Parametric Analysis of the Store Separation of a High ...€¦ · separation of the missile and include the effects of the autopilot and moving control surfaces modeled in MATLAB/SIMULINK.

Parametric Analysis of the Store Separation of a High Speed Anti-radiation Demonstrator (HSAD) Missile

E. Hallberg1

United States Naval Academy, Annapolis, MD 21402

The High Speed Anti-radiation Demonstrator (HSAD) Program intends to demonstrate key enabling technologies for inclusion in the follow-on to the AGM-88E HARM missile during one captive carry and two free-flight tests. The HSAD missile is planned for release from an F/A-18C/D aircraft at a Mach number of 0.8 and an altitude of 30,000 feet. Recent improvements to the U.S. Navy’s store separation prediction code (NAVSEP) have allowed the U.S. Navy to analyze the separation of the missile and include the effects of the autopilot and moving control surfaces modeled in MATLAB/SIMULINK. A parametric analysis of the release was conducted to account for uncertainty in the freestream and grid wind tunnel data, control surface effectiveness, mass properties, and sensor performance with the autopilot engaged.

Nomenclature Store trajectories are defined in the Aircraft Axis System, which has its origin at the store center of gravity at release. The origin is fixed with respect to the aircraft and thus translates along the current flight path at the freestream velocity. The axes rotate to maintain constant angular orientation with respect to the current flight path direction. ψ = PSI = Store yaw angle, positive nose right as seen by the pilot, deg. θ = THETA = Store pitch angle, positive nose up, deg. φ = PHI = Store roll angle, positive right wing down, deg. P = Store roll rate, positive right wing down, deg/sec. XA = Store CG location relative to carriage, positive forward, parallel to aircraft centerline, ft. YA = Store CG location relative to carriage, positive right, as seen by the pilot, ft. ZA = Store CG location relative to carriage, positive down, perpendicular to aircraft centerline, ft. XFS = Fuselage Station. Distance of the store CG from the absolute Aircraft-axis system origin in

the negative XA direction, inches, full scale. YBL = Butt Line. Distance of the store CG from the absolute aircraft-axis system origin in the YA

direction, inches, full scale. ZWL = Water Line. Distance of the store CG from the absolute aircraft-axis system origin in the

negative ZA direction, inches, full scale. CN = CN = Normal force coefficient, positive up, perpendicular to the store axis. CY = CY = Side force coefficient, positive right, looking forward along store centerline. CA = CA = Axial force coefficient, positive rearward, along store centerline. Cl = CLL = Rolling moment coefficient, positive right wing down. Cm = CLM = Pitching moment coefficient, positive nose up. Cn = CLN = Yawing moment coefficient, positive nose right. αAIRCRAFT = Aircraft Angle of Attack, deg. αS =ALPHAS = Store Angle of Attack (without induced upwash), positive nose up, as seen by the pilot,

deg. βS = BETAS = Store Sideslip angle (without induced sidewash), positive nose left as seen by the pilot, deg.

1 Assistant Professor of Aerospace Engineering, AIAA Member.

6-DOF = Six-Degree of Freedom. AEDC = Arnold Engineering Development Center CG = Center of Gravity. CTS = Captive Trajectory System. HARM = High-speed Anti Radiation Missile. HSAD = High Speed Anti-radiation Demonstrator. ITALD = Improved Tactical Air Launched Decoy. KCAS = Knots, Calibrated Air Speed. NAVSEP = Navy generalized Six-Degree of Freedom separation simulation software. TGP = Trajectory Generation Program.

I. Introduction HE AGM-88E HARM missile is the U. S. Navy’s primary weapon for the suppression of enemy defenses (SEAD) strike mission. While the baseline HARM as undergone a number of block

improvements since its inception in 1983, its basic flight profile, and specifically its fly-out speed, has remained virtually unchanged. Future Navy requirements call for the suppression or destruction of time critical mobile forces at range. In order to address this need, the U.S. Navy has taken an evolutionary approach utilizing the High Speed Anti-radiation Demonstrator (HSAD) Program. The approach taken in developing the HSAD missile was to combine the proven capability of the AGM-88E High-speed Anti Radiation Missile (HARM) with advancements in propulsion technology, specifically advanced integral nozzleless rockets and variable flow ducted rocket ramjets. Utilizing these key technologies, the High Speed Anti-radiation Demonstration Program (HSAD) expects to demonstrate a substantial increase in capabilities over the baseline HARM in both range and response time. The HSAD Program intends to demonstrate these capabilities through a series of three flight tests. The first flight test will be a captive carry of the HSAD missile. The second and third flight tests are planned to demonstrate the capabilities of the HSAD missile through free flight.

T

All three HSAD flights will be

conducted from a modified LAU-118, on station 3 of the F/A-18C test aircraft. Figure 1 shows a mockup HSAD on a baseline LAU-118. The first free flight test of the HSAD missile is planned for the July/August 2006 timeframe. The release condition will be a Mach number of 0.8 and an altitude of 30,000 feet. The second free flight intends to release the HSAD missile at the same condition, and execute an extended profile.

Prior to the store receiving an

airworthiness certification for release, a detailed simulation was conducted to estimate the HSAD trajectory immediately after launch. The simulation was based on wind tunnel testing at the Arnold Engineering Development Center (AEDC), wind tunnel testing at the Allied Tunnels 7-FT Trisonic Tunnel, and functional analysis of the autopilot provided by the manufacturer. Figure 2 shows a 40% scale model of the HSAD missile in the Allied Tunnels 7-FT Trisonic Tunnel during freestream wind tunnel testing.

Figure 1. HSAD Missile on F/A-18C (baseline launcher).

The HSAD missile and rail have significant differences in shape and size from the baseline HARM configuration. These differences have the potential to affect the trajectory immediately after release. The LAU-118 rail launcher is extended in length from a baseline LAU-118 to accommodate the extended length of the missile. The two variable flow ducted rocket ramjet inlets are positioned on the aft and bottom of the missile body introducing asymmetries in both the missile aerodynamics and the thrust dynamics about the missile body y-axis. Additionally, an advanced and modified guidance section has the capability to control four moving control surfaces mounted on the rear fins of the vehicle. At release, the fins are initially locked. Fin unlock occurs approximately 0.7 seconds after release as the autopilot takes active control of the HSAD vehicle.

Figure 2. HSAD 40% Freestream Model.

Simulations were performed by the contractor incorporating normal autopilot operation, fin lock

conditions, and autopilot malfunctions. In all cases, simulations showed that the store would remain stable and not interfere with the operation of the aircraft. Following the principle of independent verification, the U.S. Navy desired to validate the HSAD autopilot with at least one complete 6-DOF simulation code other than the proprietary one used by the contractor.

A variety of candidate Six-Degree Of Freedom (6-DOF) codes are available to simulate store

trajectories. AEDC uses a code known as the Multi-Dimensional Interpolation Trajectory Generation Program (TGP). The U.S. Navy generalized store separation code is known as NAVSEP, and is based on an early version of the AEDC TGP code. At the time, NAVSEP did not have an indigenous capability to simulate autopilot functionality in a store. Past simulation efforts utilizing NAVSEP and autopilots had required embedded modifications to the NAVSEP source code, and functional descriptions of the autopilot translated into FORTRAN sub-routines. This resulted in specifically tailored version of the NAVSEP code that had limited portability to other applications. It was desired to develop an environment that permitted autopilot incorporation in high-level, block diagram form (MATLAB /Simulink) for simulation of the HSAD missile release with the intention of improving the baseline NAVSEP code for future applications. Furthermore, it was desired to use Monte-Carlo techniques to analyze the sensitivity of the trajectory to uncertainty in the wind tunnel data, and sensitivity of the trajectory to certain performance variations in the auto pilot.

II. Development of a NAVSEP/MATLAB Iterative Execution Environment

The NAVSEP code recently underwent a major version upgrade which included translation of the legacy code into modern FORTRAN 90. Numerous upgrades were implemented to improve the user interface. After validation and verification processes were completed, This new version of the NAVSEP code was designated NAVSEP 3.0. This version of NAVSEP served as the starting point for the evaluation of the release of the HSAD missile with the autopilot off. This work is described in detail in reference (12).

Up to this point, the simulated trajectories were only valid to the time of fin unlock. At the point of fin unlock, the control surfaces commanded by the autopilot would influence the HSAD trajectory. The time of fin unlock, approximately 0.6 seconds, was specifically chosen such that the HSAD would be a safe distance in front of the aircraft. However, it was necessary to demonstrate that the autopilot would not allow the missile maneuver unacceptably. It is desirable that the trajectory of the missile not cross the extended centerline of the aircraft either laterally of vertically until the missile is a safe distance in front of the aircraft. The natural tendency of the HSAD to pitch and roll due to the influence of the aircraft flow field, off centerline thrust of the HSAD rocket motor, and asymmetric aerodynamics of the missile would need to be countered by the autopilot. The desired control should level the missile in pitch and roll as it accelerated away from the releasing aircraft prior to commencing the pre-programmed mission maneuvers.

Figure 3. Functional Diagram of NAVSEP and MATLAB/SIMULINK Iterative Execution

The Navy decided to make moderate modifications to NAVSEP to allow for its execution in a MATLAB/SIMULINK environment. It was realized that store separation with autopilot functionality analysis would be a minority subset of all store separation analysis tasks. Therefore, the developmental goals were to 1) provide robust capability to incorporate store autopilots in SIMULINK block diagram form, and 2) retain the capability to run the same NAVSEP source code (without an autopilot) in its native command-line mode. This strategy would leverage on two decades of corporate knowledge and compatibility with legacy NAVSEP data sets while providing an accepted standard environment for analysis and inclusion of control algorithms.

Initially, two approaches were taken to develop and integrated environment. First, a version of

NAVSEP was developed that ran as a MATLAB executable (mex-file) within a MATLAB/Simulink environment, and designated as NAVSEP 3.1. Second, standardized file exchange protocols were established between the two applications to allow them to run in an iterative manner. For reasons stated earlier, it was desired to maintain the ability to run NAVSEP on both UNIX and Windows XP operating systems without a requirement for a MATLAB/Simulink installation. In order to avoid a situation whereby the U.S. Navy would need to maintain two versions of the NAVSEP code, one for compiling as a MATLAB executable, and one for execution as a stand-alone FORTRAN application, the decision was made to move forward with the latter development effort. Some performance measurements indicated that this approach would execute approximately 30% slower than running NAVSEP as a MATLAB executable, and that computational accuracy was comparable. This was judged to be an acceptable compromise in order to avoid a bifurcation of the NAVSEP source code development efforts. A diagram of the process whereby NAVSEP and MATLAB/Simulink operate in an iterative manner is shown in Figure 3.

III. Simulation Results of the Baseline HSAD Release Two wind tunnel tests provided aerodynamic data for the simulation. A 6% scale HSAD and a 6% F/A-

18C aircraft model manufactured by Boeing underwent separation/loads testing in the AEDC 4T facility. The Captive Trajectory System (CTS) was used to obtain store freestream and aircraft flowfield aerodynamics. A 40% scale HSAD vehicle manufactured by Trimodels underwent freestream testing in the

Allied Tunnels 7-FT Trisonic Tunnel. Grid data was implemented into NAVSEP as “delta” coefficients; that is, they were added to baseline store freestream values to account for the influence of the aircraft. To reduce systematic errors from the Wind Tunnel (sting aft end model distortion, scale effects, etc.), the freestream values subtracted from the “total” grid coefficients are from the same model as used for grid measurement (6% scale, in this case). However, NAVSEP took advantage of the 40% scale HSAD data for the freestream database.

Control fin aerodynamics were implemented using a database provided by Nielsen Engineering and

Research, Inc. The multi-dimensional interpolation was accomplished in MATLAB, outside of the NAVSEP “kernel.” Additionally, the wind tunnel freestream data was available at three different Mach numbers from the release condition of Mach = 0.8, to a Mach of 1.2. NAVSEP prefers that freestream data be provided in grids of angle-of-attack (ALPHA) sweeps at discrete sideslip (BETAS) angles for internal interpolation. Much of the freestream data, however, was taken about the aeroballistic axis using roll sweeps. Therefore, MATLAB was used to fit surfaces to the freestream wind tunnel data as shown in Figure 4. Symmetries in BETAS can be exploited by NAVSEP, hence only the half-plane shown was required.

Figure 4. HSAD Normal Force (CN) and Yawing Moment Coefficient (CLN) Interpolated Surfaces. Original data are depicted as blue dots.

The resulting surfaces were linear interpolated for freestream Mach number and uniformly sampled for

exchange with NAVSEP at each time step. An example of the uniform sampling of Mach interpolated data for exchange with NAVSEP. Ejector force characteristics, mass properties, and rocket motor thrust profiles were obtained through separate ground testing.

The HSAD autopilot was modeled in MATLAB/Simulink based on a block diagram description of the autopilot functionality provided by the manufacturer. The autopilot was activated 0.7 seconds after release. State information was provided to the autopilot from NAVSEP with no attempt to introduce sensor noise or sensor dynamics. Autopilot fin commands including the effect of actuator dynamics were iteratively computed in MATLAB/Simulink, and their subsequent effect on the missile dynamics was determined through linear interpolation of the multi-dimensional tables provided by Nielsen, Inc. The resulting simulation is shown in Figure 5 where the trajectory of HSAD with the autopilot inactive is shown for comparison. Notice that at 0.7 seconds after release, the HSAD is both pitching and rolling considerably with the pitch attitude reaching -11 degrees and the roll attitude reaching 50 degrees. The roll motion is the most pronounced, and would continue to diverge without commands from the autopilot. The performance from the autopilot is acceptable and appropriate as it both stabilizes the nose in a lightly nose low attitude (-8 degrees) and rolls the missile in the direction of wings-level. The trajectory of the missile is also acceptable as it does not cross the extended centerline of the aircraft within the first approximately second and a half.

Longitudinal Displacement (XA)

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

Time, sec

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plac

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t, ft Autopilot Off

Autopilot On (No FS Interp)

Autopilot On (With FS Interp)

Lateral Displacement (YA)

-13

-11

-9

-7

-5

-3

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Vertical Displacement (ZA)

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IV. Analysis of Parametric Variation in the HSAD Release

Accuracy of the store separation modeling is limited in fidelity due primarily to the quality of the input data and the accuracy of the numerical integration. The latter can be effectively managed through the proper selection of step size and method. Inaccuracies in the former, however, cannot be known prior to flight. Aerodynamic coefficients returned from wind tunnel testing, both freestream and grid, will differ from those at the actual flight conditions for a number of reasons including flow angularity, wall effects, scale effects, aero-elastic effects, interference effects, and atmospheric effects to name just a few. Ejector force profiles will differ slightly from those modeled. Mounting and structural interactions between the missile and the launcher, and the launcher and the aircraft are not fully modeled. Therefore, a sensitivity analysis was used to assess parametric uncertainty in the input data, and ensure that a sufficient margin of safety exists at the release condition.

A number of approaches can be taken to address this problem and mitigate the risk involved in release

of the first release HSAD missile. Perhaps the most straight forward approach is to conduct a Monte Carlo simulation of the release. Monte Carlo simulation is a stochastic technique whereby the parametric uncertainty is modeled as the outcome of a random event, although the outcome of the event is confined to a fixed range. A random selection process is used to select the event outcome, and the result is used in the simulation. A sufficient number of simulations should provide a realistic range of trajectories, and a probability can be assigned to any one trajectory. Since the number of parameters that can vary can be quite large, this method is typically computationally intense.

Another technique that can be used to mitigate uncertainty in the modeling is to assume that errors in

the trajectory simulation will be greatest when the parametric variation is at its greatest. The simulation can be run for some, all, or combinations of the varied parameters at their limits in order to bound a “worst-case” scenario for the trajectory. This method lacks a statistical basis, but is well suited to problems that have sufficient background with which to provide the engineer an intuitive understanding of to the physics

Time, sec

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t, ft

Autopilot Off

Autopilot On (No FS Interp)

Autopilot On (With FS Interp)

1.

Time, sec

Dis

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t, ft

4

Autopilot Off

Autopilot On (No FS Interp)

Autopilot On (With FS Interp)

Yaw Attitude (PSI)

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Autopilot On (With FS Interp)

Pitch Attitude (THETA)

-15

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Time, sec

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itude

, deg

Autopilot Off

Autopilot On (No FS Interp)

Autopilot On (With FS Interp)

Roll Attitude (PHI)

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Time, sec

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itude

, deg

Autopilot Off

Autopilot On (No FS Interp)

Autopilot On (With FS Interp)

Figure 5. Comparison of Simulated HSAD Trajectories.

of the problem with insight into what parametric variation is most likely occur, and what parametric variation is most likely to affect the trajectory.

A combination of the two approaches was employed for the HSAD release. The varied parameters

were grouped into four general categories; propulsion forces and moments, aero forces and moments, mass properties, and autopilot performance. The first three groups were treated in a similar fashion. The parameters in each category were assumed to vary randomly with a Gaussian distribution. Within the calculation of the aerodynamic forces and moments, NAVSEP assumes a superposition of elements due to the freestream, grid, and control surface deflection contributions. Based on experience with other store separation applications, a conservative assumption was made in the variation of the components making up the aerodynamic forces in moments in that they were assumed to vary in a coherent manner. Experience has shown that this method can give overly conservative results. If the analysis indicates that one or more of these profiles could result in an unsafe trajectory, the more detailed (and computationally time consuming) simulation is conducted to assess the probability of the occurrence.

The performance of the auto pilot also depends on the fidelity of the wind tunnel data. This was felt to

be the primary uncertainty in the performance of the autopilot. Specifically, the auto pilot uses processed wind tunnel data as a basis for the estimation of the missile angle-of-attack and missile side-slip angle. These angle estimates, in turn, serve as inputs to the autopilot algorithms. Therefore, angle-of-attack and side-slip angle estimates were modeled as a parametric uncertainty with a Gaussian distribution and standard deviation of 10% of nominal values. A summary of the standard deviation of the variation in the parameters in each category are summarized in Table 1.

Table 1. Summary of Parametric Variation on HSAD Simulation Mass Properties Aerodynamic

Properties Propulsion Properties

Alpha & Beta Estimates

Std Dev 2.5% 10% 20% 10%

The resulting trajectories with all four groups of parametric variation can be seen in Figure 6. The resulting variation in lateral and vertical displacement is acceptable for all cases shown. The functioning of the autopilot can be seen as a pitch, and yaw, angle capture with variation of a few degrees. Roll angle capture is slower by design, but in all cases the undesirable roll rate induced by the flow field on the missile during the first 0.7 seconds of flight is countered.

0 0.5 1 1.50

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800Longitudinal Displacement (XA)

Time

Feet

0 0.5 1 1.5-9

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3.5Yaw Attitude (PSI)

Time

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0 0.5 1 1.5-12

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-3Pitch Attitude (THETA)

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Time

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Figure 6. Comparison of Simulated HSAD Trajectories with Parametric Variation and the Autopilot On.

Monte Carlo techniques were also used to assess the relative effects of the four groups of parametric uncertainty on the trajectory. As expected, aerodynamic uncertainty was the dominant group. The relative effects on yaw angle and lateral displacement are shown in Figure 7 for the case of aerodynamic or autopilot performance parametric variation alone. Trajectory variation along the other axis exhibited similar behavior. The relative effect of uncertainty in the mass properties and propulsion groups was also secondary in magnitude as compared to the aerodynamic group.

0 0.5 1 1.5-3

-2

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Time - seconds

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Autopilot UncertaintyAerodynamic Uncertainty

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ral D

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Autopilot UncertaintyAerodynamic Uncertainty

Figure 6. Relative Effect of Alpha/Beta Estimation (Autopilot) and Aerodynamic Uncertainty on HSAD Trajectory.

V. Conclusions

The release of the first HSAD missile is currently planned for late FY2006. Following this first free flight of the vehicle, flight telemetry will be used to validate and improve trajectory simulations from NAVSEP 3.1. There is a possibility that the second free flight, currently planned at a similar release condition, might change in order to better demonstrate the increased capability of the HSAD vehicle. Should this change the launch condition, the improved and validated NAVSEP 3.1 code will be important in assuring a safe release from this different, and perhaps more challenging, flight condition. In that case, the progress made in the clearance for the first HSAD release will have immediate benefits in terms of schedule and cost. The complexity of stores continues to increase, and movable control surfaces with active autopilots near or at the time of release are becoming more common. NAVSEP 3.1 provides the capability to incorporate the effects of these elements in a MATLAB/Simulink environment using block diagram formats (as opposed to replicating low-level contractor codes in Fortran) while maintaining the ability to execute the trajectory generation NAVSEP kernel as a command line application. The integrated computational environment allows the store separation engineer to quickly leverage the computational resources available in MATLAB when it makes sense to do so. For the case of the HSAD missile release simulation, wind tunnel data interpolations and Monte Carlo techniques were implemented in MATLAB alleviating the need to modify the legacy Fortran code within the NAVSEP kernel. The recent improvements to NAVSEP have helped it keep pace with the trend to more complex store separation simulations.

References

1Huhes, D., et al., “F/A-18C HSAD Test,” Proj. No. 10425, Test No. TC-1098. Arnold Engineering Development Center, Arnold AFB, TN, April 2004.

2Akroyd, G., Tutty, M., “Theory Basis for STEME – Store Trajectory Estimation in a Matlab Environment,”

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http://www.mathworks.com/access/helpdesk/help/toolbox/simulink/index.html 4MATLAB Release 14 User’s Manual: http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html 5Taverna, F. P., Cenko, A., “Navy Integrated T&E Approach to Store Separation,” Paper 13, RTO Symposium on

Aircraft Weapon System Compatibility and Integration, Chester, UK, October 1998.

6Moyer, S. A., “NAVSEP – Navy Generalized Separation Package,” AVCSTD Report 93011-6053, Sep. 1993.

7Veazey, D. T., Hopf, J. C., “Comparison of Aerodynamic Data Obtained in the Arnold Engineering Development Center Wind Tunnels 4T and 16T,” AIAA, 1998.

7Veazey, D. T., Hopf, J. C., “Comparison of Aerodynamic Data Obtained in the Arnold Engineering Development

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Aircraft,” AIAA-96-2411, June 1996. 9Ray, E., “CFD Applied to Separation of SLAM-ER From the S-3B,” AIAA Paper 2003-4226. AIAA Applied

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Sciences Meeting, January 2005. 11Tutty, M., “Aircraft Stores Compatibility Systems Engineering – The Fundamentals & Future,” Aircraft Stores

Compatibility XIII Symposium, ITEA 2003.

12Hallberg, E. N., Ray, E., Fitzwater, R “Store Separation Trajectory Simulation for the High Speed Anti-radiation

Demonstrator (HSAD) Program,” AIAA Aerospace Sciences Meeting, January 2006.