Liftoff of a Delta IV, one of the rockets in the Air Force's Evolved Expendable Launch Vehicle program. Data from this flight have been archived in Aerospace databases that also include flight data from past Atlas and Titan launch vehicle families. These data will support future validation and verification efforts. (U.S. Air Force)

Loads Analysis for National Security Space Missions

A. M. Kabe, M. C. Kim, and C. E. Spiekermann

A rocket launch is an extremely stressful event—and not just for the people involved. Aerospace has helped define a rigorous design and verification process to ensure that launch vehicles and spacecraft will withstand the severe forces encountered during launch and ascent.

During liftoff and ascent, a launch vehicle and its payload experience severe forces that cause structural deformations and vibrations. The vibrations will increase the deformations, which in turn produce internal loads and stresses in the launch vehicle and spacecraft structure. For most of the structure, these internal loads and stresses will represent the principal design requirements, dictating how strong the structure must be.

Designing launch vehicles and spacecraft to withstand these loads (and verifying that they can) is a complicated process, involving numerous organizations and diverse technical disciplines. Structural loads are a function of the dynamic properties of the entire launch vehicle and spacecraft system; but the integrated system cannot be tested prior to flight because of its size and complexity. Moreover, every substructure contributes to the dynamic properties of the system overall, so design changes in one element can result in load changes in all elements, and modeling errors in one place can cause load prediction errors in others. Also, neither the launch vehicle organization nor the spacecraft organization has control over the other's design, so neither can control the entire process.

As a result, the design and verification of launch vehicle and spacecraft structures requires a multidisciplinary, collaborative process that begins during the earliest phases of a program and does not end until the vehicle is launched and postflight data have been analyzed. The process is typically referred to as the load cycle process, and Aerospace has played a pivotal role in its development and current form.

The Load Cycle Process

The spacecraft design process begins with an initial estimate of loads based on past experience with similar launch configurations. These preliminary design load factors are used to size the load-carrying structure, and insight into both sides of the launch vehicle/spacecraft interface can be of considerable value in their development. Once the preliminary design and corresponding drawings of the spacecraft are complete, they can be used to create an analytical finite-element model. This model is in turn used to derive the structural dynamic model and internal load recovery equations. The structural dynamic model is used to calculate responses, and the load recovery equations are used to convert these responses to internal loads, stresses, and deflections. The spacecraft organization sends this information to the launch vehicle organization for use in the preliminary design load cycle.

The load cycle process has been used successfully for a long time on Air Force and other programs. Experience has shown that the space vehicle design requirements are best derived by a qualified organization that has visibility into both sides of the interface and can transfer lessons learned across many programs. Key: GSE&I—General Systems Engineering and Integration; IV&V—Independent Verification and Validation. (view larger image).

The preliminary design load cycle is the first of several such load cycles (three is typical). For each, the launch vehicle organization develops models that correspond to liftoff and the various phases of ascent. Typically, six to twelve distinct events are considered. For each event, the spacecraft model is coupled to the corresponding launch vehicle model to form a unique coupled-system model. At this point, the dynamic properties of the launch vehicle and the space vehicle merge to form the system-level properties. The launch vehicle organization will have developed distinct methodologies to analytically model the physics of each event as well as custom computer programs to numerically solve the equations of motion. The computed system responses are used with the load recovery equations (which can exceed 10,000 equations) to establish launch vehicle and spacecraft internal loads. The spacecraft loads are sent back to the spacecraft organization, and the launch vehicle loads are sent to the appropriate area of the launch vehicle organization for structural margin assessment.

The spacecraft organization will assess the preliminary design against the just-computed loads as part of its preliminary design phase. Areas with negative margins are redesigned, and any configuration changes are implemented. The drawings and the finite-element models are updated to reflect these changes, and the entire loads analysis process is repeated. After the final design load cycle, a structural assessment will confirm that the structure has adequate margin against predicted loads. The design can then be released for manufacturing.

Once the spacecraft has been manufactured, numerous tests are performed in support of the last prelaunch loads analyses that verify the flightworthiness of the system. The testing can be performed on actual flight hardware, dedicated structural test articles, or a combination of the two. Mode survey tests, for example, are used to measure the structural dynamic properties of the spacecraft. (The launch vehicle organization will also perform mode survey tests on dynamically complex substructures such as the upper stage and fairing.) The data from these tests are used to adjust the finite-element models that will form the basis of the upcoming verification load cycle. In addition, data from these tests are often used directly as part of the dynamic models. The mode survey test is typically followed by static strength tests, in which the design-phase loads are applied to the actual hardware to establish empirically the structural capability.

The verification load cycle provides a final check on the adequacy of the launch vehicle and spacecraft structural designs. The loads analysis methodologies and analysis data, if not verified during previous verification load cycles, will also be independently validated and verified. Aerospace has performed this validation and verification function for numerous Air Force programs, and has developed loads analysis methodologies, procedures, and computer codes for the Atlas II, Atlas V, Delta II, Delta IV, Titan II, and Titan IV families of launch vehicles.

After the validation, an organization such as Aerospace will also perform independent loads analyses to verify that the predicted loads are error free. The spacecraft loads are then sent back to the spacecraft organization for final flightworthiness assessment. The validated launch vehicle loads are used in a similar assessment of the launch vehicle.

The procedures and data used in the loads analyses are continually being refined and improved as flight data become available. During liftoff and ascent, a relatively large amount of data is collected for postflight analysis. Data of interest include acceleration at various locations, external pressures on the vehicle skin, engine chamber pressures, autopilot commands, and engine actuator displacements. These data are analyzed to detect any anomalous behavior and are then used to refine the analysis methodologies and models. Data from several flights are typically needed to refine the loads analysis procedures enough for routine use. For this reason, Aerospace maintains extensive databases that include data from flights of the Atlas II, Atlas IIA, Atlas IIAS, Atlas III (A and B), Atlas V, Delta II (6925 and 7925), Delta III, Delta IV, Titan II, and Titan IV (A and B) launch vehicles. One sophisticated flight data analysis tool, the Time Series Analysis Resource (TSAR), was developed at Aerospace and is used routinely to analyze flight data. Often, the data are available for real-time assessment at Aerospace as the launch vehicle lifts off the pad and flies to orbit (see sidebar, Flight Data Analysis).

Loads Analyses

The structural dynamic models used in the load cycle process are developed by coupling structural dynamic models of substructures. Typical substructures include the spacecraft, upper stage, fairing, interstage adapters, propellant tanks, liquid-fueled engines, and solid rocket motors. A launch configuration model will often consist of several dozen substructure models, each of which may have been developed by coupling still other substructure models. A spacecraft bus and its payloads, for example, are typically modeled as separate substructures, often by different organizations.

Analytical structural dynamic models are developed from structural finite-element models. Finite-element models are detailed and relatively large; millions of equations are not unusual. To be useful in loads analysis, these large models must be reduced in size to those equations (typically tens of thousands) that are required to describe the kinetic energy (motion of all the mass, including fluids) of the system as it vibrates. They can then be converted into structural dynamic models by computing the normal, or natural, modes of vibration (see sidebar, Finite-Element Models and Analysis).

The normal modes of vibration are the patterns of motion in which a lightly damped, linear-elastic structure can vibrate. When a structure vibrates in a normal mode, all points undergo harmonic (periodic) motion, reach their maximum values at the same time, and pass through their static equilibrium point at the same time. Associated with each normal mode of vibration is a natural frequency and a certain amount of damping that will cause oscillations to decay. No matter how structural oscillations are initiated, the observable or measurable vibrations in a structure will be the superposition of the motions of the individual mode shapes (see sidebar, Mode Survey Tests).

	Finite-element models are used to develop structural dynamic models along with the load recovery equations needed in the coupled launch vehicle/spacecraft loads analyses. Because of the classified or proprietary nature of many systems, the launch vehicle organization generally has little, if any, insight into the models used by the spacecraft organization—and vice versa.

Normal modes of vibration have unique properties that make them extremely useful in creating efficient system-level models. For example, they can be used to transform the substructure finite-element models into so-called mixed-modal/physical domain models. These models can be reduced in size and coupled to other models. Most large launch vehicle and spacecraft models are developed in this fashion. For example, a coupled launch system model is formed by combining the launch vehicle and spacecraft mixed-modal/physical domain models. The resulting equations are used to compute the mode shapes and associated natural frequencies and damping values of the coupled launch system.

Once the coupled-system modes are known, they can be used to develop the equations of motion that are solved to obtain loads. For lightly damped structures such as launch vehicles and spacecraft, natural modes are orthogonal to each other, which means that many modes can oscillate at the same time, but with little or no interaction. This is a relatively difficult concept to visualize because the various modes of vibration are all determined by the same mass and stiffness properties of the structure. Because the modes are orthogonal, however, the equations of motion of a structure can be transformed into a modal coordinate domain in which their numerical solution is considerably simplified. The total loads and accelerations, for example, are then obtained by summing the time-phased individual modal responses, which, for some events, can number as many as several thousand.

Liftoff Loads

The complexity of the loads analysis process can be illustrated by looking at one of the many critical events in the launch sequence. Liftoff, for example, produces significant loads in both the launch vehicle and its payload. While the launch vehicle rests on the launchpad, the propulsion system—which may comprise any combination of liquid-fueled engines and solid rocket motors—ignites and generates thrust. If the vehicle is a "fly-away" type, it is allowed to rise freely as soon as the thrust overcomes the vehicle weight. If it is a "hold-down" type, a retention mechanism prevents it from lifting off while the engines build up thrust and computer systems verify the proper performance of the engines; this takes only a second or two. The retention mechanism is then released, any solid rocket motors are ignited, and the vehicle rises off the launchpad.

The ignition of liquid-fueled engines and solid rocket motors causes the system to oscillate and produce additional internal loads. Concurrently, the system undergoes a rapid change from being fully attached to the launchpad to being fully unconstrained and free flying. This change causes additional oscillations and internal loads. Also, ground winds and ignition overpressure pulses generate even more oscillations.

The prediction of liftoff loads requires complex mathematical simulations and computer codes that model the nonlinear forces associated with the launch vehicle's separation from the pad as well as the loading caused by engine ignitions, overpressure pulses, ground winds, and gravity. Models of the thrust forces must include the lateral forces caused by flow separation in nozzles, engine misalignments, and engine thrust offsets. Models of the ignition overpressure pulses must include the components emanating from the flame duct and from the exhaust port. Forces in propellant tanks caused by pressure fluctuations are also included, as are the fluctuating forces caused by thrust oscillation and engine actuator oscillation. The forces related to propellant motion in the feed lines can also be critical, especially during a launch abort.

Atmospheric Flight Loads and Day-of-Launch Loads Analysis

Once a launch vehicle has lifted off the pad, it will rapidly accelerate, and can reach speeds greater than a few hundred meters per second while still in the atmosphere. These high speeds cause severe pressure on the launch vehicle skin, which in turn will cause the vehicle to deform and experience significant loads. As the launch vehicle approaches and passes the speed of sound, shock waves form on the vehicle and interact with the flow separation caused by geometry changes along the length of the vehicle. This interaction causes severe "buffet" vibration of the launch vehicle and spacecraft system. The launch vehicle may also encounter atmospheric turbulence or gusts, which can cause oscillations and increase loads. In addition, the launch vehicle control system, to maintain vehicle stability, will continually gimbal the engines. The side forces thus generated can also cause the vehicle to oscillate and produce internal loads.

Each of these atmospheric flight load contributors has a specialized analysis methodology requiring unique models. The methodology for analyzing atmospheric turbulence loads, for example, incorporates a control-system simulation, an aeroelastic model of the interaction between the launch vehicle structure and air (which is obtained by means of a wind-tunnel test), the structural dynamic model of the launch vehicle and spacecraft system, and representations of the atmospheric turbulence. Because of the complexity of the atmospheric flight events, each is analyzed separately, and the resulting response quantities, such as loads, are combined statistically.

Most of the loads analyses are performed well in advance of the launch date, but some are finalized just prior to launch. For most launch vehicles, reliability requirements can only be met by restricting the winds through which they are allowed to fly. This reduces launch availability, but the impact can be minimized by developing the launch vehicle steering profile using winds measured close to the opening of the launch window. In these cases, the actual winds and the resulting vehicle steering are not known until just before launch, so additional analyses are required to determine whether structural and performance limits (placards) would be exceeded if the vehicle were to launch.

These analyses typically begin several hours before the opening of the launch window and continue until the launch is either completed or scrubbed for the day. Wind speed and direction are typically determined with balloons that rise through the atmosphere. The measured wind profiles are used to derive the vehicle steering parameters. A trajectory simulation then "flies" the vehicle through the measured wind and computes loads-related data such as angle of attack, dynamic pressure, and Mach number as a function of flight time. These data are used to compute the static-aeroelastic (nonvibrating) component of the total load.

The static-aeroelastic load is then combined statistically, at all critical points along the vehicle trajectory, with the turbulence/gust, buffet, autopilot-induced, and dispersion loads, which will have been calculated in advance during the verification load cycle. The combined loads are compared to the allowable values at critical vehicle stations. If they are within acceptable limits, then the launch can proceed; if not, the launch is held, and the whole process—measuring the wind, performing the trajectory simulation, and computing the loads—is repeated until the vehicle is launched or the launch window closes.

Aerospace has been intimately involved in the development of the atmospheric flight loads analysis methodologies and their implementation in computer codes. For example, the time-domain buffet analysis approach, the Monte Carlo gust-analysis methodology, and the concept of using the structural dynamic model to perform static-aeroelastic loads analyses were developed at Aerospace and made available to the loads analysis community. In addition, the statistical approach used to verify the loads combination equations in the day-of-launch placard analyses was also developed at Aerospace. For Air Force launch vehicles, Aerospace is intimately involved in the development of the procedures and tools needed to perform the day-of-launch placard analyses. For the Titan IV vehicle, for example, Aerospace also performs the placard calculations independently on the day of launch and provides an independent launch recommendation.

Conclusion

The structural design and verification process is highly complex, involving various organizations and numerous technical disciplines. No single organization controls the entire process, so overall management is challenging. Further complicating the matter, the launch vehicle and spacecraft need to be treated as a single integrated unit, but such an integrated unit would be too large to test. Hence, mission planners must rely on copious analysis and substructure testing.

Aerospace plays a critical role in support of the structural design of national security launch vehicles and spacecraft. This includes independently validating and verifying the load cycle process loads analysis methodologies and procedures, many of which were developed at Aerospace alone or in close partnership with industry. In addition, Aerospace's cross-program involvement ensures that the structural design process remains equitable to the launch vehicle and spacecraft organizations. The high degree of structural reliability achieved by national security launch vehicles and spacecraft owes much to the load cycle process and the application of this process to each new system generation.

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