Identification of Suitable Governing Equation for Electromagnetic Fields in Aircrafts During a Lightning Strike

Lightning discharges in the atmosphere can present a severe electromagnetic threat to an aircraft in flight. For testing electrical equipment as well as to verify adequacy of protective systems, lightning current waveforms are suggested in pertinent standards. These have been emerged from ground-based lightning measurements and are broadly categorized into fast, median, slow (first and subsequent strokes). Similarly, lightning current waveforms A to D for direct effects are in force in aerospace industry for certification. Waveforms A and D have rise times of median first and subsequent strokes. Component H (fast subsequent stroke) specified in standards, although is not intended for full aircraft level testing but is usually employed for indirect effect testing. Experimental methods for quantification of a lightning threat to aircraft is expensive and time-consuming. Considering the suitability of numerical computational tools for this purpose, in literature, the solution of full-wave equations using Finite Difference Time Domain (FDTD) is considered. Seeking full wave solution for aircraft's complicated geometry would be computationally challenging. As certification for direct effects of aircraft and its major parts involve only the components A and D, in this work, an assessment is made on wave effects based on frequency spectrum of these currents and typical dimensions of aircraft. It is shown that solution of diffusion equation (eddy current field) would be quite adequate for assessing lightning effects on the aircraft. For the sake of completeness, the effect of employing an eddy current approximation for fast subsequent strokes i.e. component H is also analyzed. For these currents, fields are computed on highly simplified wire-mesh model using Time Domain Thin Wire (TDTW) solution and distributed circuit-based approach.