Simulation Study on Electromagnetic Response and Cable Coupling Characteristics of eVTOL Under Lightning Environment

Abstract

This study employs CST simulations to analyze the electromagnetic response and cable coupling characteristics of electric vertical takeoff and landing (eVTOL) aircraft under lightning conditions. Based on the SAE ARP5414B standard, lightning zoning was carried out, and three typical strike scenarios—the nose, wing, and vertical tail—were established. Referring to representative lightning current waveforms in SAE ARP5412B, Component A was selected as the primary excitation source. On this basis, the L9(3³) orthogonal design method was applied to evaluate the influence of cable structure, length, and routing method on the induced current. The results show that nose attachment produces the strongest coupling to the airframe. Shielded cables effectively reduce the induced current in the conductor core by diverting most of the coupled current through the shielding layer, while unshielded single-core cables demonstrate the weakest resistance to interference. The induced current increases with cable length, and Z-shaped wall-mounted routing produces stronger coupling than straight or suspended routing. This research provides a systematic approach for evaluating indirect lightning effects in eVTOL and offers engineering guidance for electromagnetic protection and cable design.

1. Introduction

1.1. Research Background

Lightning is a severe natural discharge phenomenon that typically occurs in strong convective weather. It releases immense instantaneous energy, characterized by high voltage, large current, and strong electromagnetic radiation. The lightning process generates a large energy release, capable of discharging hundreds of kWh of energy within microseconds [1]. The electromagnetic pulse field generated can significantly affect surrounding equipment in a very short period of time. The effects of lightning on aircraft primarily manifest in two aspects: direct effects and indirect effects. The direct effects refer to the thermal effects, mechanical damage, and structural harm caused by large currents when lightning strikes the aircraft. Indirect effects refer to the interference or even damage caused by the strong electromagnetic field generated during the lightning discharge, which induces or couples onto onboard cables, communication links, and sensitive electronic equipment, resulting in disruption of normal operation [2].

Electric Vertical Takeoff and Landing (eVTOL) aircraft, as an emerging type of aircraft, has become a key support for the development of the low-altitude economy and Urban Air Mobility (UAM) due to its advantages in vertical takeoff and landing, low carbon emissions, high efficiency, and rapid travel. eVTOL is expected to be an important solution for alleviating urban traffic pressure and improving airspace utilization in the future. Currently, many companies are actively promoting eVTOL test flights and commercial applications, exploring scenarios such as short-distance passenger transport, logistics distribution, and emergency rescue. Its safety issues have also become a central focus of regulation and research.

Compared to traditional aircraft made with metal shells, eVTOL uses lightweight composite materials, such as carbon fiber, in its structure to reduce the weight of the aircraft and improve flight performance. Composite materials have significantly lower electrical conductivity than metals and lack current dissipation and electromagnetic shielding capabilities, which notably decreases the resistance to lightning strikes [3]. Therefore, composite materials are prone to ablation, delamination, and even structural failure when struck by lightning. Moreover, the strong radiation field generated by direct or nearby lightning strikes can easily enter the interior of the aircraft through gaps or other coupling paths, coupling with sensitive equipment or signal cables, thereby interfering with or even damaging the equipment.

eVTOL typically operates in urban low-altitude airspace, which has a complex electromagnetic environment, including high-voltage power transmission, microwave communications, building scattering, and frequent thunderstorms and extreme weather conditions. Its ability to resist lightning interference is a critical part of the system’s airworthiness assessment. Therefore, there is an urgent need to focus on the coupling mechanisms of lightning’s indirect effects, based on the structural, electrical system, and operating environment characteristics of eVTOL, and develop high-fidelity numerical simulation models to provide theoretical support and technical basis for electromagnetic protection design and lightning airworthiness certification.

1.2. Current Research Status

The indirect effects of lightning pose a significant threat to the safety and electromagnetic compatibility of aircraft, especially for new composite material flying platforms like eVTOL, whose complex structures and high-density wiring make them more sensitive to lightning-induced coupling effects. Therefore, in recent years, scholars both domestically and internationally have conducted extensive research on lightning coupling paths, electromagnetic response characteristics, and cable protection strategies.

Alkasi [4] used EMA3D simulations to compare and analyze the response differences in aluminum alloy, CFRP, and copper-foil embedded composite materials under lightning indirect effects, finding that copper foil embedding effectively reduces the coupled current in cables, and shielded cables exhibit better inductive immunity. Zou, D. et al. [5], using the Su-27 as an example, studied the distribution of lightning currents at different lightning strike positions on the aircraft, providing an important basis for lightning coupling path research. Yang Z [6] conducted cable shielding performance analysis on composite aircraft bodies and verified the role of shielding structures and wiring methods in lightning protection. Aguilera [7] proposed a patch-supported macro finite element method for lightning-induced simulation of engine systems, improving the modeling efficiency for complex structural coupling paths. Qiu Yicheng [8] proposed a multi-physics field lightning modeling method combining thermodynamics, electromagnetics, and radiation coupling, revealing the formation mechanism and evolution law of lightning channels. Nie Yunke [9] modeled the lightning attachment areas and aerodynamic structures based on the CST platform, analyzing their impact on radar performance. Wang Yifan [10] studied the transient coupling of broadband electromagnetic pulses to multi-conductor transmission lines using the FDTD method, analyzing the effects of structural and boundary parameters on inductive responses. Bu Huinan [11] used a high-voltage electrode and field-circuit collaborative modeling method to systematically simulate the response of aircraft and onboard cables under lightning conditions, providing targeted protection recommendations.

Despite extensive work on lightning coupling paths, field distributions, and cable-induced currents, several gaps remain:

As an emerging platform characterized by lightweighting and electrification, eVTOL lacks dedicated studies on lightning zoning, electromagnetic response, and cable-coupling analysis specific to this class of aircraft.

Most existing studies perform single-factor analyses (e.g., cable construction or shielding parameters). Systematic assessments of joint effects—such as routing method and cable length—are scarce, as is quantitative characterization of multi-parameter interactions.

The linkage between the electromagnetic influence region of the lightning attachment and in-airframe cable coupling is underexplored; methods that integrate field-distribution analysis with cable-response evaluation are still lacking.

1.3. Objectives and Contributions

To address the above gaps, this study focuses on the electromagnetic response and cable-coupling characteristics of an eVTOL platform under a lightning environment, combining CST-based simulations with an L9(3³) orthogonal design. The main contributions are:

1.

Lightning zoning and excitation modeling.

Following SAE ARP5414B, we perform lightning zoning for the eVTOL structure and select three typical lightning attachment points—the nose, wing, and vertical tail. Per SAE ARP5412B, a representative Component-A waveform is adopted as the excitation for subsequent simulations.

2.

Airframe electromagnetic response analysis.

Time-domain simulations in CST systematically compare the surface-current and H-field distributions for different lightning attachment regions, identify that nose attachment yields the strongest coupling to the cabin region, and delineate the key coupling paths and vulnerable locations.

3.

Cable coupling analysis and design recommendations.

With an L9(3³) orthogonal array, we quantify how cable construction, cable length, and routing method affect the peak induced current. Based on the trends, we recommend prioritizing shielded cables, minimizing run length, and favoring free-hanging routing over all-hugging layouts to enhance immunity.

Overall, the results enrich modeling practices for indirect lightning effects and provide actionable guidance on cable layout and lightning protection for next-generation electric aircraft.

2. Theoretical Basis and Coupling Mechanism

2.1. Transmission Line Matrix (TLM) Theory

The Transmission Line Matrix (TLM) method is a mature, full-time-domain electromagnetic field analysis technique, widely used in the analysis of electromagnetic problems such as radiation and scattering. The basic principle of this method is based on the similarity between the propagation behavior of electromagnetic waves in space and the transmission characteristics of voltage and current in transmission lines, which forms the basis for the development of this method. Currently, the TLM method has been extended to three-dimensional spatial problems.

In the TLM algorithm, the analysis region is first discretized and represented by an equivalent transmission line network, with each node in the network modeled by lumped elements. The physical properties correspond to the actual parameters of the problem, achieving spatial discretization. Then, the propagation of electromagnetic signals is simulated by the connection methods between the transmission lines and the behavior of the lumped elements, achieving time-domain discretization. When analyzing a one-dimensional transmission line problem, its lumped-parameter model can be simplified into a specific equivalent circuit structure, as shown in Figure 1.

Figure 1 defines the voltage/current variables and sign convention, consistent with Equation (1); its relation to the numerical workflow—scattering, connection, and time-stepping—is given by Equations (3)–(5).

According to Kirchhoff’s laws, the following equation can be obtained:

$$\left\{\begin{array}{c}V\left(z+△z,t\right)-V\left(z,t\right)=l△z{\displaystyle \frac{\mathsf{\partial }I\left(z,t\right)}{\mathsf{\partial }t}}\\ I\left(z+△z,t\right)-V\left(z,t\right)=c△z{\displaystyle \frac{\mathsf{\partial }V\left(z+△z,t\right)}{\mathsf{\partial }t}}\end{array}\right.,$$

(1)

where $V$ and $I$ represent the voltage and current in the circuit, respectively; $z$ is the position; $t$ is the time coordinate; $l$ and $c$ are the distributed inductance and capacitance parameters, respectively. After rearranging, we obtain:

$$\left\{\begin{array}{c}{\displaystyle \frac{{\mathsf{\partial }}^{2}V\left(z,t\right)}{\mathsf{\partial }{z}^2}}=lc{\displaystyle \frac{{\mathsf{\partial }}^{2}V\left(z,t\right)}{\mathsf{\partial }{t}^2}}\\ {\displaystyle \frac{{\mathsf{\partial }}^{2}I\left(z,t\right)}{\mathsf{\partial }{z}^2}}=lc{\displaystyle \frac{{\mathsf{\partial }}^{2}I\left(z,t\right)}{\mathsf{\partial }{t}^2}}\end{array}\right..$$

(2)

To avoid repeating basic derivations, we present only the three implementation-oriented steps: node scattering → network connection → time-stepping/aggregation. Equation (3) gives the iterative relation between node scattering and connection, Equation (4) provides the explicit scattering formula for a 2-D equal-admittance node, and Equation (5) summarizes the 3-D Symmetrical Condensed Node (SCN) case.

In the 2-D TLM, a grid network of parallel transmission lines is constructed. Each node receives incident pulses from four directions, which enter through four line branches and undergo scattering at the node. The scattered waves then propagate along the lines to neighboring nodes, representing electromagnetic wave propagation in space. The process is described by the following equations:

$$\left\{\begin{array}{c}{\mathrm{V}}_{k+1}^i=C_{k+1}{V}^r\\ V_{k+1}^r=S_k{V}^r\end{array}\right.,$$

(3)

where ${\mathrm{V}}_k^i$ and $V_k^r$ are the column vectors of incident and reflected pulsed voltages at time step $k$; $S$ is the pulse scattering matrix of the node, and $C$ is the connection matrix that describes the network topology. The subscripts $k$, $k+1$ represent the discrete time intervals for scattering. For a 2-D equal-admittance, lossless node, Equation (3) reduces to the scattering formula in Equation (4):

$${}_{k+1}V_n^i={\displaystyle \frac{1}{2}}\left[{\displaystyle \sum _{m=1}^4{}_{k}V_m^i}\right]-{}_{k}V_m^i,$$

(4)

where $k$ represents scattering; $i$ denotes incident; $m,n$ are port numbers.

As shown in Figure 2, when the TLM method is extended to three-dimensional space, the Symmetrical Condensed Node (SCN) model is often used. In this algorithm, each node of a spatial unit is connected to adjacent nodes by short transmission line segments in six directions. Each direction is represented by two perpendicular voltage components [12]. Within one computational time step, these twelve voltage components will change, producing corresponding reflected waves, which then serve as the incident excitation for the adjacent grid nodes in the next iteration. This iterative process enables the accurate modeling and simulation of electromagnetic wave propagation in three-dimensional space.

This process can be described by the formula:

$$\left\{\begin{array}{c}{V}_r=S{V}_1\\ V_{r,k+1}=C{V}_k\end{array}\right.$$

(5)

The Transmission Line Matrix (TLM) method recasts Maxwell problems as equivalent transmission-line networks. It naturally accommodates boundaries, material properties (permittivity, loss, conductivity, permeability), and excitations without re-deriving governing equations for each new geometry, enabling efficient modeling of complex structures and varying electromagnetic environments [13].

As a time-domain solver, TLM sidesteps large frequency-domain linear systems, improving efficiency while maintaining accuracy. A single run yields rich data: transient responses to pulse excitation and—via Fourier transform—frequency-domain characteristics, including fundamental and higher-order resonances. These features make TLM well suited to broadband analyses such as lightning, EMP, high-intensity radiation, and cable/circuit coupling, and it is widely used for complex electromagnetic systems.

In this work, electromagnetic simulations are performed with the TLM solver in CST Studio Suite to evaluate coupling under lightning excitation.

2.2. Basic Characteristics of Lightning Electromagnetic Fields

The Lightning Electromagnetic Environment (LEE) refers to the electromagnetic fields generated by the large currents flowing through the lightning channel during a thunderstorm discharge and their propagation characteristics in space. These electromagnetic fields not only cover a broad frequency spectrum but also exhibit significant time variability and spatial non-uniformity, which can have important impacts on aircraft, radar, communication equipment, and more.

1.

Origin and Components of Lightning Electromagnetic Fields

The lightning process primarily includes stages such as leader development, leader breakdown, return stroke, current continuation, and multiple discharges. Each stage generates different electromagnetic radiation characteristics. The resulting electromagnetic environment is mainly composed of the following parts:

Electric Field (E-field): Primarily originates from charge accumulation in the lightning channel, with near-ground electric field strengths reaching the kV/m range.

Magnetic Field (H-field): Formed by the large currents in the lightning, with typical peak values reaching several hundred A/m, especially prominent during the sharp current changes in the early stages of the lightning strike.

Lightning Electromagnetic Pulse (LEMP): A radiation wave formed by the rapid variations in both the electric and magnetic fields, which exhibits significant transient high-frequency characteristics and can propagate over long distances, coupling with system circuits [14,15].

2.

Frequency Spectrum Characteristics of Lightning

The electromagnetic radiation from lightning covers a very wide frequency range, from DC (static electric fields) to RF (MHz range), and even extends to microwaves (GHz) and X-rays. Its main frequency spectrum features are as follows:

The peak frequency is concentrated between 5 and 10 kHz, which is the primary energy concentration region for lightning radiation in the far-field area.

The electric field spectrum decreases inversely with frequency, with stronger radiation intensity in the lower frequency bands.

The frequency range below 1 MHz has a higher coupling risk to electronic devices, communication systems, etc., and can easily couple with sensitive circuits through conductors [16].

This study prioritizes selecting excitation source frequencies that are closely related to the operating frequency bands of onboard electronic equipment, the cable induction capacity, and the structural resonance frequencies, focusing on the low-frequency range. Considering factors like electromagnetic induction capacity, coupling path clarity, system sensitivity, and standard compatibility, the lightning frequency band below 30 MHz is chosen as the main simulation frequency band.

3.

Time Characteristics and Waveform Features

Fast Rise Time: The typical rise time of the lightning electric field waveform is from tens to hundreds of nanoseconds, with the dI/dt of some return strokes exceeding 100 kA/μs.

Pulse Width: The main pulse width ranges from tens to hundreds of microseconds, followed by a slower afterglow.

Multipulse Structure: A complete lightning strike typically includes multiple sub-discharge events, such as multiple leader-return stroke cycles, forming complex superimposed waveforms.

4.

Spatial Distribution Characteristics

Near-field Region (<100 m): Primarily consisting of static electric fields and induced fields, with high intensity and complex coupling paths.

Far-field Region (several kilometers or more): Primarily consisting of radiation fields, propagating in a spherical wave decay pattern.

Ground/Aerial Structure Effects: Terrain, conductivity, and object height alter the propagation paths and distribution patterns of lightning fields.

5.

Direct and Indirect Effects of Lightning

Based on the different paths of lightning effects, they can be divided into two categories (Figure 3):

Direct Effects: Lightning current directly injected into the aircraft structure or cables, potentially causing structural ablation, thermal damage, fusion, and other severe consequences.

Indirect Effects: Lightning fields induce coupling into the system during spatial propagation, such as through onboard cables, circuits, or devices, causing voltage surges, current interference, or logic faults. In severe cases, this can also damage sensitive components.

Because indirect lightning effects are insidious, frequent, and difficult to shield, they are a primary concern in eVTOL lightning-protection design. This study therefore focuses on the electromagnetic field coupling of indirect effects, examining the impact mechanisms on the onboard cable system and outlining corresponding protection strategies.

2.3. Lightning Coupling Mechanisms

Lightning interference to onboard systems is mainly introduced via three coupling mechanisms: electrostatic, magnetic, and resistive coupling. In eVTOLs, the extensive use of composite materials weakens the shielding advantage of traditional metallic skins, making these couplings more pronounced and worthy of focused analysis.

1.

Electrostatic Coupling

During a lightning discharge, strong electric fields can penetrate the fuselage through apertures such as seams, doors, and windows, inducing charges/currents on internal conductors (e.g., cables, equipment enclosures). This mechanism is most prominent during the early charge-accumulation stage. Conventional metallic airframes provide a Faraday-cage effect that effectively shields the interior. In contrast, composites used in eVTOLs have nonuniform conductivity and reduced continuity, leading to weaker E-field shielding and elevated electrostatic coupling risk.

2.

Magnetic Coupling

Lightning current flowing on the airframe generates a strong, rapidly varying magnetic field. When this field threads structural apertures or gaps, it induces voltages/currents in internal loops and cables, especially during the main discharge phase. Compared with metals, composites attenuate magnetic flux less, allowing deeper penetration. Studies [17] indicate that composite structures can exhibit faster field rise and higher peaks, resulting in larger induced lightning currents on internal conductors than those in metallic airframes.

3.

Resistive Coupling

Resistive (ohmic) coupling arises from voltage drops (V = IR) along lightning-current paths due to finite resistance in structural materials and joints. In metallic aircraft, low resistivity generally limits this effect except at high-resistance joints/hinges. In eVTOLs, however, composite regions often have resistivity hundreds to thousands of times higher than metals, producing larger voltage drops where current traverses these areas. Elevated potentials can appear at equipment grounds and structural seams, potentially affecting sensitive equipment.

2.4. Lightning Protection Standards for eVTOL

Currently, major international aviation regulatory bodies (EASA, FAA) as well as the Civil Aviation Administration of China (CAAC) have developed or published relevant specific conditions and certification frameworks for eVTOLs based on existing aircraft standards, combined with the unique characteristics of eVTOLs. Additionally, test standards such as DO-160G, SAE ARP 5412B, SAE ARP 5414B, and SAE ARP 5416A provide important technical support for evaluating lightning resistance performance. The following is an overview of the airworthiness requirements and technical specifications for lightning protection of eVTOLs by these major organizations, which will lay the foundation for subsequent simulation analysis and compliance studies.

The European Union Aviation Safety Agency (EASA), in the context of eVTOL airworthiness, issued the “SC-VTOL-01 Small Vertical Takeoff and Landing Aircraft Specific Conditions” in 2019, based on the review of over 150 vertical takeoff and landing aircraft projects (applicable to non-pressurized aircraft with a maximum of 9 passengers and a maximum takeoff weight of 3175 kg) [18]. EASA has since published four versions of the Method of Compliance (MOC) to further explain and clarify these requirements. In 2021, EASA released SC E-19 “Specific Conditions for Pure Electric and Hybrid Electric Propulsion Systems” for the powerplants of eVTOLs. These conditions provide specific requirements for lightning protection in eVTOLs:

1.

Aircraft Level Requirements

Unless it can be demonstrated that the aircraft is unlikely to be struck by lightning, the aircraft must be capable of preventing catastrophic consequences from lightning strikes.

2.

Equipment Level Requirements

Unless it can be demonstrated that the electrical/electronic system is unlikely to be affected by lightning, the following requirements must be met: If the failure of any electrical or electronic system would prevent the aircraft from continuing safe flight and landing, the system must be designed and installed to ensure that its functionality is not adversely affected during and after a lightning strike, unless this recovery conflicts with other operational or functional requirements of the system. For aircraft authorized to operate in Instrument Meteorological Conditions (IMC), critical systems must also recover promptly after a lightning strike, ensuring the crew’s ability to respond to adverse conditions [19].

The Federal Aviation Administration (FAA) developed its first airworthiness guidelines for eVTOLs at the end of 2022 for Joby’s JAS4-1, which is equivalent to specific conditions. The final guidelines were officially released in March 2024. Furthermore, in May 2024, the FAA issued official airworthiness guidelines for Archer’s M001 model. Based on this, the FAA released Advisory Circular AC21-17-4 “Model Certification—Powered Lift Aircraft” in June 2024 (for aircraft with a maximum of 6 passengers and a maximum takeoff weight of 5670 kg), which is open for public comment [20]. This advisory circular provides a more efficient general airworthiness guideline for eVTOLs. Similarly to EASA’s requirements, the advisory circular also divides eVTOLs into Enhanced Performance Category and Basic Performance Category, with the Enhanced Performance Category being intended for commercial passenger operations. The lightning protection requirements in AC21-17-4 for eVTOLs are essentially consistent with those outlined by EASA [21].

The Civil Aviation Administration of China (CAAC) has not yet established general eVTOL airworthiness approval requirements. According to the “Interim Regulations on the Flight Management of Unmanned Aircraft,” any design, production, importation, flight, or maintenance activity for medium- and large-sized civil unmanned aircraft systems must apply for airworthiness approval from the Civil Aviation Administration of China [22]. For systems already granted airworthiness approval, any major design changes and proposed flight activities also require re-application for airworthiness approval. The “Civil Unmanned Aircraft Operation Safety Management Rules” further specify that if the CAAC has already issued airworthiness standards but the standards do not cover sufficient safety requirements, the CAAC should develop “specific conditions” equivalent to the original airworthiness standard’s safety level. These specific conditions apply to situations such as novel or unique product designs, unconventional intended uses, or potential safety concerns based on similar products’ experiences. If no airworthiness standard is available, the “specific conditions” may incorporate applicable clauses from existing airworthiness standards and other relevant requirements based on the aircraft’s design and intended use [23].

As a result, Chinese eVTOL projects generally adopt a “case-by-case” approach, referring to EASA’s SC-VTOL, CCAR-23, and CCAR-27 regulations to establish specific conditions. In recent years, the CAAC has published three airworthiness documents related to eVTOLs: SC-21-002 “EHang EH216-S UAV System Specific Conditions” in February 2022 [24]; SC-21-004 “Autoflight V2000CG UAV System Specific Conditions” in November 2023 [25]; and the draft “Aerofugia AE200-100 Electric Vertical Takeoff and Landing Aircraft Specific Conditions” for public comments in December 2023 [26]. The Southwest China Civil Aviation Administration also established a project review team, which, in conjunction with the AE200-100’s design characteristics and operational scenarios, developed applicable specific conditions for airworthiness certification. Additionally, Chapter H of the revised CCAR-23-R4, “Supplementary Requirements for Electric Aircraft Power Systems,” can also serve as a reference for the certification of eVTOL electric power systems. Both the “EHang EH216-S Specific Conditions” and the “AE200-100 Draft Specific Conditions” clearly outline lightning protection requirements for eVTOLs, which are essentially in line with EASA’s SC-VTOL-01 and FAA’s AC21-17-4.

In terms of lightning compliance testing methods, eVTOLs and other new aircraft types currently still primarily follow traditional aircraft-related test standards, including RTCA DO-160G, SAE ARP 5412B, SAE ARP 5414B, and SAE ARP 5416A. Specifically, DO-160G [27] includes Section 22 “Lightning Induced Transient Susceptibility” and Section 23 “Lightning Direct Effects.” Section 22 tests are designed to simulate the transient voltage and current disturbances induced by lightning’s indirect effects on onboard cables. This is performed by injecting different lightning pulse waveforms into the external interfaces of the equipment, assessing the equipment’s electromagnetic immunity to lightning strikes. Section 23 focuses on lightning’s direct effects, such as electrical heating and mechanical damage, typically applied to exposed structural components like radomes, connectors, and conductive rails. SAE ARP 5412B [28] defines the waveform simulation method for aircraft lightning environments and introduces typical lightning current waveforms, which include four major components representing different temporal characteristics of natural lightning, guiding the simulation of lightning strike excitation. SAE ARP 5414B [29] provides methods for partitioning the aircraft’s external surfaces to identify lightning strike exposure levels and potential attachment points. SAE ARP 5416A [30] specifies the test procedures and technical requirements for lightning effects testing, including lightning injection, verification, measurement, and evaluation. It is a crucial technical standard for testing both direct and indirect lightning effects.

This study will use the representative lightning waveforms, system protection requirements, and structural exposure partitions outlined in the above standards for simulation modeling and data analysis. The goal is to assess the electromagnetic response characteristics and cable coupling effects of typical eVTOL structures under lightning environments, providing theoretical and engineering foundations for lightning protection design of eVTOLs.

3. Simulation Model and Excitation Setup

3.1. Introduction to CST and Cable Studio

CST Studio Suite 2021 (Dassault Systèmes, Darmstadt, Germany) is a three-dimensional full-wave electromagnetic simulation software widely used in fields such as antenna design and electromagnetic compatibility (EMC) analysis. Its core feature is the integration of various electromagnetic solvers, including the Finite Integration Technique (FITT), Time Domain Finite Element Method (TDFEM), Transmission Line Matrix (TLM), electrostatic/magnetic field analyzers, and frequency domain solvers. CST enables electromagnetic modeling and analysis across the entire process from low to high frequencies, from static fields to transient behaviors. CST supports multi-physics coupling analysis through its modular structure, equipped with powerful modeling tools and optimization algorithms, allowing it to handle complex geometries and material properties.

In the eVTOL system lightning coupling modeling, CST Cable Studio, as a dedicated module within CST Studio Suite, is primarily used for simulating the coupling effects of complex cable networks under electromagnetic excitation. Cable Studio employs a hybrid modeling approach based on transmission line theory, capable of accurately modeling complex cable networks composed of shielded cables, unshielded cables, twisted pairs, connectors, and terminating loads. It combines external field sources (such as lightning, electromagnetic pulses) for induced voltage and current analysis. Cable Studio includes a variety of excitation sources (such as double-exponential pulses, waveform injection, and coupling source definitions) and frequency-domain/time-domain solvers, which can work directly with 3D simulation modules to achieve complete link modeling of field-to-port electrical responses. It is especially suitable for studying the transient interference characteristics of lightning’s indirect effects on onboard eVTOL equipment.

CST and its Cable Studio module provide a unified multi-scale modeling platform and efficient numerical solving methods for lightning effect analysis on eVTOLs, offering significant simulation support for studying electromagnetic coupling mechanisms and protection design.

3.2. eVTOL Model Setup

To carry out the analysis of coupling effects on the eVTOL under lightning environments, this study uses the AE200 electric vertical takeoff and landing (eVTOL) aircraft model developed by Aerofugia Technology Co., Ltd. (Chengdu, China), as shown in Figure 4 [31]. Based on the external dimensions and structural features of the AE200 prototype, a simplified 3D model was created on the CST Studio Suite platform. The model retains the geometric features and major external parameters of the aircraft while simplifying the internal structure and some complex components to improve simulation efficiency and focus on the aircraft’s response characteristics to the electromagnetic field.

The model retains the major external components—nose, wings, and vertical tail—while simplifying representative features such as transparent cockpit windows and landing-gear interfaces. The resulting geometry (Figure 5 and Figure 6) has an overall length of 11.76 m and a wingspan of 17.22 m. The airframe is modeled as carbon-fiber–reinforced polymer (CFRP) using the electromagnetic properties listed in

Table 1. Electromagnetic properties of the carbon-fiber composite (CFRP).

Material	$\mathit{\epsilon }\mathit{r}$	$\mathit{\mu }\mathit{r}$	$\mathit{\sigma }$ (s/m)
Carbon Fiber	3	1	1 × 104

for subsequent simulations.

3.3. Lightning Zoning

3.3.1. Introduction to Lightning Zoning

According to the SAE ARP 5414B standard, the airframe surface is classified into Zones 1–3 based on attachment probability and current-carrying role: Zone 1 covers regions most likely to experience the initial attachment/first return stroke; Zone 2 covers swept re-attachments during the lightning sweep; Zone 3 has low attachment probability and primarily serves as current-conduction paths. Zones 1 and 2 are further subdivided into A/B (with 1C additionally defined within Zone 1). See

Table 2. Lightning Attachment Zones and Their Characteristics.

Zone	Sub-Zone	Description	Lightning Attachment Characteristics
Zone 1	1A	Initial attachment, short dwell time	High attachment probability, short duration
	1B	Initial attachment, long dwell time	High attachment probability, long duration
	1C	Smaller first return stroke, short dwell time	Medium attachment probability, smaller current
Zone 2	2A	Sweeping attachment, short dwell time	Subsequent lightning, short sweep duration
	2B	Sweeping attachment, long dwell time	Subsequent lightning, long sweep duration
Zone 3		Low probability of direct attachment, only conducts lightning current	Current path, no direct strike

for definitions and characteristics.

According to SAE ARP5414B, a typical distribution for conventional aircraft is: Zone 1A at the nose, wing tips, and vertical tail tip; the adjacent aft margins are typically Zone 1B; areas downstream of 1C along the fuselage are generally Zone 2A, followed farther aft by Zone 2B; the remaining surfaces with low attachment likelihood are assigned to Zone 3.

3.3.2. Lightning Zoning Simulation

This section utilizes the lightning attachment zone classification and simulation methods outlined in standards such as SAE ARP 5416A to model and simulate the electric field distribution of the aircraft under different lightning strike scenarios. In actual flight conditions, there are two types of lightning strikes that the aircraft may experience: (1) when the aircraft traverses a natural lightning channel, cutting off the original channel and forming a bidirectional leader discharge process; and (2) the lightning leader process triggered by the aircraft itself. For these two scenarios, simulations are performed using rod-shaped and flat plate electrodes in CST’s low-frequency studio to model the electric field distribution characteristics.

1.

Flat Plate Electrode Model

To emulate an aircraft-initiated lightning leader, a parallel-plate electrode setup is adopted per SAE ARP5416A. The upper plate is biased at 3000 kV to represent the thundercloud/high-field environment, and the lower plate is set to 0 V as the ground reference. The plate length and width are each set to 2× the aircraft’s maximum overall dimension. The inter-plate spacing is 39 m, and the clearance between the upper plate and the aircraft is 30 m, satisfying the requirement that the spacing exceed 1.5× the aircraft’s maximum dimension. The computational boundary condition is Open Boundary. The resulting setup is shown in Figure 7.

The simulation yields a maximum surface electric field of approximately 1.44 × 10⁶ V/m. To better visualize the relative distribution, the field magnitude is expressed in logarithmic units (dBV/m), as shown in Figure 8. The nose, wing tips, upper fuselage crown, and vertical tail exhibit markedly higher surface fields than other regions, indicating a greater likelihood of lightning attachment at these locations.

2.

Rod-shaped Electrode Model

To emulate aircraft interception of a natural lightning channel and the formation of bidirectional leaders, a 1.5 m rod electrode biased at 3000 kV is arranged in a comparative configuration with the aircraft model. The rod-to-ground separation is 39 m, and the clearance to the airframe is approximately 30 m, representing a natural leader approaching the aircraft surface. The ground is set to 0 V, and Open Boundary conditions are applied. The resulting setup is shown in Figure 9.

The simulation yields a maximum surface electric field of 2.76 × 10⁶ V/m, substantially higher than in the plate-electrode case, indicating stronger field concentration for natural-strike attachment. The distribution in logarithmic units (dBV/m) is shown in Figure 10. Both electrode configurations exhibit a consistent spatial pattern: elevated fields at the nose, wing leading edges, vertical tail, and upper fuselage crown, implying a higher lightning-attachment likelihood at these locations.

3.

Conclusion and Analysis

In summary, both lightning-simulation configurations indicate that the nose, wing tips, and vertical tail exhibit the strongest surface-field concentration and are the most susceptible to lightning attachment. Accordingly, subsequent simulations focus on these representative attachment regions to examine the electromagnetic-interference mechanisms affecting onboard electronics and to explore shielding/mitigation optimizations.

3.4. Lightning Excitation Study

For the simulation study of lightning indirect effects, this research refers to the definition of typical lightning waveforms in SAE ARP 5412B. A typical lightning current component diagram is shown in Figure 11.

Descriptions of different lightning current components and their key parameters can be found in

Table 3. Typical Lightning Current Components and Key Parameters.

Component	Name	Key Parameters
A	First Return Stroke	Peak current: 200 kA ± 10% Action Integral: 2 × 106 A2·s ± 20% Duration: ≤500 μs
B	Intermediate Current	Maximum charge transfer: 10 C ± 10% Average current amplitude: 2 kA ± 20% Duration: ≤5 ms
C	Continuing Current	Current amplitude range: 200~800 A Charge transfer: 200 C ± 20% Duration: 0.25 s ≤ t ≤ 1 s
D	Subsequent Return Stroke	Peak current: 100 kA ± 10% Action Integral: 0.25 × 106 A2·s ± 20% Duration: ≤500 μs

.

Lightning current waveforms are typically described using a double-exponential function (Double Exponential Function), with the mathematical expression as follows:

$$I\left(t\right)=I_0\left[e^{-\alpha t}-e^{-\beta t}\right],$$

(6)

where $I_0$ is the current amplitude (A); $\alpha$ is the tail decay rate (s⁻¹); and $\beta$ is the front rise rate (s⁻¹).

Among the multiple lightning current components, Component A (First Return Stroke) has the most significant impact on aircraft and its electronic systems. To study the induced current effects of different lightning components on onboard cables, this paper selects representative Components A, C, and D for simulation modeling analysis, with their waveforms shown in Figure 12.

In the simulation setup, the nose section (Figure 13) is chosen as the lightning attachment region for indirect effects. The boundaries are set to Open. The lower boundary is a PEC plane, coextensive with the computational domain and located 3.17 m below the lowest point of the airframe. This PEC plane is treated as a reference ground and serves as a scattering boundary that provides charge balance via capacitive coupling. Under external excitation, the displacement current closes through the capacitive coupling between the airframe and the PEC plane and through the open boundary.

Two typical cable bundles, including single-core cables and shielded cables, are laid along the same position inside the aircraft, as shown in Figure 14.

After building the 3-D model, the 2D Modeling tool in CST Cable Studio is used to define the cable layout. In the Schematic editor, an External Port is inserted and connected to the discrete port. For excitation, tasks are created according to the double-exponential parameters of the selected lightning components. All cable ends are terminated with 50 Ω loads, and current/voltage probes and grounds are added. Specifically, P1/P3 terminate the unshielded single-core at its two ends, P2/P4 terminate the shielded-cable core, and P5/P6 terminate the shield. The resulting circuit schematic is shown in Figure 15, after which the simulations are executed.

The results in Figure 16, Figure 17 and Figure 18 exhibit high-frequency oscillations (ringing). This ringing arises from resonance and boundary reflections in the coupled airframe–cable system; it is governed mainly by the effective cable length and terminations, is insensitive to the choice of lightning component, and represents a physical response rather than numerical noise. These oscillations do not affect the conclusions regarding peak levels and relative trends.

From the simulation results, the following conclusions can be drawn:

The induced current from Component A has the highest overall magnitude. In unshielded single-core cables, the peak induced current is approximately 93 A; in shielded cables, the maximum induced current in the core is approximately 0.78 A, while the induced current in the shield reaches 288 A.

Component C generates the smallest induced current. In unshielded single-core cables, the maximum induced current is only 0.3 A, in shielded cable cores it is 0.0029 A, and in the shield, the maximum induced current is 0.96 A. Compared to Component A, its effect is minimal and can be considered negligible.

The induced current from Component D is between Components A and C. In unshielded cables, the maximum induced current is about 28 A, in shielded cable cores it is 0.26 A, and in the shield, the maximum is 99.2 A. The current distribution pattern is similar to Component A, showing a clear coupling effect.

From the comprehensive analysis, it can be concluded that Component A has the most significant interference with the onboard cable system, making it the most influential lightning component; Component C has a much smaller coupling effect on the cables and can be neglected compared to Component A; Component D produces induced currents lower than Component A, and its current distribution patterns in the cable core and shield are highly consistent with Component A. Therefore, to unify the simulation conditions and focus on the most representative lightning excitation scenario, Component A is selected as the typical lightning excitation waveform for further analysis in subsequent studies.

The excitation waveform of Component A set in CST is shown in Figure 19, with a simulation time of 200 μs. The current reaches its peak at 6.4 μs and decays to half-peak at 69 μs.

3.5. Cable Setup

To investigate coupling in different cable types, three representative models were built in CST Cable Studio:

Unshielded single-core cable (outer diameter 4 mm; conductor 2 mm; insulation thickness 1 mm): Simple construction, used for low-EMC-demand power/signal runs. Lacking a shield, it is susceptible to lightning-induced fields in harsh EM environments.

Unshielded two-core twisted pair (outer diameter 4 mm; each core 1 mm; insulation thickness 0.5 mm): Twisting reduces differential-mode interference and improves immunity relative to a single core, but common-mode coupling remains significant without a shield.

Shielded cable (outer diameter 4 mm; core 1 mm; shield + insulation thickness 1.5 mm): metallic shield around the core suppresses incident/leaked EM fields, offering strong EMC performance in lightning environments; commonly used for critical systems and high-immunity links.

The geometric layouts of the three cables are shown in Figure 20, Figure 21 and Figure 22 and are used for subsequent simulations of induced current under different lightning components.

The cables are arranged inside the aircraft, as shown in Figure 23.

4. Electromagnetic Response Analysis of the Aircraft Under Lightning

4.1. Modeling and Simulation for Different Lightning Attachment Regions

In Section 3.3, the lightning zoning for eVTOL was introduced and analyzed in detail. Based on these zoning results, this section selects typical lightning strike locations: the nose, wing, and vertical tail, and simplified models of lightning strikes at these three locations are established in CST for subsequent lightning coupling effect simulation studies. The model diagrams for each excitation location are shown in Figure 24.

Since the lightning excitation reaches its peak current at 6.4 µs, the surface-current and H-field monitors are configured to record at t = 6.4 µs. The computational domain employs Open Boundary conditions to emulate free-space propagation of the lightning electromagnetic wave. Simulations are then executed.

4.2. Analysis of Surface-Current and H-Field Responses on the Airframe

According to the previous setup, the simulation results are shown in

Table 4. Maximum surface current density and H-field for different lightning attachment locations.

Attachment Location	Max Surface Current Density (A/m)	Max Surface H-Field (A/m)
Nose	84,426	48,364
Wing	189,000	125,000
Vertical Tail	112,000	90,513

:

To better visualize the surface-current distribution for different attachment locations, the surface current density is plotted in logarithmic units (dBA/m), as shown in Figure 25, Figure 26 and Figure 27.

The results show that:

Nose attachment. The surface-current distribution is wide, with high-current-density regions concentrated over the forward/mid fuselage and the wings. Current density increases with proximity to the attachment point; the wing tips exhibit higher densities than the wing panels.

Wing attachment. The distribution is more localized, with high current density primarily over the entire wing, and the wing tips again showing the highest levels.

Vertical-tail attachment. Elevated current density is concentrated on the vertical tail, especially near the attachment site. A noticeable increase also appears on the wings, predominantly near the tips.

Overall, nose attachment produces the widest current spread, whereas wing and vertical-tail attachment yield more localized distributions. This also appears in the corresponding maximum surface current density: in general, the more localized the distribution, the higher the peak density. In addition, because nose attachment couples more strongly into the cabin—where cables and onboard equipment are typically located—the nose case is expected to impose a greater impact on internal cables and avionics from a current-distribution perspective.

Next, we will show the magnetic field distribution characteristics under different lightning strike locations, also expressed in logarithmic units (dB). The visualization results are shown in Figure 28, Figure 29 and Figure 30.

The simulations show that the H-field distribution broadly follows the surface-current pattern. Under nose attachment, the airframe exhibits the strongest overall H-field response: the forward/mid fuselage and wing regions rise markedly, and the high-H-field area is comparatively extensive. By contrast, wing and vertical-tail attachment produce strong fields mainly in localized regions with a confined extent.

In summary, because onboard cables and equipment are concentrated in the cabin, and coupling in the lightning band is typically dominated by magnetic-flux variation, nose attachment imposes the highest magnetic exposure on the cabin—consistent with the current-distribution results. Therefore, subsequent simulations adopt the nose-attachment case as the representative condition to further examine electromagnetic coupling to onboard cables.

5. Cable Coupling Effect Analysis Based on Orthogonal Experiment

5.1. Introduction to the DOE Method

DOE (Design of Experiments) is a systematic experimental method used to establish the relationship between influencing factors and response variables by rationally organizing experimental plans, while controlling variables and resources. Its core goal is to obtain as much useful information as possible with as few experimental trials as possible, improving experimental efficiency, optimizing system performance, and identifying key factors.

5.2. L9(3³) Orthogonal Experiment Design

In this study, the DOE method is used to analyze the influence of different cable arrangement parameters (length, cable structure, wiring method) on induced current response under lightning coupling effects, primarily analyzing the maximum induced current occurring on the cable core. The L9(3³) orthogonal experiment design is employed, with the first 9 sets as representative experimental plans, covering 3 levels for each factor. Additionally, to further analyze the independent effect of wiring method on induced current, two control test groups (Tests 10 and 11) are added, with Test 1 forming the supplementary experimental group where wiring method is the only variable.

The levels for each factor are set as follows: Cable Length: 1 m, 2 m, 3 m.

Wiring Method: Free-hanging wiring, Wall wiring, Zigzag wall wiring.

Cable Structure: Unshielded Single Wire (4 mm diameter), Unshielded Twisted Pair (2 × 2 mm), Shielded Cable (4 mm diameter).

The experimental design is shown in the

Table 5. L9(3³) Orthogonal Experiment Plan for Cable Lightning Coupling Effects.

Experiment Number	Cable Length	Wiring Method	Cable Structure
1	1 m	Wall wiring	Unshielded Single Wire
2	1 m	Free-hanging wiring	Unshielded Twisted Pair
3	1 m	Zigzag wall wiring	Shielded Cable
4	2 m	Wall wiring	Unshielded Twisted Pair
5	2 m	Free-hanging wiring	Shielded Cable
6	2 m	Zigzag wall wiring	Unshielded Single Wire
7	3 m	Wall wiring	Shielded Cable
8	3 m	Free-hanging wiring	Unshielded Single Wire
9	3 m	Zigzag wall wiring	Unshielded Twisted Pair
10	1 m	Free-hanging wiring	Unshielded Single Wire
11	1 m	Zigzag wall wiring	Unshielded Single Wire

:

5.3. Analysis of Experimental Results

Based on the experimental design mentioned above, after completing the 11 experimental simulations, the maximum induced current response results for each cable arrangement were compiled. The statistical table is shown in

Table 6. Simulation Results.

Experiment Number	Maximum Induced Current in Conductor Core (A)	Maximum Induced Current in Shielding Layer (A)
1	110.19	None
2	66.75	None
3	1.35	374.58
4	91.67	None
5	1.05	257.81
6	194.27	None
7	1.29	318.32
8	197.61	None
9	106.22	None
10	93.86	None
11	183.46	None

. For ease of subsequent analysis, the table records the maximum induced current magnitude for each group of experiments, both in the cable core and in the shielding layer (if present).

From the data above, it can be seen that the induced current in the conductor core varies significantly under different experimental conditions, indicating that experimental factors have a substantial impact on lightning coupling responses. The following analysis will explore the influence of the three main factors on the induced current to further identify the dominant factors and their behavior.

1.

Cable Structure

From the results of experiments 1–9, it is evident that the cable structure has the most significant impact on the induced current among the three factors. The results for different cable structures are summarized in Figure 31.

Among these, cables with a shielded structure (Experiments 3, 5, and 7) show very low induced current in the conductor core, ranging from 1.05 to 1.35 A, but the induced current in the shielding layer is as high as 257–374.58 A. This indicates that most of the coupling current is absorbed by the shielding layer, significantly reducing the interference exposure of the conductor core and effectively providing protection through the shielding structure.

In contrast, unshielded single-core cables show a significantly higher induced current in the conductor core, ranging from 110 to 197.61 A (Experiments 1, 6, and 8), and exhibit the weakest anti-interference capability.

Unshielded twisted pair cables exhibit intermediate performance in terms of induced current. The conductor core induced current in Experiment 2 is 66.75 A, while the maximum induced current in Experiments 4 and 9 is 97.67 A and 106.22 A, respectively. This suggests that the twisted pair structure has certain mutual coupling characteristics, and the twisted structure helps reduce the loop area, providing some suppression of the induced interference, but still not as effectively as the shielded structure.

In conclusion, the ranking of lightning coupling resistance for different cable structures is as follows: Shielded Cable > Unshielded Twisted Pair Cable > Unshielded Single-core Cable. Therefore, to improve system electromagnetic compatibility in lightning electromagnetic environments, shielded cables should be prioritized. In applications where shielded cables cannot be used, multi-core twisted pair cables should be considered. Non-shielded single-core cables should be avoided, especially in areas close to lightning strike zones or regions with severe electromagnetic leakage.

2.

Cable Length

In general, the longer the cable, the higher the induced voltage it intercepts in the lightning induction field, resulting in higher induced current. The simulation results of this study confirm this trend. In the results of Experiments 1–9, the average maximum induced current for cables of different lengths was calculated, and Figure 32 was generated.

For the 1 m cable, the average conductor current is about 59.4 A; for the 2 m cable, it increases to about 95.7 A; and for the 3 m cable, it further rises to about 101.7 A. This trend is also further confirmed by the simulation currents for both unshielded single-core and unshielded twisted pair cables.

From the simulation results, as the length of the unshielded single-core cable increases, the maximum induced current shows an increasing trend (Figure 33): 110.19 A for 1 m (Experiment 1), 194.27 A for 2 m (Experiment 6), and 197.61 A for 3 m (Experiment 8). The induced current distribution also increases with cable length. At 1 m, the induced current is the smallest, while at 2 m and 3 m, the differences are not significant due to the wiring structure, though the induced current at 3 m is slightly larger than at 2 m.

The same trend is observed with unshielded twisted pair cables (Figure 34). For 1 m (Experiment 2), the induced current is the smallest, with 2 m (Experiment 4) showing a current value between 1 m and 3 m, while 3 m (Experiment 9) shows the highest induced current value.

Thus, in lightning high-electromagnetic exposure areas, it is advisable to minimize the length of critical cables or choose more concentrated wiring schemes while ensuring system functionality. For applications where long cables are necessary, it is recommended to use shielding measures to enhance protection.

3.

Wiring Method

Compared to cable structure and length, the wiring method has the least impact on the maximum induced current. To study this factor more precisely, additional experiments 10 and 11 were set up and compared with Experiment 1 (all 1 m unshielded single-core cables). The results show that in Experiment 1 (wall wiring), the maximum current is 110.19 A; in Experiment 10 (free-hanging wiring), it is 93.86 A; and in Experiment 11 (Zigzag wall wiring), it is 183.46 A, as shown in Figure 35.

The results show that, under the same conditions, Zigzag wall wiring produces the highest induced current, followed by wall wiring, and free-hanging wiring produces the lowest induced current.

In conclusion, in lightning protection design, Zigzag wall wiring should be avoided as it produces the highest induced current under the same conditions and may result in more severe coupling effects. This complex wiring not only increases the total length of cables but may also expand their effective exposure area in space, which is unfavorable for improving electromagnetic compatibility. Free-hanging wiring should be prioritized, as it effectively reduces the coupling intensity of lightning-induced current while meeting system wiring requirements. Conventional wall wiring serves as an intermediate option. Ultimately, the cable path should be simplified, and the exposure area reduced based on the actual platform structure characteristics to improve the system’s protection against lightning indirect effects.

6. Conclusions

This study, set against the background of the lightning indirect effects on eVTOL, conducts modeling and simulation analyses around three aspects: lightning zoning, excitation comparison, and aircraft response and cable coupling effects. The main conclusions are as follows:

Lightning Zoning Analysis: Based on the SAE ARP 5414B standard, key lightning strike regions such as the nose, wings, and vertical tail were identified, providing spatial references for subsequent electromagnetic response simulations.

Excitation Comparison: Based on SAE ARP 5412B, three typical lightning components were compared in terms of their induced current effects on onboard cables. Component A, with representative waveform characteristics, was selected due to its significant impact.

Aircraft Electromagnetic Response Analysis: The results show that in the case of lightning strikes at the nose, the distribution range of the aircraft’s electric and magnetic fields is the widest, with a complex coupling path and the most significant impact on the interior of the cabin.

Cable Coupling Experiment Analysis: Based on the L9(3³) orthogonal design, the effects of different factors on induced currents were clarified:

• Cable Structure: Shielded cables provide the best protection, followed by unshielded twisted pair cables, and lastly, unshielded single-core cables. Shielded cables significantly reduce the induced current in the conductor core, offering a clear protective effect. They are the preferred structure for improving lightning resistance.
• Cable Length: The induced current is positively correlated with cable length, meaning longer cables generate a higher induced current in lightning environments. It is recommended to minimize the length of critical cables.
• Wiring Method: The wiring method also affects the induced current, with free-hanging wiring being superior to both Zigzag wall wiring and wall wiring. It is recommended to prioritize free-hanging wiring in the design.

The results of this study provide important references for lightning protection planning and wiring strategies in the early design phase of eVTOL systems.