Jack Reacher and the Deployment of an Airbag

As teachers of introductory physics and engineering courses, we are always looking for ways to bring current events into our classrooms. We are especially interested in finding examples where basic principles of physics can be used to cast skepticism or validation on assertions made by celebrities, politicians, or professional athletes. In fact, over the past several years, various articles in The Physics Teacher have shown how a forensics-style reexamination of popular or historic events can be used as a motivation to introduce fundamental concepts to students in introductory physics and engineering courses.^1–9 These exercises afford students the opportunity to apply basic principles of physics to explore significant events or unsolved mysteries and potentially settle such debates. The literature also contains many examples of how television and motion pictures also provide fertile ground for classroom exploration of introductory-level topics and critical analysis of physics.^10–12 The lessons learned and best practices of these activities have been formalized into a pedagogy for teaching topics in physics, engineering, problem solving, critical thinking, and ethics.^13,14 As 2023 came to a close, another such example aired on the Amazon Prime smash (pun intended) hit series Reacher.

The show depicts the travels of the fictitious Jack Reacher, a former U.S. Army military police major, who uses his formidable strength and skills to mete out justice as he drifts from town to town across the Unites States. On December 14, 2023, season 2, episode 2 of the series premiered. Early in the episode, Reacher spots a potential villain sitting in a parked Ford Taurus Interceptor. To capture the villain, Reacher quickly devises an ingenious plan (see Fig. 1).¹⁵ Reacher approaches the front of the parked car and kicks its front grille slightly above the Ford logo. Instantly, the airbag deploys, striking the villain in the head. The rapid inflation of the airbag renders the villain delirious, allowing Reacher to apprehend him. This scene immediately grabbed our attention—could a human being really kick a car with enough force to deploy its airbag? Clearly, the topics of collisions, impulse, and force belong in a classical mechanics course, but can we provide enough background information to our students that they can determine whether this scene is realistic? Thus, the purpose of this article is to present a unique teaching opportunity for instructors to bring current events into their classrooms and to have their students use basic principles of physics, covered in an introductory classical mechanics course, to cast doubt on the events portrayed in a contemporary hit television series.

The term “airbag” is a misnomer since these devices are not bags and do not hold air. Instead, they are carefully shaped and vented nylon-fabric cushions that fill with nitrogen or inert gas and lubricants.¹⁶ When an airbag deploys, a diagnostic unit triggers an electric charge that heats up a filament, which in turn ignites a chemical solid contained in a small tray (approximately 50 g in the driver side tray and approximately 200 g in the passenger side tray). In the past, nitrogen gas was generated by the rapid decomposition of sodium azide. Recently, sodium azide has been replaced by less toxic gas-generating materials. To assist in the opening of the airbag, nontoxic lubricants, such as talcum powder or starch, are also released. The “smoke” you may have seen in a vehicle after an airbag demonstration is the lubricant. Inflation occurs in 50 ms, but even as it is filling with gas, an airbag is already venting, through small holes, so that if a human strikes the airbag, they are not hitting a fully inflated, hardened cushion. Additionally, as the chemical reaction occurs, the gas generated by the reaction is hot, so car occupants may suffer minor burns. In general, airbags usually hold 60–80 L. Finally, at approximately 200 ms after impact, the airbag deflates through vent holes or the cushion’s porous nylon fabric. Interestingly, the entire process of deployment, inflation, and deflation is over in less than 1 s.

The patent for the first airbag was issued on August 18, 1953, to American engineer John Hetrick for “a safety cushion assembly for automotive vehicles.” Throughout the 1970s, General Motors trial-tested airbags as a supplemental restraint system, but the devices were poor-selling add-ons, and the idea was quickly abandoned. Airbags were first introduced on a large-scale basis in the late 1980s. By 1990, all new cars were required to have either a driver’s side airbag or an automatic seat belt. Prior to 1994, airbag deployment systems relied on mechanical sensors. The Rolamite model by Sandia National Laboratories is the prototypical such sensor.^17,18 In this sensor, a metal roller was held in place by a spring or magnet. When a crash occurred and the sensor was subjected to a certain threshold force, the spring or magnet could no longer hold the metal roller in place. The roller would translate to a point at which it would make contact with an electrode and send a signal for deployment of the airbag. These early airbags were inaccurate and misinterpreted minor collisions, such as hitting a pothole, as striking another automobile. Thus, the scene from the Reacher television series may well be realistic had the automobile in question been a pre-1994 model. Also, these airbags frequently deployed with a significant delay after collision. Federal regulations now require that all cars manufactured on or after September 1, 1997, must be equipped with driver and front-passenger airbags.¹⁹ 

Modern airbags use a sensing and diagnostic module (SDM) (sometimes called the airbag control module), activated when the vehicle’s ignition is turned on and usually mounted near the center dashboard of the vehicle, to evaluate a continuous stream of displacement, velocity, and acceleration data from multiple crash sensors. Normally, the crash sensors are mounted at the front and sides of the perimeter of the vehicle and collectively provide input to the SDM. This gives rise to the misconception that a blow to the center grille of a vehicle will deploy its airbags. The misconception comes from the notion that the deformation (or “crumpling”) of the front of the vehicle is what deploys the airbag, rather than the vehicle’s changes in acceleration. The crash sensors are not mounted to the grille or the bumper cover. If they were, one could more easily imagine that a kick or “fender bender” could generate a signal to deploy the airbag. Instead, the crash sensors are mounted behind the bumper, so that the entire car must be accelerated to produce the necessary signal to deploy the airbag. The crash sensors are micro-electromechanical systems (MEMS) with piezoelectric or variable-capacitance accelerometers. The SDM evaluates data from these sensors and determines if a crash has occurred in order for the airbags to deploy—the SDM decides if a crash has occurred, not the sensors. Deploying the airbags is denoted as the “fire” command. SDMs use complex algorithms to make fire/no-fire decisions based on crash severity related to the instantaneous acceleration of the vehicle. “Smart” airbags can alter their deployments and use a multistage inflation process based on the occupants’ belt status, seating position, crash severity, and other factors.¹⁸ A manufacturer, for example, may choose not to deploy the passenger airbag if no occupant is seated in the passenger seat.²⁰ Not only do the algorithms for airbag deployment during a collision depend on vehicle and airbag module specifics, but because of the proprietary nature of automobile manufacturing, they are intellectual property and depend on patents. However, in the next section, we describe how a range of frontal barrier impact speeds and corresponding acceleration thresholds for deployment can be developed for use in the introductory physics classroom. Finally, airbags are not designed to activate during sudden braking or while driving on rough or uneven pavement. In fact, the maximum deceleration generated in the severest braking is only a small fraction of that necessary to activate the airbag system.²¹ 

When discussing airbags with students, two approaches can be implemented to determine whether the Reacher television scene described in our opening remarks is realistic. Both approaches reduce the airbag deployment criterion to a simple introductory-level physics problem, ideal for a classical mechanics course:

The first approach uses the guidelines set forth by the National Highway Traffic Safety Administration (NHTSA). According to the NHTSA, “Airbags are typically designed to deploy in frontal and near-frontal collisions, which are comparable to hitting a solid barrier at approximately 8 to 14 mph,” if the driver is not wearing their seat belt.²¹ The threshold speed is increased to 16 mph if the driver is wearing their seat belt (the SDM can indeed detect if the seat belt is engaged). The NHTSA’s guidelines reduce to a typical impulse problem covered in a classical mechanics course. We can simply determine if our television scene is realistic by calculating the average force exerted by a solid barrier in stopping a car and equating such a force to that exerted by Jack Reacher’s foot. We then ask ourselves, “Is a human capable of such a force?” Reframing the problem as we would in an introductory physics or engineering class, the airbag deploys upon detection of a high-impact, front-end collision while traveling at an initial speed of v₀. After colliding with a solid barrier, the vehicle’s final speed is v = 0. The mass of the car and occupant have a combined mass of m_total. The mass of a Ford Taurus Interceptor is 1830 kg, while we can approximate the mass of a typical villain to be 90 kg. The final piece of necessary information is how much time the barrier and car were in contact. Since the airbag deployed, it must have experienced a collision comparable to that of hitting a solid barrier at a minimum of 8 to 16 mph. Such time intervals can be well approximated since research demonstrates that for low-speed collisions (i.e., v < 35 mph), the impact duration is between 0.14 and 0.195 s, while for higher speeds, the impact duration is closer to 0.12 s.¹⁸ Equating the impulse to change in momentum, we find that F_avg = Δp/Δt, or F_avg = m_total(v – v₀)/Δt. Substituting the range of initial speeds and range of low-speed impact durations into this expression, we determine a range of average forces as 35.2 kN < F_avg < 98.0 kN.

The second approach uses the guidelines set forth by the Collision Safety Institute, an independent traffic collision consulting organization, which states that airbags deploy when two consecutive acceleration pulses less than approximately –1.0g for smaller vehicles, or less than approximately –2.0g for larger vehicles, occur within a short period of time (10 ms).²² In short, a jerk has to occur. Let’s simplify our discussion and see if Reacher is even able to generate one of the necessary accelerations. Again, reframing the television scenario as a typical introductory physics problem—but this time as a second law of motion problem—we can determine if the television scene is realistic by calculating the average force needed to produce an acceleration between 1g and 2g on a 1830-kg Ford Taurus Interceptor carrying a 90-kg villain. We determine that Jack Reacher would need to exert an average force in the range 18.8 kN < F_avg < 37.6 kN.

Reviewing our calculations, we see that in order to deploy the airbag, Jack Reacher would need to exert a force in the range 19 kN < F_avg < 98 kN. Note that our calculations do not take into consideration that most of the force exerted on the front grille of the car would first deform the grille (i.e., “crumple” it) or roll the car before actually accelerating it. We now address the question of whether a human is capable of kicking a car with such a force. An average adult can kick with a force of approximately 1 kN; however, according to the mixed martial arts channel, Edson Barboza, a highly trained martial artist, is arguably the most powerful kicker in the world at this time and can kick with up to 9 kN of force.²³ Assuming Jack Reacher is capable of equally powerful kicks, his kick to the front of the villain’s car is at most capable of half of the force needed to deploy its airbag. We conclude that the events portrayed in the hit television series are simply impossible. An additional exercise to undertake with the students, and one that makes the analysis more interesting, is to consider the force required to break a person’s femur … or tibia … or to perhaps induce a compressive ankle fracture. In other words, we have been focusing on whether or not a person is capable of generating a kick powerful enough to deploy an airbag, but one might also wonder if bones in the human body are indeed capable of sustaining the forces necessary to generate the accelerations involved in deploying an airbag. Of course, so many variables are involved that giving a meaningful answer is difficult—a lot depends on the bone itself, its position in the body, its health, the angle of attack of the force, etc. However, a study by the Association for the Advancement of Automotive Medicine found that a force of 8.0 kN resulted in a 50% probability of compressive foot-ankle fracture.²⁴ Given our range of calculated values for F_avg, we can conclude that Jack Reacher not only would have failed to deploy the airbag in the scene under consideration, but he more than likely would have limped away from the villain with a broken ankle. A few other considerations to discuss with students include:

1. As noted earlier, the airbag systems only become active when the vehicle’s ignition is on, so if the vehicle is parked and the ignition is off (as it appears to be in the scene), its airbags will not deploy—another impossibility of the show!

2. Because the SDM decides if a crash has occurred based on the acceleration of the vehicle, front-end damage is not a good indicator of whether an airbag should have deployed. For example, according to engineer Sean Haight, PhD, Editor of Collision Publishing, an object protruding from the roadway surface may strike the undercarriage of a vehicle and not cause any visible damage to the front grille of a vehicle yet may still decelerate the car enough to deploy its airbag.

3. Most airbags are designed to automatically deploy in the event of a vehicle fire to ensure that the fire does not cause an explosion of the entire airbag module.

4. Front airbags are not designed to deploy in side impact, rear impact, or rollover crashes.

5. Safety belts must always be worn, even in airbag-equipped vehicles. Airbags are supplemental restraint systems and are not meant to replace a vehicle’s primary restraint system—seat belts. Seat belts are the most effective restraining device to protect occupants of a vehicle in a collision. Statistically, when used in tandem, the airbag and shoulder belt reduce serious injury for drivers by 50%, while the effectiveness of the airbag alone is only 30%.²⁵ 

Gregory A. DiLisi earned his BS from Cornell University in applied and engineering physics and his MS and PhD from Case Western Reserve University in condensed matter experimental physics. He is currently a Professor of Education at John Carroll University. His recent research focuses on using case studies as a pedagogical approach to teaching introductory physics. [email protected]

Richard A. Rarick earned his BS from Cleveland State University in electrical engineering and his MS from Cleveland State University in applied mathematics. After working in the private sector in the field of digital signal processing and control theory, he is now a member of the faculty at Cleveland State University, specializing in electronics, control theory, electromechanical energy conversion, and embedded systems.