Store Separation Trajectory Deviations Due to Unsteady Weapons Bay Aerodynamics

Transcription

1 46th AIAA Aerospace Sciences Meeting and Exhibit 7-10 January 2008, Reno, Nevada AIAA Store Separation Trajectory Deviations Due to Unsteady Weapons Bay Aerodynamics Rudy A. Johnson 1, Michael J. Stanek 2, and James E. Grove 3 Air Force Research Lab, Air Vehicles Directorate, WPAFB, OH, The combined trends toward internal carriage of weapons in modern aircraft and the design of new weapons to be neutrally stable for increased performance have increased the probability that unsteady aerodynamics will effect store separation trajectories. Reports from time accurate computational fluid dynamics trajectory simulations have shown trajectory sensitivity to time of weapon release. Typical wind tunnel data collected to support store separation analysis cannot detect this effect since the data collected consists of time averaged store loads. Flight testing to investigate effects of bay unsteadiness has not been done since it is expensive and typically there are insufficient funds to conduct repeated store drops at identical flight conditions. Carefully designed and conducted small scale drop testing in wind tunnels provides a means to identify the effect of unsteady weapons bay aerodynamics on store separation trajectories. Time accurate computational fluid dynamics trajectory analysis results on the Small Smart Bomb separating from an F-111 aircraft and a GBU-12 separation from the B-52 aircraft are reviewed. Small scale drop test data from a generic 10% scale rectangular cavity in a flatplate and from a 6% scale B-1B are introduced to provide experimental evidence of the effect of unsteady flow on the store separation trajectory. I. Introduction n this paper a growing volume of evidence related to unsteady flow effects on the store separation trajectory is I reviewed and new small scale experimental results are documented. Store separation trajectory analysis is focused on the initial half second of flight after the weapon (or store) is released from the aircraft. In a clean separation event the store will have traveled between 10 to 15 feet in this time and is no longer likely to impact the aircraft. During this short time period the aerodynamics of the weapon being released are modified by the influence of the aircraft aerodynamics which can significantly modify the expected store performance. The modified store aerodynamics can become sufficient in magnitude to produce unexpected trajectories with the result being anything from a benign separation to store collision with the aircraft. Stores have been carried both externally and internally for many years. Both carriage arrangements have advantages and disadvantages as far as range, stealth, and load out are concerned. From an aerodynamics point of view the stores to be dropped from an aircraft have been designed to fly in a steady freestream flowfield. For external store separation the typical analysis involves the use of time averaged store aerodynamic loads to estimate the effect of the aircraft flowfield on the store trajectory. In most cases this works fine, but there have been sufficient excursions to justify flight testing to validate the analysis. For internal separation the store must fly in the weapons bay & shear layer before it even gets to the aircraft flowfield. Both are unsteady environments that the store has not been designed to fly in. Traditional production store separation analysis techniques do not account for unsteady flow computationally or during wind tunnel testing. Current techniques used to feed store trajectory analysis employ time averaged aerodynamic loads. Theoretical and empirical models provide rough aerodynamic estimates to support parametric trajectory analysis. CFD is asked to provide time averaged aerodynamic loads to supplement wind tunnel data. Time accurate trajectories are done at 1 Aerospace Engineer, Integration and Demonstration Branch, AFRL/RBAI. 2 Associate Technical Advisor, Aeronautical Sciences Division, AFRL/RBA, Senior Member AIAA. 3 Team Lead, Weapons Integration Team, AFRL/RBAI. 1 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

2 a very limited number of flight conditions due to cost and time restrictions. These are typically to verify a specific trajectory from the steady model or in an attempt to identify what went wrong during a flight test. The wind tunnel is the workhorse that provides time averaged loads for separation trajectory analysis. The captive trajectory system (CTS) places the store to be separated on a sting or strake that allows positioning of the store in the aircraft flow field. This technique is capable of generating both quasi-time accurate separation trajectories and a grid of store aerodynamic coefficients. Mechanical limitations prevent fully time accurate trajectory modeling with CTS testing. Drop testing small scale stores in the wind tunnel environment has also been used to model the separation event. Typically this technique is not used for production weapons separation analysis due to the required approximations in the scaling laws which make extrapolation of small scale trajectories to the full scale difficult. The drop test scaling techniques are well documented 6 and can be used to generate time accurate trajectory data. The remainder of the paper will review existing theoretical and computational fluid dynamics results and introduce experimental results related to unsteady flow effects on store trajectories. First a short description of a combined theoretical and numerical technique that has identified a pitch bifurcation in the store trajectory will be discussed. Then time accurate CFD coupled with a six degree-of-freedom model are described for two aircraft-store combinations. Experimental results from small scale drop testing are presented as further evidence as to the dramatic effect unsteady flow can have on separation trajectories. II. Theoretical Evidence The combined asymptotic and numerical analysis (CANS) approach to modeling the separation of internally carried stores developed by Shalaev, Fedorov, and Malmuth 4,8 provides insight into the sensitivity of the store trajectory to small perturbations such as those caused by the unsteady shear layer in the opening of the weapons bay. The CANS model splits the separation problem into three separate aerodynamics models, 1. store in the bay, 2. store crossing the shear layer, and 3. store in external flow as indicated in Figure 1. While slender body theory and asymptotic methods are applied in Phases 1 and 3, the shear layer is modeled as a steady inviscid vortex sheet. This is rationalized by observing that the unsteady motions of the shear layer are three orders of magnitude faster than the time scale of the separating body 4. The developers of this model identify sensitivity in Phase 3 to the entry conditions from Phase 2 (angular velocity, vertical speed and their rates) which they labeled a pitch bifurcation. The plot in Figure 1 demonstrates the bifurcation caused by reversing the sign of the pitching moment applied in Phase 2 of the model. Essentially this model indicates that the weapons bay shear layer determines which path of the bifurcation the store follows. The critical piece of information to take from this is, under the assumptions of the model, that the store trajectory is sensitive to small perturbations such as those generated by a weapons bay shear layer. III. Time Accurate Coupled CFD/6-DOF Evidence With the notion of trajectory sensitivity to the unsteady weapons bay shear layer established theoretically, evidence from time accurate CFD/6-DOF models will be reviewed. Initially 2-dimensional results for a store separating from a generic bay are reviewed. Then full aircraft results from an inviscid model of an early version of the small smart bomb (SSB) separating from the weapons bay of an F-111 aircraft are discussed. The SSB in this case is an extremely stable 250 pound class store and is expected to be insensitive to small disturbances. At the other extreme we will look at a marginally stable GBU-12B (fins retracted) separating from the B-52H aircraft. In this case the CFD is fully viscous. 2

3 s l d V Phase 1. Store in the bay. Phase 2. Store crosses shear layer. Phase 3. Store in external flow α [deg] Experiment [8] α=α(m) α=α(-m) Phase 2 t [sec] -0,020,000,020,040,060,080,100,120,140,160,180,200,22 Figure 1. CANS Model and trajectory bifurcation result. A. Two Dimensional Trajectory Example Jordan and Denny 3 document the time of release effect using a 2-dimensional CFD model of a generic store separating from a rectangular bay. The goal of the study was to develop an estimate of a trajectory envelope that would bound the deviations due to unsteady flow. For a cavity with L/D of 4.5, a ten foot long store, and freestream Mach number of 0.95 four trajectories are computed. The time of release is evenly distributed over the period of the unsteady cavity flow based on the first Rossiter mode. The results indicate maximum differences in x and z displacements are 6 and 7 feet, respectively and 20 degrees in pitch at 0.4 seconds from the time of release (Figure 2). While this clearly demonstrates unsteady flow effects on the trajectory, the deviations are relatively small compared to the distance the store has traversed (35 feet) and are considered insignificant from a store clearance perspective. Figure 2. Two dimensional store separation trajectories from a generic bay L/D=4.5. 3

4 B. F-111/SSB Trajectories Coleman 1 presented fully time accurate inviscid store separation trajectory simulations done to support a flight test program. At the time the unsteady carriage loads on the SSB were monitored (Figure 3) and multiple release times were chosen to examine time of release effects on the store trajectory. Arbitrary times and release times corresponding to maxima and minima in the store aerodynamic loads were selected and time accurate store trajectories generated. Coleman noted only a slight effect on store translation but the store orientation definitely displayed sensitivity to time of release. The plots of pitch and yaw in Figure 4 show orientation deviations up to 5 degrees. While these changes are not typically considered significant to the practicing store separation engineer they are present and isolated such that the only cause is unsteady aerodynamic loads. It should also be noted that large end of stroke ejection velocities (36 ft/sec) and a static margin estimated to be 270% make the SSB trajectory artificially insensitive to the aerodynamic loads relative to conventional weapon separations. Figure 3. SSB Carriage Loads (CFD), Forward Location in the F-111 Bay. Figure 4. SSB Pitch and Yaw Results from Time of Release Study. C. B-52/GBU-12 Trajectories Freeman, Keen, and Jolly 2, 5 report on fully viscous time accurate GBU-12B separation trajectories from a B-52H weapons bay. They note that the store separation modeling is accomplished with the fins folded and that there is no weapons bay spoiler present (Figure 5). In contrast to the SSB the GBU-12B is neutrally stable at low angles of attack and unstable at higher angles of attack. This is a gravity drop from a deep bay. 4

5 Figure 5. B-52H geometry with open bay and GBU-12B folded fin configuration. In Figure 6 the carriage load plot indicates that the moments reverse sign and this prompted a small time of release study. Four separate trajectories were computed by initiating separation at the times indicated. Figure 7 has several snapshots of the store below the aircraft. The 4 stores in each image are at the same time level, relative to time of release, in frames (a-d). In frame (e) the yellow store has stopped and in frame (f) the blue store has also stopped (due to the simulation ending). The only difference between these 4 simulations is the time of release, i.e. the relative position of the unsteady weapons bay flowfield and shear layer. Clearly the store trajectory is sensitive to the unsteady flow and as the authors indicate the possible trajectories are not limited to the four computed. Figure 6. GBU-12B Carriage Loads. 5

6 a. b. c. d. e. f. Figure 7. Superimposed GBU-12B trajectory images from four separation events. IV. Evidence from Small Scale Wind Tunnel Tests Theoretically it has been shown that the store trajectory is sensitive to small perturbations, computationally results have isolated unsteady flow, through time of release studies, as the sole source of trajectory deviations. To build credibility in these models the same unsteady effects need to be verified experimentally. Unfortunately the collection of unsteady store separation data is not a standard practice during weapons integration testing due to both the difficulty in data collection and the justification of additional cost when the current quasi-steady process works most of the time. This section will look at acoustic data, store loads, and trajectory data collected from several different programs to provide insight into the effect of unsteady flow on store separation trajectories. The initial unsteady data discussed is store loads data collected during acoustic testing in the Lockheed-Martin Compressible Flow Wind Tunnel (CFWT). This is followed by discussion of 10% scale drop test data collected on the MK-82 JDAM during separation from a generic weapons bay in the Boeing Polysonic Wind Tunnel (PSWT). Six percent scale drop test results are also discussed for the CBU-105 separating from the rear bank of the B-1B intermediate weapons bay without the spoiler present. A. Unsteady Wind Tunnel Store Loads Measured With A Strain Gauge Balance Typically, time averaged quasi-steady store loads are collected with a strain gauge balance in the wind tunnel to provide aerodynamic data for store trajectory analyses using six degree-of-freedom (6-DOF) models such as FLIP- TGP. Unsteady store loads are almost never obtained with five or six component balances, because to properly collect the data, the system from the store through the balance and sting must be correctly designed to properly account for inertias and prevent unwanted oscillations. In this reported case, six component store loads data were collected during cavity acoustic testing in the Lockheed-Martin Compressible Flow Wind Tunnel (CFWT), as spare high frequency data collection channels were available, so the store balance was sampled at the same rate as the Endevco dynamic pressure transducers in the bay. The cavity was inches long with a length to depth (L/D) of approximately 6.0, which approximated a 1/5 th scale F-111 weapons bay, and the metric store was a generic 1/5 th 6

7 scale model of a 500 pound laser guided weapon with a body diameter of 2.15 inches and a length of inches, as shown in Figure 8. The dynamic pressure data and balance data were obtained from Hz to 50,000 Hz in Hz steps. The tunnel test conditions were Mach 1.45, with a dynamic pressure of approximately 10.9 psi and a total temperature of approximately 70 degrees F. Store balance and acoustic data were collected with several pneumatic flow control concepts in front of the cavity leading edge, and with several spoilers, and a baseline cavity with no flow control. Figure 8. Baseline cavity and store in wind tunnel. In Figure 9, the baseline cavity sound pressure level (SPL) data is shown at a transducer position on the cavity ceiling 62% aft of the cavity front bulkhead, along with store normal force data (in volts) reduced with the same FFT program. The SPL data clearly shows the first three cavity Rossiter modes at approximately 135, 270 and 425 Hz. The balance normal force data (N2 gauge) are shown at three store vertical (z) positions in and out of the bay, with the zero position defined as the store center line at the water line (WL) of the cavity edge, and positive being outside the bay. The store normal force data clearly shows a response at the first Rossiter mode of the cavity (135 hz), even when the store is 3 inches (~1.5 store diameters) outside the cavity, and shows a small response to the second Rossiter mode when the store is even with the cavity lip, at WL=0. In Figure 10, the Slot 2 leading edge blowing concept SPL data is shown, along with store normal force data, at a blowing rate of 0.06 lbm/sec. Compared to the SPL plot in Figure 9,the cavity acoustic levels are clearly reduced, although the first three Rossiter modes are still evident. The response of the store normal force to the first Rossiter mode is still visible at all three store positions, but the levels are greatly diminished, as compared to Figure 9. The results clearly show a correspondence between the unsteady pressures seen on the cavity ceiling and the unsteady store loads. The magnitude of the unsteady store loads also appear to be dependent on the magnitude of the acoustic levels in the cavity. 7

8 SPL (db) Baseline Cavity - Port 3 (62 % X/L) SPL03 N2 Balance Gauge (volts) Baseline Cavity - Store at WL = -2 in N N2 Balance Gauge (volts) Baseline Cavity - Store at WL = 0 in N2 N2 Balance Gauge (volts) Baseline Cavity - Store at WL = 3 in N Figure 9. Baseline Cavity Sound Pressure Level and Store Normal Force vs. Frequency SPL (db) Cavity with Slot 2 Blowing - Port 3 (62% X/L) SPL 03 N2 Balance Gauge (volts) Cavity with Slot 2 Blowing - Store at WL = -2 in 0.35 N N2 Balance Gauge (volts) Cavity with Slot 2 Blowing - Store at WL = 0 in N2 N2 Balance Gauge (volts) Cavity with Slot 2 Blowing - Store at WL = 3 in N Figure 10. Cavity SPL and Store Normal Force vs. Frequency with Leading Edge Blowing 8

9 B. MK-82 JDAM Small Scale Drop Testing from a Generic Rectangular Bay Drop testing of ten percent scale MK-82 JDAM models from a generic rectangular weapons bay (L/D=7.24) were preformed in the Boeing PSWT 7. Figure 11 depicts the weapons bay, ejector system, and the drop test model. The ejector consists of two springs compressed onto load washers to monitor ejector forces. A burn bolt compresses the springs by holding the store model until sufficient current is applied to vaporize the bolt, initiating the ejection. The drop test models were designed using light scaling laws which results in store dynamics representative of a store at 5,000 ft altitude while the aerodynamics are representative of that at 15,000 ft. Understanding of this scaling is critical when trying to infer how the drop test trajectories would scale to a real separation scenario, however for the purpose of this paper we will simply note that the aerodynamic forces are much stronger relative to inertial loads than what would be seen at full scale. The wind tunnel flow conditions and store properties are detailed in Table 1. Theoretical design conditions are given in the first row of the table, the rest are measured flow conditions and store properties given to emphasize how closely the experiments were controlled. The only significant deviation from nominal is the rolling moment of inertia, due to the model design (mass concentrated on the store axis). It is consistent among the models and not a significant source of error for comparison within the data collected. Small deviations in the weapons bay pitch angle and tunnel dynamic pressure do not result in a consistent change in store trajectory and are not considered significant. (a.) (b.) Figure 11. (a) Generic rectangular weapons bay configuration, (b) MK-82 JDAM drop test model with ejection mechanism. Table 1. Freestream Release Conditions and Drop Test Model Properties. 9

10 The store separation is initiated by vaporizing the burn bolt then and recording the separation using high speed photography. The nominal and achieved ejector forces are listed in Table 2. The total force variations were within 5% of nominal while the imparted pitching moment varied up to 7.1% of nominal. Deviations in ejector forces and moments between runs are less than those compared to nominal. The photogrametric processing is completed by assuming either a three degree (3D) or six degree (6D) of freedom store motion. Computer software is used to track targets placed on the drop test models and resulting trajectories are plotted in Figure 12. The plot indicates the store center of gravity displacement from the carriage location. The Z axis is vertical displacement and the X axis is streamwise distance from carriage. Solid lines are generated using the full six degree of freedom reduction while the dashed lines are for the three degree of freedom approximation. The breaks in the solid lines occur when the required number of tracking targets are not visible in the images. The separation trajectories for all five runs start the same but result in different trajectories. Run 2 is the only clean separation, while runs 1 and 3 actually generate enough lift to fly back and strike the weapons bay model. Runs 4 and 11 generate sufficient lift to fly but do not impact the model. Figure 13 has a plot of the store pitch achieved as a function of time after release. Once again the initial trajectories are similar and the deviations grow in time without a clear initiation mechanism. Figure 14 is a series of images off of the high speed film from run 1 (upper) and 2 (lower). In frame (a) from this series there is a visible deviation in pitch by the time the store is partially through the shear layer. The store in run 2 has completely exited the bottom of the image by the time the store in run 1 starts flying back toward the bay in frame (g). Table 2. Nominal and Measured Ejector Parameters. 10

11 2 Run 1-6D Photo Run 2-6D Photo Run 3-6D Photo Run 4-6D Photo Run 11-6D Photo Run 1-3D Photo Run 2-3D Photo Run 3-3D Photo Run 4-3D Photo Run 11-3D Photo 0-2 Z (in) X (in) Figure 12. Photogrametric Drop Test Trajectories. pitch (deg) time (ms) Figure 13. Store Pitch Histories. 11

12 (a.) (b.) (c.) (d.) (e.) (f.) Figure 14. MK-82 JDAM trajectory images from Run 1 (upper) and 2 (lower). C. B-1B/CBU-105 Small Scale Drop Testing Drop testing from a 6% B-1B model was conducted in the Boeing PSWT facility as part of a program to develop an improved flow control methodology to enhance store separation characteristics. 9 The data shown here is for a light scaled CBU-105 store with stowed fins being separated from the aft bank of the intermediate bay without the B-1B spoiler. This data was collected to provide a baseline for the clean bay in order to compare the existing spoiler performance with that of the clean aircraft and new flow control concepts. The store to be separated is shown mounted in the carriage position in Figure 15. Averaged side wall and aft wall pressure transducer outputs are shown in Figure 16. The averages plotted are taken over consecutive 1024 sample windows from the test data (recorded at 20,000 samples per second for 20 seconds). The burn bolt is initiated at time equal to zero and takes approximately a half a second to release the store. A change in the time histories can be seen which corresponds to the time of release but not much insight is gained regarding the unsteady flow. Figure 16 does indicate the repeatability of the ejection mechanism and acoustic data collection from run to run. The CBU-105 separation trajectories are depicted using images from three instances in time in Figure 17. Run 24 is the top image in each frame (a,b,c), Run 25 the middle, and Run 26 the lower image. The movies have been synchronized as closely as possible to time of release. As in the previous case tunnel and ejector parameters were tightly controlled with the result once again being different trajectories for each separation event. Run 24 impacts the aft bay bulkhead, Run 25 is a clean separation, and Run 26 shows significant yawing as the trajectory progresses. 12

13 Figure 15. B-1B without spoiler and the CBU-105 mounted on the aft centerline ejector (Run 26). (a.) (b.) Figure 16. Pressure transducer outputs from Runs 24, 25, and 26. (a.) Bay side wall (b.) Aft bulkhead. D. Discussion of Experimental Data Clearly experimental results presented here provide insight into the effects of unsteady flow on the store separation trajectory. Experimentally measured unsteady loads for a sting mounted store indicate that the store experiences unsteady forces at the same frequencies seen by acoustic sensors within the weapons bay. This unsteadiness is seen not only with the store in the bay, but also while the store is within 1.5 diameters of the bay opening. Additionally drop testing indicates significant trajectory deviations are possible but at the same time raises questions about the reliability/repeatability of the ejection mechanism. Drop testing also introduces light scaling with the consequence being the importance of the aerodynamic forces tends to be exaggerated relative to full scale. Sources of variation of the ejector mechanism are possible but not indicated by data collected from the load washers or acoustic monitoring. There is a slight elongation of the burn bolt as it heats up prior to release and the bolt requires approximately 0.5 seconds to release once current is applied which makes it difficult to obtain the exact time of release with the present ejection set-up. The ejector forces monitored are not capable of measuring any effect of forces imparted on the store due to the bolt vaporization or any effect the vaporization has on the local aerodynamics. Inclusion of an expendable small telemetry package in the drop test model to measure accelerations 13

14 and the use off body flow diagnostics would provide increased confidence in the experimental results and should be included in future efforts. It is well known that the light scaling laws used to develop the store model increases the sensitivity of the store trajectory to the aerodynamic loads over that which would be seen at full scale. Unfortunately cost prohibits repeated full scale store separation flight testing to isolate this effect and conventional CTS wind tunnel testing is not currently capable of the unsteady data collection needed support the analysis. The drop test deviations are in fact a worst case scenario since aerodynamic loads are magnified relative to other forces that affect the trajectory at full scale. At full scale it is expected that unsteady forces will cause trajectory deviations, but not with as large of a magnitude as that witnessed in the wind tunnel. With the move to more unstable stores due to both performance requirements and packaging for internal carriage the full scale aerodynamics become more important and drop test results are more meaningful. Fortunately for the purposes for this work we are comparing a consistent set of data at the same scale to identify trajectory deviations so the scale-up difficulty is avoided. The coupled CFD/6-DOF models are capable of simulating the light scaled set-up to provide consistent code verification and flowfield information. With careful control of the drop test model fabrication, the wind tunnel parameters and ejector parameters small scale drop testing can be effectively used to generate time accurate separation trajectory data. This data may prove difficult to extrapolate to full scale separation clearance work but can provide a significant source to validate coupled CFD/6-DOF and empirical models. (a.) (b.) (c.) Figure 17. Light scaled CBU-105 separation trajectory images for runs 24, 25, and 26. V. Conclusion Theoretical, computational, and experimental data indicate unsteady aerodynamics can have significant effects on store separation trajectories. Theoretical results identify a pitch bifurcation evidenced by trajectory sensitivity to small flow perturbations (weapons bay shear layers). Computational results demonstrate unsteady effects on realistic geometries that cannot be measured in traditional CTS separation testing. Experimentally unsteady store loads collected with a CTS system indicate that a store in the vicinity of the weapons bay experiences aerodynamic forcing at the same frequencies seen by acoustic sensors in the bay. In addition, experimental drop testing further demonstrates the unsteady effects on store separation trajectories. Trajectory data collected on 5 identical small scale store drops show no significant deviations in initial trajectory, ejector data, or tunnel conditions, and the initial 14

15 store pitching trends are similar, yet significant trajectory variations are observed. Three identical store drops from the 6% scale B-1B without a spoiler also show significant trajectory variations. The probable cause is unsteady flow inducing small variations in aerodynamic forces and moments from one drop to the next. The accumulation of these small variations due to unsteady flow early in the trajectory results in the significant deviations at later times. Future drop testing should include monitoring of weapon bay acoustics during separation, instrumenting the drop test models with expendable telemetry packages, improved photogrametric camera placement and analysis, and the inclusion of off body diagnostics techniques to observe the unsteady shear layer interaction with the store. Additional development of the ejection system to avoid the burn bolt approach could improve data collection synchronization of the various diagnostic equipment. Combined CFD/6DOF modeling needs to be validated against new experiments in order to incorporate unsteady effects into the Store Separation Certification process. Acknowledgments The authors would like to thank Ganesh Raman from Waveflows, Andrew Cary from The Boeing Company, and David Benjamin from Boeing Enterprise Laboratories for their continued discussions of the small scale drop test data. References 1. Coleman, L. A., F-111 / Small Smart Bomb Trajectory Predictions for Safe Separation Analysis using Computational Fluid Dynamics, Aircraft-Stores Compatibility Symposium, March 5-8, 2001, Destin, FL. 2. Freeman, J. A., Keen, J. M., and Jolly, B. A., Quick-Reaction Computational Fluid Dynamics Support of Aircraft-Store Compatibility," presentation slides 19-24, ITEA Aircraft Store Compatibility Symposium, FT Walton Beach, FL, April 11-13, Jordan, J.K. and Denny, A.G., Approximation Methods for Computational Trajectory Predictions of a Store Released from a Bay, AIAA , Applied Aerodynamics Conference, Atlanta, GA, June V. Shalaev, A. Fedorov, and N. Malmuth, Dynamics of Slender Bodies Separating from Rectangular Cavities, AIAA Journal, 40, No. 3, March 2002, pp Freeman, J. A., Applied Computational Fluid Dynamics for Aircraft-Store Design, Analysis and Compatibility, 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA , 9-12 January 2006, Reno, Nevada. 6. K. S. Keen, C. H. Morgret, and R. L. Arterbury. An Analytic Investigation of Accuracy Requirements for Onboard Instrumentation and Film Data for Dynamically Scaled Wind Tunnel Drop Models. AEDC TR-96-7, March Cary, A.C. and Wesley, L.P., Airframe Integration of Modern Stores (AIMS), Delivery Order 0031: Phase II & III Analytical Predictions & Validation Testing, Air Force Research Lab, Dayton, OH, January 2006, AFRL-VA-WP-TR Malmuth, N., Fedorovf, A., Shalaevt V., Cole, J., Khokhlov, A., Hites, M.,and Williams, D., Problems in High Speed Flow Prediction Relevant to Control, Part 3. Store Separation from Cavities, AIAA , Theoretical Fluid Mechanics Meeting, 2nd, Albuquerque, NM, June 15-18, Bower, W. W. and Kibens, V., Separation Enhancement and Acoustic Reduction (SEAR) Phase I, Air Force Research Lab, Dayton, OH, November 2006, AFRL-VA-WP-TR