Developing Improved Civil Aircraft Arresting Systems (2009)

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

189 Figure G-1. Simplified diagram of the APC. Figure G-2. Aircraft dynamics transformed into suspension model. Arrestor Prediction Code (APC) (MATLAB) Metamodel Data Performance Predictions Tire Load- Deflection Data Aircraft Library Arrestor Design Definition x z Direction of Travel FV,MG FD,MG FD,NG FV,NG Main Gear Wheel/Axle Fuselage Nose Gear Wheel/Axle Strut Strut Tire/Arrestor Interface Tire/Arrestor Interface Wing Mass Main Gear Rut Nose Gear Rut u1u2 u3 u4 u5 u6 x θ (2) (3) (4) (5) (6) (1) DNG VNGVMG DMG

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

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

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

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

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