Overvoltage Protection Matlab

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This document outlines the position of the International Astronomical Union (IAU) Centre for the Protection of the Dark and Quiet Sky from Satellite Constellation Interference (CPS) regarding the impact of low-earth-orbit (LEO) satellite constellations on scientific and public access to the night and radio sky. The intended audience includes government organisations, space industry, the public, and the astronomy community. While it does not delve into technical details extensively, it focuses on presenting the overall context, key concepts and recommendations.

The document comprises sections at three levels of detail, with the Executive Summary providing the briefest,

The Chapter Summary And Recommendations A More

comprehensive, and the main body of the document a detailed explanation of the position of the CPS. As the situation with LEO satellites is constantly evolving, the CPS may issue an update to this position in the future.

The Views Expressed In This Document Are Those

of the IAU CPS and may not necessarily reflect the opinions of the individual contributors or the affiliated Institutes mentioned in the Acknowledgements..

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Introduction: Low-Earth-orbit Satellite Constellations and Astronomy

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The Importance of Astronomy and Astrophysical Research

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The Impacts of LEO Satellite Constellations on Astronomy

[ Executive Summary ]

1 In the following we refer to the radio-quiet sky as simply the ‘quiet sky’. The growing number of satellite constellations in low Earth orbit (LEO) enhances global communications and Earth observation, and support of space commerce is a high priority of many governments. At the same time, the proliferation of satellites in LEO has negative effects on astronomical observations and research, and the preservation of the dark and quiet sky. These satellite constellations reflect sunlight onto optical telescopes, and their radio emission impacts radio observatories, jeopardising our access to essential scientific discov- eries through astronomy. The changing visual appear- ance of the sky also impacts our cultural heritage and

Environment. Both Ground-Based Observatories And

space-based telescopes in LEO are affected, and there are no places on Earth that can escape the effects of satellite constellations given their global nature. The minimally disturbed dark and radio-quiet sky1 is crucial for conducting fundamental research in astronomy and important public services such as planetary defence, technology development, and high-precision geolocation.

Some Aspects Of Satellite Deployment And Opera-

tion are regulated by States and intergovernmental

Organisations. While Regulatory Agencies In Some

States have started to require operators to coordi-

Nate With Their National Astronomy Agencies Over

impacts, mitigation of the impact of space objects on astronomical activities is not sufficiently regulated.

Quiet Sky And Prevent Catastrophic

loss of high quality observations.

Vatory Operations And Implement Mitigation

measures at observatories and in software.

Practices In Interference Mitigation, Leading To

widely adopted standards and guidelines.

And Reduction Of Unwanted Radiation In The

radio regime for spacecraft manufacturing.

Industry Best Practices That Mitigate The Neg-

ative impacts on astronomical observations.

Operated In Ways That Minimise Adverse Effects

on astronomy and the dark and quiet sky.

Of Space Debris Will Also Benefit The Field Of

astronomy and all sky observers worldwide.

And Astronomy

In recent years, numerous projects to deploy large ‘constellations’ of small satellites have been proposed by the satellite industry and by governments.

A satellite constellation is a set of spacecraft that share a common design, distributed across different orbits to provide a service and geographical coverage that cannot be achieved by a single satellite . Applications of satellite constellations range from civil and military

Telecommunications To Remote Sensing And Earth

observation, global navigation, and meteorology. As of the end of 2023, there are more than 5000 satel- lites from large constellations in low Earth orbit (LEO) . Filings in respect of over one million satellites at the International Telecommunication Union (ITU) indicate an ambition for possibly hundreds of thou- sands of satellites in LEO in the coming decade .

Astronomy today is conducted by almost 1000 largely publicly funded observatories and spacecraft, ranging from small metre-size telescopes to large-scale projects like the Square Kilometre Array and the Extremely Large Telescope, worth billions of dollars. Tens of thousands of astronomers around the world use such facilities to make scientific discoveries that benefit humanity.

Even Larger Amateur Community, With Commercially

available equipment capable of supporting critical amateur–professional scientific collaboration. As a result of the ability to easily view the night sky and make important discoveries even with modest equip- ment, astronomy remains one of the most accessible sciences, particularly for developing countries.

The negative impact of artificial satellites on astronomy has been an issue for many years. However, the paradigm shift to an industrial use of LEO, with an expected 20- to 100-fold increase in the number of satellites, is becoming a much larger threat to science. The visibility and bright- ness of a satellite depend on the altitude of its orbit, its size, shape and surface reflectivity, its orientation with respect to an observer, and the orbital configuration of the system. LEO satellites reflect sunlight and can be detected as moving spots, particularly at twilight. Satellites at higher altitudes are visible for much of the night. They emit radio waves ubiquitously and can outshine cosmic sources by millions of times, which becomes an issue when they appear in direct line of sight to a radio tele- scope. The growth of LEO satellites has a direct impact on professional and amateur astronomy, and, without appropriate mitigations, it will have a significant and detrimental effect on the dark and quiet sky across the globe, even rendering some observations impossible.

Industry leaders have made substantial investments to reduce the optical and radio visibility of their satel- lites. They are entering into agreements with individual national governments to explore efforts to do so .

At the time of writing, the effort seems to be making progress. Measurements in 2023 of the brightness of SpaceX’s Starlink Generation 2 mini-satellites have shown that the visibility in operational orbit with the specular coatings and darkening efforts is reduced compared to the satellites initially deployed in 2019, although bright Generation 2 satellites at final orbital height can still be observed . There are many other satellite constellations in development, however, which will require brightness mitigations and partnerships with the astronomy community to validate those mitigations.

Satellite companies are developing various constellations to provide internet and telephony access, as well as Earth monitoring, some of which utilise dedicated ground-based antennas as user terminals. This growing novel and dense communication ground segment is in itself an added source of radio interference. More recently, there are growing efforts to develop systems that connect directly to common mobile/cell phone handsets. These satellites have a much larger surface area compared to those sys- tems designed to connect to larger, less mobile ground stations. Without mitigation, these new satellites could outshine even the brightest stars and planets in the opti- cal regime . Currently, without voluntary cooperation, radio-quiet zones around sensitive radio telescopes are also not protected from satellite emissions, in particular direct downlinks. Moreover, the widespread transmis- sion of radio signals, as well as unintended radiation in the radio regime in all directions, adds progressively more noise to the radio interference background .

And Astrophysical Research

Astronomy plays an irreplaceable role in advancing fundamental physics and driving technological inno- vation in current and future industries. It serves as an accessible avenue for technical and scientific research and education in developing and developed countries.

Earth-based astronomy is essential for providing the high-precision celestial reference frame needed for navigation and geodesy, monitoring potentially harmful space weather, and detecting and tracking potentially hazardous asteroids, comets and interstellar objects.

Scientific Significance

Both historically and in the present, astronomical observations have driven breakthroughs in the under- standing of the physical Universe and the mathematics required to describe it. Likely influenced by criticism of the Ptolemaic cosmology by the Persian and Syrian astronomers Al-Urdi, Al-Tusi and Ibn al-Shatir — all members of Maragheh observatory funded in what was then Mongolia, now Iran — Copernicus revived the idea that the Earth orbits around the Sun and not vice versa.

Kepler’s laws of the motions of the planets were the first mathematical description of a physical phenomenon, subsequently bolstered by Galileo’s first observations of the heavens through a telescope. Newton developed a whole modern branch of mathematics to connect those motions to physical laws. All those giant leaps in scientific understanding depended entirely on direct observation of the cosmos under the dark sky. Einstein’s general theory of relativity, which posits that mass changes the shape of space, was initially validated by observations of the apparent shift in the positions of stars close to the Sun during a solar eclipse. Today’s observations of black holes and gravitational waves probe the fundamental nature of gravity itself. The existence of Dark Matter and Dark Energy, the main constituents of our Universe, has been inferred through astronomical experiments.

Continued recognition of these critical contributions to fundamental understanding is exemplified by the fact that half of the Nobel Prizes in Physics awarded between 2017 and 2022 went to astronomers and astrophysicists.

Although we cannot predict the specific outcomes of today's fundamental research, history leads us to expect that it will significantly impact technological innovation and society in the coming decades and centuries.

Furthermore, astronomy's aesthetic appeal often serves as a means to engage young individuals in scientific and technical subjects. The accessibility of astronomy, cou- pled with the allure of the night sky, offers opportunities for both developed and developing nations worldwide.

Imaging And Image Processing Now Found In Many

aspects of everyday life, including medical imaging,

Mobile Phone Cameras, Telecommunication, Airport

scanners and high-sensitivity radio receivers. The positive impact of astronomy on the development

Of New Disruptive Technologies And The Economy Is

even more direct. For example, digital photography and WiFi technology have been pioneered in astron-

Omy, As Well As Various Medical Image Processing

techniques. The next generation of observatories are driving innovations in ‘big data’, by creating tech- niques to process vast amounts of scientific data.

Fundamental discoveries are possible with small-aperture telescopes of modest cost. While LIGO made the first detection of gravitational waves, their origin was identified by a large number of small telescopes providing optical confirmation. Some of the first known exoplanets were discovered with telescopes smaller than 0.25 metres.

Astronomy hence offers a low-cost entry point to fun- damental physics and technological development.

Cultural Significance

Culturally, astronomy holds immense significance as it is, and has always been, deeply intertwined with the knowl- edge and daily lives of different societies across time.

Celestial observation forms the basis of rich mythological and religious narratives across cultures. Archeological sites dating back to Neolithic and Chalcolithic times, to at least 6000 BCE, bear witness to connections to the sky, and numerous cultural artefacts depict stellar constella- tions. Ancient civilisations and many documented early human settlements developed astronomical observatories and built early astronomical knowledge for their daily lives, technology advances, and cultural and religious development. Major modern religions refer to the stars in their holy books, and many religious and cultural groups

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still depend on access to the night sky for wayfinding, ritual timekeeping, and more. Astronomical discovery was the origin of the fundamental transformation in western civilisation that led to the blossoming of exact sciences, which would later be called the Copernican revolution.

Astronomical discovery permeates popular culture through compelling imagery as well as imaginative science fiction. Advertisements feature astronomical imagery, and commer- cial products are named after astronomical objects. Access to the natural dark sky is a key component of many cultural practices ; thus preserving and protecting a pristine night sky are crucial for safeguarding our cultural heritage.

Significance

Beyond fundamental research and technical development, astronomy has substantial economic implications.

Astronomy Is An Important Component Of Many Gov-

ernments' space objectives and plans, along with other space-based activities, including the satellite commu-

Nications And Earth Sensing Sectors. Ground-Based

astronomical observatories play a critical role in protecting our society’s infrastructure and even life on Earth. In order to provide navigation services for GPS receivers on Earth and also spacecraft operating in Earth orbit and beyond, we need precise knowledge of the Earth’s shape and location. This is challenging, as Earth continuously changes its shape and orientation on various scales.

We Can Measure Minute Shifts Of Earth’S Shape And

spin by knowing the positions of radio telescopes on the ground and the orientation of the Earth’s rotation axis; this is done by observing a number of extremely distant radio sources (quasars), beacons of relativistic particles emanating from black holes. This forms the single most reliable reference system against which other navigation systems can be calibrated.

Observations of the radiation from these quasars with a terrestrial network of radio telescopes establish the basis for navigation, precision geolocation, continental drift measurements, climate change monitoring, and biodiversity assessment. These observations then require corrections supplied by the theory of general relativity — another discovery fundamentally supported by astronomy — for these precise applications. This service is currently a free contribution, financed by States, that provides an invisible foundational support to the worldwide economy.

Space Environment Is Vital For Much Of The Modern

economy, with infrastructure worth billions of dollars or euros at stake. Adverse space weather events can, for example, affect power grids on the ground and disable spacecraft in any orbit, potentially causing catastrophic cascades of destruction. With space weather monitoring, countermeasures can be initiated, and astronomy again provides a pivotal service to the worldwide economy.

Our Planet Has Experienced Multiple Catastrophic

impacts with asteroids and comets in the past . Despite substantial international efforts, we still know only a fraction of the potentially hazardous objects

Devastation . Discovering Unknown Objects And

monitoring the highly non-linear trajectories of near- Earth objects is the prime purpose of planetary defence, which relies primarily on optical telescopes.

Additionally, astro-tourism is developing a positive

Minimum Impact From Ground-Based Light Pollution,

desiring unhindered views of the natural night sky.

Constellations On Astronomy

Satellite-induced light and radio pollution affects the night sky globally. This environmental impact means that a pristine night sky is being affected everywhere in the world by satellite reflections and space debris.

Even traditionally remote observatory locations will be affected just as severely as any other area. Figure 1: Bright streak left in an astronomical image of a group of galaxies with the Hubble Space Telescope. The streak was generated by a satellite crossing the field of view during the exposure. Courtesy of NASA/STScI .

Visibility Of Satellites In The Sky

Most satellites in LEO are constructed of materials that reflect sunlight and as a result they can often be seen by the unaided eye. Depending on the satellite's alti- tude, orientation, and surface characteristics, and the darkness of the viewing site, these reflections can be observed throughout the entire night. The larger satellites that are intended to communicate directly with cellular phones are expected to be among the brightest objects in the night sky if mitigations are not implemented.

Efforts have been made by industry to identify and develop novel approaches to spacecraft design and mechanisms to reduce the brightness of satellite systems. However, the technology to reduce brightness is still in its early stages and is not yet broadly adopted by all constellation oper- ators and consequently many systems already deployed are often visible to the naked eye in a moderately dark sky. The proposed and deployed LEO satellite systems are causing changes in the appearance of the night sky worldwide, impacting the cultural heritage associated with it in every country and every location on Earth .

Observations

LEO communication satellites, at their current levels of brightness, will adversely affect optical and infrared astronomical observations by reflecting sunlight.

As satellites move across the sky, they can reflect sunlight and leave bright streaks on astronomical images (see Figure 1). Depending on the brightness, such interference has the potential to invalidate whole datasets. Satellites in lower orbits enter the Earth's shadow earlier after sunset, ceasing to reflect sunlight to the ground and disappearing from view, at least from the perspective of an optical observer.

Generally, the lower the orbit, the shorter the period of visi- bility after twilight, although the visible period also depends strongly on the geographical latitude of the observatory and the season. Orientation, size and the reflectivity of the mate- rials it is made of also play important roles in determining the brightness of a satellite as seen by astronomical observers.

Depending on the field of view of the telescope (the por- tion of the sky it observes), it might not be possible to avoid the negative impact of streaks of reflected sunlight on professional and amateur astronomical observations, particularly in twilight. Studies show that the extent of the impact depends on the telescope’s characteristics, science plans, and observing strategies. For instance, simulations that assume some 60 000 LEO satellites in realistic orbital configurations predict that Vera C. Rubin Observatory, hosting a large optical telescope with a wide field of view that is scheduled to commence operations in 2024, may be impacted by at least one satellite streak on up to 30% of observations at the beginning and end of each night

. Current Asteroid Population Models Suggest That

unknown potentially hazardous objects reside in greater numbers in locations that are accessible only through observations conducted during twilight, shortly after sunset or before sunrise. But it is exactly during twilight that the sky is most affected by LEO satellite constellations .

The combined effect of current satellites in orbit and

The Accumulation Of Space Debris May Already Be

causing an approximately 10% increase in the bright- ness of the night sky compared to natural levels . This exceeds the classification threshold established by the International Astronomical Union (IAU) in 1979, which should not be surpassed at large astronomical observatory sites. Consequently, the effective sensi- tivity of optical and infrared astronomical telescopes

On Earth May Have Already Decreased As A Result

of the unprecedentedly high activity in LEO. Any increase in space debris resulting from the grow- ing use of low Earth orbits also impacts astronomy.

Sunlight reflecting off debris brightens the night sky in a similar way to nearby city lights increasing the level of light pollution. Even small reflections from uncon- trolled objects in LEO will also cause false detections of transient events of astrophysical interest .

In addition to constellations of many smaller satellites, there is a growing interest in larger structures in

Space, Including Space-Based Solar Power Systems,

LEO space habitats, and larger satellites that con-

Countermeasures, All These Plans Would Result In

sources of even greater interference to astronomy. Unmitigated LEO satellite systems, with a steadily increasing density in the sky, are hence a threat to optical and infrared astronomy, and therefore to a

Radio Astronomy

As in the optical, satellites can also reflect radio emis- sions from the Sun or terrestrial anthropogenic radio signals towards radio telescopes, resulting in a reduced quality of observations and the loss of data. Far more significant, however, are the active radio transmissions by the satellites and the unnecessary leakage of radiation from on-board electrical equipment and electronics.

Even a perfect radio transmitter will always produce some emissions at frequencies outside the designated carrier signal's band. These can be reduced with filters or other techniques, but only to a certain level. Better suppression is usually tied to increased effort and thus costs. The same is true for the emissions of an antenna. While most of the power is beamed towards a certain area — the main beam — there is always a fraction of the power that goes into other directions (see Figure 2). This means that any transmitting satellite visible to a radio observatory will cause a signal with the potential to disrupt radio observations, even at frequencies other than the nominal carrier frequencies of the satellite. The strength of the detected signal depends on the pointing orientation of both systems. As they move over the sky, satellites can appear in the direct line of sight of a radio telescope, which will amplify their emissions by a huge factor compared to terrestrial transmitters, which are usually located at (or behind) the horizon. Furthermore, even in the most remote observing sites, far from terrestrial transmitters, satellites will still be high in the sky and will be a potential source of harmful interference. This results in distortions of astronomical measurements, from sub- noise-level features that can become apparent with long observing times (e.g., multi-year observations of the cosmic microwave background) to the loss or prevention of entire datasets. In extreme cases, spaceborne Earth or weather exploration radars can damage radio astronomical receiver systems . Satellite emissions can also mimic or interfere with observations of transient astronomical radio sources.

Large satellite constellations hence pose a challenge to the traditional operation of radio observatories. Many observations make passive use of a wide range of fre- quencies outside of those explicitly allocated for radio astronomy by international regulation. This includes bands explicitly allocated for use by satellite systems. Radio astronomy’s passive observation in these bands does not interfere with other uses of the spectrum. However, observations at these frequencies are affected by active transmissions by other users and there are no official rights of protection from interference from authorised services.

These opportunistic observations of cosmic radio sources in parts of the spectrum not allocated to radio astronomy are in many cases made possible thanks to national or regional protection zones, as well as geographical separation and natural shielding against terrestrial anthropogenic radio emissions. However, no existing or potential radio obser- vatory sites benefit from such protection zones in the case of satellite constellations, which are designed to transmit signals to everywhere on Earth. No international regula- tion exists to protect those zones or radio observatories outside the limited bands allocated to radio astronomy.

Furthermore, the aggregate unintended radiation or leakage radiation emitted by electronic systems on satellites is less regulated and can occur in bands allocated to radio astronomy. This leads to, at best, a significant loss in sensitivity and may severely affect certain ground-based radio observations .

Towards Intended Target Zone

Figure 2: Illustration of the illumination pattern of antennas of satellites in large constellations. The radiation is emit- ted not only in the intended direction, but also at lower power level in a much wider cone, at some level even in any direction. Since radio telescopes are, to some extent, also susceptible to radio emission from any direction, they detect emission from all satellites that are above the horizon. Image credit: IAU CPS/NOIRLab/SKAO.

Research Come From Ground-Based Observatories, As

do those used for planetary defence and a census of orbiting objects. In addition, major observatories are funded by international consortia; there are currently 40 large ground-based optical telescopes with primary mirrors between 3 and 11 metres in diameter, representing a worldwide investment. In contrast, there is only one telescope this size in space. Facilities in space cannot replace ground-based telescopes, owing to a wide vari- ety of prohibitive technical and cost challenges .

Astronomers Are Working To Mitigate Data Loss

due to satellite constellation interference in the optical/infrared and in the radio regime. Support is required for the development, deployment and maintenance of software packages to identify and mask out satellite streaks. Accurate predictions of the positions of satellites on the sky in a given direction and at a given time of night are essential. Those can accelerate identification of streaks in wide-field images without requiring a blind search of the full image. Some satellites will be so bright that they must be avoided on the basis of such predictions, in order to prevent the complete loss of an image. Development is required for applications to make access to operator-supplied position data routinely available to observatories. Coordinated observations of the apparent brightness of constel- lation satellites provide feedback to operators on the effectiveness of their efforts to dim the spacecraft and can feed into the predictions to provide both position and brightness as they would impact a planned obser- vation. The IAU Centre for the Protection of the Dark and Quiet Sky from Satellite Constellation Interference (CPS) provides the organising structure, but continuing support to observatories around the world is required.

Unwanted effects by human-made radio transmissions have affected radio astronomy since its inception. Accordingly, the astronomical community has always had to put significant resources into the implementation of various countermeasures, a long-standing, ongoing effort.

Three methods can be used. The simplest is to avoid the impeding signal. However, the possibility of minimising direct observations of satellites at radio frequencies by sophisticated observation strategies is more limited than in the optical regime, as radio antennas are susceptible to radio emission from the entire sky. Even if the sensi- tivity decreases rapidly beyond the pointing direction, it never vanishes. A second method, subtracting the interfering signal from astronomical observations, has been attempted, but with very limited success. To achieve good results, each interfering signal should be observed to a better accuracy than the astronomical source, which is virtually impossible. The third method is the removal of both the astronomical signal and the interfering signal when the latter occurs, and then restricting any analysis to the remainder of the data. The task is to identify the false signals from interfering sources, and several techniques have been developed. They can be slightly optimised if the satellite's position is known well enough, again an effort being undertaken in the scope of the CPS.

All mitigation methods have in common that the deg- radation of the astronomical signal cannot be avoided, ranging from an increase of the noise against which a signal needs to be detected, over false detection of astronomical sources, to the total loss of the observation.

In both the optical and the radio regime, further resources are needed by astronomers and the satellite community to develop new, and optimise existing, mitigation strategies and techniques so that they are affordable, accessible and effective. Many governments actively support the development of space activity broadly, including the use of satellite-delivered services, satellite launch and manufacturing and investments in ongoing scientific discovery in optical and radio astronomy. Considering the interdependencies of the space ecosystem and the consequences for astronomy and space sustainability generally, mitigation then becomes a whole-of-gov-

Ernment Balancing Challenge, And Ongoing Support

from government is necessary to find and implement effective solutions for all parties concerned to coexist.

Collaboration With Industry

Satellite constellation systems are being launched and deployed more rapidly than before, as a result of

Access To Launch Facilities, Competitive Market

forces, and international and national regulations

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

0.150

Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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