DELTA-V AS A MEASURE OF TRAFFIC CONFLICT SEVERITY

Transcription

1 DELTA-V AS A MEASURE OF TRAFFIC CONFLICT SEVERITY Steen G. Shelby Senior Research Engineer, Econolite Control Products, Inc., Tucson, AZ, USA, e-ail: [email protected] Subitted to the 3 rd International Conference on Road Safety and Siulation, Septeber 4-6, 0, Indianapolis, USA ABSTRACT Delta-V ( ) is a easure of the seerity of a traffic collision, defined as the change in elocity between pre-collision and post-collision trajectories of a ehicle. Delta-V eerged in the 970s in the context of crash reconstruction analysis, and is considered by soe researchers to be the best single predictor of crash seerity. Howeer, this indicator has not been applied to the analysis of traffic conflicts, until recently when it was incorporated into the autoated conflict analysis algoriths of the Surrogate Safety Assessent Model (SSAM). This paper introduces Delta-V and deonstrates how it oercoes shortcoings present in seeral traditional easures of traffic conflict seerity. We discuss the abiguity present in the literature on the topic of traffic conflict seerity, and suggest the adoption of alternatie terinology and definitions. We deonstrate a new approach, incorporating Delta-V, to estiate the collision propensity and potential collision seerity of a traffic conflict. Keywords: traffic, safety, conflicts, surrogate easures, delta-, seerity, collision propensity, coprehensie econoic costs. INTRODUCTION Delta-V ( ) is coonplace notation used in atheatics and particularly in physics to denote a change or difference in elocity. In the context of a otor ehicle crash, specifically refers to the change in elocity between pre-collision and post-collision trajectories of a ehicle. = after before Delta-V eerged in the 970s in the context of crash reconstruction analysis, and is considered by soe researchers to be the best single predictor of crash seerity. Howeer, this indicator has not been applied to the analysis of traffic conflicts, until recently when it was incorporated by the author into the autoated conflict analysis algoriths of the Surrogate Safety Assessent Model (SSAM). () Traffic conflict studies hae historically been conducted with a tea of obserers trained to identify and characterize the seerity of narrowly-aerted traffic collisions as they watch traffic fro the roadside. Howeer, with the eergence of algorithic software to

2 conduct this task, uch ore sophisticated easures of safety, such as, can be calculated. We note that our estiation of in the SSAM software was an oerly crude first effort, but nonetheless a aluable first step toward the ideas outlined herein. We continue the introduction of in the next (second) section, and then in the third section show this single alue can be used to estiate the full range of collision outcoes across the seerity spectru. Howeer, a constructie discussion of conflict seerity easures requires a coon understanding of what exactly is the seerity of a traffic conflict. We find the literature abiguous and conflicting in this regard, and thus deote the third section to defining new terinology and clarifying the concept. The fourth section contrasts with traditional seerity easures, illustrating its adantages, and deonstrates how to estiate in the context of a traffic conflict. The final sections show how the seerity profile lends itself to the aggregation and coparison of conflicts, using coprehensie econoic costs to weigh the risks. The paper is written assuing that readers are already failiar with traffic conflict techniques. Howeer, for the benefit of unfailiar readers, we proide a ery concise synopsis and suggest reiewing a brochure describing the Swedish Traffic Conflicts Technique for a quick oeriew, (, 3) or the recent dissertation by Archer for ore coprehensie coerage. DELTA-V The utility of for characterizing collision seerity eerged in the 970s, in the context of crash reconstruction analysis. The National Highway Traffic Safety Adinistration (NHTSA) coissioned deelopent of a crash reconstruction progra called CRASH (Calspan Reconstruction of Accident Speeds on Highways). (4, 5) This progra is used to estiate the Delta-V of ehicles inoled in a crash based on easureents of their structural deforation. (6) The original ersion of CRASH was able to estiate ehicle ipact elocities to within about % of actual elocities. We present a siplistic equation for as follows. Suppose that ehicle with ass is traeling at a pre-collision elocity and is encroaching on ehicle, a slower oing ehicle with ass and pre-collision elocity. The post-collision elocities are arked with an oerlaid tilde (~). Then, for each ehicle is siply the change between the pre-collision elocity and the post-collision elocity, as written in Equation. = ~ = ~ () Figure below illustrates two conerging ehicles to an ultiate collision (the splat shape draw in the iddle), and their post-collision trajectories (eanating fro the splat), in order to isualize the notion of.

3 3 Figure. Illustration of Delta-V ectors for two colliding ehicles. To keep the presentation siple, suppose that both ehicles are traeling in the sae direction (unlike the preious illustration). One ehicle traeling at higher speed catches up with the other, and we are assuing an inelastic collision, which can be enisioned as the collision of two clay balls, which then stick together after the point of collision (with cobined ass ) and proceed along the sae post-collision trajectory at elocity ~ (i.e., ~ ~ ~ = = ). The equation for this relationship, which conseres oentu, is proided in Equation, where the oentu of ehicle is, the oentu of ehicle is, and the oentu of the two ehicles stuck together post-collision is ( ) ~. () The alues can be written as in Equation 3. (3) We characterize this as a siplistic presentation because this is a one-diensional scenario (with both ehicles traeling in the sae linear diension), whereas typically we would consider twodiensional trajectories. Furtherore, this is an inelastic collision scenario. In reality, collisions exhibit a soewhat elastic effect, where the ehicles rebound off each other. A purely elastic collision could be enisioned like the collision of two billiard balls. This rebound effect is odeled with a coefficient of restitution, which equals zero (0.0) for an inelastic collision and one (.0) for a purely elastic collision. In practice, collisions tend to hae a coefficient of restitution of about 0.4 at low-speed for buper-to-buper collisions, reducing perhaps to 0. for higher speed collisions where the ehicle body begins to cae-in on collision. (7) ( ) ~ ~ = = ( ) ( ) ~ ~ = = = = = = = =

4 We note that the original CRASH progra assued an inelastic collision. This was later identified as a reason for underestiating alues by 0% to 30%, and a subsequent ersion of the CRASH software was updated to account for the coefficient of restitution, which was then said to estiate initial ipact elocities within about % of their true alue. (8) This gies a feel for the raifications of aking the siplifying assuption of an inelastic collision. We will assue inelastic collisions for the calculations in this paper, as our focus is on introducing the basic concept to a new field of application, and not burying the reader in unnecessarily coplex analysis. PREDICTING INJURY OR FATALITY OUTCOMES Researchers in the 970s were deeloping odels to predict the likelihood that a crash would result in injuries or fatalities based on ariables such as ipact speed and ehicle ass, and began exploring the use of to predict injuries and fatalities. (9) It becae eident that was a strong predictor of crash seerity. One of the earliest efforts in 977 explored the relationship between (a) the alues estiated fro the crash analysis of 73 side-ipacted ehicles and (b) the ean injury seerity of their corresponding occupants, rated using a easure referred to as the Abbreiated Injury Scale (AIS). (9) A least squares linear regression of this relationship yielded an R alue of Howeer, perhaps the ost well known result is by Joksch, who presented an approxiate odel he characterized as a rule of thub, as shown in Equation 4, stating that ean rate or percentage (P) of two-ehicle collisions resulting in a fatality is approxiately proportional to to the fourth power, based on his efforts to fit a odel to crash data fro the National Crash Seerity Study (NCSS). (0) 7 P = Other ore coplex functional fors hae also been considered, but additional studies hae confired that Joksch s rule proides a ery good approxiate fit. For exaple, O Day and Flora found a siilar power function of based on analysis of 0,000 crashes in the NCSS database fro 970 to 979. Also, Eans analyzed oer 4,000 crashes fro the NCSS database fro the years 98 to 99, and fit the generalized functional for in Equation 5 to data for both injury prediction and fatality prediction, conditioned on whether occupants wore seat belts or not. 4 (4) P = α k (5) The result of Eans effort to fit this odel to crash data is illustrated in Figure. These equations, as drawn, are referenced later in the paper, and thus we will work with U.S. custoary units to aoid conersions for this original figure fro Eans. We note that all of these odels were also based on the assuption of inelastic collision dynaics, and siply used the scalar alue (agnitude) of. 4

5 Figure. Illustration of actual crash outcoes to predicted outcoes. (Source: Eans, 994) Researchers oer the years hae stated great confidence in as an indicator of crash seerity with stateents such as the following: Epirical data show unequiocally that injuries and fatality rates increase as a power function of ipact speed or Delta-V. () It is well known that the is the best single predictor of injury and fatality risk in a crash. () [Delta-V] is the best aailable easure of crash seerity for ehicles that hae not been specially instruented for crash testing. (3) SEVERITY Notions regarding the seerity of an actual crash are fairly well-established; howeer, the concept of seerity is uch ore abiguous in the context of traffic conflict literature. This section reiews these two seeingly incongruent perspecties and we suggest specific terinology and interpretations with the ai of clarifying future discussion. When speaking of otor ehicle crashes, seerity is defined in ters of the agnitude of aderse consequences, which for the ost part could be characterized as daages, to both property and health. Crashes are typically classified as a fatality crash, an injury crash, or a property-daageonly (PDO) crash based on the seerity of the worst injury aongst all people inoled in the 5

6 crash. Howeer, in the context of traffic conflicts, the notion of seerity often takes a different character. Perhaps this alternatie perspectie arises fro the reality that outcoes in ters of bodily har and property daage are not directly easurable in a narrowly-aerted crash scenario. It is ore natural to say, That was a close one. Indeed, the literature on traffic conflict seerity tends to utilize ters such as nearness, closeness, or proxiity to express seerity. Conflicts are also coonly characterized as serious or seere when a ore or less arbitrary seerity threshold has been exceeded. Notions of traffic conflict seerity that appear in the literature can generally be classified into one of the following four caps: Seerity is the probability of crashing. Seerity is the agnitude of the daages fro a potential collision. Seerity is both of the aboe. Seerity is equated to a quantitatie alue, with no explicitly defined interpretation. The following subsections present exaples of the ter seerity used in each of the senses. Seerity as a probability of crashing Gettan and Head hae said, The sizes of the surrogates TTC, PET, and DR indicate the seerity of the conflict eent, that is, the probability that a collision could result fro a conflict, such that a lower TTC indicates a higher probability of a collision, a lower PET indicates a higher probability of a collision, and a higher DR indicates a higher probability of a collision. (4) Likewise, Saunier et al. odel a conflict collision probability as an exponential function of a tie-to-collision estiate, saying, The collision probability can be considered as the noralized seerity diension of the safety hierarchy. (5) Seerity as the agnitude of daages fro a potential collision Gettan and Head state, It is iportant to distinguish both the seerity of the conflict and the seerity of the resulting collision. Whereas their definition of the seerity of a conflict was based on the probability that a conflict would result in a collision, they suggest other indicators for the resulting collision seerity as follows. MaxS and DeltaS are used to indicate the likely seerity of the (potential) resulting collision if the conflict eent had resulted in a collision instead of a near iss. (4) Sensson suggests, The seerity should be related to the probability of serious injury. (6) Sennson says this while discussing the Swedish Traffic Conflicts Technique and its corresponding seerity indicator, gien by a ratio of the Tie-to-Accident (TA) to the Conflicting Speed (CS). These ters are defined as follows: Tie-to-Accident (TA) is the tie that reains to an accident fro the oent that one of the road users starts an easie action if they had continued with unchanged speeds and directions. Conflicting Speed (CS) is the speed of the road user taking easie action, for who the TA alue is estiated, at the oent just before the start of the easie action. 6

7 Figure 3 presents the notion of the unifor seerity leel, where the bold red cure delineates serious conflicts fro non-serious conflicts. Unifor seerity zones are bands of equialent seerity. Figure 3. Bands of unifor seerity leels defined by the ratio TA/CS. Source: (Archer, 005). Seerity as both a crash probability and the agnitude of potential daages Sennson teaed with Hyden to publish another paper on the topic of conflict seerity, wherein the sae easure of seerity, TA/CS, is characterized differently as follows. The ai ust, furtherore, be to construct a seerity hierarchy for traffic eents so that for each eent a seerity, i.e. the eent s closeness to a crash, can be estiated. (7) While this description suggests the probability that a conflict results in a crash, the paper goes on to say, At this ery oent we can say that an unknown eent with a certain location in the seerity hierarchy has a certain closeness to an injury crash, i.e. a certain probability of resulting in an injury crash. Thus, Sensson and Hyden refer to the TA/CS indicator as proiding both the probability of an unqualified crash of any type and also the probability that this crash includes an injury. The inforation we get fro each interaction and its seerity, is how close this particular interaction was to a crash, i.e. how iinent the danger was. Seerity as an ordinal quantitatie easure, with no explicit interpretation Sayed has suggested, The TTC alue represents the conflict seerity. The saller the TTC alue the ore seere the conflict. Conflicts with TTC alue less than second are usually considered to be seere conflicts. (8) Thus, seerity has been expressed purely as a quantitatie alue, without any particular eaning being ascribed to the indicator. Siilarly, Chin and Quek suggest the reciprocal of TTC is a easure of seerity, stating, since tie-to-collision decreases with increasing seerity, it would be better to represent the conflict easure in ters 7

8 of the reciprocal of tie-to-collision, which increases with increasing seerity. (9) They additionally suggest that the deceleration rate necessary to aoid collision also reflects the seerity of the conflict, since the higher the alue of the deceleration, the ore serious is the conflict. We hae shown that the notion of seerity as discussed in the traffic conflict literature takes a range of abiguous and conflicting definitions fro one paper to the next, and in soe cases within the sae paper. We present the following terinology and definitions to bring soe clarity to the noenclature in this paper, and hopefully to future literature on this topic. Collision propensity is the probability that an eerging conflict results in a collision. Collision seerity or potential collision seerity is the expected agnitude of the consequences of a collision, gien that a collision occurs. Conflict seerity is the expected consequences of the eerging conflict eent, considering the estiated distribution of no collision and collision outcoes. We briefly discuss soe of the otiation behind this noenclature. We prefer to keep usage of the ter seerity in the context of traffic conflicts consistent with its usage in the context of actual crashes, where it already has a uniersal connation of the agnitude of resulting consequences. In the context of a traffic conflict, outcoes are not known, and thus seerity takes the for of an expectation. We suggest refraining fro using the ter traffic conflict seerity as a collision probability, since that is not consistent with notions of crash seerity. We feel it is crucial to explicitly acknowledge that collision propensity and potential collision seerity are two distinct diensions in the character a traffic conflict. As we deonstrate later in this paper, two traffic conflicts with the sae collision propensity ay exhibit draatically different potential collision seerities. We refer to these two separate diensions by two different naes for clarity, as opposed to the confusion created and prolonged by referring to both diensions as seerity. We prefer the ter propensity to the ter proxiity, which iplies physical or teporary closeness. Propensity captures the probabilistic estiation we truly seek, whereas proxiity iplies relatie or ordinal relations that are often not true. For exaple, it is coonly stated that shorter tie-to-collision (i.e., teporal proxiity) corresponds to a higher probability that a conflict results in a collision. Howeer, we will show that this is not true in the following section. Siilarly, two closely-spaced ehicles in conflict do not necessarily present a higher probability of collision than two ehicles with relatiely distant spacing. While these notions ay often be true, they are certainly not always true, whereas a higher probability of collision does, by definition, always correspond to a higher probability of collision. We also adopt the ter propensity in faor of the ter probability, as it sees soewhat odd to obsere a traffic conflict which does not result in an actual collision in the ast ajority of cases and then subsequently speak of that conflict s collision probability being nonzero, when we already know 8

9 that it did not result in an actual collision. The notion of propensity is rather ore loosely and pragatically defined, but can be taken as the long-run relatie frequency of collisions, gien a sufficiently large nuber of replications of the sae situation. This focus on the generating conditions is also consistent with our suggested ethodology of calculating propensity based on the situation the location and elocity of the inoled ehicles at the oent the traffic conflict eerges. COMPARISON WITH TRADITIONAL SEVERITY MEASURES The section copares and contrast Delta-V with seeral traditional easures of seerity, elucidating their respectie shortcoings, and thereby highlighting the oerall robustness of Delta-V to a broad range of conflict scenarios. The easures hae been diided into two categories of alues: (a) directly easurable indicators, and (b) estiated indicators. Directly Measurable Indicators Directly easurable indicators can be directly obsered fro the trajectories of two conerging ehicles. They proide useful indications of relatie seerity in liited scenarios, but as we will show, they also fail to accurately distinguish seerity when faced with a broader range of traffic conflict situations. Maxiu Speed (Max S) Maxiu Speed (Max S) indicates the axiu obsered speed of either ehicle during a conflict eent. (4) This is considered an indicator of collision seerity, with the understanding that speed kills. Its strengths and weaknesses are illustrated by the follow cases: Case Vehicle A is traeling eastbound (EB) at a speed of 40 ph, and rear-ends ehicle B, which is stationary. The Max S alue is 40 ph. Delta-V can be calculated assuing an inelastic collision, which is a collision where both ehicles stick together after the collision. This siplifying assuption is adopted throughout this paper. In this case, assuing equal ass ehicles, both ehicles would hae a post-collision EB trajectory at 0 ph. Both ehicles would hae a of 0 ph. Case This is the sae as case, except ehicle A is traeling 0 ph, in which case the Max S alue is 0 ph, which suggests a less seere collision. Delta-V is 0 ph in this case, for both ehicles, also indicating lower seerity than Case. Case 3 Vehicle A is traeling EB at 40 ph and crashes head-on into ehicle B, which is traeling westbound (WB) at 30 ph. The Max S alue for this collision is 40 ph. The post-collision trajectory of both ehicles is EB at 5 ph. The for both ehicles is 35 ph. Max S is successful in distinguishing that Case is ore seere than Case. Note that it is possible to directly estiate the probability of an injury, and the probability of a fatality, based on, using the equations proided in Figure. We will assue that all ehicle occupants are 9

10 wearing seat belts. Note that both seerity easures in Case are half of their respectie alues in Case. Howeer, the probabilities of injuries and fatalities are a power function of, and thus differences in the probability of injuries are uch greater than 50% between Cases and. The probability of injury is 0.04 in Case, and in Case. Case 3 illustrates the shortcoing of Max S. In Case 3, the probability of an injury is 0.80, whereas the probability of an injury in Case is 0.04, despite haing the sae Max S seerity indicator. Siilarly, the probability of a fatality in Case 3 is 0.044, whereas the probability of fatality in Case is 0.003, despite haing the sae Max S seerity indicator. A fundaental weakness of the Max S indicator is that speed is a scalar alue, with no notion of direction of trael, whereas elocity is a ector, which has both agnitude and direction. Thus, can distinguish the extree seerity of a head-on collision fro the inor seerity of a rear-end collision, whereas the Max S indicator cannot. Relatie Speed The easure Delta S ( s) is the axiu difference in speeds between the two ehicles during a conflict eent. (4) This is considered an indicator of collision seerity, with the understanding that the higher the difference in speeds in a rear-end accident, the higher the seerity. This easure suffers the sae fundaental shortcoing as Max S, in considering only the agnitude of speeds and not the direction. Using the cases fro the Max S discussion, s is 40 ph in Case and s is 0 ph in Case. So, s is successful in distinguishing that Case is ore seere than Case. Howeer, s is 0 ph in Case 3, which suggests that Case 3 is less seere than Case. Howeer, using, we calculated a probability of fatality of for Case 3, and for Case. Thus, Delta S has utterly failed in this case. Post-Encroachent Tie Post-encroachent tie (PET) is the elapsed tie between the departure of a leading ehicle and the arrial of the trailing ehicle at the sae location. Consider a crossing conflict where one ehicle turns in front of an oncoing ehicle. A shorter elapsed tie between the departure of the turning ehicle and the arrial of the oncoing ehicle suggests greater risk of collision. Howeer, there are coonplace scenarios where PET does not accurately portray relatie seerity. Suppose a left-turning ehicle is just entering an intersection and begins steering into its turn when the drier reconsiders the speed of an oncoing ehicle and decides to abruptly stop and wait for the oncoing ehicle to pass. The oncoing ehicle in this case is closely followed by two trailing ehicles, and thus seeral seconds pass before the left-turning ehicle copletes its turn. While the crossing conflict presents a potentially ore seere consequence than a lowspeed rear-end scenario, this crossing conflict presented a uch larger PET alue, suggesting a less seere consequence. PET ay also fail in the context of an easie lane change. For exaple, suppose a ehicle encroaches on a standing queue of ehicles, and briefly is on a rear-end collision course, but changes to an adjacent lane to aoid collision. In this case, the trailing ehicle neer encroaches 0

11 on the stationary position held by the last ehicle in the standing queue. There is no PET alue, and hence no seerity indication whatsoeer in this case. Obsered Deceleration The initial deceleration rate (Initial DR) quantifies the agnitude of the easie deceleration action of a trailing ehicle in a conflict. It is the instantaneous deceleration rate of the trailing ehicle at the oent it begins an easie braking aneuer. (4) A greater deceleration rate suggests that the trailing ehicle has less tie to decelerate to aoid a collision, and thus suggests a greater likelihood of collision. Siilarly, the axiu deceleration (Max D) is the axiu deceleration rate obsered by the trailing ehicle during the conflict eent. (4) Both easures are confounded when the trailing ehicle elects to change lanes to aoid a rear-end collision instead of decelerating. Also, in the case of turning ehicle crossing in front of an oncoing ehicle, the turning ehicle ay accelerate through the turn to aoid a collision, and thus it is possible that neither ehicle decelerates. Thus, these easures are not consistently useful in proiding seerity indications. Estiated Indicators Estiated indicators consider directly obsered attributes fro the trajectories of two conerging ehicles, such as their position, instantaneous speed and heading, and apply soe odeling assuptions to copute a seerity etric. These easures are ore robust than the directly obserable easures, but we will show that they also exhibit shortcoings in their seerity indications. Tie-to-Collision (TTC) Tie-to-collision (TTC) was introduced by Hayward in 97, and is defined as: The tie required for two ehicles to collide if they continue at their present speed and on the sae path. (0) For exaple, if a ehicle traeling 45 ph (66 feet/sec) encroaches on another ehicle traeling in the sae direction at a pace of 5 ph ( feet/sec), and there is a space of 88 feet between the ehicles, then the TTC at that oent would be.0 seconds. Oer the course of a conflict eent, the instantaneous speed, direction, and spacing of the ehicles inoled ay change each tie step, thus presenting new TTC alues each tie step. When we speak of an unqualified TTC easure fro a gien conflict eent, we refer to the iniu TTC alue obsered oer the entire course of the conflict eent. We present a hypothetical conflict scenario actually three ariations of the sae scenario in order to deonstrate the character and shortcoings of TTC in a concrete exaple. Figure 4 presents an intersection in Tucson, Arizona, where the author recently experienced a traffic conflict ore or less as follows, while driing westbound (WB) on Speedway. Figure 4 illustrates the scenario just as the conflict eent eerges, where an EB ehicle in the left turn lane has just entered the intersection with the ultiate intention to turn left across opposing WB lanes. The EB ehicle is decelerating at a rate of 0 ft/sec as it crosses the stop line and enters the intersection at a pace of just under 0 ft/sec (about ph). It appears to be on track to stop in the iddle of the intersection, using the short, straight trajectory indicated in Figure 4, to let

12 oncoing WB ehicles pass before copleting its turn. Howeer, the ehicle suddenly accelerates and initiates the left turn in front of the oncoing WB ehicle, using the path indicated by the sweeping arc across the intersection. Its path cuts across the path of the oncoing WB lane at approxiately a 45-degree angle. The conflict area is the white rhobusshaped zone with cross-hatched arking in the iddle of the intersection. This hypothetical conflict resoles itself without incident, due to the turning ehicle accelerating at a axiu acceleration pace through the reainder of the oeent. We assued a linearly decreasing acceleration odel. () The projected collision anishes after.3 seconds (reaching a iniu TTC of.5 seconds), when the ehicle has accelerated to nearly 7 ph. The turning ehicle clears the conflict area just a oent before with the WB ehicle arries, without the WB ehicle haing to decelerate. Figure 4. Left-turn crossing conflict scenarios. Background iage fro Google Earth. There are three ariations of this scenario. Each entails only a singular ehicle in the WB through lane that reaches a iniu tie-to-collision of.5 seconds, with specific ariations as follows:

13 Scenario A The WB ehicle, arked A, is traeling at 30 ph when a collision course eerges with a TTC of.8 seconds, at a distance of 3 feet fro the conflict area. The conflict reaches its iniu TTC of.5 seconds at a distance of 66 feet fro the conflict zone when the left turning ehicle has accelerated to a pace at which it would clear the conflict zone before the WB ehicle arries. The WB ehicle and EB ehicle are both typical id-size sedans weighing 3,487 pounds and easuring 5.8 feet in length with 6.0 feet wide. Scenario B The WB ehicle, arked B, is traeling at 45 ph when a collision course eerges with a TTC of.8 seconds, at a distance of 85 feet fro the conflict area. The conflict reaches its iniu TTC of.5 seconds at a distance of 99 feet fro the conflict zone when the left turning ehicle has accelerated to a pace at which it would clear the conflict zone before the WB ehicle arries. The ehicles are equally sized, with diensions as in Scenario A. Scenario C The WB ehicle, arked C, is traeling at 45 ph when a collision course eerges with a TTC of.8 seconds, at a distance of 85 feet fro the conflict area. The conflict reaches its iniu TTC of.5 seconds at a distance of 99 feet fro the conflict zone when the left turning ehicle has accelerated to a pace at which it would clear the conflict zone before the WB ehicle arries. The WB ehicle is a typical large SUV, weighing 5,4 pounds, while the EB ehicle is a typical copact car weighing,979. We now consider the relatie collision propensity and potential crash seerity of these scenarios, which all hae identical TTC alues of.5 seconds (i.e., identical traditional easures of seerity). Consider the calculation of, adopting the TTC assuption that seerity can be gauged by assuing ehicles aintain their speed and path until ipact. The elocity of the turning ehicle at the iniu TTC oent is approxiately 7 ph, in the north-easterly direction. Purely in the interest of a ore tractable exaple, we will siplify atters into a onediensional real (along an East-West axis), and thus consider only the EB coponent of the elocity, which would hae a speed of approxiately 8.5 ph. In Scenario A, the WB ehicle was traeling at a pace of 30 ph. The for this scenario is 9.5 ph, which corresponds to a probability of injury of and a probability of fatality of In Scenario B, the WB ehicle was traeling at a pace of 45 ph. The for this scenario is 6.75 ph, which corresponds to a probability of injury of and a probability of fatality of In Scenario C, the WB ehicle was traeling at a pace of 45 ph, and in this case the WB ehicle ass is approxiately.8 ties the size of the EB ehicle. The for the larger WB ehicle is 9 ph, which corresponds to a probability of injury of and a probability of fatality of The for the saller WB ehicle is 34.5 ph, which corresponds to a probability of injury of 0.73 and a probability of fatality of

14 Despite the indication by the TTC alues that these three conflict scenarios hae identical seerity, these siplistic calculations suggest that Scenario B is 4.3 ties ore likely to result in a fatality than Scenario A, and Scenario C is 4 ties ore likely to result in a fatality than Scenario A. While these calculations ery siplified, it reains clear that these scenarios hae draatically different potential collision seerities. We now turn our attention to an estiation of collision propensities. To calculate a credible expectation of collision, we suggest returning to the point where the traffic conflict eerged, which is to say to first oent when a collision course seeed possible. This occurred with a TTC alue of.8 seconds. In contrast, typical applications of TTC only consider conflicts below a specified TTC threshold, which ost coonly is.5 seconds. In that context, it would only be necessary to project ehicle trajectories.5 seconds into the future, looking for possible collisions. Our exaple scenarios hae been constructed explicitly to illustrate the arbitrariness of the TTC threshold approach. With just the slightest adjustent to speed or spacing, each of these exaple scenarios would exceed the threshold, and thus be entirely discarded, despite haing only the slightest reduction of their collision propensity and potential collision seerity. Higher speeds, such as freeway facilities, warrant longer thresholds. Howeer, setting TTC thresholds to higher alues results in the identification of any safe conflicts, which do not indicate hazards (another shortcoing of the TTC approach). As an alternatie to a fixed, arbitrary threshold, we suggest a projection horizon (i.e., the duration of the look-ahead for a potential collision) that is based on the tie to trael, at current speed, oer the distance necessary to identify a hazard and decelerate to a coplete stop. In our exaple, ehicles were traeling as high as 45 ph, which would correspond to a projection horizon of 4.7 seconds. This assues an aerage perception-reaction tie (PRT) of.3 seconds, which is based on studies of recognizing and responding to stiulus to decelerate fro a forward-looking perspectie. () A ore robust projection horizon would incorporate uncertainty, such as recognizing that 95 th percentile reaction tie, which would be about.45 seconds, extending the projection horizon to 5.3 seconds. It is also eident that reaction ties are dependent on the situation, and are often longer for recognizing a threat coing fro the side. Siilarly, a longer projection horizon could be warranted by large trucks, which would not be capable of stopping as quickly as passenger cars. In this exaple, the conflict with a TTC of.8 seconds was identified as it eerged. Fro this point in tie, we consider the log-norally distributed perception reaction tie behaior, which fro huan factors studies assue in this case to hae a ean a.3 seconds, and a standard deiation of 0.6 seconds. () Table considers quantizing the probability distribution of the WB ehicle s perception reaction tie into quintiles (i.e., 5 equal portions of the distribution). The perception reaction tie could certainly be quantized to a finer resolution than quintiles for better accuracy, though that increases the coputational burden, so we hae chosen quintiles as a practical atter to keep this exaple siple to anually-calculate, both for the author and readers interested in replicating the exaple calculations. Each quintile can be ealuated by considering its idpoint percentile. For exaple, the first quintile considers the shortest perception reaction ties in the range of 0 percentile to 0 th percentile. The idpoint of this range is the 0 th percentile, which corresponds to reaction tie of 0.67 seconds. We calculate the ipact elocity (if any) assuing that the WB 4

15 ehicle begins decelerating 0.67 seconds after the conflict eerges, at an eergency rate of 4.8 ft/sec (as suggested by AASHTO). Howeer, for the first quintile, Scenario A does not result in contact, since the WB ehicle could decelerate to a stop before the conflict zone if it reacted that quickly. Table. Distribution of reaction ties and resulting outcoes. Scenario Quintile Percentile PRT (sec) P{collision} Delta V P{PDO} P{injury} P{fatality} E[loss] A $ - A $ - A $ - A $ 3,0 A $ 6,386 B $ - B $ - B $ 7,468 B $,8 B $ 5,638 C $ - C $ - C $ 7,634 C $ 3,058 C $ 74,047 A All 5 All 5 All $,897 B All 5 All 5 All $ 9,065 C All 5 All 5 All $ 4,748 A No reaction $ 3,399 B No reaction $ 49,067 C No reaction $ 47,4 A Mean $ - B Mean $ 9,04 C Mean $,669 Inspecting Table, it is eident through this quintile approxiation schee that Scenario A will not result in a collision if reaction ties of the WB drier are within the first 3 quintiles. The fourth quintile, with a idpoint reaction tie of.5 seconds, did result in a collision, though the WB ehicle was able to decelerate to a low speed. Had we quantized the reaction tie distribution with greater resolution, we could hae deduced that for a reaction tie of.3 or ore, the WB ehicle in Scenario A would not be able to stop in tie. That would be a 59 th percentile reaction tie, which suggests a collision propensity of 0.4; howeer, with the quintile approxiation, we were able to estiate a propensity of 0.40, which was fairly close. Note that the higher speed ehicles in Scenarios B and C presented an approxiate collision propensity of A higher resolution quantized distribution would reeal a ore precise collision propensity of Fro this analysis, it is plainly eident that the collision propensities of Scenarios B and C were significantly higher than the propensity of Scenario A, despite haing the sae TTC alues. There are a couple other iportant obserations fro Table. First, by considering the ean reaction ties, and explicitly accounting for deceleration, we would see that the potential 5

16 collision seerities are uch less than if we assued no reaction, as is the ost coon assuption in estiating the iniu TTC. We would also see that Scenario A would not be expected to result in a collision, whereas Scenarios B and C were expected to result in a collision. Thus, just considering the ean reaction tie and its corresponding deceleration iproes results. Howeer, in consider the distribution of reaction ties, een with a crude quintile approxiation ethod, we were able to iproe the potential collision seerity estiates of all scenarios, and show that Scenario A still had a chance of producing an injury, if poor reaction ties occurred. One final disclaier is that the estiates of Table are based solely on consideration of the reaction ties of the WB ehicle, while still assuing that the EB turning ehicle aintained the constant speed of ph that was obsered when the conflict first eerged. To coplete the proper estiation of collision propensity and potential collision seerity, it would be necessary to also consider the easie aneuers aailable to the turning ehicle an exercise we leae to the reader in consideration of space liitations. We would suggest a uch shorter ean reaction tie for the case of the turning ehicle. For exaple, Koppa suggests a ean PRT of 0.54 seconds to respond when the need for easie aneuers is anticipated. () Consideration of the acceleration of the turning ehicle will reduce the collision propensities, though it ay slightly increase the potential collision seerity slightly, since ipact would occur at higher opposing speeds. Fro Table we can extract the three alues defined earlier: collision propensity, potential collision seerity, and conflict seerity. The conflict seerity for Scenario A appears in the row arked All 5 quintiles. This is expressed in ters of an expected, and expected probabilities of PDO-, injury-, and fatality crashes, considering a distribution of possible drier PRTs which could hae occurred under the sae eerging conflict conditions and resulted in a distribution of outcoes, fro no collision to a fatality collision. The conflict seerity is generated fro the conolution of the collision propensity distribution and the corresponding potential collision seerity distribution. For exaple, the potential collision seerity suggests that if Scenario A had resulted in a collision, it would hae a 0.03 probability of an injury; whereas, the conflict seerity only represents a probability of injury, since the eerging conflict conditions only reflected a collision propensity of Tie-to-Accident (TA) Tie-to-accident (TA) was introduced by Hyden in 987, and is defined as the tie reaining to collision fro the oent the first easie action is taken by one of the road users. (3) This approach iproes on the TTC easure in that it utilizes a speed-cognizant threshold depending on the speed of the releant user, as shown by the Conflict Seerity Leel in Figure 3. In our prior exaple, the WB ehicle would be that releant user. Thus, it is not inalidated by a range of different trael speeds, as is the TTC approach. Keying off the easie aneuer sees to be this ethod s strength and weakness. In this anner, it is soewhat effectie in assessing the propensity of collision, since the TA alue reflects the reaction tie. Howeer, it only reflects a singular obsered reaction tie, aongst a distribution of possible outcoes. As shown with the TTC analysis, ealuation of the distribution of outcoes that ight result fro an eerging conflict proides a ore useful assessent of 6

17 the collision propensity and collision seerity than were obtained by just considering the ean reaction tie. A reaining issue is how exactly to discern when an easie action occurs. This issue is analogous to the course projection issue with TTC, where huan obserers can naturally perceie an easie aneuer fro a non-easie aneuer; howeer, codifying this technique for autoated algoriths presents a challenge. In our preious exaple, it is not clear where the easie aneuer begins. The turning ehicle was accelerating throughout the conflict. Thus, there was a change in speed, which fro one perspectie ay be an easie reaction, but not an easily distinguished change in strategy or intention since the acceleration was steady. After.3 seconds of acceleration, the turning ehicle reached a pace where the collision course anished. Since the ean reaction tie of the WB ehicle was.3 seconds, and the collision course was no longer present at the end of that response tie, it is possible that the WB ehicle would not hae reacted at all, exhibiting no easie aneuer. If we assue that the acceleration of the turning ehicle constitutes the easie action, then the TA alue would be.8 seconds. For Scenario A, with the WB ehicle approaching at 30 ph (48.3 k/hr), we can see fro Figure 3 that a TA of.8 seconds leaes too uch tie reaining (i.e., does not exceed the Conflict Seerity Leel), and thus Scenario A would not be counted as a conflict. The other scenarios with a 45 ph (7.4 k/hr) approach speed would just exceed the iniu seerity leel. It sees inappropriate to abandon Scenario A, which exhibited a significant collision propensity (although those calculations were not copleted to incorporate the behaior of the turning ehicle). Howeer, such is the nature of any binary threshold based schee, that a hazard is either a conflict or it is not (i.e., black or white). Note that our suggested projection horizon casts a uch wider net, with a 3.-second horizon for Scenario A, as opposed to the.0 second threshold iposed by the Swedish ethod. By explicitly calculating a collision propensity (i.e., spanning whole grayscale spectru), the approach we deonstrate is able to incorporate less serious conflicts into the oerall safety assessent. The abiguity of the definition of easie aneuer is perhaps what ake soe researchers call the TTC approach ore objectie (than TA). (3) We will assue, for the sake of arguent, that the WB ehicle did decelerate, and that this happened.3 seconds after the conflict eerged. At that oent, the reaining TA alue was.5 seconds. In this case, the TA/CS seerity indicator accurately differentiates Scenario A as less seere than Scenarios B and C. Howeer, the TA/CS alue would be the sae alue for both Scenario B and Scenario C. In the last section, we showed the Scenario C was 3 ties ore likely to result in a fatality than Scenario B. Thus, in oerlooking the ipact of relatie ehicle ass on seerity, the Swedish Traffic Conflict Technique exhibits a significant shortcoing in discerning seerity leels. Siilarly, were it the case that the heaier ehicle were unable to decelerate as fast as the lighter ehicle, perhaps the collision propensities of scenarios B and C would be different, with Scenario C being ore likely to result in an accident. It does not see that TA accounts for the different characteristics of different ehicles. It is also eident that the TA approach would not distinguish a crossing ehicle that was accelerating at a partially opposing angle (as in our exaple) fro a crossing ehicle at a perpendicular angle that was not accelerating. Certainly, the cobination of both ehicles taking easie action would tend to reduce the collision propensity ore so than 7

18 just one ehicle reacting. TA and TA/CS indicators hae no echanis to account for this difference in collision propensities. We hae shown an exaple where the estiated indicators of seerity, TTC and TA, both rated two traffic conflicts (Scenario B and Scenario C) with identical seerity alues, yet these scenarios presented drastically different seerities, with Scenario C being ore than 3 ties ore likely to result in a fatality. NOT ALL CRASHES ARE EQUAL RIGHT? Safety assessents soeties aount to a siple coparison of intersection crash rates. Often, analysts also distinguish crashes types resulting in property daage only (PDO), injuries, or fatalities. Qualitatiely, fatality crashes are worse, but for perspectie, consider the quantified coprehensie econoic costs by seerity, using the abbreiated injury scale (AIS), as illustrated in Figure 5 below. $4,000,000 $3,500,000 $3,366,388 $3,000,000 $,500,000 $,40,997 $,000,000 $,500,000 $,000,000 $500,000 $0 $73,580 $34,04 $57,958 $,53 $,96 $5,07 PDO MIAS 0 MIAS MIAS MIAS 3 MIAS 4 MIAS 5 Fatality Figure 5. Coprehensie econoic costs by seerity (AIS). The nubers fro Figure 5 proided the added perspectie that a collision resulting in a fatality (at a cost of $3.4 illion) is approxiately,330 ties ore seere than a property daage only collision (at a cost of $,500). NOT ALL CONFLICTS ARE EQUAL ARE THEY? Incredible as it is, traffic conflict analyses often consider only total conflict counts or rates, instead of recognizing that a potential fatality has consequences 330 ties that of a inor fender bender. The siple truth, as illustrated in the preceding pages, is that current techniques often cannot tell the difference. This paper has presented a new approach to assessing the 8

19 seerity of traffic conflicts through the estiation of Delta-V. This approach also directly estiates of collision propensity, as a distinctly different characteristic of a traffic conflict, by incorporating estiates of the distribution of drier reaction ties at the oent a traffic conflict eerges. Whereas preailing techniques using TTC or TA alues utilize a threshold to classify a ehicle encounter as either a conflict or not, the approach deonstrated in this paper gauges each encounter with a collision propensity spanning the whole range fro zero to one. Furtherore, this approach deonstrates utilizing Delta-V to gauges the probability of injuries of different seerities. By cobining a collection of obsered conflict encounters, their distribution of collision propensities, their distribution of potential collision seerities, and the associated coprehensie econoic costs of each potential outcoe, it would certainly see plausible to better assess the relatie safety of two traffic facilities than possible by eploying current schees that often fail to distinguish all of these iportant characteristics. The rightost colun of Table proides the expected copressie cost (i.e., loss) for our exaple. CONCLUSIONS This paper introduced the concept of Delta-V ( ) as a easure for the seerity of traffic conflicts, and showed how it oercoes significant shortcoings present in seeral of the ost coonly used surrogate safety indicators, including tie-to-collision and tie-to-accident easures. We reiewed arious conflict seerity ters used in the literature, and proposed alternatie ters and interpretations to bring clarity to the topic. An exaple was presented to deonstrate how to directly estiate collision propensity, and use to estiate the probability of PDO, injury, or fatality outcoes. This technique also introduces a full spectru of shades of gray, aluing each conflict differently, instead of the traditional binary (black/white) classification schee of using a threshold to judge an encounter as an official conflict or not. Finally, we hae suggested cobining coprehensie econoic costs with explicit estiates of collisions of different seerities, to obtain a ore uniersal coparison of the full profile of traffic conflicts of different types, obsered at different traffic facilities that are copeting for a coon pool of safety reediation funds. We feel that these new directions in traffic conflict analysis ay yield substantially iproed safety assessent results. REFERENCES. Gettan, D., Pu, L., Sayed, T., and Shelby, S., Surrogate Safety Assessent Model and Validation: Final Report. Report No. FHWA-HRT FHWA, Hyden, C., The Swedish Traffic Conflicts Technique. Lund Uniersity, accessed Archer, J., Indicators for traffic safety assessent and prediction and their applicaiton in icro-siulation odelling: A study of urban and suburban intersections, in Departent of Infrastructure. Royal Institute of Technology: Stockhol, Sweden, McHenry, R.R. The CRASH Progra - A Siplified Collision Reconstruction Progra. in Motor Vehicle Collision Inestigation Syposiu. 975: Calspan, 5. Shara, D., Stern, S., Brophy, J., and Choi, E.-H. An Oeriew of NHTSA s Crash Reconstruction Software WinSMASH. in 0th International Technical Conference on the Enhanced Safety of Vehicles. 007, 6. Capbell, K.L., Energy Basis of Collision Seerity. SAE Technical Papers,

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