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188 APPENDIX G Arrestor Prediction Code G.1. APC Overview was not inherently capable of simulating the aggregate and aggregate foam systems, which do not behave as an analog to The APC was developed to simulate aircraft arrestments for either crushable foams or soils. The APC was, therefore, more the different arrestor concepts. The APC allows experimenta- generalized than ARRESTOR and could simulate a broader tion with different aircraft, arrestor geometries, and material variety of system concepts. strengths. Built with a generalized framework, essentially any arrestor bed concept could be simulated with the APC. Figure G-1 shows that the APC has four principal inputs: G.3. Suspension Model G.3.1. Concept Description 1. Metamodel data, which defines the aircraft landing gear interaction with the arrestor bed; At the core of APC is an aircraft suspension model that cal- 2. Tire load-deflection data, which defines the landing gear culates the dynamic loads and motion of an aircraft as it rolls interaction with solid surfaces; through an arrestor bed. The arrestor bed exerts loads on both 3. Aircraft library, which defines the aircraft dimensions, the nose and main gear, and the aircraft responds by pitching weights, and other properties; and forward, bouncing, sinking into the bed, and decelerating to 4. Arrestor design definitions, which define the bed dimen- an eventual stop. The upper portion of Figure G-2 illustrates sions and aircraft conditions for a given scenario. the loads on the aircraft during such an event. The dynamic behavior of the aircraft was represented Using these four inputs, the APC runs a time-marching mathematically using the component model illustrated in simulation to predict the dynamic loads on the aircraft, the the lower portion of Figure G-2. The component model is arresting distance, and so on. A typical APC simulation for an composed of lumped masses, springs, and damper elements aircraft arrest takes 1.5 to 2 minutes to run. After completion in order to approximate the aircraft fuselage, wings, and of the simulation, the APC provides graphical plots and tab- landing gear. Although an effective wing mass, spring, and ular data output. damper were included, this was done as a placeholder provi- The APC was written in MATLAB, a scientific programming sion within the mathematical framework of the model. In language and coding environment. Overall, the APC has nine modules (m-files) with nominally 1,500 lines of code. practice, the wing motion was neglected by using null values for those parameters. G.2. FAA ARRESTOR Code G.3.2. Scope of Capabilities The FAA previously developed the ARRESTOR code, which performed similar predictions as the APC. It featured The APC was developed specifically to simulate aircraft three aircraft (B707, B727, and B747) and could be used to arresting scenarios. Consequently, its intended capabilities model different foam arresting bed geometries. Initially, and limitations were defined a priori. General performance modification of the ARRESTOR code was considered in lieu objectives for the suspension model include: of developing a new predictive tool. If the evaluation had been restricted to crushable foam materials only, this could Allowing the modeling of general arrestor beds of various have proven advantageous. However, the ARRESTOR code geometries,

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189 Tire Load- Aircraft Library Deflection Data Arrestor Design Metamodel Data Definition Arrestor Prediction Code (APC) (MATLAB) Performance Predictions Figure G-1. Simplified diagram of the APC. DMG DNG VMG VNG u6 (6) Wing Mass u1 u2 (2) Fuselage u3 (3) (1) x u4 Strut u5 Strut Main Gear (4) FD,MG Nose Gear (5) FD,NG Wheel/Axle Wheel/Axle FV,MG FV,NG Tire/Arrestor Tire/Arrestor Interface Interface Main Gear Rut Nose Gear Rut z Direction of Travel x Figure G-2. Aircraft dynamics transformed into suspension model.

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190 Modeling of material response accomplished through freedom are included in the governing equations. This pro- metamodels, duced a system stiffness matrix that was 10 x 10. Prediction of gross loading on landing-gear struts for dam- Additionally, linear approximations were made for the age estimation, angle () and the angular velocity () that were accurate to Prediction of stopping distance for arrestor concepts, within less than one percent for the angle range specified. Prediction of porpoising effect with transient load spikes, Prediction of arrestor efficiency compared with idealized deceleration, and G.3.4. User-Defined Problems Prediction of fleet-wide performance (versatility) of an The APC permits the user to define arrestor scenarios using arrestor. many parameters, as summarized in Table G-1. General limitations for the suspension model include: No steerage (yawing) or other lateral motion effects, G.4. Aircraft Parameter Definition No tire slippage or heat generation effects, The aircraft library indicated in Figure G-1 was developed to No lateral load prediction on gear struts, and provide input parameters required by the suspension model No higher order effects or frequency analysis. for the three test aircraft: the CRJ-200, B737-800, and B747- 400. These properties included aircraft weights, landing G.3.3. Simplifying Assumptions gear configuration, design strengths of the struts, and overall In light of the APC scope of capabilities, the mathematical dimensions. In all, 36 parameters were required to define suspension model involves several simplifying assumptions: each plane. These properties were obtained from published manufacturer data, a generalized aircraft model, and the FAR The fuselage only pitches at relatively small angles, less requirements for passenger aircraft. than +/10 degrees; The motion is two-dimensional with no yawing; G.4.1. Published Manufacturer Data The airframe remains effectively rigid; and The landing-gear struts can be approximated with con- Published aircraft data generally included information stant stiffness and damping factors. regarding aircraft weight, gross dimensions, landing gear strut configurations, and the types of tires used. This infor- These assumptions were appropriate because the simula- mation was acquired through open-source websites and air- tions assume an aircraft in a ground rolling state. Non-linear port guidance documents published by the manufacturers strut spring and damping factors were considered, but ulti- (42, 60). Goodyear also provided load curve data for the tires mately were not necessary due to the relatively low loading used by the three subject aircraft. rates and minimal strut travel. Aircraft manufacturers were approached directly for addi- Given these assumptions, the model has seven degrees of tional information regarding strut properties and landing gear freedom. Since the two rut-depth degrees of freedom are design strengths. However, these requests were ultimately un- implicitly defined by the metamodel data, only five degrees of fruitful due to the proprietary nature of the specifications. Table G-1. User-defined parameters for simulations. Aircraft Arrestor Simulation Controls Type Type Time step for computations and data output intervals Initial speed Bed length and depth Plotting and tabular data Braking conditions inside and Depth at which the bed is saving options outside of the bed recessed vertically Setback distance Tapering length for bed thickness Increase or decrease arrestor material strength

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191 G.4.2. Generalized Aircraft Model G.4.4. Summary of Aircraft Parameters In the absence of the remaining properties, which were Based on the preceding discussion, the different aircraft needed to complete the aircraft definitions, alternative means parameters and related data sources can be summarized as were sought to develop reasonable estimates. Sources found in Table G-2. during the literature review provided the means to calculate For inline wheel sets, "shadowed wheels" were those behind approximate values. the leading wheel. The leading wheel was responsible for pro- Chester outlines a modeling approach for a generalized ducing the drag load when interacting with the arrestor bed, aircraft of arbitrary size, with a focus on landing gear while the shadowed wheels were assumed not to contribute dynamics and overall airframe response (16). Based on this drag load. method, properties such as strut stiffness, the pitching moment of inertia, and various unspecified dimensions G.5. Arrestor and Tire Interface were estimated. Currey provided excellent guidance with regard to landing G.5.1. Contrast of APC and ARRESTOR gear mechanics (14). Non-linear strut compression curves The APC uses a different premise than ARRESTOR for were developed based on oleo-pneumatic strut design prin- calculating the landing-gear loads. The ARRESTOR method ciples. Ultimately, however, constant spring stiffnesses were calculated the loads on the tire based on the geometry of used for simplicity. Statistical information in this reference interface and the foam compression strength (radial spring regarding typical landing gear weights was used to estimate tire assumptions) (63). These loads were calculated in real-time, the travelling mass for the wheel assemblies of each strut. during the course of the simulation. This quasi-analytical The strut damping coefficients were estimated as a per- method proved sufficient for crushable foam arrestors (cellu- centage of critical damping, assuming the estimated strut lar cement, polymer foam, etc.). However, the approach is stiffness and a mass equivalent to the vertical static load on not as well-suited to more chaotic and non-linear arrestor the strut. Generally, damping factors less than 1.0 (under- materials (aggregates, foam aggregates, etc.). damped) produced oscillatory behavior, noise, and instabil- The APC method uses high-fidelity numerical models of the ity. After experimentation, it was determined that a simple tire/arrestor interface to build a large database of loads for a factor of 1.0 (critically damped) would suffice for the simu- broad range of conditions, which are defined in the metamod- lations. Aside from basic system stability, the damping els discussed in Table G-4. Because high-fidelity models are factor was not found to have a substantial effect on the used for the load calculations a priori, the load predictions have predictions. higher accuracy than using a simplified analytical model. Fur- ther, there is no inherent limitation on the arrestor beds that G.4.3. Federal Aviation Regulations can be assessed; a suitable numerical code can be chosen for whatever system is desired (LS-DYNA, EDEM, others). The The load limits for the landing gear were among the most contrasts of the APC and ARRESTOR methods are summa- critical properties to define for each aircraft. Such values were rized in Table G-3. not available from published data or the aircraft manufactur- ers. Discussions with the manufacturers and the FAA pro- G.5.2. Metamodel Interface duced a straightforward alternative: the limit and ultimate with Suspension Model landing-gear loads as specified by the FAR were taken as design strengths for the aircraft. During each simulation, the loads on a tire are determined The limit/ultimate loads were calculated for the nose and based on the penetration depth of the tire into the arrestor, the main gear from multiple criteria in FAR Part 25. Vertical load speed of travel, and the arrestor bed depth. Given these condi- limits were not of high importance since the rolling arrestments tions, the APC queries the correct metamodel for the vertical did not substantially affect them. The rearward drag load limits and drag loads on the tire. This process is essentially a database were critical, however, particularly for the nose gear. lookup except that the database is a multi-dimensional meta- For the nose gear, the highest drag loads resulted from model. When the tire was on a hard surface, rather than in an Section 25.509, "Towing Loads," conditions 1 and 2. For the arrestor bed, tire load-deflection data was used in place of the main gear, the highest drag loads resulted from Section 25.493, metamodel data. "Braked Roll Conditions." Values for drag-direction limit Figure G-3 illustrates the transformation of the tire/arrestor and ultimate loads based on these two criteria were employed interface into a virtual spring/roller assembly in the suspen- in the APC as performance thresholds. sion model (refer to Figure G-2).

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192 Table G-2. Summary of aircraft parameters. Group Parameter Source Overall Mass Weight (maximum take-off) Published data Aircraft Pitching moment of inertia Generalized model Dimensions Wheel base Published data Distances from center of gravity (CG) to nose and main gear Supplemented using generalized model Height to CG Main & Nose Configuration Number of struts Gear Wheels per strut Published data Number of shadowed wheels Mass Travelling weight Generalized model Strut Stiffness Generalized model Damping Tire Diameter Static deflection Static load Published data Maximum deflection Maximum load Load limits Drag limit load FAR Part 25 Drag ultimate load Wings Mass Weight Spring Stiffness Not used properties Damping Table G-3. Contrast of ARRESTOR and APC methods for landing-gear load calculations. ARRESTOR APC Tire Model Radial spring analytical model Numerical model, dependent on software choice LS-DYNA: finite element tire model EDEM: rigid tire form, with deflection adjustment Arrestor Material Simplified quasi-analytical Numerical model using appropriate method Model crushable foam model Crushable: LS-DYNA smooth particle hydrodynamics (SPH) formulation Aggregate: EDEM discrete element (DEM) formulation Load Calculation Analytical calculation based on Batch simulations utilizing numerical model Method area of tire/arrestor interface Many simulations to create data set Metamodel for loading created as a fit to the data set Timing of Load Real-time, during simulation A priori, using high-fidelity models to create Calculation metamodels. Metamodels referenced in real-time during simulation.

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193 Wheel/Tire Mass Main Gear Strv Wheel/Axle FD FV Tire/Arrestor Arrestor Bed Interface Rut z Direction of Travel x Figure G-3. Arrestor interface dynamics transformed into suspension model. G.5.3. Metamodel Dimensions of significant interest when compared with the overall drag loads. Given the soft nature of the arrestor materials, this The metamodels generated for each arrestor type had three assumption was reasonable. independent variables: speed, bed depth, and depth of pene- Additional metamodel data could be generated to include tration into the bed. For each condition set, two response vertical speed and could be implemented with little alteration values were available: the drag and vertical loads (Table G-4). of the software. However, this additional complexity was Considered from the standpoint of the suspension model, deemed unnecessary for the current effort. there were additional parameters that could have been included as additional variables, such as wheel spin, vertical translation velocity, braking torque, and so on. For simplic- G.6. Overall Program Function ity, these variables were neglected in the current analysis. The overall process followed by the APC is illustrated by Therefore, the current metamodels were four-dimensional, Figure G-4. Starting from the initial conditions specified by having three independent variables and one response variable the user (upper left), the program calculates a steady-state each. Ultimately, metamodels could be seven-dimensional if rolling solution for the aircraft, including initial strut and tire the additional independent variables were included. deflections, weight distribution for the aircraft, and so on. The primary limitation of the metamodel data used in these The program then enters the main loop, which computes simulations is the lack of vertical speed as an independent the time-marching dynamic behavior of the aircraft and variable. Without vertical wheel velocity information, high arrestor bed. The loop calculates the current load state based frequency response predictions, such as small bumps and on the component locations and velocities. Using the core noise, could be realistically simulated. The overall assump- suspension model stiffness matrix (gray box), the system tion for the metamodel data was that steady-state loading at various penetration depths was sufficiently accurate for the velocity matrix is determined. Numerical time integration required predictions. Overall, transient vertical loads were not produces new displacements from the velocity matrix. After updating the stiffness matrix constants, the loop begins a new iteration. This process continues until the aircraft comes to Table G-4. Metamodel variables and responses. rest. At that point, data files and plots are output per user specifications. Variables Responses Included in Metamodels Forward speed Vertical load G.7. Conclusions Bed depth Drag load Penetration depth of tire The APC effectively simulated aircraft arrestments across Neglected in Metamodels Vertical speed Torque on tire a wide range of aircraft and for a set of dissimilar arrestor mediums. Because it was not dependent on simplified analyt- Spin rate ical tire or arrestor material models, it provided a generalized Braking torque framework suitable for simulating nearly any arrestor design.

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194 Input Initial Conditions Calculate Forces for for Case Tire/Ground/Arrestor (Aircraft Parameters, Interface Arresting Material (Tire Load Curves or Parameters, etc) Metamodel Data) Calculate Velocities & Calculate Initial Steady- Accelerations State Solution (Suspension Model Matrix Solution for u-dot matrix) Integrate Over Time Step & Calculate Displacements Update Suspension Model Constants (Non-Linear Coefficients) Simulation Complete Output Data & Plot Files Figure G-4. Simplified process diagram for the arrestor prediction code.