Military Aircraft Configurations CFD solutions on complete military aircraft configurations have become a routine requirement. CFD solutions are used to augment test data or provide data that is difficult or impossible to obtain otherwise. Because CFD can model actual flight conditions, problems that arise with sub-scale ground testing are not a concern. Reynolds number effects, tunnel blockage effects, and support hardware effects do not exist with CFD. Obtaining flow field data near flight test vehicles is extremely difficult, while such data is inherent in the CFD solution. The CFD-FASTRAN flow solver has been widely used for aerodynamic predictions over complete and partial aircraft configurations. Block structured, chimera overset, and unstructured meshes have all been used with CFD-FASTRAN for analyses over a wide range of flight conditions. ESI Group engineers have considerable experience in applying CFD technology for aircraft aerodynamic analysis and design support. The F/A-18 results shown here were obtained from separate studies for buffet and control analysis and for store loaded aircraft aerodynamic predictions.

Business Jet Configuration Analysis The CFD-FASTRAN flow solver has been used for aerodynamic flow field predictions of civil transport and business jets. The flexibility of using block structured, chimera overset, and unstructured meshes, and the availability of several turbulence models and high-order schemes make the software a very attractive tool for business jet applications. ESI Group engineers also provide consultation services to the aircraft industry in the area of aerodynamic analysis and design support. The results shown here were obtained from a study conducted to optimize the wing design and inlet duct placement on a new business jet.

Rotorcraft Hover Aerodynamic Predictions The helicopter rotor flow-field presents many challenges for flow prediction computational tools. Several flow phenomena including turbulence, blade stall, rolling vortices, and wildly disparate velocities on the retreating and advancing blades make rotorcraft flow fields some of the most difficult to predict. ESI Group has developed several technologies for rotorcraft flow field predictions. Some of these technologies are embedded in the CFD-FASTRAN code, which provides a powerful tool for modeling rotorcraft aerodynamics. The chimera/overset grid methodology can be used to model the moving rotor-blade. The motion model dependencies capability can be used to model complex rotor motion such as lead, lag, and flapping. The code's high order schemes and several turbulence models can be used to model the highly viscous phenomena such as tip-vortex generation. The simulations shown here were performed to predict the flow field of a generic ROtor Body INteraction (ROBIN) helicopter body with a four-bladed rotor in a hover configuration. The animation shows the time accurate predictions of the blade motion and its effects on fuselage surface pressure distribution.                      Click image for movie Generic Helicopter Body with Four-                Bladed Rotor in Hover

Aerodynamic Analysis of X-35B VSTOL Effects VSTOL aircraft in ground effect produce a very complex flow. High and low temperature gases impinge on the ground, spread, and mix in very intricate patterns. In the early stages of the design process, predictions of this type of flow are critical for analyses of ground crew safety, hot gas ingestion, twin-jet fountain effects, and VSTOL suckdown. ESI Group has developed and implemented into the CFD-FASTRAN code a structured chimera overset mesh technology for complex geometry modeling and moving body applications. This overset mesh technology has been successfully applied to many types of problems. In a recent project for the U.S. Navy, the overset capability was used to model a complete X-35B aircraft in VSTOL mode. This capability allowed the modeling of all the open doors, inlets, landing gear and deflected surfaces of the aircraft in the complex flow field generated by the downward directed jets.

Inlet Aerodynamics This analysis is an example of the use of CFD in preliminary design studies. This CFD-FASTRAN analysis coupled internal and external flows to determine the effectiveness of a splitter plate at the inlet face and the flow uniformity at the compressor face of an aircraft engine. Detailed information on the inlet flow was obtained without an expensive wind tunnel test. Using the data obtained from this analysis, the inlet geometry was altered and the flow uniformity through the inlet was improved.                Engine Inlet                        Engine Face

This moving airfoil case demonstrates some of the moving body capabilities of CFD-FASTRAN. In this solution, the motion of the flap relative to the airfoil was prescribed using the Prescribed Motion Module. The aerodynamic loads on the system were calculated and used by the Rigid Body Motion 6-DOF Module to determine the motion of the entire airfoil-flap system. This type of solution process is easily applied to more complex geometries, enabling the simulation of maneuvering aircraft or moving control surfaces.

            
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Wing flutter occurs as a result of exchange of energy between different modes of the structure because of fluid-structure interactions. Flutter is a growing oscillation of a wing surface leading to large amplitudes and stresses, and which can lead to structural failure.

The MDICE environment coupled with the CFD-FASTRAN flow solver has been widely used to analyze wing flutter. A modal solver module based on the mode shapes of the wing or FEMSTRESS module may be used as the structural solver.

CFD-FASTRAN was used to perform an aeroelastic analysis of static and dynamic flutter of an AGARD 445 wing. The computed flutter point was observed to be at 0.9 times the experimental flutter point. The following figure shows visualization of actual flow data on the wing surface. The left hand side (reflected wing) shows the pressure, while the right hand side shows deflection (including deflection vectors) on the fluid-structure interface.

The limit cycle oscillations (LCOs) have been a persistent problem and are generally encountered on aircraft carrying external store. Several aircraft models have experienced store-induced LCO for certain attached wing store configurations which result in restricting their intended mission. The LCO characteristics of the fighter aircraft impose safe limits in addition to those defined by structural strength and stability requirements. These limits significantly reduce the effectiveness and maneuverability of fighter aircraft, limit the flight envelope of these aircraft, and risk the aircraft and pilot.

The MDICE environment coupled withthe CFD-FASTRAN  flow solver and internally developed nonlinear structural module has been used to study LCO in nonlinear aeroelastic system with fluid nonlinearities, dynamic and kinematics nonlinearities.

CFD-FASTRAN was used to perform an aeroelastic analysis of LCO of nonlinear aeroelastic systems. The results were extensively validated against wind tunnel data.

CFD-FASTRAN, coupled with MDICE  and a structural module based on influence coefficients was used to study aeroelasticity of the F16 wing-body configuration. The computational analysis predicted a wing-tip displacement of 65 mm. The Experimental Displacement is 68mm.

Besides influence coefficients, our structural modules use beam models, linear, and nonlinear FEM models.

In fighter aircraft such as the F/A-18, the leading-edge extension (LEX) of the wing maintains lift at high angles of attack by generating a pair of vortices that trails downstream over the aircraft. At some flight conditions, the leading-edge vortices break down ahead of the vertical tails. In these cases, the breakdown flow impinges upon the vertical tail surfaces, causing severe structural fatigue and premature failure. The buffet characteristics impose limits in addition to those defined by structural strength and stability requirements. The limiting factors may include vibration levels and frequencies at critical airframe locations where items like tracking radar antenna or a gyro might be located.

An integrated environment was developed for the prediction of tail buffeting of fighter aircraft. The environment comprises of a CFD fluid dynamics module (CFD-FASTRAN), a structural dynamics module (FEMSTRESS), and a conservative fluid-structure interfacing module. The modules are integrated into the MDICE environment for seamless loosely coupled analysis of various aeroelastic phenomena.

CFD-FASTRAN was used to predict the vertical tail buffeting of F/A-18 aircraft over wide range of angles of attack. The results were extensively validated against flight and wind tunnel data.

Crew escape systems are an integral feature in combat aircraft. Two main concerns with such systems are their aerodynamic stability, and the potential injury level to which their occupants are exposed.

CFDRC, sponsored by the US Navy and the SBIR program, has been on the forefront of developing CFD technology for escape system aerodynamic analysis, design support and injury reduction. CFDRC engineers have worked very closely with the U.S Navy and major ejection seat manufacturers on developing and applying CFD technology to support major escape system programs including ejection seat upgrades, mishap investigations and design of new systems. Areas of applications include ejection seat and canopy trajectory simulation, windblast protection, stabilization devices, head and neck injury assessment, helmet mounted Display (HMD) and goggles, inflatable restraint systems and rocket plume interference. The developed numerical technologies and related capabilities have been incorporated into the CFD-FASTRAN code.

The US Air Force and U.S. Navy, as well as commercial ejection seat manufacturers, are constantly investigating new concepts and devices to stabilize ejection seats and their occupants in high-speed flows.

CFD plays an integral role in early trade studies and in down selection of potential designs. The data generated from CFD computations includes aerodynamic forces and moments for evaluating the stability and controllability of the seat with and without the stabilization device, and surface pressures for assessing the windblast loads and potential occupant injuries. Additionally, the near-field flow-field solution data can be used to determine the effects that stabilization devices would have on the sensors that are installed in the seat, such as the Pitot tubes.

During egress from an aircraft, the occupant of an ejection seat is exposed to severe windblast effects from the oncoming flow. The US Department of Defense, as well as manufacturers of ejection seats, have been continuously working on developing better ways of shielding the occupants from these effects.

CFD-FASTRAN was used to provide analysis and design support during the development and optimization of new windblast protection concepts. Our engineers have investigated ways of stagnating the flow over the helmet region through the use of brim designs. Methods of protecting the occupant's torso have also been investigated. These methods include the use of flow deflectors, and raising of the legs of the occupant towards the torso. The data generated by CFD computations includes aerodynamic forces and moments for use in analyzing the stability of the ejection seat, and surface pressure data for use in determining the head and neck loads, and flow-field information required to determine the readings of on-board sensors.

The presence of a helmet-mounted display (HMD) and night vision goggles adds another level of complexity to the crew escape sequence. Before such devices can be safely used , any harmful side effects they may have must be determined.

CFD-FASTRAN was used to analyze the effects of the attachment of various devices to helmet-head configurations. The computations enabled the prediction of the additional loads experienced by the occupant, prediction of the overall effect on the aerodynamic characteristics of the seat, and prediction of the near-field interference effects on the seat control sensors.

Understanding the aerodynamic characteristics and loads on a canopy and an ejection seat during their separation and emergence from an aircraft is necessary to determine the potential for occupant contact with the aircraft canopy. Because of the high costs of escape system evaluation using ground or flight-testing facilities, it has become increasingly cost effective to use computational methods to simulate the actual event. CFD-FASTRAN was used to perform various canopy separation analyses. These analyses combined the CFD flow-solution module with an aerodynamically-coupled rigid-body motion model to yield accurate trajectory predictions.

CFD-FASTRAN capabilities include motion constraints that represent the slides and hinges that control the motion of the canopy during the initial phases of separation, and ockets that are used to force the canopy away from the body of the aircraft. The figure and animation on the right shows the results from an analysis for an F/A-18 rocket-jettisoned canopy. The figure shows the close agreement between the computational results predicted with CFD-FASTRAN and the corresponding hardware test data.

  
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As an ejection seat and its occupant exit an aircraft, the configuration enters a highly complex and transient flow field. Understanding the emergence effects encountered during the initial stages of the ejection sequence requires high fidelity analysis. Our engineers have developed and successfully applied computational simulation tools to model the complex phenomena associated with emergence and full sequence ejection events.

The figure and animation on the right show results from simulations using CFD-FASTRAN for an SIIIS seat emerging from an AV-8B aircraft. The simulations utilized the code's overset chimera algorithm and its rigid-body dynamics model. The simulations also utilized the features in CFD-FASTRAN that allow the user to specify motion constraints, and time- and distance-dependent point forces. The data generated included aerodynamic forces and moments for stability and control analysis, surface pressures for determining head and neck loads, and kinematics and dynamics data for trajectory analysis. The head loads predicted in these simulations compared well with the corresponding sled test data.

      
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SIII Ejection Seat and Occupant Separating From AV-8B Aircraft

Rocket propulsion systems are an essential part of ejection-seat escape systems. The thrust applied by the rockets propels the seat out of the aircraft, and stabilizes the seat during and after the ejection sequence. CFD-FASTRAN was used to perform analysis and support several programs involving controllable propulsion systems. Some of the problems considered required analysis of the influence of the rocket plumes on the aerodynamic behavior of the seat.

ESI Group has recently developed a unique, well-integrated, ready-to-use, high-fidelity multidisciplinary tool for the control of aeroelastic problems of aerospace vehicles.

The integrated environment includes:

• CFD-FASTRAN for the fluid dynamics
• FEMSTRESS for the structural dynamics
• Conservative-consistent interfacing for the fluid-structure interaction
• Grid interpolation algorithm for the grid motion due to the flexibility of structures
• Finite element modeling of piezoelectric actuators for suppression of vibration
• Matlab® control laws for deriving the piezoelectric actuators

Our engineers have significant experience in the analysis of aeroelastic and control problems of aerospace vehicles, including passive flow control, active flow control, and structural control devices. The links below lead to some examples of analysis.

Further developments to CFD-FASTRAN were implemented  for the analysis of passive flow control techniques used for flowfield improvements or dynamic loads alleviation. The passive flow control devices include LEX fences, vortex generators, flow dividers, control surfaces extension, and others.

LEX fences were used to alleviate vertical tail buffeting of F/A-18 aircraft. The LEX fences are placed along the path of the primary LEX vortex in order to restructure the vortical flow over the aircraft. Recent results obtained compared well with several flight and experimental data.

Further developments to CFD-FASTRAN were implemented  for the analysis of active flow control techniques used for flowfield improvements or dynamic loads alleviation. The active flow control techniques may include blowing and/or suction.

Flow control devices, such as blowing jets, were used to alleviate vertical tail buffeting of F/A-18 aircraft. In the simulation, a high-momentum fluid is injected from the upper surface of the LEX of the wing. The fluid is injected tangential to the LEX surface and parallel to the LEX vortex. The injection is aimed at restructuring the vortical flow of the F/A-18 aircraft in order to produce stronger vortices and alleviate the vertical tail buffeting.

Further developments to CFD-FASTRAN were implemented for the analysis of active smart materials control systems used for active structure control of vibrations of aerospace vehicles. Active strengthening of the structure is achieved by attaching smart material patches into the structure. The use of smart materials, such as PZT, gives an actuation system that is independent from the flight control system. It also has the ability of structural actuation over larger frequency band.

Piezoelectric actuators were used to strengthen the vertical tail of the F/A-18 aircraft to alleviate vertical tail buffeting. The PZT actuators were distributed over the inboard and outboard surfaces of the vertical tail as shown in the figure. Each set of PZT actuators on the sides of the tail is being commanded by a control law to strain in opposite directions simultaneously, enabling the vertical tail to bend. The PZT patches near the root of the tail increase control authority in the first bending mode. The PZT patches near the tail tip increase control authority in the torsional mode.

Vehicles flying through the atmosphere at hypersonic speeds excite the air surrounding them to very high temperatures in the post-shock and boundary layer regions. Various chemical reactions associated with the elevated temperatures of these regions are initiated as a result. These reactions in turn affect the thermodynamic and transport properties of the air, as well as the lift, drag, and surface temperatures experienced by such vehicles. Accurate and efficient numerical solutions of the aerothermochemistry equations are therefore needed to predict these viscous, chemically-reacting flows, and to predict the aerodynamic and thermal loads experienced by such vehicles.

The CFD-FASTRAN code employs fully-coupled finite rate chemistry with an arbitrary number of species, as well as thermal non-equilibrium models. It is designed to handle flows with a calorically perfect gas model, or with thermo-chemical non-equilibrium gas models. The code takes into account either thermal equilibrium, or two-temperature thermal non-equilibrium.

In addition to the CFD-FASTRAN software, ESI Group provides engineering consulting services for problems involving aerothermodynamic and aerothermochemical analysis. ESI Group's application engineers are highly experienced and skilled at applying CFD technology to a wide range of problems involving aerothermodynamic and aerothermochemistry predictions.

Reusable Launch Vehicle (RLV) Simulations with CFD-FASTRAN

CFD-FASTRAN was used to conduct time-accurate, coupled CFD and rigid body dynamics simulations of the staging event of NASA's X-43-A hypersonic research vehicle. The objectives of the analysis were to assist NASA in evaluating the stability of the vehicle and assess the re-contact risks during the staging event. The X-43A vehicle separates from the Pegasus booster at Mach 7 and an altitude of 95,000 ft. Hydraulic pistons push the flyer forward and away from the booster to initiate the staging, while the tail control surfaces increase their deflection up to 8 degrees to trim the vehicle to the 2-degree angle-of-attack required to activate the vehicle's scramjet.

This computation was made possible by the coupling between the flow and body motion modules of CFD-FASTRAN. The code has a sophisticated motion module, which can simultaneously handle multiple bodies executing either prescribed or aerodynamically controlled rigid-body motion. Thus, CFD-FASTRAN was able to simulate the full physics of the problem, incorporating the combined effects of the hypersonic flow, with the vehicle interference effects, the forcing of the hydraulic pistons, and the deflection of the tail control surfaces. Full Navier-Stokes computations, with the K-e turbulence model, were used on grids with 2.5 million points. The accompanying images show the Mach number plots at various points in the staging sequence.

        
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CFDRC and Martin Baker engineers used CFD-FASTRAN to generate a static aerodynamic-coefficient database for the Beagle 2 Mars probe. The database covers the probe's entire entry trajectory, over which the speed varied from Mach 1.5 to Mach 28. More than 50 reacting and non-reacting flow cases were computed for the database. An eight-species (CO2, CO, N2, O2, NO, C, N, O), nine-reaction, thermo-chemical non-equilibrium model was used for all cases with Mach numbers of 7 and above. The aerodynamic coefficients were then provided and used to generate a blended aerodynamic database for vehicle EDLS development.

The CFD-FASTRAN code was ideally suited for these calculations. It employs fully-coupled finite rate chemistry with an arbitrary number of species, as well as thermal non-equilibrium models. It is designed to handle flows with a calorically perfect gas model, or with a thermo-chemical non-equilibrium gas model, depending on the flow regime. Additionally, the code employs higher order differencing schemes, a robust and efficient laminar flow model, and several turbulence models for accurate predictions of high speed flows.

In this study, time-accurate computations were performed using the CFD-FASTRAN code to generate dynamic derivatives of the aerodynamic coefficients for the Beagle 2 Mars probe. Simulations were performed for the full-scale vehicle at the Mach-1.5-entry trajectory point, and for a 1/15 scale wind tunnel model in pure CO2. The wind tunnel case was modeled both with and without a sting mount. A steady state solution at an angle of attack of 2 degrees provided the initial condition for the time accurate analysis. The pitch-damping coefficient was extracted from the pitch angle time history over three cycles.

The computation relied on the automated chimera overset grid technique implemented in CFD-FASTRAN, together with its rigid body motion module. The computation also relied on the higher-order-accurate schemes of CFD-FASTRAN, and the presence of appropriate turbulence models for accurate prediction of the separated flows that occur around blunt body configurations such as the Mars entry vehicle.

CFD-FASTRAN wsa used to generate aerodynamic force and moment coefficients for an inflatable hypercone deceleration system for Mars atmospheric entry. The generic vehicle geometry consisted of an inflatable torus supporting the edge of a flexible-fabric conical surface skirting a cylindrical cargo vessel. Two configurations were analyzed; one with the fabric cone in an undeformed conical shape, and one with the fabric surface deformed in response to the aerodynamic forces. The flow field was predicted for various angles of attack at a Mach number of 2.5 in the Martian atmosphere. These types of simulations allow analysts and design engineers to conduct quickly trade studies to evaluate aerodynamic and structures characteristics of various concepts.

Satellite flow simulations were conducted to predict the flow field and critical heat loads on satellite components exposed to the upper atmosphere at an altitude of 90 kilometers and velocities in excess of 2400 m/sec (corresponding to a Mach number of 8.8). The flow was at the limit of the continuum flow regime (with a Knudsen number of 0.01).  The computations revealed highly complex heating patterns due to the shock system that forms around the satellite.

These complex computations were obtained using CFD-FASTRAN, which employs finite rate chemistry and thermo chemical non-equilibrium models to handle hypersonic reacting flows.

Hypersonic Reacting Flow Over a Sphere

Missile launching, staging and maneuvering present unique numerical modeling and simulation challenges to CFD codes. These challenges are because of the complex geometry, complex physics, and relative motion between different bodies. A chimera overset grid methodology, a sophisticated rigid-body motion module, and state-of-the-art numerical solution algorithms and physical models make CFD-FASTRAN the code of choice for an extensive range of missile transient events, including launching, staging, and maneuvering.

In addition to developing and supporting software technologies, ESI Group provides engineering consulting services for a full range of missile transient events and aerodynamics problems, including those involving multiple moving bodies and moving control surfaces. Our engineers are highly experienced at applying CFD technology to these problems.

At high altitudes and low ambient pressures, the rocket plumes of missile control jets expand much faster and wider than at sea level. The plume expansion may even interfere with the targeting sensors in the nose of the missile. The CFD-FASTRAN code employs models for finite rate chemistry and thermal non-equilibrium to allow it to accurately predict such effects. In addition to these models, the code also employs models for surface reaction. This enables the modeling of reacting flow fields in hypersonic flows, as well as the surface reactions that are caused by the aerodynamic heating in such flows.

In this study, CFD-FASTRAN was used to compute the interaction of a control jet with the hypersonic flow field around the AIT interceptor missile at an altitude of 110,000 feet and a velocity of 3.5 km/sec (corresponding to a Mach number of 8.2). The jet exit Mach number was 3.5. Reacting and non-reacting simulations of the mixing of the solid propellant exhaust jet with the external flow showed the potential for external afterburning of the plume gases.

This simulation computes the trajectory of a guided missile nose cone with and without an active-fin control autopilot. In one case the autopilot was inactive and the control surfaces remained stationary. In the other case, an autopilot model was coupled with CFD-FASTRAN and was used to direct the motion of the control surfaces. The simulation algorithm is shown on the right, while the movies below show the relative effect of the autopilot on the trajectory and alignment of the missile.

The coupled aerodynamics and rigid-body dynamics solvers, together with the automatic chimera overset grid capability allow the simulation of such complex problems. This type of simulation enables designers and analysts to test control modules and maneuvering capability in real-life type situations where aerodynamics, flight dynamics and controls are fully coupled.

                                        
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CFD-FASTRAN's multiple moving body capability was used to predict the trajectories of the canard covers for this projectile, and to assess the potential impact of the covers with the tail fins. The ejection of the canard covers is initiated under the influence of spring mechanisms. The covers then rotate on hinges for a short duration, before being released into the ambient high-speed air-stream.
The covers experience rotation rates of up to 15000 degrees per second.

The code's motion models enable full specification of the time-dependent forces or constraints applied by the spring mechanisms, the hinges, and the release mechanisms. Such constraints and point forces can be intuitively and easily specified in the code's GUI. This computation relies not only on the motion model, but also on the ability of the automated chimera overset grid to handle multiple moving bodies in relative motion.

         
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This case demonstrates the ability of CFD-FASTRAN to model moving control surfaces on a missile. In this simulation, the missile is counter-acted by a point force, while the canards on the sides of the missile increase their angle-of-attack at a prescribed rate. The entire missile moves under the combined effect of the aerodynamic forces on the body of the missile, the simulated thrust, and the forces generated by the canards.

          
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CFD-FASTRAN employs several physical models and solver technologies that allow the modeling of the complex unsteady flows that occur during missile launch. The code has several features and capabilities that are essential for accurately modeling the behavior and dynamics of a missile during launch. These include coupled aerodynamics and rigid-body-motion solvers, and an automated chimera overset grid methodology. The code also allows the specification of time-dependent thrust forces, and can account for the variation of the mass of the missile with time.

This 2D demonstration shows a generic missile ejecting out of a canister. The thrust forces were specified using a time dependent pressure and temperature profile at the nozzle exit of the missile. This type of simulation allows the analyst or design engineer to evaluate potential contact between the missile and the canister and to evaluate the separation dynamics as the missile exits from the canister while accounting for all the physics and body dynamics.

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CFD-FASTRAN can be used with structured or unstructured meshes. The missile high angle-of-attack solution on the right was obtained using structured single block grid techniques, while the solution at the bottom was obtained using an adaptive Cartesian mesh technique. Because of the high angle-of-attack, vortices are shed from the nose region. The solution was initiated on a coarse Cartesian mesh, which was then adaptively refined to the flow gradients as the solution progressed, thus increasing the accuracy of the prediction, while keeping the number of cells to a minimum.

CFD-FASTRAN was used for the time accurate simulation of this F-16 with multiple bombs carried on a rack mounted under the wing. The objective of the simulation was to calculate the trajectory of the bomb as it separate from the rack and assess its potential collision with the fuel tank.

CFD-FASTRAN was used to calculate the steady state captive loads on the aircraft and stores, as part of the U.S. Navy CFD challenge to predict the viscous flow fields of a JDAM store separating from the F/A-18 aircraft. Time accurate simulations were also conducted to calculate the trajectory of the JDAM as it separates from the aircraft.

The CFD-FASTRAN software package is used by many of our customers for store separation analyses and in many cases certification of new weapons on fighter aircraft. The flexible and well-proven automated moving-body capabilities of CFD-FASTRAN make it the code of choice for store separation analysis problems.

            
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This Air Force Eglin Wing/Pylon/Finned Store configuration is a benchmark test case commonly used in the industry for 6-DOF models validation. This test case was used to validate CFD-FASTRAN's moving body capabilities. As seen on the right, the trajectory results show excellent comparison to test data.

     
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