm as LAUNCH5.  As the vehicle configuration is developed a pre-processor tracks mass properties for inertias of loaded and dry weights including locations; a post processor provides estimates of control moment loads.

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 4. BISTAR: Developed to determine stability of planetary motion around binary star systems, this program models the restricted elliptic three-body problem by advancing the two primaries with Keplerian motion about a barycenter with two ellipses of given eccentricity with semi-major axes inversely proportional to their mass ratios. The third body is integrated inertially with its orbital parameters calculated about one or the other primary from the resulting state vector updates. Program defaults initiate the planetary orbit in near circular motion about one or the other star based on input position in Astronomical Units or a thermal flux condition. A data base of known binary stars plus many recently discovered stars with brown dwarf or Jovian planet companions is provided.

For additional background see (hyperlinked)

ACROBAT file:  ASTRO97.pdf

Power Point Slide Show: Lunar&Extrasolar_3BodyProblems111706.pdf

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5. SUNANG: An on-orbit six degree of freedom simulation, this program models spacecraft environmental and control torques based on inertial properties, drag cross sections, gravity gradient forces and upper atmosphere (or exosphere) drag models.  Magnetic field and damper models are included.

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 6. JACOBEM: Derivative of BISTAR and AEXTRAP, this program simulates third body motion in the restricted elliptic 3-body problem with Earth, Moon and a spacecraft as the 3 bodies.  Default cases examine Earth departure and Earth return trajectories, plus stability or motions near the five Lagrangian points.  The program can be used to assess lunar mission design requirements based on trajectory analyses. Features under development are finite burn simulations and means to conduct parametric investigations for varied system true anomalies.

For additional application background see

PDF file: Lunar&ExtraSolar_3BodyProblems111706.pdf

Power Point Slide Show: Lunar&ExtraSolar_3BodyProblems.

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 7. DAYPLOT: Provides orbital decay histories based on drag-weight parameters and high altitude atmospheric density (>80 kilometers) based on solar extreme ultra violet flux and terrestrial magnetism parameters.  The program provides quick estimates of orbital lifetimes for low orbiting satellites.

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 8. PROXIM: Launch vehicles at staging or spacecraft in orbit rely on jet thrusters to rotate or maintain attitude control. The thruster installations require a jet selection logic for translational, rotational and failure modes, a phase plane logic for evaluating errors and a dynamic models for environmental effects and rotational schemes.  This program focuses on  evaluating jet thruster configurations for a given rigid body spacecraft.  Typical use evaluates angular accelerations provided, thruster "chatter", phase plane stability, motions in rotational maneuver corridors, cross-coupling and  propellant consumption 

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External Trajectory and Celestial Mechanics  Programs

1. GMAT:  The General Mission Analysis Tool under development by the Goddard Spaceflight Center provides means to generate powered or coasting trajectories. GMAT employs an open architecture to generate new technology through an innovative an open collaboration of NASA, universities, businesses such as Triton and private citizens.

To participate in its development or obtain more information, contact http:/gmat.gsfc.nasa.gov.

2. ALCYONE* Ephemeris: an accurate and fast astronomical ephemeris calculator. Covering the period from 3000 BC to AD 3000, it calculates heliocentric, geocentric and topocentric positions of the Sun (Earth), Moon, planets, minor planets and comets in ecliptic, equatorial and horizontal coordinates with optional corrections for parallax and refraction;  rectangular coordinates, velocity, apparent diameter, magnitude phase and orbital elements...JPL and other ephemeris tables are provided. 

For additional information, contact: www.alcyone-ephemeris.info

*Named for η Tauri, the brightest star in the Pleiades open cluster.  

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Industry Tools

 1.  ALIBRE: Design Standard is a fully featured 3D CAD application, allowing designers to create 3D mechanical designs and generate and detail associative 2D drawings. Along with a full set of advanced modeling tools and parametric modeling functionality, Standard comes with the capability to create interactive 3D PDFs and import & export designs in industry standard formats. 

For more information visit  http://www.alibre.com/products/

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 2.  CEA: the chemical equilibrium and application program is combustion and compressible flow analysis tool in steady development at the NASA Glen Research Center since the 1950s.  As described in NASA RP-1311, the program obtains chemical equilibrium for assigned thermodynamics states; calculates theoretical rocket performance for specified combustion chambers; calculates Chapman-Jouguet detonation effects or calculates shock tube parameters for both incident and reflected shocks.

For more information visit  http://www.cea.grc.nasa.gov/

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3.  DATCOM: provides aerodynamic coefficients and stability derivatives for subsonic, transonic and supersonic aircraft flight based on overall vehicle configurations or via component (wing, body, stabilizer, flap...) analyses.  The coefficients for classical perturbation equations of motion, both lateral and longitudinal, are parameters of these coefficients, based on wind tunnel, flight test or computed evaluations with DATCOM methods as one means of obtaining the values in the early design phase.

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 4.  MATHCAD: provides both symbolic and numerical calculation capabilities with a large library of engineering and mathematical functions and operators. The software employs conventional mathematical notation for clarity, importing and exporting product files to other applications such as MATLAB and spreadsheets. It is capable of compiling FORTRAN or C output.

For more information visit  http://www.integratedpdg.com/

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 5. MATLAB: a high performance language for technical computing, the package integrates computation, visualization and programming in an easy-to use environment for mathematics and computation, algorithm development, data acquisition, modeling, simulation and prototyping, plus scientific and engineering graphics.  Currently, Triton Systems is exploiting three of the MatLab "Toolboxes":

Aerospace Toolbox: extends the MATLAB technical computing environment by providing reference standards, environment models and aerodynamic coefficient importing (e.g., from DATCOM) for performing advanced design aerospace analysis on the Stellar-J variants or other study vehicles.

Control Systems Toolbox: Detailed modeling beyond 3 degree of freedom simulation of flight vehicles requires subsystem design and control based on classical and modern control system algorithms.  This toolbox provides an extensive array of linear time-invariant analysis packages for both single and multiple input and output (SISO & MIMO) systems drawing both from classical and modern control methods.

Optimization Toolbox: A set of algorithms or software functions capable of performing minimization or maximization on general non-linear multi-variable functions.  This includes non-linear equation solving and least square (data fitting) problems.  This toolbox is used to support GMAT trajectory analysis problems involving searches for minimum time, change in velocity or expenditure of propellant.

For further information on MATLAB, contact www.mathworks.com.