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Lightning Effects and Structure Analysis Tool (LESAT) Steve Peters

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What Is LESAT? LESAT - Lightning Effects Structure Analysis Tool –Computational methodology implemented in MATLAB to analytically predict actual transient current levels and voltages on aircraft wiring and structural elements. –Assists designers in protecting aircraft against the indirect effects of lightning strikes. –Implements the methodology used successfully for MH-47 lightning analysis.

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Outline Motivation Objectives Methodology Results Conclusions and Future Work Questions?

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Motivation Lightning is a severe threat (up to 200 kA peak). More reliance on electronic systems. Technology evolution from metallic aircraft structure to composite structure. High cost aircraft-level testing and hazardous aspect of experiments in laboratories.

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Objectives Input system geometry in a CAD format. Circuit analysis approach - apply Kirchhoff’s laws to obtain linear equations that can be solved in matrix form. Predict induced currents and voltage drops on wiring and structural elements.

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Lightning Indirect Effects Waveform MIL-STD-464C Severe Stroke in both Time and Frequency Domains

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Why Kirchhoff Rather Than Maxwell? Since the source frequency is very low, we have a Quasi-static (near steady state) situation. Dimensions of the conducting network are much smaller than the wavelength. Tool gives good results for aircraft dimensions up to ¼ the wavelength of the maximum frequency. Drawing not to scale

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Code Analysis Methodology Read Geometry & Electrical Characteristics From Mesh Files Break Up Structure Into Linear Segments Compute System of Linear Equations Calculate Frequency Domain Impulse Response for Each Branch Calculate Time-Domain Solutions (Induced Currents and Voltages) Plot Results Compute Resistances Calculate Self & Mutual Inductances Compute Impedance Matrix Calculate Laplace Responses

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Input Geometry Input system CAD geometry as a series of mesh files used to represent skins, pylons, and other routed cabling and electrical equipment inside the aircraft. Example Mesh Geometry Input for a Structure

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BULK RESISTIVITY Ω-m LENGTH (L), WIDTH (W), THICKNESS (H) Fundamental Resistance Data SKIN RESISTIVITY Ω/ □ LENGTH RADIUS Line/Cable Resistivity Ω/m 1.Lines/Cable Resistivity is measured in Ohms per meter ρ – to get Ohms use: R c = ρL 2.Skin/Mesh Resistivity is measured in Ohms per square ρ – to get Ohms use: R skin = ρL/W 3.Bulk Resistivity is measured in Ohm- meters ρ – to get Ohms use: R bulk = ρL/(WH) 4.Equivalent resistance for a branch use: R = R bulk X R skin /(R bulk + R skin )

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Attachment Points lightning detachment point lightning attachment point

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Model Circuit Approach: The airframe is represented by an equivalent R,L circuit network. R2R2 R3R3 L2L2 L3L3 L4L4 L1L1 R1R1 R4R4 M 12 M 34 M 23 M 12 Kirchhoff’s Laws are enforced: Piece of the mesh has 5 nodes and 4 branches. x B y I1I1 I2I2 A C D M 12 z 3D representation Each branch is a resistive, mutually inductive circuit element. Code calculates mutual inductances

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Five-Branch Four-Node Circuit Example E1E1 IsIs IsIs E3E3 E4E4 E2E2 Z 11 I L1 (jω) I L2 (jω) I2I2 I1I1 I4I4 I3I3 I5I5 Z 44 Z 33 Z 22 Z 55 System of linear equations

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Matrix Notation Topology Topology T 0 Z I = E 0 IsIs Input Output Ax = b Physics (square matrix) Number of Branches Number of Nodes Number of Branches Number of Nodes A x b

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Reduction To Transformed Currents System reduces to: branches – (nodes – 1) transformed currents.

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Solution for Multiple Frequencies Solution for a specific branch current at each frequency. Branch Current Laplace Transform – represents the frequency-domain Transfer function between the Injected lightning current and the current of the “victim” component.

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Lightning Time Dependence Lightning Laplace Transform Frequency Domain Transfer Function Branch Current Laplace Response Time-Domain Solution

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Note the addition of the purely resistive part a o Branch Current Time Dependence

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Cable Inside A Conducting Box Rectangular volume of material with dimensions (13.6m x 2.5m x 2.5m). Skin Thickness: 1.6mm Bulk Resistivity: 2.65x10 -8 Ohm- meters Skin Parallel Mesh Resistivity: 1.35x10 -4 Ohms/sq Skin Perpendicular Mesh Resistivity: 1.35x10 -4 Ohms/sq Cable Resistivity: 1.728x Ohms/meter Cable Radius: 2.54cm

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Results for Aluminum Conducting Box Blue curve represents cable current and voltage drop on cable for blue bolt strike location. Magenta curve represents cable current and voltage drop on cable for magenta bolt strike location. Driving Waveform

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Conclusions and Future Work Validation: compare calculated results to experimental data. Apply methodology to: –Ground systems –Buildings –Electromagnetic Pulse (EMP) excitation Relate predicted Lightning Effects to structural damage.

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Questions? Steve Peters

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