Effects of Solid Rocket Booster Case Breach on Vehicle and Crew Safety

Transcription

1 26th AIAA Applied Aerodynamics Conference August 2008, Honolulu, Hawaii AIAA Effects of Solid Rocket Booster Case Breach on Vehicle and Crew Safety Shishir A. Pandya * NASA Ames Research Center, Moffett Field, CA, The structural failure of a Solid Rocket Booster (SRB) in the form of a breach can result in venting of burnt solid rocket fuel during the ascent phase of a manned mission. Such venting can cause a substantial side force resulting in loss of thrust in the main nozzle, loss of vehicle controllability, and possible structural failure. This paper describes a strategy to analyze the effects of such a breach using high-fidelity simulation. The effects of the breach on the overall safety of the vehicle are analyzed by quantifying loss of thrust, resulting pitching moment, and pitch acceleration. The warning time is also computed to examine the effects on crew safety. It is found that while the loss of thrust in the main nozzle is negligible, substantial force and pitching motion are generated by a breach and can cause a vehicle failure if not countered by the thrust vector control system available on the main nozzle. α = Angle of attack α = Pitch acceleration ρ = Density ω = Angular velocity h = Height m = Mass r = Radius D inner = Diameter of the fuel chamber D outer = Diameter of the rocket C. G. = Center of gravity F = Force H = Angular momentum I = Moment of inertia M = Moment MET = Mission Elapsed Time Q = Dynamic pressure of the external air Re = Reynolds number W = Weight N Nomenclature I. Introduction ASA has embarked on a mission to design and build a new spacecraft in response to the current administration s Vision for Space Exploration. As a part of this vision, Ares-I, the Crew Launch Vehicle (CLV), is a rocket that will be used for manned missions after the retirement of the Space Shuttle. As shown in Figure 1, the astronauts travel in the Crew Exploration Vehicle (CEV), which includes a capsule atop the rocket stack similar to the one atop the Saturn-V rocket used in the Apollo program. 1 A Launch Abort System (LAS) attached to the top of the capsule is designed to separate Orion from the rest of the launch stack and return the astronauts back to earth safely in case of deployment due to a catastrophic failure during ascent. One possible failure during ascent involves the development of a breach in the steel casing of a Solid Rocket Booster (SRB), which allows burnt rocket fuel to vent orthogonal to the vehicle axis resulting in a substantial side force. 2 In the event of such a case breach, an abort may be necessary due to the imminent dangers from loss of thrust in the main nozzle, loss of vehicle controllability, and overstepping structural limits. * Aerospace Engineer, NASA Ames Research center, M.S. T27B, AIAA Senior Member. 1 of 14 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

2 This paper describes the results of an analysis to determine the effects of a case breach on the loss of thrust and vehicle control and structure. Two breach sizes and three breach locations are analyzed. Steady-state inviscid computational fluid dynamics (CFD) simulations are used with and without a breach in the geometry of the SRB to directly compute the loss of thrust. Thrust loss due to growth of breach size is addressed in Ref. 3, but is not addressed in this paper. Next we consider loss of controllability. A thrust vectoring system is available on the SRB in order to keep the vehicle on a planned trajectory. The nozzle of the SRB can be gimbaled up to 7 to provide control authority for pitch and yaw. To assess controllability, we use forces and moments computed in the CFD simulations to obtain the angle of attack and pitch rates. The computed moment values of the full gimbal case are compared to the moments caused by the breach to determine if loss of control has occurred. Finally, the structural limit is examined. The structure of a rocket is designed to withstand a given set of loads. The limits of these loads are often characterized as a maximum angle, or a maximum rate of motion. The most sensitive of these is the pitching motion or yawing motion due to buckling problems at high pitch or yaw rates. To prevent the rocket from buckling, the rocket must fly at pitch rates lower than a given threshold. For the Apollo program, the pitch-rate threshold was at 3 /sec. 4 The moment data from CFD is used along with the mass properties to determine the time it would take to reach the pitch rate limit. This data can then be used to determine the amount of thrust required for the Launch Abort System to pull the capsule away from the stack during an abort maneuver. In addition, the time to failure is also computed to guide the design of the LAS. It should be noted that the presence of the plume from the breach modifies the aerodynamics in the viscinity of the breach resulting in substantial changes in forces and moments. These effects are Launch Abort System Spacecraft Adapter J-2X Upper Stage Engine properly captured in a high-fidelity fluid flow simulation. However, if these aerodynamic effects are not important, one could compute the moments with only the breach and the nozzle thrust values. With the moments, and moments of inertia, one can make similar conclusions without the use of high-fidelity simulation. In addition to the steady-state solutions, preliminary simulations are conducted to test the current capabilities of 6-degrees of freedom (DOF) time-dependent moving-body methodology. An earlier CLV design involving a 4- segment SRB geometry (with a raceway) is used. The scope of the simulations is to test the current capability of the flow solver and to evaluate its possible future use. The rocket is released by the 6-DOF simulation at M=2.75 in nominal flight (without a breach) at 76,600 ft. altitude. During upward flight, the SRB develops a breach and the solid rocket chamber vents through this breach. The dimensions of the breach are 70 in. axially and 4 in. in the azimuthal direction in the aft segment of the SRB. The SRB nozzle is held fixed at the 0 gimbal position. A second 6-DOF simulation consist of the same breach with added gimbaling of the SRB s main nozzle to compensate for the moment generated by the breach. The purpose of this simulation is to determine if the rocket can 2 of 14 Ares l Figure 1. Ares I representation Orion Crew Exploration Vehicle (Crew Module/ Service Module) Instrument Unit Upper Stage Interstage First Stage (5-Segment RSRB)

3 be controlled using the TVC system. The nozzle is gimbaled at a fixed rate of 8deg./sec. until the 4 gimbal position is reached. Gimbal positions between 4 and 7 are not investigated and a gimbal feedback algorithm is not applied. II. Breach geometry and locations A series of inviscid computational fluid dynamics (CFD) simulations are performed on a representative Ares-I geometry (as shown in Figure 1). Note that a clean configuration without protrusions is used (no Reaction Control System (RCS) or cable trays). The simulation cases are outlined in Table 1 and 2. Table 1 shows the variations in geometries. Three types of variations are used: breach size, breach location, and gimbal position. First, the solution without a breach is compared to solutions obtained with two different breach sizes at all three breach locations. The comparison of the resultant thrust is used to determine the loss of thrust due to the breaches. For solutions with a breach, the nozzle is fixed in the 0 gimbal position. However, for the nobreach case, the 7 gimbal position is also simulated to obtain the maximum gimbal authority values. This helps determine the vehicle controllability. The final geometry variation involves the position of the breach. The SRB under consideration has 5 segments. Thus, breaches in the forward segment (1), the middle segment (3), and the aft segment (5) are considered as shown in Figure 2. Table 2 shows the flow condition variations. Four Mission Elapsed Times (MET) are considered, corresponding to different altitudes and Mach numbers. For each MET, the Mach number is varied by a given percentage. The angle of attack is also varied about a nominal of 0 to determine the effects of angle of attack on the results. These variations about the nominal condition are used to determine the uncertainty in the moments. All dimensions and flight conditions used in this paper are based on early designs or Space Shuttle data. The weights, center of gravity locations, and moments of inertia used in this study are approximations based on the diameter and height of each component of the Ares-I stack. III. Vehicle properties At the time of this analysis, CLV component sizes, weights and moments of inertia were not available. Therefore, approximations were made based on similar vehicles. Reference 1 is used in order to approximate the mass, and moments of inertia of the CLV. A representative trajectory and the 1976 Standard Figure 2. SRB breach locations (4 x70 breach shown) Breach Size Gimbal Breach Location 0 No gimbal - 7 gimbal - 2 x70 No gimbal Forward Middle 4 x70 No gimbal Aft Forward Middle Aft Table 1. Geometry variations MET Altitude Q Re Thrust Mach (x10 6 ) (x10 6 ) number α 15 2, ±10% 0± , ±20% 0± , ±5% 0± , ±11% 0±1 Table 2. Flow conditions Body Weight [lbm] Weight [Kg] CEV system 59,000 26,760 CEV to orbit 48,000 21,770 Payload 34,485 15,640 Upper stage fuel 245, ,130 Upper stage inert 40,475 18,360 SRB fuel 1,105, ,580 SRB steel 179,800 81,570 GLOW 3 of 14 1,616, ,410 Table 3: Manned CLV weights from reference

4 Atmosphere 5 are used to determine the flight conditions of the vehicle at the four MET s of interest. The Shuttle ascent flight table is used to determine the point in the trajectory when half of the SRB fuel is spent. A. Weights Since the total operating time of the SRB is approximately 2 minutes, half the solid propellant is assumed to be expended at MET=60 s. Therefore, the weight data is computed at this MET by adding the CEV system weight and upper stage system and fuel weight 1 to an inert SRB weight and the weight of half of the SRB fuel. The approximate component weights are obtained from Ref. 1 and tabulated in Table 3. This computed weight is used for all MET s used in the simulations. Additional details necessary for the simulations are presented in Table 4. Body ρ[kg/m 3 ] D Outer [m] D Inner [m] Height[m] Weight[Kg] CEV system ,760 Upper stage (LOx/LH 2 ) ,000 Upper stage inert ,000 SRB fuel (rubber) 1, ,000 SRB casing (steel) 7, ,570 Total 236,443 Table 4: Crew Launch Vehicle weights B. Center of gravity The CEV C.G. is derived based on our experience with the Apollo CEV. The upper stage C.G. is assumed to be halfway down the stage and the C.G. of the SRB is assumed to be 12% lower than the geometric center due to the presence of the large skirt, rocket motor, and nozzle assembly at the bottom. The C.G. locations used in this study are tabulated in Table 5. The center of gravity of the entire vehicle is computed using component center of gravity and weight as follows, C.G. W Component C. G. [m] CEV Upper Stage 17.8 SRB 60.1 Table 5. Component center of gravity = C.G. CEV W CEV + C.G. UpperStage W UpperStage + C.G. SRB W SRB Using the weights from Table 4, the C.G. of the entire CLV is computed to be 47.3 m. C. Moments of inertia The CEV inertias were obtained from an early capsule design and therefore are representative numbers. The inertias of the rocket were computed assuming cylindrical bodies. For reference, moments of inertia for a cylinder can be calculated using the following formulas: 6 I xx = 1 2 mr 2 ( ) I yy = I zz = m 12 3r2 + h 2 The steel casing for the SRB is a cylindrical shell for which the moments of inertia are computed by subtracting the moments of inertia of the inner-diameter cylinder from the moments of inertia for the outer-diameter cylinder. The mass of the vehicle is based on the density of the material (steel for the SRB casing, solid rubber fuel for the SRB fuel, etc.) and is computed using the formula m = ρv = πρr 2 h. The resulting moments of inertia are shown in Table 6 for each component. 4 of 14

5 Body I xx I yy I zz I xy I xz I yz Capsule 30,000 26,700 24, Upper stage 487, e6 7.8e SRB Fuel 58, e7 3.4e SRB Steel 7, e7 1.15e Table 6: CLV moments of inertia about the component axes [Kg.m 2 ] D. Transferring moments of inertia to the center of gravity The moments of inertia for the upper stage and the SRB in the above section are calculated about the geometric center of the cylinder. These moments of inertia need to be transferred to the center of gravity of the entire vehicle by noting that: I xx = I xx,cc I yy = I zz = I yy,cc + m( c.g. c.g. cc ) where the subscript cc denotes the center of the cylinder such that I xx,cc is the moment of inertia about the center of the cylinder. Thus, the moment of inertia for the complete vehicle is: I yy = I zz = I yy,cev + m CEV ( c.g. c.g. CEV ) + I yy,us + m US ( c.g. c.c. US ) ( ) +I yy,srb + m SRB c.g. c.c. SRB where CEV is the crew escape vehicle, US denotes the liquid upper stage and SRB denotes the solid rocket booster. The moments of inertia for the entire CLV are tabulated in Table 7. I xx I yy I zz I xy I xz I yz 583, e e Table 7: Vehicle moments of inertia IV. Simulation methodology The surface geometry is extracted from a CAD model of the vehicle using tools described in Ref. 7. The resulting surface triangulation is then used in the Cart3D package to generate a suitable telescoping Cartesian mesh that is used in the Cart3D flow solver to generate inviscid steady state solutions. 8 These inviscid flow solutions provide values for the forces and moments on the vehicle. The forces in the axial direction are compared for the breach cases with the no-breach cases to obtain the loss of thrust. The moments for the 7 nozzle gimbal cases is compared with the cases with 0 gimbal to see if the TVC has enough control authority to counter the additional moment generated by rocket fuel venting through the breach. Finally, the moments of inertia are used with the pitching moment from the simulations to determine the pitch rate. This pitch rate is compared to the maximum allowable pitch rate to determine if abort must be executed for the given breach size, position, and flow conditions. To obtain the specified thrust corresponding to the MET, a thrust chamber is included in the model as shown in Figure 3. A chamber pressure computed with 1-D nozzle analysis is imposed at the top face of the chamber as a boundary condition (see Ref. 9 for boundary condition details). The chamber is connected to the atmosphere through the SRB nozzle and the breach. Figure 3. Schematic of the SRB geometry Flow is computed in the chamber and through the nozzle resolving airflow through the throat and capturing the shape of the plume. Note that chemical reactions in the plume are not modeled. When a breach is present, some of the high-pressure gas in the chamber escapes through the breach resulting in a loss of thrust. The vented gas and associated plume results in a change in the forces and moments on the vehicle. 5 of 14

6 A moving-body version of Cart3D is used to solve the Euler equations in a time-accurate manner. 10 Coupled with the fluids module, a moving body module integrates the forces and moment on the vehicle and assesses the new position of the vehicle based on 6-DOF solid body dynamics and user input. 11 A time-dependent Cart3D run of the rocket is started from M=2.75. It is assumed that the rocket is moving straight up. In other words, gravity is pointing down the rocket. After a few meters of movement upwards, a breach is introduced in the aft section of the SRB casing. The breach is 4 wide and 70 long with the opening connecting the SRB thrust chamber to the atmosphere. In real life, the TVC system attempts to compensate for the resulting side force using nozzle gimbal. We impose a nozzle movement to gimbal the nozzle to 4 over a period of 50 time steps resulting in 8 /sec. gimbal rate. The resulting pitch rate is then assessed to see if the side force generated due to the breach can be compensated for by the nozzle gimbal. V. Results A. Loss of thrust Table 8 shows the thrust produced and percentage loss of thrust as a function of the size and position of the breach for MET=15 s. The largest deviation in thrust due to a breach in the SRB is 1.39% or 53,000 lbf. This is not very large compared to a total thrust of 3.2 million lbf. The thrust loss is also noted to be lower for the aft breach. This is due to the presence of the aft-skirt in the vicinity of the breach. MET Breach Size Breach Position Thrust [Million lbf] % Loss Fore x70 Mid Aft Fore x70 Mid Aft Table 8. Loss of thrust for MET=15 due to a breach in the SRB Figure 4 shows the thrust as a function of MET for the 4 x70 forward breach. To illustrate the loss of thrust, the no-breach case is also plotted. During ascent, the thrust lost due to a breach does not vary greatly. Thus, loss of thrust is not an issue for the size of breach considered in these simulations. Note that breach-growth is not dynamically addressed. Instead, increasing breach sizes are examined to mimic breach growth. Figure 4. Thrust produced by the SRB with and without a breach as a function of MET 6 of 14

7 B. Loss of control authority The thrust produced by an SRB in the present simulation is shown in Table 9, along with the side force generated due to breaches at different axial locations for MET=15 s. Although the side force generated is not vastly different for a given breach size, the position of the breach changes the moments generated on the vehicle. The resultant moments can be computed from the side force and moment arm to the C.G. and are listed in Table 10 for MET=15 s. The uncertainty based on variations of α and Mach number are seen to be small. Figure 5 shows the moments generated as a function of MET for both breach sizes at all breach locations. The worst-case scenario for a 2 x70 breach is the aft location at MET=101 s. which produces a moment of 31 million ft.-lbf. The flow solution with the SRB nozzle gimbaled to 7 (gimbal hard-over case) yields a moment of 48 million ft.-lbf. This indicates that there is sufficient control authority to overcome the moments generated by the 2 x70 breaches. The worst-case scenario for the 4 x70 breach also occurs for the aft breach location at MET=101 s. In this case, 47.8 million ft.-lbf of moment is generated. This is just below the moment from the gimbal hard-over case. While it is sufficient for control, it does not leave a comfortable margin. MET Breach Size Breach Position Thrust [Million lbf] Side Force [lbf] x70 Fore Mid Aft x70 Fore Mid Aft Table 9. Side force generated due to breach MET Breach Size Breach Position Moment [Million ft.-lbf] Uncertainty [Million ft.-lbf] Fore x70 Mid Aft Fore x70 Mid Aft Table 10. Moments generated due to SRB case breach C. Structural integrity limit To compute the pitch rate induced by a breach in the SRB, we use the moment values shown in Figure 6. A derivation for computing the pitch rate, pitch angle and pitch acceleration generated due to the breaches is shown in the Appendix. The pitch acceleration results are listed in Table 11 for all MET, breach sizes and positions along with the gimbal hard-over (7 gimbal) case for each MET. The results indicate that gimbaling is sufficient to control all breach cases considered here. The time to abort, defined as the time required to reach the pitch rate limit after a breach occurs, can also be computed using the same analysis for deriving pitch acceleration. Table 2 shows time to abort for all MET values and two abort criteria. The first criterion of 3 /sec. pitch rate is used, as in the Apollo program. 4 The second criterion of 5 /sec. (also an Apollo criterion for MET=50+ sec.) is presented here as a more realistic estimate of the CLV program target. The times shown are computed at 0 gimbal. It is predicted that the times will increase with the use of nozzle gimbal. 7 of 14

8 (a) Forward location (b) Mid location (c) Aft location Figure 5. Moment generated due to SRB case breach 8 of 14

9 MET Breach Size Breach Position α α due to gimbal hard-over [1/sec 2 ] Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Table 11. Pitch acceleration due to SRB case breach and gimbal hard-over Pitch rates can also be viewed as a function of MET and time from breach. Figure 6 shows the pitch rate as a function of MET for various times for all breach locations. Figure 6(a) shows pitch rate for the forward breach position. No gimbaling is employed for this analysis. The acceleration due to the breach is assumed to be constant, and is, therefore, a conservative estimate. At MET=59 and 101 sec., the pitch rates generated are below the limit of 3 /sec. At MET=39 s., the pitch rate limit is exceeded for the 4 x70 breach approximately 2 seconds after breach. At MET=15 s., the limit is exceeded for the 2 x70 breach after 2 s. and for the 4x70 breach after 1.5 s. 9 of 14

10 MET Breach Size Breach Position Time to abort [sec.] 3 /sec. Time to abort [sec.] 5 /sec. 15 Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Fore x70 Mid Aft Table 12. Time to abort based on the pitch rate Figure 6(b) shows pitch rate as a function of MET for a breach near the middle of the SRB. Again, curves corresponding to several times from breach are represented based on a constant acceleration value. The possibility of failure at MET=15 s. does not change from the forward breach case. However, at higher MET values of 59 s. and 101 s., failure can occur with lead times of 2 and 1 seconds respectively. Figure 6(c) shows pitch rate for the aft breach position where the failure lead times have dropped to less than 1 second. Once again, this analysis is done without gimbaling. Use of the thrust vector control system would certainly help lengthen the time to failure since in all cases the moment generated by the breach can be completely counteracted with nozzle gimbal. 10 of 14

11 (a) Forward breach (b) Mid breach (c) Aft breach Figure 6. Pitch-rate due to SRB case breach 11 of 14

12 D. 6-DOF simulations The first scenario simulated with the 6-DOF method is a CLV rocket in ballistic flight (flying straight up) at M=2.75 with half the fuel in the SRB expended (Figure 7(a)). A 4 x70 breach is introduced in the aft section of the SRB (Figure 7(b)). A plume quickly develops and the rocket begins to tumble (Figure 7(c)). It continues to tumble till it is out of control and the pitch rates exceed the structural limits (Figure 7(d)). In this test case, thrust vector control is not used to counter the force and moment generated by the presence of the breach. A time-dependent, inviscid simulation to assess if SRB nozzle gimbal can control the attitude of the rocket is then considered. In this second scenario, the SRB s nozzle is gimbaled at 8 /sec. to a 4 gimbal position to counter the pitch rate resulting from the breach. The gimbaling is effective, as the pitch rate of the rocket is reduced greatly when compared to the case without thrust vector control. In order to illustrate the differences, two frames of the simulation that correspond to the time indices of Figure 7(c) and (d) are shown in Figure 8(a) and (b). Although the vehicle does not attain as high a pitch rate, extending the time of the simulation reveals that the vehicle begins to roll due to the presence of the raceway on the SRB and the non-zero moments of inertia (Ixz, Ixy, Iyz). Without a feedback loop for the TVC and a reaction control system, the attitude of the rocket will deviate from its intended path. (a) Rocket on a ballistic path (b) Breach in the aft section (c) Tumble due to breach (d) Loss of control (high pitch rate) Figure 7. 6-DOF simulation of loss of control due to an aft breach 12 of 14

13 (a) Tumble due to breach (time: same as Fig. 7c) (b) Slower tumble due to gimbal(time: same as Fig. 7d) Figure 8. 6-DOF simulation of the CLV with 4 gimbal VI. Concluding remarks The possibility of an abort during ascent due to SRB case-breach is explored with loss of thrust, loss of control, and structural failure in mind. A series of inviscid computational fluid dynamics simulations are used to perform the analysis. The values of thrust, pitching moment, pitch acceleration are computed with and without breach for 2 breach sizes and 3 breach locations. The analysis shows that the loss of thrust due to a breach is a negligible effect for the breach sizes in consideration. However, substantial force is generated by propellant flow through the breach in the pitching plane resulting in moments that induce a pitching maneuver. If not counteracted by the thrust vectoring system available on the SRB, loss of control is imminent. However, when employing the nozzle gimbal mechanism, enough control authority is available at the full 7 gimbal to mitigate the problem, although the margin in some cases is small. Substantial pitch acceleration is also noted due to a case breach. Though the forward breach location is relatively benign due to the fact that it is close to the center of gravity of the vehicle, the aft location can result in as little as a half second of warning time. The TVC system is, however, capable of generating larger pitch acceleration and thus can be used to avoid large pitch acceleration if deployed in time to counteract the pitching motion induced by the breach. Computation of pitch angle and rate Appendix The linear momentum of an object in a fixed frame of reference is defined as mv, where m is the mass of the object and v is the velocity. Subsequently, the angular momentum, H, is defined as Where r is the position of the object. Now, v = Differentiating H, we get Since a vector s cross-product with itself is zero, Now, Newton s second law states that r. So, H = r mv H = r m r H = r m r + r m r H = r m r F = ma = m r 13 of 14

14 Thus, H = r F which we recognize as the moment, M, applied on an object by a force. Thus, H = M Now, we also know that the relation between angular velocity and angular momentum is Thus, For the case of pitch rate, H i = I ij ω j M i = I ij α, induced by the moment, M z, we have the relation M z = I zx ω x + I zy ω y + I zz ω z For I zx = I zy = 0, and ω z = α, the pitch acceleration M z = I zz α Thus, and α = j j ω j α can be obtained from the relation M z I zz dt M z I zz α = M z Δt 2 I zz 2 Acknowledgments The author wishes to thank Donovan Mathias for technical discussions and guidance, and the SARA project for supporting this work. Thanks also go to Veronica Hawke and Alexander Te for CAD support and to Scott Murman for supporting the 6-dof version of Cart3D. Finally, thanks to Goetz Klopfer, William Chan, and Ken Gee for looking over my shoulder, keeping me on track, and helping me edit the report. References 1 W. J. Rothschild, D. A. Bailey, E. M. Henderson, and C. Crumbly, Shuttle-derived Launch Vehicles Capabilities: An Overview, AIAA Paper , Jan Beaty, J. R., Starr, B. R. and Gowan, Jr., J. W., Ares-I-X Vehicle Preliminary Range Safety Malfunction Turn Analysis, AIAA Paper No , Jan Gowan, Jr., J. W., Ascent Trajectory Simulation for the Space Shuttle Launch Area Risk Assessment, AIAA Paper No , Aug Crew Safety Section, Crew Safety and Procedures Branch, Manned Spacecraft Center, Houston, Apollo Abort Summary Document,, MSC Internal Note 67-IN-2, November, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., D. T. Greenwood, Principles of Dynamics, International Series in Dynamics, 2 nd ed., Prentice-Hall, New York, July W. M. Chan, The OVERGRID interface for Computational Simulations on Overset Grids, AIAA Paper , M. J. Aftosmis, M. J. Berger, and J. E. Melton, Robust and efficient Cartesian mesh generation for component-based geometry, AIAA Paper , Jan S. A. Pandya, S. M. Murman, and M. J. Aftosmis, Validation of Inlet and Exhaust Boundary Conditions for a Cartesian Method, AIAA Paper , Aug S. M. Murman, M. J. Aftosmis, and M. J. Berger, Simulation of 6-DOF motion with a Cartesian method, AIAA Paper , S. M. Murman, W. M. Chan, M. J. Aftosmis, and R. L. Meakin, An Interface for Specifying Rigid-Body Motions for CFD Applications, AIAA Paper , Δt 14 of 14