Numerical simulation of aircraft lightning attachment zone using the enclosing ball method

Abstract

The initial stage in aircraft lightning protection design and safety certification involves delineating the lightning attachment zone. The lightning leader’s development is inherently random, favoring the shortest path to the aircraft fuselage. In response, we employ the enclosing ball method to establish the lightning attachment zone. First, define the center point of the aircraft as the coordinate position for the sphere’s center, creating a sphere with a specified radius. The leader’s initial position is then selected from any point on the sphere. Second, by calculating distances between the leader’s position and various areas on the aircraft surface, we determine the shortest path. The corresponding aircraft surface area along this path is identified as the lightning attachment zone for the leader. Subsequently, choose a new leading position on the sphere and iterate through the calculation process until all sphere positions are considered. Finally, tally the occurrence frequencies for all calculated attachment areas, representing the attachment probability of each area based on its frequency of occurrence. This paper not only compares our method with the electrostatic field simulation method but also contrasts it with the probability distribution of lightning attachment points obtained from aircraft flight experiments. The comparison results are highly favorable, providing robust verification for the correctness of our approach.

Keywords

Attachment point lightning attachment zone enclosing ball method leader progession model

1. Introduction

The division of an aircraft’s lightning attachment zone serves as the initial phase in designing lightning protection systems. This critical step provides a foundational framework for crafting comprehensive protection measures and conducting lightning risk assessments. By thoroughly analyzing the aircraft’s susceptibility to lightning strikes and its electromagnetic field characteristics, it becomes possible to pinpoint the precise locations where lightning is most likely to attach. These areas, in turn, guide the implementation of tailored lightning protection strategies, minimizing the potentially detrimental effects of lightning strikes on the aircraft.

At present, in the experiment of aircraft lightning attachment zone [1,2], high voltage discharge experiments are carried out on the full size or scale model of the aircraft in the laboratory based on SAE-ARP5416, SAE-ARP5412 and MIL-STD-464A standards [3–5], and the attachment zone is recorded. However, this experimental method is time consuming and costly, and the tester is prone to electric shock. With the rapid development of computer technology, numerical simulation research has been increasingly applied to the protection of aircraft lightning effects [6–10]. The empirical developed by BAe is based on the rolling sphere model [6]. The input parameter is the radius of the sphere which is evaluated by service lightning strike experience for a given aircraft, but it is difficult to determine the radius of the new aircraft sphere with a large change in shape [7]. Another approach is based on the physical description of the lightning strike on an aircraft [8]. However, this method does not consider the randomness of lightning leader development. The problem of calculating the lightning attachment zone of aircraft by electrostatic field method has become mature and the simulation can obtain more accurate results. However, electromagnetic numerical calculations are intricate for large and complex geometries. Some scholars have developed a numerical simulation method for aircraft lightning strike attachment points based on the fractal theory lightning leader development model [9]. However, the fractal dimension of the three-dimensional lightning leader is difficult to determine.

As an important method in computational geometry, the Enclosing Ball Method (EBM) has been widely used in preserving privacy, quantum cryptography [11] and dealing with outliers in large data [12,13] etc. On the one hand, the idea of the enclosing ball method involves finding the smallest sphere that contains a set of points in a multi-dimensional space. On the other hand, the lightning leader development model believes that the leader always develops in the direction of the maximum spatial electric field with the shortest breakdown path [14,15]. In this situation, the enclosing ball method, a three-dimensional geometric topology method based on the shortest breakdown path, is applied here to quickly and efficiently determine the lightning attachment points on aircrafts.

The rest of this article is organized as follows. In Section 2, we delve into the process of aircraft triggering and intercepting the lightning leader, elucidating the fundamental concept of the enclosing ball method. Section 3 presents the simulation model and employs the enclosing ball method to generate both top view and over view of the aircraft’s lightning strike zone. Section 4 involves a comparative analysis with the lightning attachment zone obtained through the electrostatic field method and the lightning strike probability points derived from flight experiments. Finally, Section 5 concludes this article.

2. Methodology

2.1. Aircraft-intercepted attachment

When the thunderstorm’s lightning leader approaches the aircraft, depicted in Fig. 1, a natural lightning strike forms [16]. The leader’s electric field strengthens, inducing a discharge at the aircraft’s tip and initiating a connecting leader. Originating from the main tip, this leader connects to branches of other lightning leaders. The point on the aircraft’s surface where these connections form is the initial lightning strike attachment point, or the lightning strike entry point. Simultaneously, connection leaders from other tip positions move away from the aircraft towards areas of opposite charge, known as lightning strike exits. The aircraft becomes part of a lightning channel several kilometers long, with its progression determined by the thunderstorm cloud’s conditions.

Fig. 1.

Schematic diagram of natural lightning leader attached to aircraft. During natural lightning, the leader’s approaching electric field intensifys its influence on the aircraft’s tip, causing tip discharges and connection to the leader. This connection initiates from the primary tip, attracting multiple connection leaders. The points on the aircraft where these connections start are the initial lightning attachment points. Meanwhile, other connection leaders may propagate away from the aircraft, commencing from points known as lightning exit points.

The positive polarity long air gap discharge process, mainly includes four physical stages: (1) corona initiation; (2) streamer leader transition; (3) continuous leader development; (4) the final jump. This paper assumes that an initial corona has already occurred at the location to be analyzed. When the electrons generated by the initial corona process pass through the streamer bottom, they continuously collide with neutral particles in the streamer bottom and heat the streamer. When the temperature exceeds the thermal ionization critical temperature of negative ions, the conductivity of the streamer channel increases significantly, and the streamer transforms into an unstable leader [17]. Among them, the critical charge required for the transformation of the initial corona into an unstable leader is about 1 μC [18]. After the streamer is transformed into an unstable leader, electrons from the streamer region in front of the leader are still required to maintain its growth. Approximate the distorted background potential U _back due to initial corona generation as a straight line with an intercept of U ₀ and a slope of E _back. The charge of the initial corona area ΔQ ⁽⁰⁾ and the head position of the corona area $l_{s}^{(0)}$ are respectively [19] $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle U_{back}\approx E_{back}Z+U_{0}\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\rm\Delta}Q^{(0)}\approx K_{Q}\frac{U_{0}^{2}}{2(E_{str}-E_{back})}\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle l_{s}^{(0)}=\frac{U_{0}^{2}}{E_{str}-E_{back}},\end{eqnarray}$ (3) where z is the distance from the corona position to the electrode; K _Q is the geometric factor characterizing the relationship between the charge amount and the potential distribution in the corona region, which is taken as 4 × 10⁻¹¹ C/(V ⋅ m); U ₀ and E _back are the approximate intercept and slope of the background potential line, respectively; E _str is the average electric field strength in the positive-polarity streamer region, which is taken as 4.5 × 10⁵ V/m [20].

If the charge in the corona region reaches a critical value of 1 μC, the positive-polarity leader onset condition is satisfied, and the unstable leader begins to develop. When the unstable leader develops to step i, its head potential $U_{tip}^{(i)}$ is [21] $\begin{eqnarray}U_{tip}^{(i)}=l_{L}^{(i)}E_{\infty }+x_{0}E_{\infty }\ln \left[\frac{E_{str}}{E_{\infty }}-\frac{E_{str}-E_{\infty }}{E_{\infty }}e^{-l_{L}^{(i)}/x_{0}}\right].\end{eqnarray}$ (4) In the above equation $l_{L}^{(i)}$ is the total leader length at the current simulation step, E _∞ is the final quasi-stationary leader gradient, taken as 3 × 10⁶ V/m and x ₀ is a constant parameter given by the product v𝜃, which is taken as 0.75 m, where v is the ascending positive leader speed and 𝜃 is the leader time constant [21].

When the unstable leader develops to the i-th step, the calculation expressions of the head position $l_{s}^{(i)}$ and charge ΔQ ⁽ⁱ⁾ of the streamer region in front of it $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle l_{s}^{(i)}=l_{s}^{(0)}+\frac{E_{str}l_{L}^{(i)}-U_{tip}^{(i)}}{E_{str}-E_{back}}\end{eqnarray}$ (5) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\rm\Delta}Q^{(i)}\approx K_{Q}\{[E_{str}(l_{L}^{(i)}-l_{L}^{(i-1)})+U_{tip}^{(i-1)}-U_{tip}^{(i)}](l_{s}^{i-1}-l_{L}^{(i)})\}.\end{eqnarray}$ (6)

The development distance ${\rm\Delta}l_{L}^{(i)}$ of the unstable leader in the i-th step and the length of the unstable leader $l_{L}^{(i+1)}$ in the i +1-th step are calculated as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\rm\Delta}l_{L}^{(i)}=\frac{{\rm\Delta}Q^{(i)}}{q_{L}}\end{eqnarray}$ (7) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle l_{L}^{(i+1)}=l_{L}^{(i)}+{\rm\Delta}l_{L}^{(i)}\end{eqnarray}$ (8) where q _L is the amount of charge required to form an unstable leader per unit length, which is taken as 65 μC/m [22]. When the length of the unstable leader reaches 2 m, the unstable leader meets the conditions for transforming into a stable leader, and the simulation process of the positive upward leader ends.

2.2. Aircraft-initiated attachment

Generally, when an aircraft is close to a thunderstorm charge zone, a strong enough atmospheric electric field nearby will cause an upward-developing positive leader to be generated on the surface of the fuselage. At the same time, a negative charge will be induced on the surface on the other side of the fuselage, so that the entire The system (aircraft and positive leader) remains electrically neutral. As the negative charge on the surface of the fuselage gradually accumulates, a negative polarity step leader will be generated at the other end of the aircraft, which forms a lightning strike process triggered by the aircraft. These leaders propagate between regions of opposite polarity charge while directing the lightning current through the aircraft. The positive leader begins as a current typically on the order of several amperes and progresses at a speed of 10⁴ m/s. When the leader accelerates to 10⁵ m/s, it will continue to propagate in the form of pulses [16]. The negative leader is an isolated pulse with a higher step and exhibits hundreds of amps for the first few hundred microseconds. The starting position of the two-way leader is also called the starting entrance and exit. The protruding parts on the aircraft are likely to be the entrances and exits triggered by lightning. They generally exist at the front end (nose), wings, tail tips, tail cones, propellers and rotors of the aircraft, Blades and engine nacelles, etc.

2.3. Theory of the enclosing ball method

In general, the development of leader is random, and the leader always tries to find the shortest path to connect with the aircraft fuselage. Take the center point of the aircraft with the length L of the fuselage as the coordinate position of the center of the sphere, and make a certain distance R as the spherical radius, and select any point on the sphere as the starting position of the leader to satisfy the randomness of the leader development.

Since the size L of a given aircraft is fixed, the size of the sphere must be first defined when using this method to determine the lightning strike attachment point. The enclosing ball method requires that the sphere must include the aircraft, so it must be ensured that the size of the sphere is larger than the size of the body. At the same time, the size of the sphere cannot be expanded indefinitely; otherwise it will seriously affect the delineation of the attachment zone. Due to the wide variety of aircraft and the complex and diverse geometry, specific analysis of specific aircraft models is required to determine the value of the spherical radius R.

Both the spherical and aircraft surfaces are discretized by triangular surface elements. All the triangular face elements of the sphere and the surface of the aircraft are numbered respectively. It is assumed that the number of face elements owned by the sphere and the surface of the aircraft are m and n, respectively, then i = 1,2,3, …m; j = 1,2,3, …n. Represent the geometric position of each triangular surface element with centroidal coordinate C (x, y, z) and calculate these coordinates for each element on the sphere. Define these coordinates as the location of the lightning leader. Calculate the distance between the spherical surface and the centroid of each plane element on the aircraft surface. Introduce a specified margin in this calculation. The final simulation then derives the lightning strike attachment area of the aircraft based on these considerations. $\begin{eqnarray}C(x,y,z)=C\left(\frac{x_{1}+x_{2}+x_{3}}{3},\frac{y_{1}+y_{2}+y_{3}}{3},\frac{z_{1}+z_{2}+z_{3}}{3}\right).\end{eqnarray}$ (9) Equation (9) is a centroidal formula of the triangular surface element, (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x ₃, y ₃, z ₃) are the three vertices of the triangular surface element. S _i(x _i, y _i, z _i) represents the centroid coordinate of the i-th triangular surface element of the sphere, and A _j(𝜂_j, 𝜎_j, 𝜉_j) represents the centroid coordinate of the j-th triangle face element on the surface of the aircraft. $\begin{eqnarray}|S_{i}A_{j}|=\sqrt{(x_{i}-{\eta}_{j})^{2}+(y_{i}-{\sigma}_{j})^{2}+(z_{i}-{\xi}_{j})^{2}}.\end{eqnarray}$ (10) Equation (10) is the distance formula of any surface element on the sphere to any surface element of the aircraft surface.

Then, the centroid of the first triangular face element is selected on the sphere as the starting position of the leader, and its coordinate is S ₁(x ₁, y ₁, z ₁). Calculate the distance between the starting position and all triangular surface elements of the aircraft surface by Eq. (10), |S ₁ A ₁|, |S ₁ A ₂|, |S ₁ A ₃|, …|S ₁ A _n|.

By comparing the above calculation results, the shortest path can be obtained. Assume it is |S ₁ A _q| that the q-th triangular face element of the aircraft surface can be used as the most likely hit point of the leader at the S ₁(x ₁, y ₁, z ₁) on the sphere, that is, the lightning strike attachment point on the surface of the aircraft.

The development of the lightning leader is inherently unpredictable, leading to an uncertain final connection process. Consequently, surface elements adjacent to the q-th face element of the aircraft are also susceptible to leader attachment. To more accurately delineate the attachment area corresponding to the leader, it becomes essential to introduce a designated margin, denoted as 𝜆 along the shortest path. For those aircraft surface elements falling within the calculated distance range [|S ₁ A _q|, |S ₁ A _q| + 𝜆], they represent potential points where the leader may attach. This, in turn, contributes to defining the lightning strike attachment area on the aircraft’s surface relative to the leader’s position. The conceptual representation of this process is depicted in Fig. 2. Notably, when |S _i A _p| equals |S _i A _p| + 𝜆, where p denotes the centroid of the p-th face element of the aircraft surface, it signifies the area on the aircraft surface to which the leader corresponds. This region takes the form of a circular zone with the center positioned at A _q and a radius equal to |A _q A _p|.

Fig. 2.

Schematic diagram of a single leader attachment zone.Positioned on the aircraft, the circle signifies susceptibility to leader attachment for surface elements near the q-th face. To precisely outline the attachment area related to the leader, we introduce a designated margin, denoted as 𝜆, along the shortest path. Aircraft surface elements within the calculated distance range [|S ₁ A _q|, |S ₁ A _q| + 𝜆] are potential attachment points for the leader.

It must be pointed out that the determination of the margin 𝜆 needs to be considered in combination with the shape and size of the aircraft and the spherical dimensions, in order to be able to show the best simulation results of the attachment area. 𝜆 = 1 is taken in this paper. The second triangular facet centroid is selected as the starting position of the leader on the sphere, and its coordinate is S ₂(x ₂, y ₂, z ₂). The distance between the starting position and all triangular face elements of the aircraft surface are calculated again by Eq. (10).

Comparing the calculation results, taking the shortest path and giving a certain margin, the leader corresponding to the lightning strike attachment area at the position can be obtained. The points S ₃, S ₄, S ₅, …, S _m on the sphere are sequentially used as the starting position of the leader, and the above calculation steps are repeated, and finally, the lightning strike attachment zone corresponding to the leader at the centroid of each triangular face element on the sphere is obtained.

The triangular surface element is used to discretize the sphere and the surface of the aircraft respectively, and the geometrical position of the triangular surface element is represented by the coordinate of the centroid of the triangular surface element C (x, y, z), and the coordinates of the centroid of each triangular surface element on the sphere are defined as the position where the leader is located. By calculating the distance between the sphere and the centroid of each surface element of the aircraft surface, and giving a certain margin 𝜆, the simulation will obtain the lightning strike attachment zone of the aircraft.

3. Simulation

3.1. Establishment of simulation model

When employing the enclosing ball method for simulating the division of the lightning strike attachment zone, it’s imperative to construct a three-dimensional geometric model of both the aircraft and the sphere. Most of these models can be conveniently generated using 3D modeling software. In this study, the three-dimensional geometric model was created using SolidWorks, representing a passenger aircraft with a fuselage length of 63 meters, a fuselage diameter of 6 meters, and a wingspan of 61 meters. The enclosing ball method is also represented as a surface model with a radius of 50 meters. Utilizing triangular face elements for discretization, the resulting mesh models were derived.This article simulates the lightning attachment zone of a passenger aircraft. As shown in Fig. 3, the center position of the aircraft is the center of the sphere. The aircraft mesh model has 25538 triangular surface elements, and the spherical mesh model has 10120 surface elements.

The hardware employed in the simulation comprises a PC with an Intel Core i5 processor running at 3.20 GHz, paired with 8.00 GB of RAM. Based on the MATLAB, the calculation program of the above algorithm is compiled. The coordinate data of the surface mesh model of the aircraft and the sphere are imported into MATLAB in turn. After all the triangular centroid coordinates of the above mesh model are obtained, the shortest path of each leader starting position on the sphere and all the face elements of the fuselage surface is calculated and a margin 𝜆 is given. Finally, the frequency of the triangular face surface of the aircraft surface being attached by the leader is counted. The final result of the lightning strike attachment zone of the aircraft is displayed by the colour bar function in MATLAB.

Fig. 3.

Schematic diagram of the simulated lightning strike attachment zone using the enclosing ball method. The center position of the aircraft is the spherical centre. The aircraft mesh model has 25538 triangular face elements, and the spherical mesh model has 10120 face elements.

3.2. Procedure of simulation

The development of lightning leader is random, and the leader always tries to find the shortest path to connect with the aircraft fuselage. The enclosing ball method primarily ascertains the lightning strike attachment point by sequentially executing the following steps, as it is shown in Fig. 4.

Take the center point of the aircraft with the length L of the fuselage as the coordinate position of the center of the sphere, and make a certain distance R as the spherical radius, and select any point on the sphere as the starting position of the leader to satisfy the randomness of the leader development. For the passenger aircraft model used in this paper, the spherical radius R > 2∕3L is appropriate through multiple simulations.

By calculating the distance between the position of leader and the various areas of the aircraft surface, a shortest path is finally obtained, and the surface zone of the aircraft corresponding to the path serves as the lightning attachment zone corresponding to the above leader. Select the leader position again on the sphere and repeat the above calculation process until the positions on the sphere are all selected.

Fig. 4.

Simulation flow chart of aircraft lightning attachment zone.

By tallying the occurrences of triangular face elements within the calculated attachment zones, it becomes evident that the most frequently occurring triangular face elements are more likely to experience lightning attachment, while the least frequent ones exhibit a lower probability of attachment. Visualizing this data, the frequencies of each triangular face element are represented by a spectrum of colors, transitioning from red to blue in decreasing order of frequency. This color-coded representation provides a more intuitive depiction of the aircraft’s lightning strike attachment zone.

The lightning leader’s development is unpredictable, making the final connection process uncertain. As a result, surface elements near the q-th face of the aircraft can also be susceptible to leader attachment. To precisely outline the attachment area related to the leader, we introduce a designated margin, denoted as 𝜆, along the shortest path. Aircraft surface elements within the calculated distance range [|S ₁ A _q|, |S ₁ A _q| + 𝜆] are potential attachment points for the leader. This helps define the lightning strike attachment area on the aircraft surface relative to the leader’s position.

3.3. Results and analysis

In the simulation process, the passenger aircraft model is centrally positioned within the simulation area. Subsequently, the aircraft model’s position is fine-tuned based on its orientation. For each of the 55 orientations, 10 simulated discharges are executed, resulting in a total of 550 discharges per simulation. The simulation results show different perspective views of the lightning strike attachment zone of the passenger aircraft calculated by the enclosing ball method. The simulation process calculates the frequency of all triangle face elements on the surface of the aircraft subjected to lightning strike attachment, and then counts the frequency of attachment of each face element. Finally, the triangular face elements are marked by the colors, which makes the results of the aircraft lightning strike attachment zone more intuitive. Figure 5 shows a schematic diagram of the lightning attachment zone of a passenger aircraft. It can be seen from the figures that the red area on the surface of the passenger aircraft is most likely to be attached by the leader, and the blue area of the surface of the fuselage is less likely to be attached by the leader. This distribution is consistent with the actual situation. This is because the surface electric field intensity of the aircraft at these tip parts is very strong. When it enters an area with a sufficiently strong background electric field, it is easy to ionize the surrounding air, generate a discharge leader, and attract a lightning leader, forming discharge channel.

Fig. 5.

The aircraft lightning strike attachment zone. The red area on the surface of the passenger aircraft is most likely to be attached by the leader, and the blue area of the surface of the fuselage is less likely to be attached by the leader.

4. Validation

4.1. Comparison to flight experiment

The probability of lightning striking a specific part of the aircraft is calculated by dividing the number of times lightning strikes that part by the overall occurrences of lightning strikes on the aircraft. The head, wing, tail tip, engine compartment and other significant protruding structures of the passenger aircraft are more susceptible to the leader attachment, with the highest frequency of lightning strike attachment on the passenger aircraft head and wing, up to 161 and 159 times. The lightning strike attachment frequency of the tip of the passenger aircraft tail is second only to the head and wing of the passenger aircraft, up to 111 times. The frequency of lightning strike attachment on the engine of the passenger aircraft is slightly lower than that of the tail of the passenger aircraft, up to 89 times, and other parts up to 30 times, as shown in Table 1.

It can be seen from Table 1 that the lightning strike probability distribution results of the passenger aircraft obtained by numerical simulation are consistent with the actual measurement results of the F-4 flight test. However, compared with the F-4 aircraft, the engine of the passenger aircraft is more prominent due to the larger cabin. It is prone to lightning strikes, which is more in line with the actual situation. Other errors may be caused by the fact that the flight experiment uses an aircraft to fly through a thunderstorm area [23,24], and the number of experiments is limited, so the number of samples used to calculate the probability, that is, the total number of lightning strikes, should be smaller than the number of samples simulated by the method in this paper. In addition, the aircraft may encounter multiple lightning strikes when passing through a thunderstorm area. Each lightning simulation in each simulation process in this article has only one starting point. However, it can be seen that the probability of lightning strikes in various parts of the aircraft is basically the same.

Table 1
Comparison of lightning strike probability results for various parts of the aircraft

Attachment point location Frequency of leader attachment The simulation probability F-4 measurement probability [17 ]

Head 161 29.3% 33.0%

Wing 159 28.9% 32.0%

Tail tip 111 20.2% 25.7%

Engine 89 16.2% –

Other parts 30 5.4% 9.3%

Attachment point location	Frequency of leader attachment	The simulation probability	F-4 measurement probability [17 ]
Head	161	29.3%	33.0%
Wing	159	28.9%	32.0%
Tail tip	111	20.2%	25.7%
Engine	89	16.2%	–
Other parts	30	5.4%	9.3%

4.2. Comparison to electrostatic method

To validate the method presented in this article, we utilize the electrostatic field method to simulate the lightning strike attachment area of the aircraft, akin to the lightning strike attachment point test experiment [18]. First, the aircraft model is placed between the high voltage electrode and the ground plane. The relative position between the aircraft and the electrodes is adjusted by changing the pitch and azimuth of the aircraft to simulate different lightning strikes. It has one position at every 30° on the sphere of the center of the aircraft. The high voltage electrode uses a metal ball electrode to simulate the leader, which is loaded with a voltage of 3000 kV; the ground plane is loaded with a voltage of 0 V. This creates a high potential distribution map between the electrode and the ground, as shown in Fig. 6.

Fig. 6.

Schematic diagram of aircraft position using the electrostatic field method. The electromagnetic simulation software CST EM studio based on finite element method is used to simulate the lightning strike attachment zone of the aircraft. The spherical electrode, aircraft material and ground plane in the simulation model are pure conductors (PEC).

Fig. 7.

The aircraft lightning strike attachment zone. The aircraft head, the engine compartment edge area, the smaller wing tip area, the horizontal tail tip and the vertical tail electric field all reach the maximum, indicating that these zones are most likely to be attached by the leader.

After fine-tuning the electrode position and conducting numerous simulation calculations, we obtained the electric field distribution results on the aircraft surface through the electrostatic field method. Figure 7 shows the top view and the full view of the aircraft lightning strike attachment zone. In combination with the two figures, it can be seen that the aircraft head, the engine compartment edge area, the smaller wing tip area, the horizontal tail tip and the vertical tail electric field all reach the maximum, indicating that these zones are most likely to be attached by the leader.

In contrast to the electrostatic field method, the enclosing ball method simplifies the calculation process, resulting in a simulation that demands minimal time. The entire process, from calculation to obtaining partition results, is completed within a few seconds. With low computer hardware requirements, the simulation yields accurate lightning strike attachment points for the aircraft.

5. Conclusion

In this study, the enclosing ball method based on the shortest breakdown path is employed here to simulate the lightning attachment zone. Our analysis focuses on the development of aircraft-triggering/intercepting lightning leaders. When the leader approaches the fuselage, we utilize the enclosing ball method to precisely pinpoint the lightning strike location. Subsequently, we determine some key parameters—such as the discharge gap, lightning strike starting coordinates, aircraft attitude, and number of discharges—following regulations for the aircraft lightning strike attachment point test. The resulting distribution of lightning attachment points on the aircraft considers the potential for the aircraft triggering/intercepting the leader. Our findings reveal that the primary concentration of aircraft lightning attachment areas occurs around key features like the nose, wings, tail tips, engine nacelles, and other significant structural elements.

Example analyses demonstrated that the probability distribution of lightning attachment points obtained through simulation aligns consistently with the distribution measured in the aircraft flight experiments. To validate the accuracy of our method, we applied the electrostatic field method to calculate the probability distribution of lightning strike attachment areas on the aircraft. A comparison of the results from both algorithms demonstrated strong agreement, and both methods can identify the highest probability of lightning strike attachment in common areas, including the aircraft’s nose, wings, tail tip, and engine nacelle. This concordance between the two methods serves to validate the precision and reliability of the enclosing ball method in assessing aircraft lightning attachment zone.

Considering that the above-mentioned key parts of the aircraft are more harmful after lightning strikes,the methodology aims to address risks in specific aircraft areas during simulation should be proposed. Strategies include structural and electromagnetic analyses for the forward fuselage, aerodynamic simulations for the tail rudder, and thermal analyses for the air entry area. Iterative design optimization based on simulation insights ensures continuous improvement of the aircraft’s lightning resilience in these critical zones.

Footnotes

Acknowledgements

The authors would like to acknowledge The Construction Project of High-Level Higher Vocational Colleges with Chinese Characteristics and Training Project for Outstanding Young Backbone Teachers of “Qing Lan Project” in Colleges and Universities in Jiangsu Province for providing fund for conducting the experiments.

Conflicts of interest

The authors declare that there are no conflicts of interest regarding the publication of this study.

Data availability

No data were used to support this study.

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Bacchiega

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