WHY PASSENGER SURVIVABILITY CANNOT BE COMPLETELY ASSURED IN HEAD-ON VEHICLE IMPACTS AT CURRENT LEGAL SPEED LIMITS

Gustavo Zini School of Engineering – University of Buenos Aires Argentina Paper Number 09-0210

ABSTRACT weeks in hospital after severe crashes and many will never be able to live, work or play as they used to do. “This impact is intended to represent the most Current efforts to address road safety are minimal in frequent type of road crash, resulting in serious or comparison to this growing human suffering”. (World fatal injury. It simulates one car having a frontal im- Health Organization, [1]) pact with another car of similar mass”. (EuroNCAP frontal impact procedures). Safety first. It can be argued that human bodies are poorly No one doubts this should be the ground rule in prepared to support direct hits from hard objects. On every aspect of automobile transportation. Yet, it is the other hand, there are proofs of resistance to very important to meditate on this: is it possible to, always, high decelerations, provided they are held for ex- put safety first? tremely short periods of time. Yet, in front-to-front It is understood that the question cannot be an- vehicle impacts, a third phenomenon that can be swered simply, and will not be responded here. What compared to direct hits takes place: instantaneous will be regarded instead, is if putting safety first is changes of speed. applicable to head-on collisions. On top of that, and Most modern vehicles are nowadays tested thor- deeming that head-on impacts are intended to repre- oughly to evaluate their capability to protect their sent the most frequent type of road crash resulting in occupants in case of frontal impacts. But these tests serious or fatal injury, some reasons will be high- are performed under the premise that the vehicle is lighted, explaining that survivability cannot be com- having an impact with another car of similar mass pletely assured when mentioned impacts take place. that is traveling at the same speed. These conditions To begin with, it can be said that when a collision lead to an incomplete analysis of the complex phe- occurs —no matter if is is a head-on one, or other— nomena that take place in a real front-to-front vehicle passenger survivability depends on how kinetic en- since it is statistically improbable that a vehicle will ergy is managed. Speed and mass of the colliding crash with another one that has both the same mass vehicles will determine how much kinetic energy will AND speed —and in this scenario, the vehicle with be transformed during the phenomenon. And depend- the lesser kinetic energy will unfailingly suffer an ing on the way in which the structure of the vehicle instantaneous change of speed—. absorbs this kinetic energy, the car will deform and This paper will confirm the lastly mentioned issue passengers will be exposed to potentially dangerous using basic physics models (namely mass-spring directs impacts, or deceleration phenomena. models), and will discuss the the way of combining As it will be explained with more detail later on, it structural integrity and occupant restraints to ensure can be argued that direct impacts produce more dam- the maximum possible protection. This will be done age to human organs than high levels of acceleration from a general and synergistic point of view, and will during extremely short periods of time. Moreover, a point out some aspects that should be developed thor- third event can harm passengers in a manner that is oughly within the corresponding settings and using closer to direct impacts than to extreme decelerations: appropriate resources. instantaneous changes of speed. Unfortunately, at current speed circulation, and with the type vehicles that are used the three mentioned events occur in INTRODUCTION most car impacts. That is to say passengers are com- monly exposed to direct impacts, instantaneous “Every day thousands of people are killed and changes of speed, and high levels of decelerations. injured on our roads. Men, women or children walk- ing, biking or riding to school or work, playing in the It can be argued that there are certain procedures streets or setting out on long trips, will never return that can be implemented to avoid both direct impact home, leaving behind shattered families and commu- and potentially deadly decelerations, specially under nities. Millions of people each year will spend long the circumstance of impact against direct objects. On

ZINI 1 the other hand, it can be proved from a Physics points Among many others, the 1934 Chrysler Airflow of view that there is no way to avoid that one of the case can be mentioned. It was full of engineering in- two vehicles of a head-on impact suffers an instanta- novations —an aerodynamic singlet-style fuselage; neous change of speed. So, if this is the case, and steel-spaceframe construction; near 50-50 front-rear considering what experts in the biomechanics of weight distribution; light weight—. However, as it trauma know about injury mechanisms: was, the car's dramatic streamliner styling antago- ➡ is it possible to design automobiles in order to nized Americans on some deep level, and sales were avoid exposing passengers to mortal instantane- abysmal. ous changes of speed during head-on collisions? ➡ if this is not situation, shouldn`t speed limits be lowered to assure survivability?

PUTTING SAFETY FIRST “And, by the way, there is only one goal, no mat- ter what the company”. (Eliyahu Goldratt, [2]) The Great God Car. It can be said that an automobile is a complex product for a variety of reasons. Firstly, it is the result of more than a hundred years of technical evolution, yet in many aspects resembles closely the cars that were sold at the beginning of the 21st century. Re- garding road safety, it is true that nowadays cars could be called safer than their predecessors, but they Figure 1. Many experts agree that the failure of Ford’s make allow drivers to travel a lot faster, and passengers are Edsel was a combination of bad marketing and deficient styling. involved in impacts with much higher kinetic ener- Photo source: Internet. gies to manage. Therefore, it can be argued that pre- sent automobiles are still not able to protect their oc- cupants in order to assure their survivability in the Lastly, every time an automobile company event of a road impact. launches a new model it spends a enormous amount Secondly, automobile users do not, in general, put of financial resources, in numbers ranging from few safety first. Over the years drivers proved to demand to several billion dollars, and there is little margin for cars that have grown faster and more powerful, and mistakes. Radical innovations are seldom understood there are very few potential owners which would re- or welcomed by mass consumers, and timing plays a fuse to drive the quickest Ferrari or Lamborghini if vital role in the success of any extreme modification they were able to pay for —and maintain— one of in a car —’ EV1 failed electric vehicle these fantasized automobiles. Then, there is the can be mentioned as an example of an audacious Peltzman effect which is the hypothesized tendency of launch made 15 years ahead of its time—. people to react to a safety regulation by increasing Before concluding this section, an appraisal about their risky behavior. For example, if some drivers an Eugene O’Neil’s play is presented. In “The Great with a high tolerance for risk who would not other- God Brown” the characters wear masks which serve wise wear a seatbelt respond to a seatbelt law by driv- two purposes: they help the characters hide and thus ing less safely, there will be more total accidents. protect their vulnerable inner selves while, at the Thus, in many cases, the safer the car, the reckless the same time, allowing them to project pleasing public driver, the fastest the impacts, the bigger the necessity images in an attempt to restore their confidence in to add safety devices, the heavier the cars, the higher themselves. Similarly, there are two key issues auto- the energies involved in road accidents, the more mobile generally hide behind their mask of freedom, dangerous the impacts, and so on. individuality and prosperity: damage to Earth’s eco- Thirdly, in the automobile world, beauty does system, and the tragedy of everyday road victims. matter. Many engineers may allege a style designer’s These two issues are way too complex to address in tyranny when arguing about who’s the one that makes this paper, yet it is the intention of this paper to zero the core decisions about the product. Nevertheless, in the fact that there are still some major improve- the truth is that there are a lot of good automobile ments to be introduced to enhance passenger protec- which were rejected by consumers simply because tion in the event of a road impact. And while for the they were not appealing enough. last few years many concept cars which focused on fossil fuel-consumption reduction were presented, the

ZINI 2 last —and arguably one-time-only from a major car INJURY MECHANISMS manufacturer— concept car which pivoted on road safety (the Volvo SCC) was introduced as far behind “The current state of the field of biomechanics of as 2001. trauma can be compared to the state of the celestial mechanics before Kepler: it is composed of a multi- Bottom line, putting safety first in automobile tude of measurements and experimental data that design is no easy target. Some reasons that explain lacks in unifying theories that would be able to pre- this were shown above, yet need more space to be dict the outcome of a new situation. In this way, the thoroughly developed. Therefore, in this paper a se- alleged tolerances of the human body are based al- ries of steps that could eventually lead to ensure the most exclusively on empiric results, or are elaborated maximum possible protection to passenger in head-on from tests using dummies or other mechanical devices collisions, taking into account that safety should be which do not represent accurately the response that a put first. This will be started by highlighting the rea- human body would show to the given situation. In the sons why car design should not begin by thinking better of cases, they do represent it only for a certain about exterior design: percentage of the population”. (Alvin Hyde, [3]) The more you know, the more you realize how much you don’t know. The incredible and enormous biodiversity of the human beings is of such extent that the experts have not been able yet neither to understand completely how injuries happen nor to determine with precision the biological tolerance to direct impacts and accel- eration phenomena. Therefore, in this paper only an overview to the topic will be presented, aimed at making a general approach to some relevant aspects for the upcoming discussions. On top of that, and for better following of the arguments of this paper, the mentioned approach is shown in Appendix I, and its conclusions are presented in the following figure:

Figure 2. Sketch of a concept car. Photo source: Internet. type of event injury potential

very high accelerations And why the following should be the first thing de- during very short periods of signers think about when they start designing a new car: time (no direct impacts)

instantaneous changes of speed

direct impacts (specially to head, neck, chest and abdomen)

Figure 4. Alleged risk factors according to their injury potential in a road crash.

This means that the primary thing to avoid in a road crash is direct impacts to the human body. Al- Figure 3. Spring (during an impact, the structure of an auto- though impacts to the head, neck, chest and abdomen mobile behaves as an inelastic spring). are the most harmful, it could be said that any part of Photo source: Internet. the body must be protected from them. Then, once this has been assured, the structure of the automobile should prevent passenger being exposed to dangerous

ZINI 3 instantaneous changes of speed. Lastly, assuming place phrase, but it is impossible to design a structure neither direct impacts nor unsafe instantaneous for an automobile that should keep deceleration rates changes of speed took place, deceleration rates should within human tolerance if there are no standards to be kept under human resistance levels. begin the calculations. And it can be argued that this At this point, two key issues arise: standards regarding human tolerance to deceleration either do not exist, or are not publicly known. ➡ what is the limit in which an instantaneous change of speed becomes unsafe? Therefore, on behalf on the object of this paper, some standards will be set. Yet, this will be done in a ➡ which deceleration rates can be tolerated for the very approximative way, considering only partial in- vast majority of the population? formation from tests held at the Holloman Air Force Furthermore, in a road crash there is commonly a Base and at the Aero Medical Laboratory of Wright- combination of direct impact and acceleration phe- Patterson Air Force Base [5]. These tests allege that nomena. Most body organs are viscous and gelati- human being could tolerate the following: nous, so direct impacts generate relative movements ➡ 12 G during 240 seconds (Wright-Patterson). and consequent deceleration processes. On the other ➡ 15 G during 4 seconds (Wright-Patterson). hand, restrain devices apply a certain amount of force in localized parts of the body, as in the case of the ➡ 25 G during 1,1 seconds (Holloman) thin strip of the seatbelt fastening the chest. These ➡ BRIEF46 G during ARTICLE 0,2 seconds. (Holloman) restrain actions combine a deceleration process with a determined degree of pressure that, depending on the This setTHE of AUTHORdata can be transformed into a curve by severity of the road crash, can lead to direct impacts. extrapolating the potential tendency of the group of points, as shown in this graphic: Hence, and considering all of the above, a brief review of the human tolerance limits —both to decel- eration and instantaneous change of speed— will be m1x1!! = k1(x2 x1 l1)(1) approached. 5,0 − − (2) 4,5 4,0 m2x2!! = k1(x2 x1 l1)+k2(x3 x2 l2)(3) − 3,5− − − − DECELERATION RESISTANCE(4) 3,0 2,5 m x!! = k (x x l )(5) “There are only two models [male and female] of 3 3 − 2 3 − 2 − 2 the human body currently available,(6) with no immedi- 2,0 ate prospects of a new design; any finding in this re- 1,5 (7) search should provide permanent standards”. (John 1,0 0,5 Stapp, [4]). time of exposure [seconds] π m (8) 0 t = 2 K Every day, around the world, tenths of thousand 10 20 30 40 50 60! 70 80 90 100 (9) human beings are exposed to decelerations that pro- decceleration [G] voke them either fatal or permanent injuries. 2 testedK on human beings (10) aavg = vo On the one hand, there is little experts know about π !potencialm tendency human response to high levels(11) of deceleration during short periods of time. Appendix II, gives some gen- Figure 6. Supposed human deceleration resistance based on a small number of empirical tests. K eral details about deceleration resistance(12) based on the amax = vo consulted references, focusing on which directions ! m and senses result in more damage(13) to human organs. On the other hand, almost everything expert do know aavg + amax (14) The above graphicdec = present the fact that the maxi- about deceleration resistance comes from NASA re- mum time of exposure decreases2 exponentially as search done at the U.S.A. Holloman(15) Air Force Base. deceleration increases. If a function to relate maxi- And most of the information is derived from tests mum time of exposure and deceleration2,5 was to be mte = 700dec− made on , a career U.S. Air Force officer, stated, the following expression could describe it: USAF and pioneer(16) in studying the ef- 2,3 fects of acceleration and deceleration forces on hu- mte = 1000dec− (i) mans. His above mentioned words declare a partial (17) truth —the one being that there are only two models where mte = maximum time of exposure [seconds] of the human body— and a landmark axiom —the dec = deceleration [G] one being that standards should be provided—. And why the latter is so? Because in the world of Nevertheless, it is crucial to understand that the engineers, in the world of design, standards are vital. above function is base on a very small number of The recent sentence can be considered a common-

1 ZINI 4 BRIEF ARTICLE

THE AUTHOR

m x!! = k (x x l )(1) 1 1 1 2 − 1 − 1 (2)

m x!! = k (x x l )+k (x x l )(3) 2 2 − 1 2 − 1 − 1 2 3 − 2 − 2 (4)

m x!! = k (x x l )(5) 3 3 − 2 3 − 2 − 2 (6) (7) π m (8) t = 2 K ! (9) empirical tests, and that the2 personsK involved in the car passengers will continue to be exposed to decel- (10) trial do not necessarilyaavg = representvo the response other eration rates under which some will survive un- π m human beings could produce, !so a correction will be harmed and others will not. (11) made to the curve. This modification is done under Lastly there is another delicate issue that arises the premise that the vast majorityK of human beings when considering deceleration resistance. On the one (12) will resist a determinateamax deceleration= vo for an amount of ! m hand, testing on human beings can be seriously mor- (13) time that is 1/2 the one indicated indicated in Figure 6 ally questioned. Before John Stapp’s test of Holloman for the lowest decelerations, and 1/4 of the indicated aavg + amax Base, a series of experiments were performed with (14) ones for the highestdec = decelerations. This transforms monkeys, some of which died during them. For Stapp expression (i) into the following:2 (15) himself the experience was tough: the safety harness 2,5 painfully dug into his shoulders at low magnitudes; as mte = 700dec− (ii) decelerations got larger, the harness cracked his rib; (16) he suffered a number of concussions, lost dental fill- where mte = maximum time of exposure2,3 [seconds] ings, broke his wrists a couple of times, and suffered mte = 1000dec− dec = deceleration [G] a contusion to his collarbone; at decelerations greater (17) than 18 G, when facing backward, vision became Thus, finally, a new curve can be plotted, this time blurry and eventually white as the blood in the eyes considering determinate safety coefficients so that, at was forced into the back of his head; when facing least in what regards this paper, a design threshold forward he experienced red outs, as blood was forced can be outlined: against his retinas breaking capillaries, hemorrhaging, and pulling his eyelids up [6].

0,10 0,09 1 0,08 0,07 harmful 0,06 deceleration 0,05 rates 0,04 0,03 safe 0,02 deceleration 0,01 rates time of exposure [seconds] 0 10 20 30 40 50 60 70 80 90 100 deceleration [G]

deceleration resistance potencial tendency design threshold

Figure 7. Supposed human deceleration resistance based on a Figure 8. John Paul Stapp in the rocket sled at U.S.A. Hollo- small number of empirical tests, corrected by safety coefficients. man Air Force Base () Photo source: Internet.

From now on in this paper, certain deceleration rates will be considered safe, and other will be con- On the other hand, though, and as said in the be- sidered harmful —and consequently avoidable—. ginning of this section, thousands of experiments are Just to mention an example, it will be deemed that a being held everyday in roads around the world, which 50 G deceleration can be safely undergone by a hu- can be also seriously morally questioned. That is to man being for a period of time of up to 0,04 seconds. say, if cars are designed without a proper knowledge Similarly, a 50 G deceleration will produce serious or of human resistance to decelerations, isn’t it the same fatal damage if exerted upon a person for more than as exposing passengers to quotidian experiments 0,04 seconds. It is important to notice that John Stapp when they are subjected to potentially harmful events was able to support 46 G during 0,2 seconds (5 times in case of an impact? more than the design threshold), but the limit was set To conclude, automobiles should not be designed considering the vast majority of automobile passen- without taking into account a design threshold for gers will support it. As it can be seen, this is a delicate deceleration resistance, and it is the opinion of this issue. For if tests are not performed to deepen the paper that this lack of information should be filled knowledge either designers should consider large with accurate and thorough testing. safety coefficients to cover the gap of uncertainty, or

ZINI 5 HUMAN RESISTANCE TO INSTANTANE- speed. Hence, the few examples that can be found to OUS CHANGE OF SPEED begin understanding human resistance to changes of speed should be found outside the world of everyday "If a virtually safe system is going to be designed, automobiles. either the harmful event must be eliminated, or it should not reach the limit of the human tolerance. In Regarding this, two paradigmatic cases in For- the Vision Zero concept, it is assumed that accidents mula 1 races that can be mentioned. The first one is cannot be totally avoided, hence the basis for this Ayton Senna’s crash, back in 1994, which lead to his concept is built around the human tolerance for me- death in the San Marino Grand Prix. chanical forces”. (Sweden’s “Vision Zero”, [7]) An instantaneous change of speed can be com- pared to a direct impact. This is so, because in the case of a road impact, when passengers are exposed to changes of speed, the are pulled in the direction of the change of speed by the restrain devices. So, bottom line, a violent change of speed will violently pull passengers by means of the safety belts, impacting their chests. On top of this, most organ fluids will also suffer instantaneous changes of speed thus potentially damaging the or- gans. Finally, the head will generate relative move- ments that will not only affect the brain, but also the neck and spine. Therefore, the problem is to find which is the limit for human tolerance to a change of speed. Neverthe- Figure 10. Example of deadly injuries caused by instantaneous less, it can be stated that this is harder to acknowledge change of speed (1994 Ayrton Senna Formula 1 accident). than deceleration resistance. On the one hand, a Photo source: Internet. change of speed in real-life road crashes is a phe- nomenon that has to be studied in a three-dimension space frame. The other one is Robert Kubica’s crash in the 2007 Canadian Grand Prix.

Figure 9. Real head-on collision expose passengers to 3D movements. Photo source: Internet. Figure 11. Example of survival after a high speed impact under the protection from direct impacts and under safe instantaneous change of speed (2007 Robert Kubica Formula 1 accident). On the other hand, there are very few cases in Photo source: Internet. which a change of speed happens without severe cockpit deformation which exposes passengers to direct impacts. In fact, vehicles are being designed It is important to highlight that although the speed with crumple zones that look for avoiding changes of at which Kubica crashed the concrete wall at Canada

ZINI 6 was similar to the one of Senna, Kubica crashed in a mentioned improvements allow drivers to travel different angle than the first one. While Senna im- faster, and passengers get involved in impacts with pacted almost perpendicularly to the wall, Kubica did higher kinetic energies, thus with greater damage it angularly, thus suffering a lesser change of speed. potential. As a result, Kubica recovered from the injuries in Moreover, the the tree main improvements in im- around two weeks. pact protection have still some development to per- These two cases show that when there is no de- form. For the first two which were mentioned (seat- formation of the cockpit, a human being can resist an belts and airbags) the pending tasks is to adapt the instantaneous change of speed, given certain condi- response of these devices to the actual crash and not tions which are, in general terms, unknown. to an average previously defaulted one. That is to say, when an airbag actives it does not take into account the position of the passenger, nor its weight or size, nor —and most important of all— the speed of the GENERAL GUIDELINES TO ENHANCE SUR- impact. It just deploys with a certain force that will VIVABILITY IN ROAD IMPACTS protect an average passenger in an average impact, “The consumer's expectations regarding automo- but this fact presents two problems: if the impact is tive innovations have been deliberately held low and slower than the average one, the force of the deploy- mostly oriented to very gradual annual style ment will outweigh the force of the human being im- changes”. (Ralph Nader, [8]) pacting the airbag, thus will have the potential to harm the passenger; in the contrary case, the airbag Sir Francis Bacon once said: “He that will not will not absorb the forward movement of the passen- apply new remedies must expect new evils; for time is ger thus performing an incomplete function. Simi- the greatest innovator”. larly, the seatbelts should adapt their reaction to the The mentioned above Raplh Nader’s words were same parameters than airbags. pronounced several decades ago. Since then automo- biles grew safer. A lot safer. Specially in impact pro- tection, where the main improvements had been the following three: ➡ widespread compulsory use of seatbelts. ➡ widespread provision of airbags (not in every country). ➡ redesigned crumple zones that enhanced passen- ger and pedestrian protection in impacts up to 64 km/h. Even so, it can be highlighted that seatbelts were introduced in the 1950’s, that airbags were introduced in the 1970’s, and that protection in impacts up to 64 km/h seems to have reached a point were no major improvements are produced. In this regards, Michiel van Ratingen, Secretary General of EuroNCAP ex- Figure 12. In order to successfully complain its target, and air- plains why protection ratings are being modified “We bag should know the position, mass an size of the passenger, and also the speed of the impact, and be capable of deploy in a differ- acknowledge that this new rating scheme is more ent way according to the actual crash conditions. challenging in some areas, but it does offer lead time Photo source: Internet. to manufacturers in others. We call this ‘smart pres- sure’. We need to raise the bar, but consider the cur- rent environment and give carmakers the opportunity to implement the best safety features into their vehi- Now it is time to assess the third of the three ma- cles. These manufacturers have shown that they are jor improvements mentioned before: the modification meeting all of our early targets. We look forward to of the crumple zones of automobiles. And the focus seeing where they go next”. will be made in head-on collisions, since they are intended to represent the most frequent type of road In other words, since the 1970’s, there hasn’t crash, resulting in serious or fatal injury. The alleged been any milestone breakthrough in impact protec- improvements base on the fact that in NCAP-type tion. On the one hand it can be said that automobiles tests, newly designed automobiles keep getting better are less liable to get involved in a road crash due to scores. But the problem is that, although the NCAP great improvements in safety devices that prevent frontal test is designed to simulate one car having a impacts from occurring. But on the other hand, this

ZINI 7 frontal impact with another car of similar mass, it is pit should be rigid enough to avoid deformations that statistically improbable that a vehicle will crash with would eventually lead to direct impacts to passengers. another one that has both the same mass AND speed And after this is achieved, there is still the target to —and in this scenario, the vehicle with the lesser ki- prevent the cockpit from undergoing instantaneous netic energy will unfailingly suffer an instantaneous changes of speed, or potentially harmful decelera- change of speed—. tions. And as stated before, instantaneous changes of The objective of the following two sections is to speed are an unwanted phenomenon when it comes to determine wether the latter is possible or not. protecting passengers from getting hurt. So a key issue arises, is there a way in which automobiles can be designed to avoid potentially harmful instantane- ASSURING SURVIVABILITY FOR ONE ous changes of speed from happening? Before an- VEHICLE, FIXED OBJECT COLLISION swering this, and considering injury mechanisms, the principles of impact survivability will be stated: “A more synergistic view or approach to motor vehicle safety design aspects is needed”. (Malcolm ➡ maintain the structural integrity of the occu- Robbins, [9]). pants' vital volume, assuring enough survival space to avoid any direct impacts. Firstly, a model for addressing deceleration issues ➡ avoid the penetration of objects to the occupants' will be adopted. In order to do so, a series of simplifi- vital volume. cations should be considered, namely: one dimension movements; reference of coordinates in the center of ➡ avoid any contact with the potentially dangerous mass of the target vehicle; and the use of a system surfaces of the interior of the vehicle. formed by a single mass and an inelastic spring ➡ absorb the whole kinetic energy both of the ve- which, according to what many experts agree, is the hicle and of the occupants to avoid or instanta- model for the description of the behavior of an auto- neous changes of speed, maintaining the decel- mobile in a crash that suits properly the purpose of eration within safe levels. this work [10]. The modelm1x1!! =fork 1a( xsingle2 x 1vehiclel1)(1) crash- ing into a fixed object can be described− as− follows: To demonstrate if this premises can (2)be fulfilled, a special type of vehicle will be used: m2x!! = k1(x2 x1 l1)+k2(x3 x2 l2)(3) 2 − − − − − (4) m1x!! = k1(x2 x1 l1)(1) 1 m x!! = k (x x l )(5) − − 3 3 − 2 3 − 2 − 2 (2) (6) m x!! = k (x x l )+k (x x l )(3) deformable2(7) 2structure− 1 2 − 1 − 1 2 3 − 2 − 2 (4) (maintain deceleration π m within human(8) tolerance) t = m3x3!! = k2(x3 x2 l2)(5) 2 K − − − ! (6) (9) (7) 2 K (10) a = v π m avg π o m (8) vtO1= ! (11) 2 K m ! (9) 1 K undeformable(12) cockpit amax = vo 2 K m (10) (avoid direct impacts) a = v ! (13) avg π o m k!1; l1 (11) 2 2 (1 + )vo (14) Figure 14. Adopted model for onedec vehicle= collisionπ against a fixed object. K 2√l (12) amax = vo (15) ! m (13) m Figure 13. Proposed type of structure to avoid (16)direct impact to Secondly, and2 as 2 a spring-massA = systemsvo behaves (1 + )vo K passengers, and maintain(14) deceleration within human tolerance. dec = π ! in a harmonic way,√ the equations that will be used (17) from now on will2 bel presented: (15) (18) The above type of structure does not exist in the m vo 2 (16) (19) A = v ⇒ K =( ) m (iii) real world of automobiles. It is just a theoretical con- o K A figuration considered to fulfill the above premises. ! (17) (20) Because if direct impacts are to be avoided, the cock- (18) (21) vo 2 (22) vo 2 K =( ) m (19) K =( ) m l A ZINI 8 (20) (23) a + a (21) (24) dec = avg max 2 vo (22) (25) K =( )2m l 2,5 (23) mte = 700dec− (26) a + a (24) dec = avg max 2,3 2 mte = 1000dec− (25) 1 (27) 2,5 mte = 700dec− (26) 2,3 mte = 1000dec− (27) 1 m x!! = k (x x l )(1) 1 1 1 2 − 1 − 1 (2)

m x!! = k (x x l )+k (x x l )(3) 2 2 − 1 2 − 1 − 1 2 3 − 2 − 2 (4)

m3x!! = k2(x3 x2 l2)(5) 3 − − − BRIEFBRIEF ARTICLE ARTICLE (6) BRIEF ARTICLE

(7) THE AUTHOR THETHE AUTHOR AUTHOR π m (8) t = 2 K ! (9) mm11xx1!!!!==kk11((xx22 xx11 ll11)(1) )(1) 2 K m1x1!! = 1k1(x2 x−1− l1−−)(1) (10) aavg = vo (2)(2) − − π(2)! m (11) mm22xx2!!!!== kk11((xx22 xx11 ll11)+)+kk22((xx33 xx22 ll22)(3) )(3) m2x2!! = 2 k1−−(x2 x−1− l1−−)+k2(x3 x−2− l2−−)(3) (4) − − − − − (4) (4)K (12) amax = vo m mm33xx3!!!!== kk22((xx33 xx22 ll22)(5) )(5) ! m3x3!! = 3 k2−−(x3 x−2− l2−−)(5) (13) (6) − − − (6) (6) BRIEF ARTICLE (1 + (7)2 )v2 (14) dec = (7)π(7)o where A = amplitude of harmonic2√l movement [m] THE AUTHOR ππ mm (8)(8) ttπ== m (15) vo = speed of impact(8) [m/s] t = 22 KK (v) 2 K!! m = mass of the vehicle(9)m [kg] ! (16) K = stiffnessA coefficient=(9)v (9) of spring [N/m] o K ! 22 KK (10)(10) m1x!!aaavg= k2=1=(x2vvoKx1 l1)(1) (vi) (17) (10) aavg1 =avg voπ o m Since it is desired that no instantaneous change of π π −m!! m− (18) (2) ! speed take place, it will(11) be(11) (11) supposed that the ampli- tude of the harmonic movementvo (A) has to be smallerm x = k (x x l )+k (x x l )(3) (19) K =( )2m 2 2!! 1 2 1 1 2 3 2K 2 that the length of the spring (l). Therefore, the stiff- − − − −K K− (vii) (12)A(12)(12)(4) a aamaxmax= v==vvoo ness coefficient (K) will be set according to the next max o mm (20) ! m!! equation: (13)(13) m3x3!! = k2(x3 x2 l2)(5) (21) (13) where t = time of acceleration− − [s]− (6) aaavgavg++aamaxmax vo(14)(14)2 m = massdecdec aof==avg the+ vehicleamax [kg] (22) K =((14)) m dec = 2 l (7) (iv) K = stiffness coefficient2 2 of spring [N/m] (15)(15) 2 (23) (15) aavg = average accelerationπ [m/sm ] 22,5,5 where K = stiffness coefficient of(8) spring [N/m] vo = speedmtemte of impact== 700 700t 2=[m/s]a,a5− aavg + amax mte = 700a− −2 K (24) vo =dec speed= of impact [m/s] a = maximum acceleration! [m/s2] 2 (16)(16) max l = length of spring(16) [m] (9) (25) 22,3,3 m = mass of the vehicle [kg] mtemtemte= 1000== 1000 1000a 2a,a3−− 2,5 Additionally, another consideration− 2 K will be done, mte = 700dec(17)(17)− (10) aavg = vo (17) regarding the exposure to deceleration.π ! m As an extra (26) The next step in this argument(11) is to assume that safety coefficient, the deceleration exposure during the automobilemte proposed= 1000dec in figure2,3 13 will impact a the time of the harmonic movement will be consid- fixed object under the model− in figure 14 and consid- K (27) 1 (12) ered as the average betweenamax = thevo average acceleration ering the following parameters: and the maximum acceleration: ! m ➡ mass (m) of the vehicle: 1.000(13) kg. a + a ➡ length of spring (l): 0,75 m.(14) dec = avg max (viii) 2 speed of impact (v ): 17,8 m/s (64 km/h) 1 ➡ o (15) 1 1 where dec = deceleration of passengers2,5 [G] The last parameter needed for the calculations (the aavg = averagemte acceleration= 700a− [G] stiffness coefficient) needs an explanation. On the one (16) amax = maximum acceleration [G] hand, the stiffer the coefficient, the lesser the possibil- 2,3 ity of instantaneous change of speed. But on the other mte = 1000a− hand, the higher the deceleration.(17) Therefore, if K is Equations (v) and (viii) are used to compare the set according to the highest possible speed impact deceleration rate of the cockpit of the proposed vehi- against a fixed object this will produce high decelera- cle against safe decelerations rates as determined in tion, even if the speed impact is lower than the one Figure 7: used to define the stiffness coefficient. That is to say, if K is set to avoid an instantaneous change of speed when a vehicle impacts a fixed object at 35,6 m/s 0,10 (128 km/h), when the crash occurs at 17,8 m/s (64 0,09 0,08 km/h), the deceleration will be higher than if K was 1 harmful set using the latter speed. But then there is the fact 0,07 deceleration 0,06 that it is not possible (at east in a mass-scale produc- rates tion sense) to design automobiles with adaptive stiff- 0,05 ness coefficients for their frontal crumple zone. So, a 0,04 0,03 choice has to be made. To enhance this point, a first 0,02 numeric example will be presented. In this example, 0,01 the stiffness coefficient will be set for a maximum time of exposure [seconds] 0 impact speed of 17,8 m/s (64 km/h). Using equation 10 20 30 40 50 60 70 80 90 100 (iv) the last parameter is set: deceleration [G] ➡ stiffness coefficient (K): 565.000 N/m. design threshold Now the model is complete, and the safety of this 17,8 m/s (64 km/h) impact prototype automobile can be asserted. To do so, the 8,9 m/s (32 km/h) impact deceleration rates for two impact speeds will be evaluated, using the following equations, which char- Figure 15. Deceleration rates for the cockpit of the first pro- posed vehicle undergoing an impact against a fixed object at acterize the harmonic movement of a spring-mass different impact speeds. system:

ZINI 9 m xm!! =1x1!!k =(xk1(xx2 xl1 )(1) l1)(1) 1 1 1 2 − 1−− 1− (2) (2)

m xm!! =2x2!! =k (xk1(xx2 xl1 )+l1k)+(xk2(xx3 xl2 )(3) l2)(3) 2 2 − 1 − 2 − 1−− 1− 2 3 − 2−− 2− (4) (4) There are two conclusions that can be made from Yet thism not3x !!true.= Itk 2can(x3 be xproved2 l2 )(5) that the mass of the m3x3!! = 3 k2(−x3 x2− l2)(5) − Figure 15. Firstly, if a vehicle(6) has the indicated pa- vehicle does− not influence− − the deceleration rate, as rameters it is possible (6) to keep deceleration rates in equations (v) and (viii) can de rewritten using only impacts bellow 17,8 m/s(7) (64(7) km/h). Secondly, when the length of the crumple zone and the maximum the stiffness coefficient(8) is set(8) for 17,8 m/s, an impact speed impact: at half the speed generates a safer rate of deceleration. π l π l Therefore, if this was the case,(9) why not design a ve- t = (9) t = 2 v (ix) hicle with a stiffness coefficient proportional to a 2 vo o higher impact speed? (10)(10) 2 22 2 To answer this, a second experiment will be done, (1 +(1) +v π )vo (x) (11)(11) dec =dec = π o this time with the next parameters —it is important to 2√l 2l remember that equation (iv) (12)is used to define K—: (12) where t = time of deceleration [s] (13) ➡ mass (m) of the vehicle:(13) 1.000 kg. l = length of crumple zone [m] ➡ length of spring (l): 0,75 m. vo = speed of impact [m/s]m (14) A = vmo (14) dec = decelerationA = vo of passengersK [G] ➡ speed of impact (vo): 35,6 m/s (128 km/h) K! (15) ! ➡ stiffness coefficient(15) (K): 2.255.000 N/m. Therefore, for each length of the crumple zone (16) (16) there is a maximum speed at which the vehicle can vo 2 The results of the second(17) theoretical experiment impact. After that speed,K v=(o deceleration) m rates will be (17) K =( )2mA are presented on the following graphic: unsafe for the passengers.A Furthermore, if equations (18) (18) (ix) and (x) are combined with equation (ii) the (19) maximum impact speed can be obtained for two dif- (19) 0,10 ferent lengths of the crumplev ozone:2 (20) K v=(o 2 ) m 0,09 (20) K =( ) ml l 0,08 (21) harmful 0,07 (21) deceleration aavg + amax 0,06 (22) decaavg= + amax (22) rates dec = 2 0,05 2 (23) 0,04 (23) 2,5 0,03 mte = 700dec2,5 − mte = 700dec− 0,02 (24) 0,01 (24)

time of exposure [seconds] 2,3 0 mte = 1000dec2,3 − mte = 1000dec− 10 20 30 40 50(25)60 70 80 90 100 (25) deceleration [G] design threshold 60 17,8 m/s (64 km/h) impact km/h 8,9 m/s (32 km/h) impact 50 cm 1 1 Figure 16. Deceleration rates for the cockpit of the second pro- posed vehicle undergoing an impact against a fixed object at different impact speeds. 90 km/h In this second case, deceleration rates prove to be 150 cm more dangerous. Specially the rate for the 35,6 m/s (128 km/h) which is out of the ranges of the graphic being its numeric value 141 G for a time exposure of Figure 17. Maximum impact speeds against fixed objects ac- cording to the length of the crumple zone, given that decelera- 0,0331 seconds. tion rates must be maintained under the limits set in Figure 7. Therefore, another key issue arises: is it possible to set the parameters of the car in a way in which an impact at 35,6 m/s generates safe deceleration rates? The results obtained after solving the set of equa- To answer this, another consideration must be tions mentioned in the last paragraph lead to a very made. In a first look, there are three parameters which important conclusion: automobiles should not impact can be set to maintain deceleration rates within safe fixed objects at speeds higher than 60 km/h if their limits: the mass of the car, the length of the crumple crumple zones can deform around 50 cm (that is what zone and the stiffness coefficient of the crumple zone. most modern cars can offer). And this is so even in

ZINI 10 m x!! = k (x x l )(1) 1 1 1 2 − 1 − 1 (2)

m x!! = k (x x l ) +(3) 2 2 − 1 2 − 1 − 1 +k (x x l )(4) 2 3 − 2 − 2 (5)

m x!! = k (x x l )(6) 3 3 − 2 3 − 2 − 2 the better of cases, when the whole(7) length is used, To solve the model, Newton’s second law will be and when the stiffness coefficient(8) is set to this impact used: speed. (9) F = ma (xi) Survivability at higher speeds can be only assured (10) by extending the crumple zone to larger lengths, and where F = Force [N] considering that this length cannot(11) be greater than m = mass [kg] 150 cm for a series of reasons (namely total overall a = acceleration [m/sπ2]l (12) t = length, structural requirements, among others), frontal 2 v impacts against a fixed object should only remain o (13) Which in terms of this model results in a three- safe at speed impacts of around 60/70 km/h for most equation system: cars, and only for the larger one at speeds of around (1 + 2 )v2 (14) dec = π o 90 km/h. The former are the speeds at which modern 2l m1x1!! = k1(x2 x1 l1)(1) cars are being tested, and they (15) have proven to per- m1x1!! = k1(x2 −x1 −l1)(1) (xii) form adequately. (2) − − (16) (2) Yet, and this is the main issue of this paper, the m2x2!! = k1(x2 x1 l1) +(3) m2x2!! = −k1(x2 −xm1 −l1) +(3) (xiii) problem arises when it comes to head-on(17) collisions. −A =+kvo(−x −x l )(4) ++kk2((xx3K xx2 ll2)(4) )(4) 2 !3 −− 2 −− 2 (18) (5)(5) ASSURING SURVIVABILITY FOR TWO m3x3!! = k2(x3 x2 l2)(6) (xiv) (19) m3x3!! = −k2(x3 −x2 −l2)(6) VEHICLES, HEAD-ON COLLISION − v − − (7)(7) o 2 (20) where m1 ; m3 =K masses=( of) eachm vehicle [kg] “The alternation of motion is ever proportional(8) to A (8) m2 = insignificant mass [kg] the motive force impressed; and (21)is made in(9) the direc- (9)(9) x1 ; x2 ; x3 = displacement of each mass [m] tion of the right line in which(22) that force is im- π l (10) k1 ; k2 = stiffness coefficientst = ofπ eachl vehicle [N/m] pressed”. (Isaac Newton, [11]) (10)(10) vo 2 tt== (23) l1 ; l2 = lengthK =( of crumple) m zone of2 veacho vehicle [m] l 2 vo As said before, an impact against a fixed(11) object (24) (11)(11) cannot be compared to a head-on collision, mainly 2 2 Additionally, an important(1 consideration +2π )v2o will be because in a head-on collision there is always an in- aavg + amax(1 + π)vo (25) (12)(12) made. The dec model= willdecdec be == evaluatingπ taking into ac- stantaneous change of speed. This will be proven us- 2 22ll (13) count that once one of the vehicles’ spring length is ing the following model: (26) (13) zero, the system becomes one where the three masses (14) 2,5 (14)(14) will continuemte to move= 700 asdec a single− body: (27) mm (15) A = vo (15) A2,=3 vo K mte = 1000dec− !K (16) v1 v!1 (28) (16)(16) (17) 1 (17) m1 m + m 2 vo 2 3 (18) K =(vo )22m (18) K =( A) m v v A O1 O3 (19)(19) k1; lf1 (20)(20) m1 m3 m2 vvo 2 (21)(21) KK=(=(o ))2mm Figure 19. In a first step, the systems behavesll according to the adopted model. Then, when one of the spring lengths is zero, (22)(22) k ; l k ; l the system behaves as a single body system. 1 1 2 2 aaavg++aamax (23)(23) decdec== avg max 22 (24) Figure 18. Adopted model for a two vehicles head-on(24)(24) collision. The system formed by equations (xii), (xiii) and 2,5 mte = 700dec−2,5 (xiv) has to be solvedmte using= differential 700dec−− equations. For the purpose of this paper, Mathematica© Software (25)(25) It is important to highlight that the mass in the was used. The object of the section 2 is,3 to prove that mte = 1000dec−2,3 middle of the two springs serves only the purpose to during a head-on collisionmte = 1000 wheredec − the− two colliding generate a reference point for the model,(26)(26) and that it vehicles do not share the mass and the speed, there will be considered insignificant in terms of the other will be an instantaneous change of speed. Further- masses (numerically speaking, when mass 1 and 3 more, the extension of the change of speed will be have values of either 1.000 kg or 1.5000 kg., mass 2 considered. In order to do so, five different pair of 1 has a 1 kg. value). vehicles were compared: 1

ZINI 11 ➡ Two small cars traveling at the same speed (Ta- ble 1). This represents the test being performed Table 3. in NCAP-type programs. Modeled impact between a small car and a medium car travel- ing at the same speed. ➡ Two small cars traveling at different speeds (Ta- ble 2). This is to know the instantaneous change stiffness crumple impact change of mass of speed of the car with the smaller speed. coefficient zone speed speed ➡ A small car and a medium car traveling at the [kg] [N/m] [cm] [km/h] [km/h] same same speed (Table 3). This is to know the instan- 1.500 1.500.000 75 64 taneous change of speed of the car with the direction smaller mass. 1.000 1.250.000 50 64 86 ➡ A small car and a medium car traveling at dif- ferent speeds, the medium car going faster than the small one (Table 4). This is to know the in- stantaneous change of speed of the car with the smaller speed and the smaller mass. Table 4. ➡ A small car and a medium car traveling at dif- Modeled impact between a small car and a medium car travel- ferent speeds, the medium car going slower than ing at different speeds. the small one (Table 5). This is to know which stiffness crumple impact change of mass one of the two will suffer an instantaneous coefficient zone speed speed (knowing a priori that greater speeds beat [kg] [N/m] [cm] [km/h] [km/h] greater masses). same 1.500 1.500.000 75 80 The results of each modeling are presented bellow direction (in red the vehicle that endures the instantaneous 1.000 1.250.000 50 48 96 change of speed, thus whose passengers will suffer indeterminate injuries):

Table 1. Modeled impact between two small cars traveling at the same Table 5. speed. Modeled impact between a small car and a medium car travel- ing at different speeds. stiffness crumple impact change of mass coefficient zone speed speed stiffness crumple impact change of mass [kg] [N/m] [cm] [km/h] [km/h] coefficient zone speed speed [kg] [N/m] [cm] [km/h] [km/h] 1.000 1.250.000 50 64 0 1.500 1.500.000 75 48 56 1.000 1.250.000 50 64 0 1.000 1.250.000 50 80 same direction

The important issue about this is that although the Table 2. considered impact speeds are not very high, the in- Modeled impact between two small cars traveling at different speeds. stantaneous change of speed are considerable. It has been already stated that these mentioned changes of stiffness crumple impact change of mass speed are much more dangerous that high decelera- coefficient zone speed speed tions. Apart from this, in the previous sections it has [kg] [N/m] [cm] [km/h] [km/h] been said that for automobiles with crumple zones same that are 50/75 cm. long the maximum impact speed 1.000 1.250.000 50 80 direction should not exceed 60 km/h in order to survive un- harmed from the deceleration phenomena in impacts 1.000 1.250.000 50 48 89 against fixed objects. Therefore, it is vital to take into consideration that every change of speed suffered by one of the vehicles in the last four models exceeds that limit . Worst of all, there is no way to avoid this from happening. Every time there is a head-on collision, one of the

ZINI 12 vehicles will suffer a considerable change of speed, unless the cars impact at low speeds. How low should these speed be? This is no easy question to answer and has to be analyzed thoroughly within the corre- sponding settings and using appropriate resources.

CONCLUSIONS “The vulnerability of the human body should be a limiting design parameter for the traffic system and speed management is central”. (World Health Or- ganization, [1]) During this paper a series of questions were posed: ➡ is it possible to design automobiles in order to avoid exposing passengers to mortal instantane- ous changes of speed during head-on collisions? ➡ if this is not situation, shouldn`t speed limits be lowered to assure survivability? ➡ what is the limit in which an instantaneous change of speed becomes unsafe? ➡ which deceleration rates can be tolerated for the vast majority of the population? The answers to them are (in order): apparently no, apparently yes, apparently it is unknown, apparently it is unknown. Furthermore, it has to be understood that automo- biles are being designed without proper knowledge about human tolerance to deceleration and instanta- neous changes of speed. And that they are being tested under the precept that they behave in a similar way in the most common of road impacts, when it is not the case. Additionally, to avoid passengers from being exposed to these dangerous phenomena, speed limits should be lowered, which in practical terms is very difficult to perform. Finally, it is probable that a many other conclu- sions could be made considering the issues mentioned here. Yet, and although I should not use the first per- son in a written technical paper, I humbly ask permis- sion to express that my personal main conclusion is that putting safety first is no easy target.

ZINI 13 APPENDIX I (INJURY MECHANISMS): men, the peritoneal cavity gathers many vital organs and glands such as the liver, the spleen and the pan- Head, neck and spine injury mechanisms creas; except for the mouth and esophagus, the entire Injuries in these vital organs are devas- digestive tract is contained within the peritoneal cav- tating, and generally lead either to the ity or is partially covered by peritoneal membranes; automobilist’s death or to various forms also, the abdominal aorta and vena cava are located of permanent physical impairment. on the posterior wall of this cavity. Most of these or- gans are soft and crumbly, and a great quantity of Direct impacts in the head can severely blood circulates through them —specially through the affect the brain and most of the sensory liver—, so their damage often results in losing the organs located within it. It is both prob- organ or in catastrophic bleeding. able and frequent to observe brain harm without any cranium fracture, since the In the case of the chest, most of the organs resid- relative movement between the rugose ing within it (as the heart and the lungs), or transiting base of the cranium and the brain can torn blood ves- it (as the esophagus, and, again, the aorta and the sels and nerves entering and exiting the head, causing cava) are vital, so any damage to them has the poten- cognitive and behavior deficiencies as well as mem- tial to generate very serious or fatal injuries. It is ory disorders. Regarding sensory organs, smell, taste, worth mentioning that injuries to this body region sight, sound and balance can be affected by direct and may be fatal in the short-term, but they bear no con- indirect impacts —even minor ones— to the cranial sequences in the long-term —precisely the contrary to nerves or to the organs situated in the head. Compres- what happens with the extremities, as it will be dis- sion forces in the neck can provoke fractures in the cussed—. Damage to the chest can provoke either first vertebrae of the vertebral column damaging the respiratory or circulatory complications. As regards arteries that circulate through them. This damage se- the first ones, direct impacts may injure the intrapleu- riously compromises the blood supply to the brain; ral membrane, affecting air movement into the lungs, besides, tears of the vertebral arteries are often fatal. and resulting in death if not treated immediately. Tension forces caused by hyperflexion or hyperexten- Moreover, any injury that affects the capacity of the sion (namely when whiplash, or severe flexion of the diaphragm to contract or that damages lung tissue neck take place) generate cervical sprains with the may lower the quantity of oxygen in blood (as a result potential to provoke fatal injuries, or functional dis- of deficient respiration) affecting other organs that are abilities which may arise years after the crash took sensitive to oxygen insufficiency. Brain tissue is spe- place. cially sensitive to this kind of insufficiency, so con- current lung injuries directly and adversely affect Finally, direct impacts can also damage the spinal brain injuries. As regards the circulatory complica- cord severely; furthermore, this type of injury cannot tions caused by direct impacts, they are also ex- be treated medically, as no therapy results in recovery. tremely harmful. There are estimations that state that Crash injuries involving the spinal vertebrae are often only 30% of the victims of injuries to the heart or violent events in which the flexed spinal column is main blood vessels survive long enough to be able to additionally subjected to coupled forces of rotation and receive medical attention. lateral bending. Damage to the lower section of the spinal cord may derive in paraplegia or serious urinal and sexual problems. Injuries above the lumbar region Lower and upper extremities injury mechanisms add breathing disorders to the mentioned conse- quences. Lastly, injuries in the higher section of the Injuries in the extremities (arms and spinal cord frequently derive in quadriplegia, with a legs) may be seldom the cause of death total loss of many essential body functions. in a road crash, but they are surely a major —if not the main— cause of permanent physical impairment. Inju- Abdomen and chest injury mechanisms ries in these organs are generally a con- sequence of direct impacts, and while Injuries in these vital organs are also they do not involve particularly risky devastating. Harm in the abdomen is situations, it has to be taken into ac- caused when suffering a direct impact, count that the movement of fractured with the aggravating circumstance that bone fragments generates serious damages to the as it is an incompressible hydraulic cav- muscular tissues and massive internal hemorrhages ity, a blow in a sector of the abdomen that, unless treated expeditiously, can provoke severe can generate a serious damage in an- injuries. other place, away from the impact point. As regards the organs that can be It is worth mentioning that the extremities are not affected by a direct impact in the abdo- restrained in any case, and that even in the event of

ZINI 14 crashes at moderate speeds they are liable to strike the interior surfaces of the vehicle. Moreover, the upper extremities can also strike the body of the other occu- pants of the car, exposing the latter to potential dam- age –specially in the head–.

APPENDIX II (DECELERATION RESIS- TANCE): Figure N3. Most dangerous directions and senses for accelera- Empirical evidence demonstrates that human be- tion of the head. ings can be exposed to high levels of accelerations with a resistance that diminishes as the time of expo- sure to it increases, and that there are senses and di- rections more favorable than others. In other words, it REFERENCES is possible to survive without serious damage from extremely high levels of accelerations given that: (1) World report on road traffic injury prevention. firstly, the time of exposure remains below extremely World Health Organization – 2004. short periods of time; secondly, the direction of the (2) The goal, a process of ongoing improvement. Gol- movement is transverse to the body, and in the sense dratt E.; Cox J. – North River Press. – 1984. of pushing the person backwards; and thirdly (and the least common of all), the process is not combined (3) Crash injuries – how and why they happen. Hyde with direct impacts. The following figure shows the A.S. – Hyde Associates Inc. – 1992. direction and senses that may damage seriously a (4) Address delivered to National Safety Forum. Stapp human being that is being accelerated, and that coin- J.P. – 1955. cide with frontal and lateral impact movements (3): (5) History of research in space biology and biody- namics at the Air Force Missile Development Center, , New Mexico, 1946-1958. Historical Division of the Holloman Air Base Force – 1958. (6) Effects of mechanical force on living tissue. Stapp J.P. – Journal of Aviation Medicine, 26(4) – 1955. (7) Vision Zero – An ethical approach to safety and mobility. Tingvall C., Haworth N. – 6th ITE Inter- national Conference Road Safety & Traffic En- forcement, Melbourne –1999. Figure N2. Most dangerous directions and senses for accelera- (8) Unsafe at any speed. The designed-in dangers of tion processes. the American automobile. Nader R. – Grossman Publishers – 1965. (9) Synergistic Motor Vehicle Safety. Robbins M. – Furthermore, it can be stated that when it comes to SAE Paper 970488 – 1987. acceleration resistance, a sudden acceleration of the head can lead to hyperflexion or hyperextension of (10) Engineering analysis of vehicular accidents. the neck, and that the most harmful movements are Noon R.K. – CRC Press – 1994. the following (3): (11) Philosophiae Naturalis Principia Mathematica. Newton, I. – 1687.

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