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face currents and voltages on the aircraft body). ... fields in closed form [1] as well as by numerical methods [2] is of interest in designing engineering .... the lightning channel at the front radome and at the tail end of the aircraft. ... term Q/V , where V is constant with the aircraft being an equipotential surface because of the ...
International Journal of Applied Electromagnetics and Mechanics 47 (2015) 911–925 DOI 10.3233/JAE-140082 IOS Press

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A software test-bed for electrical dynamics of direct cloud-to-ground and ground-to-cloud lightning flashes to aircraft: Initial results P.R.P. Hoolea , S. Thirukumaranb and S.R.H. Hoolec,∗ a Department

of Electrical and Communications Engineering, Papua New Guinea University of Technology, Lae, Papua New Guinea b Department of Physical Science, Vavuniya Campus of the University of Jaffna, Vavuniya, Sri Lanka c Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA

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Abstract. This work presents a self-consistent and self-contained model to study and analyse aircraft-lightning electrodynamics. An aircraft-circuit-model-based estimation of lightning currents is reported when the aircraft is struck by cloud-to-ground (CG) and ground-to-cloud (GC) lightning flashes. A distributed transmission line model for the aircraft and the return stroke channel of the lightning channel is used to simulate the return strokes of CG and GC flashes. It is observed that a higher magnitude of the rate of change in currents is produced due to the rapid discharge of electric charges on the lightning leader channel. Many GC return stroke currents eventually result in a steady state current along the channel resulting in a large build up of induced voltage in avionics. It is further observed that the severity of threat to airborne devices is great in the case of the initial wave-front of CG return strokes. Previous lightning return stroke simulation units failed to consider the inclusion of aircraft as part of the long CG or GC lightning channel, which is crucial when considering the engineering design of the aircraft body and the protection of internal electronics where shielding is weakened by weakly shielding aircraft bodies. We report here for the first time a computer software simulation tool for studying lightning-aircraft dynamics for engineering analysis and design. Keywords: Lightning-aircraft dynamics, lightning return stroke, aircraft model transmission line model, aircraft-lightning interaction, frequency spectrum

1. Introduction

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The atmospheric lightning environment interacts with an aircraft both directly (direct lightning flash to the aircraft) and indirectly (through the lightning radiated electromagnetic pulse, LEMP, inducing surface currents and voltages on the aircraft body). The computation of lightning radiated electromagnetic fields in closed form [1] as well as by numerical methods [2] is of interest in designing engineering systems [3–5]. This paper is confined to the direct effects of lightning on an aircraft body, especially, the currents and voltages induced on an aircraft body from a direct strike of lightning to the aircraft. Moreover this paper reports on the differences of lightning threat parameters (e.g. return stroke currents) due to CG and GC lightning flashes. ∗ Corresponding author: S.R.H. Hoole, Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA. E-mail: [email protected].

c 2015 – IOS Press and the authors. All rights reserved 1383-5416/15/$35.00 

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Fig. 1. Return Stroke Interacts with (a) The real time scenario addressed (b) Aircraft, power line and windmill blade (http://www. thenational.ae/news/uae-news/transport/lightning-strike-on-emirates-a380-during-flight-caught-on-video).

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The lightning currents flow through the conductive parts of the aircraft and thus the aircraft becomes a part of the lightning event. Scientific evidence is available to trace the initial lightning channel leader initiated by an aircraft during landing or take-off under a thundercloud. A video frame of a lightning strike to an aircraft on takeoff, for instance, was clearly observed from the Kamatzu Airforce Base on the coast of the Sea of Japan during Winter [4]. Many lightning events have been reported directly hitting the aircraft during flight hours at least once a year [4,5]. Figure 1(a) shows the Emirates aircraft A380 being struck by lightning prior to landing at Heathrow Airport in London in May 2011. The interaction of lightning-aircraft currents generates electromagnetic threats associated with the lightning current flowing along the discharge channel and on the skin and structure of the aircraft [6]. The electric circuit model of lightning return strokes may be used to estimate the surges produced in an electric circuit model of the aircraft attached to lightning [7,8] using aircraft dimensions in the public domain [9]. The earth resistance was included in the model [10]. This paper simulates and investigates both Cloud-to-Ground (CG) and Ground-to-Cloud (GC) types of lightning return strokes which generate large currents, using the transmission line model (TLM) of the channel [7]. The magnitudes of the return stroke electric current, rate rise of current, and induced voltage, and the frequency spectrum of lightning return strokes are important aircraft performance parameters for obtaining deeper insights into the lightning phenomenon and to determine its interaction with aircraft and other systems such as wind turbine blades and grounding systems. Since the measurement of these parameters is almost impossible above ground level, a reliable lightning simulator that includes the aircraft is of critical importance. In this paper, the return stroke of the lightning strikes which was modelled in [10] is used to develop a simulator for aircraft-lightning electrodynamics and to determine performance parameters for CG-, GC- and aircraft-coupled earth flashes. The electromagnetic analysis of the lightning return stroke was reported in [12], where the current pulse travelling along the channel was considered as a transverse magnetic wave. By establishing the validity of representing the lightning return stroke by a transverse magnetic wave [12], and comparing results obtained by simulation with measured lightning currents for direct CG lightning strokes modelled as transmission lines, the validity of the transmission line circuit model to represent the lightning return stroke was established and the detailed validation of the model is given in references [7,10]. Moreover it reports on parameters such as electric current and voltage transients induced on an aircraft body during lightning attachment to the aircraft.

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2. Aircraft model and charge distribution

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This paper further employs the transmission line model for the Transverse Magnetic (TM) lightning return stroke dynamics [7] and the electric charge simulation method reported elsewhere for aircraft capacitance calculations [11], to determine the transmission line model computation of currents and voltages along the aircraft surface in Sections 2 and 3 respectively. Finally in Section 4 the impact of both CG and GC lightning return strokes are considered in detail for their importance to aircraft electric surges. The simulator contains the following three units as one system: first, for simulating the lightning return stroke using a dynamic, self consistent transmission line model; second, a unit that models an aircraft body which may be inserted into the lightning module at any position between the cloud and ground; and third, the unit that calculates the electric and magnetic fields radiated by the lightning return stroke, including near, intermediate and distant electric and magnetic fields. The work may be appropriately and readily extended to include lightning strikes to tall towers and wind turbine blades.

n  1 ⎢ 1 ⎥ ⎢ √3.53 qi + qj ⎥ ⎣ 4πε0 rij ⎦ ΔRi j=1

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Vi =

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An electrostatic charge simulation dipole model of an aircraft electric charge distribution is used to determine the capacitance distribution along the aircraft skin when the aircraft enters a thunderstorm environment. Figure 1(b) illustrates a typical passenger aircraft’s dimensions [9] and its geometrical parameters such as overall length and the diameter of the cylindrical fuselage of the aircraft attached to the lightning channel at the front radome and at the tail end of the aircraft. We note that material property is assumed to be that of perfectly conducting metallic materials which is part of the assumption of fixed voltage along the fuselage. The effects of other materials like carbon composite on capacitance calculation are not considered in this paper. We further state that the important effects of aircraft altitude or height from ground are also not considered in these initial results corresponding to a fixed height although the effects of altitude on the model can be incorporated by varying the height as in [7]. The effect of striking point [1] in this model may be allowed for by varying the length of the line from the striking point to the lightning channel from the aircraft. These effects are being presently considered in an ongoing doctoral work under the first and third authors. The cylindrical structure of the aircraft is divided into a number of small surfaces. Each subsurface i, being of area ΔRi (in m2 ), contains the unknown charge qi (in Coulombs). This charge on each subsurface, given the potential Vi (in volts), is calculated by the following set of equations obtained from the integral solution of the electrostatic potential [8]: ⎡ ⎤ (1)

i=j

where rij (in m) is the distance between element i and neighbouring element j . Both π and ε0 are standard constants. The factor 3.53 appears from the integration of 1/r over a rectangular area and applied to other shapes because the contribution to the relevant integral is from parts where r is close to 0 [8]. A linear electric circuit equation expressing the aircraft voltage while in flight in terms of all the unknown charges on the surface of the aircraft as expressed in Eq. (1) can be solved to obtain the q/Va ratio. As expected, it is found that the charges are more concentrated on the vertical extremities of the aircraft’s skin during its flight under the thundercloud (Fig. 2). Since the geometry of the outer conductor of the aircraft is largely cylindrical, more charges accumulate on the upper and lower curvature of the

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Fig. 2. Charge distribution along the surface of the aircraft.

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aircraft’s skin. Thus, the charge distribution is not symmetrical all around. This is the case for the mostly metallic body of commercial aircraft [9]. In the new A380 aircraft, about 70% of the body is metallic. In this paper the aircraft body is assumed to be entirely metallic. Future work is expected to include nonmetallic parts of the body made of carbon composite materials. Although in this paper, reporting initial results, the effect of the leader stroke electric charges on the electric charges induced on the aircraft surface is ignored, this may be readily included by extending the leader channel from the thundercloud or the aircraft. The charge distribution along the surface of a typical aircraft is shown in Fig. 2, and those results are used for subsequent computations in the model developed here. The charge distribution at the extremities of the aircraft is large, as expected and is approximately constant in the mid-portion of the aircraft body. The geometry of the aircraft radome and tail (or fins) is critical in lightning-aircraft electrodynamics. Hence, a higher electric field can be observed near the sharp end points of the aircraft modelled. The constant potential Va of the aircraft which is oriented horizontally between the cloud and the earth is solved using the finite difference numerical method [8]. Thus the total capacitance Ca of the aircraft is computed by using: n qi Ca = i=1 (2) Va The distributed capacitance values may be determined by leaving distributed capacitances without summing. The non-linear electric charge density over the aircraft surface (which, for instance, is dependent on the aircraft geometry) is captured by the values of the dipole electric charge calculated using this method, as seen in Fig. 2. Indeed the capacitance varies because Q on aircraft charge and varies in the term Q/V , where V is constant with the aircraft being an equipotential surface because of the fuselage being a good conductor. As for space charge density, that is charge that is scattered around the aircraft since the thundercloud region has space charges, these charges were not taken into account, they being negligibly small compared to the cloud charge which induces charges on aircraft surface and which we account for. In this paper both distributed and lumped, circuit model capacitances are obtained using a single cylindrical fuselage and a short tail. The effect of wings on the fuselage capacitance has also been investigated. In the future more detailed analyses of aircraft wings and body material will be reported. The focus here is on a transmission line simulator employing distributed line models for both lightning and aircraft. The main fuselage, the sharp radome cone and the tail alone, are accounted for in the results reported herein. These results are compared for validation to those from a similar laboratory model aircraft tested in a high voltage laboratory as reported in [11].

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Fig. 3. Aircraft-Lightning interaction profiles of a model aircraft in Texas lab test (a) Current (b) Voltage (From [11]).

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Fig. 4. Aircraft-Lightning interaction profiles of a lumped aircraft (a) Current (b) Voltage.

3. Current and voltage surges on the aircraft

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The aircraft is assumed to be at a height of 500 m above ground, below a 1000 m altitude thundercloud from which the lightning strike hits the aircraft. The structure of the aircraft is divided into three segments and plugged into the distributed circuit model of the lightning channel as shown in Fig. 1(b), where the aircraft is part of the lightning channel and both the aircraft and the channel are modelled by electric circuit elements. The current flow distribution on each of the segments is determined from the transmission line parameters described in [10]. The current and voltage waveforms on the three-element aircraft surface compared from the aircraft-lightning model are shown in Figs 3, 4 and 5. In Fig. 3 are given high voltage laboratory test results: indirect measurements made of the current (magnetic field) and voltage (electric field) on an aircraft model with fuselage and tail only [11]. These laboratory experimental results were used to validate the transmission line model of the aircraft in [11]. Figure 4 shows the transmission line simulator results for the aircraft modelled as a single lumped-circuit element. Figure 5 shows the results for the distributed aircraft circuit model. In Fig. 5(a), the current is very high at the connection point in the first segment of the aircraft where the transient current flow through the aircraft’s skin has a steep rise to its peak at 61 kA, with a 2.5 μs

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rise time and then it drops gradually with some oscillations. The current distribution in the middle and last segments has steeply risen to the peak at 43 kA and 30 kA respectively over a very short rise time. The time interval between the two half peak points is 1.5 μs. The lumped aircraft surface current rises to a peak value of 45 kA as shown in Fig. 4(a). The Figs 3(a) and 3(b) show that the waveforms of magnetic and electric fields correspond to the electric current and voltage magnitudes along the surface of an aircraft model in a laboratory test [11]. In Fig. 5(b), the maximum voltage magnitude of 63 MV is reached in 7 μs on the distributed model of the aircraft. It is clearly observed that the voltage on the surface of the aircraft obtained in the aircraft segments for a distributed model (Fig. 5(b)) differs from the measured waveform (Fig. 3(b)). The voltage waveform on the lumped aircraft surface is shown in Fig. 4. All circuit parameters for the aircraft were calculated for the dimensions of the laboratory model in [11]. The electric circuit model of the aircraft was validated by comparing computed currents and voltages with measured values [11]. The current and voltage waveforms observed in the simulations are similar to the waveforms measured from the laboratory test. The differences in magnitudes are due to the electrical parameters used for the distributed TLM of the lightning channel. The current and voltage surges computed are important in designing measures to combat electromagnetic interference that couples into the aircraft wiring thereby upsetting computerized navigation systems, and to prevent damage to electrical and electronic equipment and any surface damage to the aircraft body from current flows. 4. Return stroke simulator results and discussions 4.1. Preamble This section reports the results obtained for return stroke simulation for both CG and GC lightning strikes. The R, L and C values are obtained as outlined in Part I of the paper [10]. The valid TLM for

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Table 1 Peak current at ground for CG flash Reference [13,24] [15] [16,23] [17] [18-20] [21,22] Present work

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Table 2 Peak current and time at the peak along the lightning return strokes Return stroke of CG lightning Peak current (kA) Time to peak (µs) 28.03 (at ground) 0.63 21.51 8.43 21.45 8.83 21.61 9.23 21.32 9.63 21.11 10.03 20.85 10.43 20.59 10.44 20.66 11.23 20.90 (at cloud) 11.63

Return stroke of GC lightning Peak current (kA) Time to peak (µs) 60.16 (at cloud) 0.65 58.87 1.13 56.08 1.59 52.90 1.97 49.69 2.50 46.28 2.73 44.17 3.32 41.21 3.61 34.08 3.90 26.55 (at ground) 4.50

4.2. Current profiles

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the common type of CG lightning strike is used to determine the electrical characteristics of that rare event of a GC lightning strike and compare both return strokes. The effects of aircraft altitude and its material properties are left for future studies. The peak current with rise time, induced voltage, current rate of change and the frequency spectrum of the transient current of the GC and CG return strokes are accounted for in the simulation and presented here.

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Quoting the International Electro-technical Commission, the values for the most important lightning return stroke parameters are primarily obtained from ground level measurements reported in Berger et al. [13]. That work has stated that among 101 events observed, 50% of the cases exceed a peak current of 30 kA. The mean first-stroke peak current measured by Berger et al. for negative discharges at Mount San Salvatore in Switzerland, is 30 kA [13]. However, the IEEE Guide for Direct Protection of Substations [14] suggests that the observed median current for lightning strike to a flat ground is around 24 kA with the recommendation based on the analysis carried out in [15]. Recently, the median peak current of 29 kA was reported in a total of 120 current waveforms for negative first strokes directly measured on 60 transmission line towers (at the top) whose heights varied from 40 m to 140 m in Japan in the period 1994 to 2004 [16]. This peak value is similar to that reported by Berger et al. Poplansky [17] reported that among 1015 events, the 50% value of the arithmetic mean value of peak current observed in the objects of 25–140 m height in Czechoslovakia is 28 kA. Table 1 from Refs. [15–24] summarizes the measured peak current values presented by various authors for the return stroke of cloud to ground lightning strike. The peak value obtained in this simulation is comparable with the reported works. It is observed that CG and GC lightning strikes have different peak values.

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Consider the TLM simulation results we obtained in Figs 4 and 5, as well as those reported in Table 2. The return-stroke current is characterized by a rapid rise to the peak current, within a few microseconds in both cases of CG and GC lightning strikes. The current has distinctly a concave wave-front with the greatest rate of change near the peak. Among the significant results, a much higher rate of current surge is observed for the return stroke of the upward lightning flash and a much sharper collapse of the electric charges in the case of the ground to cloud return stroke. In contrast, the downward CG flash collapse of the electrostatic charge is not severe, thus allowing for more subsequent flashes to occur over the same lightning channel. The return stroke current peaks at 28 kA with a rise time 0.63 μs (Fig. 6(a)) and 60 kA in 0.65 μs (Fig. 6(b)) for CG and GC lightning strikes, respectively. Peak currents are obtained at the ground and at the cloud end for both CG and GC flashes. The peak electric current of the CG return stroke drops off to about 46 kA at midpoint about 500 m above ground, the midpoint being where an aircraft would be attached to the lightning channel. The results with aircraft attached were presented and discussed in the previous section of this paper (Section 3, Figs 3 and 4). This current value agrees well with the average result simulated for current along the aircraft skin when it interacts with lightning strike as explained in Section 3. A higher capacitance is obtained near earth in the return stroke of the CG lightning model due to the impact of the earth on the leader electric field at its tip just above the ground, at the instant when lightning-ground closure is made. These results show that the waveforms are different between segment 1 and the other segments as shown in Fig. 6(a). However, in the GC lightning return stroke, the waveforms in each segment are similar as shown in Fig. 6(b). The difference in the initial current waveform of the CG flash (Fig. 6(a)) is due to the earth resistance, which is very different from the lightning channel resistance. The capacitance along the channel from two segments above ground to near cloud remains constant as explained in Part I of this two-part paper [10] and the zero potential is used for the lightning leader for the GC stroke since the leader stroke travels upward from ground to cloud at a low potential until making connection with the cloud. The peak current for the CG return stroke is higher than for the

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Fig. 7. First return stroke currents of (a) Positive CG flash (b) Negative CG flash and (c) Microsecond-scale waveform of positive CG [27].

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GC return stroke since the thundercloud resistance element is small, curtailing ohmic power loss. Hence an aircraft will receive intensive electromagnetic pulses (LEMP) from the cloud end of the GC flash. Figures 7(a) and 7(b) show two examples of the first return stroke measured current waveforms of positive and negative downward lightning [26]. Rapidly rising currents are observed in the wave-front of the return stroke current. This is followed by the slowly dropping wave tail. Figure 7(c) shows another category of the lightning current waveform of positive downward lightning in the millisecond-scale with long rise times up to 100 μs [26]. The double exponential waveform is clearly observed in the measured current waveforms (Fig. 7), as well as in the TLM simulated currents (Fig. 6). The current work is confined to the most common negative CG and GC lightning strokes, although it is expected that the extension to positive strokes, to be further explored, will not impose drastic changes in the model. The effect of the leader, as commented here, may be included as as extension thin conductor from the thundercloud or aircraft as appropriate – its effects will be studied in future as a separate study, since it will affect the capacitance close to the contact point. The return-stroke current is specified by its peak value and its wave-shape. The wave-shape in turn is specified in terms of rise time as given in Table 2. It is observed from the results of Table 2 that there is a delay in the time to reach the peak current between each of the segments in the respective lightning channel segments. This condition shows that the lightning current is propagated along the lightning channel from one segment to the next segment, and from the first segment to the last segment, at a velocity slightly less than that of light. For instance, in the CG flash, between segments 4 and 5, the velocity of the wave is 100 m/(9.63–9.23) μs = 2.5 × 108 ms−1 . The return stroke current and the time

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4.3. Voltage profiles

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to reach the peak current in each segment of the two types of lightning flashes are tabulated in Table 2. The peak current magnitudes for the return stroke of both CG and GC lightning strikes decrease steadily over the lightning channel.

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A cloud voltage of about −50 MV is used for these results from our simulator, which influences the magnitude of the potential changes along the return strokes [11]. A negative value is used for cloud voltage since the CG lightning leader emanates from the negative charge centre at the bottom of the cloud region. The GC leader connects with the similar negative electric charge centre at the bottom of the cloud. The following discussion considers only the magnitude of the voltage changes depicted in Fig. 8 since the negative sign is used to represent the negative electric charge of the cloud. In both cases of CG and GC lightning strikes, the voltage magnitude drops for subsequent segments from the return stroke source as illustrated in Fig. 8. The voltage magnitude of the return stroke as shown in Fig. 8(a) gradually drops from 50 MV to 28 MV over the first 7 μs, close to ground (segment 1) but after that increases slightly before reaching a constant value. At the ground level, the potential reduces linearly as expected. However, a very steep increase from 0 to around 50 MV is observed closer to the cloud (segment 10) for the return stroke as shown in Fig. 8(b). In the upward lightning strike, since the leader propagates from the earth, the initial voltage of the leader is set to zero. At the same time, the downward lightning leader has a voltage magnitude of similar value to the cloud potential along the channel until it makes a connection to the ground. In both cases the small voltage drop along the leader is ignored, although if necessary it can be incorporated. As shown in Fig. 8(b), right after the attachment with the cloud in the GC lightning, the potential of the return stroke reaches −50 MV in the vicinity of the cloud while the other segments between the cloud and the earth have a voltage maximum ranging between −40 MV and −50 MV before reaching saturation. In both cases of the CG and GC return strokes, the potential difference between the earth and cloud (the first and last segments) is 15 MV at 20 μs as indicated in Fig. 8. A fluctuation of voltage is observed

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4.4. The current rise rate

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for 10–15 μs and thereafter the voltage decreases steadily along the channel. A much deeper collapse of the electrostatic potential is observed in the return stroke of GC lightning strike. The fluctuations observed in the voltage profile illustrate that the potential change along the return stroke channel is valid.

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The rate of current change in the lightning channel is a significant parameter for devices that present an impedance, such as arresters or conductors in the electronic systems of an aircraft or ground systems, to safeguard them from lightning strikes [25,27]. Figure 9 shows the current rise rate (dI/dt) in the return stroke of the CG and GC lightning strikes. The voltage V(t) across a length of conductor will be proportional to the rise rate of the lightning current with respect to time, dI(t)/dt, along the conductor (V(t) = LdI(t)/dt, where L represents inductance). Thus, the peak inductive voltage is proportional to the maximum rate of change of current. This will happen during the initial rise to peak value of current. The extremities (1, 2 and 10) and middle (5) segments of the lightning return stroke channel are considered for comparing the rates of current rise along the lightning channel and aircraft. When the return stroke of the CG lightning discharge starts, it produces nearly a 167 kA/μs current rise rate along the channel close to the attachment point at ground (segment 1) while in the middle and last segments it is observed that the values drop to 10 kA/μs and 12 kA/μs respectively as shown in Fig. 9(a). In GC lightning, since the cloud level current is higher, the first segment near the cloud exhibits a current rise rate of about 168 kA/μs. In the middle and at ground, the computed values are 60 kA/μs and 23 kA/μs respectively (Fig. 9(b)). The magnitude of radiated electric fields is determined by the rate of rise of currents. These radiated electric fields interact with the electronic systems in the airborne vehicles whereas the current magnitude is associated with the heat dissipated and the force that punches large holes on structures. Table 3 lists the magnitude of maximum rate-of-change of current in each segment for both CG and GC return strokes.

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4.5. Frequency spectrum

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The frequency spectrum is important in designing filters and in shielding the avionics used within an aircraft. Moreover, it will determine the energy transferred to charged particles inside the ionosphere, resulting in sprites. The spectrum can be associated with a particular lightning process according to the shape of the waveform. The frequency spectra of the two types (i.e. CG and GC) of the return stroke currents are shown in Fig. 10. The frequency spectrum that would interact with avionics and ionospheric charged particles is calculated from the return stroke currents for the first 20 μs. The frequency spectra of Figs 10(a) and 10(b) for the currents of Figs 6(a) and 6(b) in each of the ten distributed transmission line segments are calculated to determine the significant frequencies radiated by the CG and GC lightning flashes. The zero frequency (DC) component of the spectrum captures the current that will continue to flow after the initial transient part of the return stroke is over; the steady part continues current that transfers much of the electric charge from the lightning leader channel and the cloud to the aircraft and to the ground. The major portion of the energy transferred is due to this continuous current. The negative frequencies, resulting from the Fourier transform of the impulse currents which rotate clockwise (needed for mathematical completeness) combine with the anti-clockwise rotating positive frequencies to yield the real-time sinusoid at each given frequency. In both cases, as seen from Fig. 10, a higher magnitude of power is observed at lower frequencies when the return strokes initiate current and voltage impulse propagation. It has also been observed that the maximum difference of the power magnitude radiated along the channel between cloud and ground is approximately 150 dB for both CG and GC lightning strikes in the frequency range of 0–25 kHz and 0–0.5 kHz respectively. There are four significant changes in radiated power over frequency bands observed in the power spectrum of the CG lightning return stroke currents (Fig. 6(a)): 0–5 kHz, 5–10 kHz, 10–15 kHz and 15–25 kHz. In the CG return stroke, a significant drop in power amplitude has been observed (Fig. 6(b)) during the frequency changes 0–0.05 kHz, 0.05–0.2 kHz and 0.2–0.5 kHz. The frequency spectrum of the lightning return stroke indicated that the low frequency equipment or systems, including the 400 Hz power system, are most exposed to indirect effects. A wide frequency band is observed for the induced current due to lightning flashes. The return stroke current imposes a higher power dissipation and generates noise due to impulse current propagation. The significant frequencies radiated by the cloud and ground lightning flashes determine a reasonably high energy transfer to charge particles inside the ionosphere as well as produce frequency-dependent interference with communication devices held within the aircraft.

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Magnitude Squared (dB)

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Fig. 10. The frequency spectrum of the return stroke current. (a) CG and (b) GC lightning.

5. Conclusion

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The characteristics of Cloud-to-Ground and Ground-to-Cloud return stroke currents with and without an aircraft attached to the lightning stroke are presented and compared (Figs 6 and 8). Rounded peak currents of 28 kA, 22 kA and 21 kA are observed at the ground, middle and near-to-cloud locations with rise times 0.63 μs, 9.23 μs and 11.63 μs respectively for the return stroke for a GC flash (Fig. 6(b)). In the case of the CG return stroke, the rounded peak currents reported are 60 kA, 50 kA and 27 kA closer to the cloud, middle of the lightning channel and at the ground with a rise time 0.65 μs, 2.50 μs and 4.50 μs respectively (Fig. 6(a)). It shows that a large current is produced in the less common GC strikes right after the attachment to the cloud charge centre. The maximum current rise rate of about 167 kA/μs has been observed closer to ground and at the cloud end for the CG and GC lightning strikes respectively (Table 3). A significant increase in segment currents and voltages is observed (Figs 4 and 5) when the lightning segment is replaced by an aircraft body. The data observed along the aircraft involves an average peak current of 45 kA with a 2.5 μs rise time. A maximum current derivative of 42 kA/μs and a maximum

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potential of 63 MV in the very first 7 μs are observed on the aircraft structure during lightning attachment (Figs 4 and 5). The high current at the attachment point and the very high voltage may cause electrical and electronic equipment damage or malfunction and surface damage to the aircraft body depending on the material used. The work presented in this paper is useful for designing aircraft geometry and material for aircraft-lightning electrodynamics, and to gain important knowledge for the protection and shielding of electrical and electronic equipment and systems in an aircraft. The simulator presented in this paper consists of a three unit system that includes a unit to determine the transient currents, voltages, rates of rise of voltages and currents, and the frequency spectrum of the currents of the lightning return stroke. The second unit which is readily slotted into the return stroke model characterizes the aircraft as an electric circuit which is compatible with the lightning channel model, accounting for the aircraft geometry and material properties. The third unit makes use of the currents calculated by the first unit to determine the lightning radiated electromagnetic fields at any point in space specified by the user. Employing inverse methods to improve the RLC model from measurements [28] is being presently examined. Since the electric dipole method used herein (Section 2) allows for different shapes of aircraft, the impact of aircraft shape on lightning-aircraft dynamics will also be explored in the future using the simulator unit reported herein. Further, the effect of the leader, as commented, may be included as an extension of a thin conductor from the thundercloud or aircraft – its effects will be studied in future, since it will affect the capacitance close to the contact point. References

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