Lightning Effects and Structure Analysis Tool (LESAT)

1. Lightning Effects and Structure Analysis Tool (LESAT) Steve Peters 410-273-7722 steve.peters@survice.com www.survice.com

2. 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. What Is LESAT?

3. Motivation Objectives Methodology Results Conclusions and Future Work Questions? Outline

4. 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. Motivation

5. 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. Objectives

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

7. 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

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

9. Input Geometry Example Mesh Geometry Input for a Structure • 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.

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

11. Attachment Points lightning attachment point lightning detachment point

12. z D I1 M12 I2 A C M12 y M23 L2 R2 L1 R1 R3 L3 R4 M12 M34 L4 Model • Circuit Approach: The airframe is represented by an equivalent R,L circuit network. B 3D representation Piece of the mesh has 5 nodes and 4 branches. Each branch is a resistive, mutually inductive circuit element. Code calculates mutual inductances x Kirchhoff’s Laws are enforced:

13. Five-Branch Four-Node Circuit Example System of linear equations Is E1 Z11 Z22 I L1(jω) I1 I2 I5 E4 Z55 E2 Z44 Z33 I4 I3 I L2(jω) Is E3

14. Matrix Notation Ax = b Number of Branches Number of Nodes x A b Z TopologyT I 0 Number of Branches Physics (square matrix) = Topology 0 Input Number of Nodes E Is Output

15. - Z Z Z Z Z é ù 1 0 0 1 é ù I é ù 0 11 12 13 14 15 1 ê ú ê ú ê ú - Z Z Z Z Z 1 1 0 0 I 0 ê ú ê ú ê ú 12 22 23 24 25 2 ê - ú ê ú ê ú Z Z Z Z Z 0 1 1 0 I 0 13 23 33 34 35 3 ê ú ê ú ê ú - Z Z Z Z Z 0 0 1 1 I 0 ê ú ê ú ê ú 14 24 34 44 45 4 ê ú ê ú ê ú - = Z Z Z Z Z 0 1 0 1 I 0 15 25 35 45 55 5 ê ú ê ú ê ú - Is 1 1 0 0 0 0 0 0 0 E ê ú ê ú ê ú 1 ê ú ê ú ê ú - 0 0 1 1 0 1 0 0 0 0 E ê ú ê ú 2 ê ú - Is 0 0 1 1 0 0 0 0 0 E ê ú ê ú ê ú 3 ê ú ê ú ê ú - - - 0 1 0 0 1 1 0 0 0 0 E ë û ë û ë û 4 Reduction To Transformed Currents System reduces to: branches – (nodes – 1) transformed currents.

16. 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.

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

18. Branch Current Time Dependence Note the addition of the purely resistive part ao

19. 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: 1.728x10-15 Ohms/meter Cable Radius: 2.54cm Cable Inside A Conducting Box

20. 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

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

22. Questions? Steve Peters 410-273-7722 steve.peters@survice.com www.survice.com