Modeling of Lightning Attachment to Aircraft and a Novel Methodology to Quantify Strike Rate

Abstract

Air transport plays a vital role in global economic growth and long-distance commutation. The aviation industry is found to double its fleet size every fifteen years. According to Air Transport Action Group (ATAG), 45 million aircraft took off worldwide in 2019, which translates to 1.5 lakh per day. Similar numbers are reported for other years under normal circumstances. Therefore, aviation appears to be an indispensable part of modern human civilization. Lightning is known to be one of the serious environmental threats to aircraft. Past incidents show that lightning strikes can lead to structural damage, operational interruption, and loss of lives. Field data suggest that, on average, an aircraft can get struck by lightning once or twice a year. Further, according to NOAA, The lightning strikes typically cost approximately two billion dollars to airline operators annually. Therefore, lightning protective measures are considered a crucial aspect of aircraft design. Design of suitable lightning protective measures involves Zoning of aircraft’s outer surface. Aircraft Zoning intends to differentiate lightning attachment points, channel slipping regions, and regions that carry just the stroke current. The first step in Zoning is to identify the initial attachment points. For the same, different methods like laboratory experiments, similarity principle, Rolling Sphere Method (RSM), and field-based approach are suggested in the standard, Aerospace Recommended Practice (ARP)-5414. Several aircraft accidents attributed to lightning strikes during the mid-20th century encouraged engineers to investigate the phenomena more closely. Therefore, several in-flight measurement campaigns were carried out in the late 80's, where the aircraft were flown inside the thunderstorm with the intention of getting struck by lightning. Field observation from these campaigns suggests two modes of lightning attachment, Aircraft-initiated and aircraft-intercepted. In the former one, under the influence of a thundercloud or descending lightning leader, the aircraft initiates bipolar leaders that lead to a strike. These leaders are deemed to propagate hundreds of meters to complete the lightning strike. In aircraft-intercepted strikes, the aircraft intercepts a descending lightning leader and hence gets struck. The methods suggested in the standard for identifying initial attachment points on aircraft are simple and have limitations. − The laboratory experiments on scaled aircraft models or isolated aircraft parts cannot portray all the aspects of discharges leading to the attachment. Therefore, the laboratory results cannot be directly extended to actual aircraft.

− The similarity principle suggested in the standard is qualitative and can’t be extended to aircraft of any size and shape. − The field-based approach is not properly described in the standard, and hence, lacks clarity. − The 25 m Rolling Sphere Method (RSM) is routinely employed to determine the initial attachment points. Being a striking-distance-based approach, RSM only depicts the last stage of aircraft- intercepted attachment and, thus, doesn’t consider aircraft-initiated leaders. However, it is reported that 90% of the lightning strikes to aircraft are attributed to aircraft-initiated mode, which involves significant connecting leader activities. Therefore, precise assessment of initial attachment points requires considering the aircraft-initiated leader discharges. From the above discussion, it is evident that modeling bipolar leader discharges from aircraft is imperative in the context of lightning protection design. In literature, it is difficult to find a model for bipolar leader discharges from aircraft. However, works on either negative or positive leader discharge from energized electrodes in laboratory gaps and their extension to grounded objects are well-regarded in the literature. Knowledge from these works is found to be helpful to the present work. In spite of being responsible for most attachments, a model for bipolar leader discharges from aircraft is hard to find in the literature. Therefore, this work aims to develop a model for the inception and propagation of bipolar leaders from aircraft. Electrical discharges being field-driven phenomena, field computation is essential. Identifying the problem in hand as an open-geometry problem, a boundary-based method, Surface Charge Simulation Method (SCSM), is chosen for field computation. SCSM provides the global field distribution around the aircraft. Aircraft extremities are the most probable regions that can initiate discharges and, therefore, requires capturing the field around them in detail. The same is achieved by employing sub-modeling at the extremities. Sub-model charges are calculated using Charge Simulation Method (CSM), while the boundary condition on the sub-model is extracted from the global field solution. Modeling aircraft-initiated leader discharges involve modeling positive and negative leader discharges. Several models for positive and negative leader discharges in laboratory gaps are available in the literature. The latest model available in the literature for a positive leader discharge was developed by Becerra and Cooray. To reduce the computational burden, a simplified version of the model, which is also suggested by them, is considered in the present work. For negative leader discharge, a simplified physical model proposed by Z.Guo et al. is considered. Using the constructed model, the mechanism involved in the inception and propagation of the aircraft-initiated leader discharges is investigated and quantified. In contrast with discharges from energized electrodes or objects on the grounds, a few salient aspects of bipolar leader discharge from aircraft are pointed out. It is shown that aircraft potential changes with the development of connecting leaders, which modifies the field around it. As a consequence of the same, unipolar stable leader discharge from an aircraft is not viable. Therefore, the aircraft-initiated positive and negative leader discharges in a mutually supporting form are essential for the stable propagation of connecting leaders. The minimum ambient fields required for the stable propagation of bipolar leaders from a medium (DC-10) and a small aircraft (SDM) are determined. The values are well within the fields measured during different measurement campaigns. Subsequently, the dependency of this threshold field on permissible pitch and roll angle, aircraft flying altitude, and humidity are quantified. The aircraft-intercepted lightning strikes are also accounted for in this work. It is shown that, being electrically floating, the magnitude of aircraft potential increases, keeping the polarity the same as the descending leader tip potential. However, it is not the case for objects on the ground (i.e., buildings, towers, etc.). Therefore, the striking-distance-based approach, routinely employed for designing lightning protection for grounded objects, cannot be directly extended to aircraft. This also indicates a possible limitation of RSM while applied on aircraft. Further, The critical stroke current below which aircraft-intercepted mode of attachment is most probable is determined for two aircraft models, DC-10 and SDM. Unlike structures on the ground, the weight and volume of the lightning protection for aircraft should be constrained. Therefore, to provide adequate protection, it is absolutely essential to quantify the probability of lightning strikes to aircraft. Thus, based on the above model for lightning attachment, this work develops a methodology for estimating the rate of lightning strikes to aircraft. This method takes aircraft dimensions and spatial densities of lightning flashes and thunderstorms along its route as input. The proposed method is employed to estimate the average annual number of strikes to aircraft worldwide. Subsequently, the dependency of the strike rate on aircraft size and flying altitude are investigated. The entire exercise is carried out for medium-sized (DC-10) and small (SDM) aircraft. The estimated strike rates are well within the range of reported field data. Further, the estimated variation of strike rates with altitudes (below 3 km) correlates well with the data published by Boeing. The small deviations observed in the estimated strike rates are attributed to the assumption of cloud heights and takeoff/landing trajectory. Therefore, given exact data on thunderstorms, lightning flashes, and the operational behavior of an aircraft, the methodology can reliably estimate the rate of lightning strikes to aircraft. In summary, this work has developed a model for the inception and propagation of bipolar leaders from aircraft and also correctly picturizes the direct streamer mode of bridging involved in aircraft-intercepted attachment. The role of the air density (hence, altitude) is incorporated in the model, along with selected humidity values. The proposed model provides a discharge-physics-based method of identifying initial attachment points on aircraft. Therefore, the limitations of the methods suggested in the standard are overcome.The work has also developed a methodology for estimating the strike rate as a function of altitude, aircraft size, thunderstorms, and lightning flash density. The estimated strike rates correlate well with the reported data from field observation.