With the merit on representing traffic conflict through examining the crash mechanism and causality proactively, crash surrogate measures have long been proposed and applied to evaluate the traffic safety. However, the driver’s Perception-Reaction Time (PRT), an important variable in crash mechanism, has not been considered widely into surrogate measures. In this regard, it is important to know how the PRT affects the performances of surrogate indicators. To this end, three widely used surrogate measures are firstly modified by involving the PRT into their crash mechanisms. Then, in order to examine the difference caused by the PRT, a comparative study is carried out on a freeway section of the Pacific Motorway, Australia. This result suggests that the surrogate indicators’ performances in representing rear-end crash risks are improved with the incorporating of the PRT for the investigated section.
Citation: Kuang Y, Qu X, Weng J, Etemad-Shahidi A (2015) How Does the Driver’s Perception Reaction Time Affect the Performances of Crash Surrogate Measures? PLoS ONE 10(9): e0138617. https://doi.org/10.1371/journal.pone.0138617
Editor: Xiaosong Hu, University of California Berkeley, UNITED STATES
Received: April 27, 2015; Accepted: August 31, 2015; Published: September 23, 2015
Copyright: © 2015 Kuang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Data Availability: Data underlying the findings of this study is provided by the Queensland Department of Transport and Main Roads. Individuals interested in obtaining this data should contact Alan Graham (email@example.com).
Funding: The authors have no support or funding to report.
Competing interests: The authors have declared that no competing interests exist.
Abbreviations: CPIi, CPI value for ith car-following scenario; d2, Deceleration rate of following vehicle; D1–2, Distance gap between the leading and following vehicle; DRAC, Decelerate rate to avoid a crash; DRACi(t), DRAC value for ith car-following scenario at discrete time t; GEH, Result of Geoffery E. Heavers (GEH) test; F, Field data; IRij, Individual risk of the discrete scenario i measured by surrogate j; MADRi, MADR value for ith car-following scenario; MCPIi, Modified CPI value for ith car-following scenario; MDRAC, Modified decelerate rate to avoid a crash; MDRACi(t), Modified DRAC value for ith car-following scenario at discrete time t; MMSD, Modified minimum stopping distance required; MPE, Mean percentage error; MPSD, Modified proportion of stopping distance; MSD, Minimum stopping distance required; N0, Number of observations; PSD, Proportion of stopping distance; R, Reaction time of the following vehicle; RD, Distance between the initial point and the potential point of collision; RMSE, Root mean square error; RMSPE, Root mean square percentage error; S, Simulation data; SRj, Societal risk of surrogate j; T, Total time duration inspected; TTC, Time to collision; U, Theil’s inequality coefficient; V1, Speed of the leading vehicle; V2, Speed of the following vehicle; , Simulation value of the nth vehicle in the VISSIM model; , Field value of the nth vehicle; τsc, Time-scan interval; Δt, Time duration of time interval
The increase in motor-vehicle crash has been well recognised as a major health problem by World Health Organization (WHO). It is stated that around 1.24 million people lost their lives and 50 million were injured in crashes on the roads around the world each year. Further, as the leading cause of death for young people aged 15–29 years, road crashes take an enormous toll on individuals and communities as well as on national economies . In Australia, it was reported that the social cost of vehicle crashes was estimated as AUD 27 billions per annum with devastating social impacts . Among these crashes, those on motorways are recognized as more severe than crashes on urban streets in terms of their consequences. According to the crash data provided by Department of Transport and Main Roads (DTMR) of Queensland, there are over 70% fatal crashes occurred on rural and inter-city roads each year. Inter-city motorways are usually designed to carry the travel demands among cities with high speed. Crashes occurred on motorways would potentially cause significant traffic delay and health, economic and environmental problems. In this regard, it is of great importance to investigate the traffic safety on motorways. The road safety has become a high-priority issue to traffic engineers and traffic authorities for decades. Researchers and engineers proposed many methods to improve road safety such as: the application of Intelligent Transportation System (ITS) programs [3, 4], the synergy of traffic energy saving [5–7] and autonomous vehicles [8, 9].
In order to reduce the crashes, many researchers have been contributed to find the possible reasons related to the crashes. Traditionally, a range of safety-related concerns are addressed by establishing the relationship between discrete crash counts and traffic/geometric parameters [10–13], relying heavily on historical crash data and statistical techniques [14–16]. However, as pointed out by Chin and Quek  and Tarko et al. , these traditional prediction models have some drawbacks and restrictions. First, due to the infrequence and sporadic occurrence of accidents, significant efforts are consumed on collecting and maintaining the appropriate data. Second, accidents are not always uniformly reported, which can produce biased conclusions. Third, these prediction models are purely dependent on statistical techniques and historical crash data, without taking into account the crash mechanism. Further, crash records for safety analysis are considered as a reactive approach, which requires a sufficiently large number of serious accidents to take place in advance. Consequently, surrogate indicators are proposed as a supplementary method of the accumulation of crashes in safety evaluation.
Surrogate indicators are firstly proposed and used to evaluate the treatment beforehand in medical sciences, and then utilized to reduce or eliminate the crashes by traffic engineers and researchers [19–28]. As suggested by Tarko et al. , surrogate events should satisfy two basic requirements: 1) surrogate events should be exacted from observable non-crash events by using some practical method (surrogate measure); 2) it is feasible to examine the relationship between these surrogate events and corresponding crash frequency and severity. Crash surrogate indicators have been well recognized as good safety indicators for analysing and predicting crashes. Firstly, surrogate events occur much more frequently than crashes with strong probabilistic properties. Secondly, as states between safe and crash, surrogate events can reflect the potential crash causality and mechanism. Last but not least, surrogate indicator is regarded as a proactive rather than reactive approach, which can proactively assess safety before crashes occur.
Although many surrogate indicators are proposed and applied to traffic safety during the past half century, to the best of our knowledge, little if not none takes into account the driver’s perception-reaction time (PRT). The primary objective of this study is to examine whether or not the incorporation of the PRT could improve the performance of a surrogate indicator. To this end, we firstly propose the modified surrogate indicators by taking into account the PRT. Based on the collected trajectory data on Pacific motorways, we validate the VISSIM simulation model by the error tests and trajectory comparison. Lastly, we evaluate the performances of the modified surrogate indicators based on the crash data on the motorway.
Various surrogate indicators, including Time To Collision (TTC), Deceleration Rate To avoid Crash (DRAC), Crash Potential Index (CPI) and Proportion of Stopping Distance (PSD), are proposed and applied in safety evaluations. Based on the assumption that both vehicles keep the speeds unchanged during the process, the surrogate indicator TTC is defined as the time remains until a collision between two vehicles would have occurred [19, 20, 28], mathematically, (1) where D1−2 represents the distance gap between the leading and following vehicle; V1 and V2 denote the speeds of the leading and following vehicles at the initial time, respectively. TTC has become one of the most well-recognized microscopic safety indicators, and been widely applied to evaluate the level of safety in different situations of traffic [27–31]. Further, Minderhoud and Bovy  develop the extended time to collision as the measures for traffic safety assessment based on TTC notion which can evaluate the risk more comprehensively by taking into account the full course of vehicles over space and time .
DRAC is another widely-used surrogate indicator. It is defined [20, 33] as the minimum deceleration rate required by the following vehicle to avoid a crash with the leading vehicle if the speed of leading vehicle is unchanged during the process. Mathematically, DRAC can be denoted as: (2)
DRAC is recognized as an effective measure of safety performance in safety evaluation [32, 34]. The AASHTO  suggests that a given vehicle is in conflict if its DRAC exceeds a threshold 3.4 m/s2. Higher value of DRAC indicates a more dangerous car-following scenario.
CPI is defined [20, 36] as the aggregated probability for those car-following sceanrios where the following vehicles’ DRAC values exceed their braking capacities or Maximum Available Deceleration Rates (MADR) during a given time period, mathematically, (3) where DRACi(t) and MADRi are the DRAC and MADR value for the following vehicle of ith car-following scenario at discrete time t respectively; N and Δt are the total number and the duration of time interval inspected; T is the total time duration investigated, where T = N ⋅ Δt. MADR is vehicle and scenario-specific, and usually represented by truncated normal distributions [36, 37]. The surrogate indicator CPI is broadly used to evaluate the road risk in safety analysis [34, 37]. By taking into account the deceleration capacity of vehicles, CPI can deliver more comprehensive results due to the MADR distribution.
PSD is defined [20, 26, 34, 38] as the ratio between the remaining distance RD and the minimum acceptable stopping distance MSD, mathematically, (4) where the remaining distance RD denotes the distance between the initial point and the potential point of collision, while the minimum acceptable stopping distance MSD represents the minimum stopping distance required based on the assumption of maximum deceleration rate used. PSD is measured by comparing the available and minimum acceptable stopping distances, all scenarios with PSD less than 1 are regarded as unsafe, where the collisions cannot be avoided with maximum acceptable deceleration rate taken. PSD is regarded as a good surrogate indicator and has been used for safety evaluation [34, 39].
Although the selected surrogate indicators are widely used in traffic safety evaluation, none of them takes into account the PRT. The PRT, which is defined as the minimum time required for the driver to react, is an important parameter in traffic safety and designing. For example, the National Association of Australian State Road Authorities (NAASRA) is currently using the PRT as the standard in the area of geometric road design for the visibility. Besides, it is used to estimate the stopping distance in the computation of horizontal and vertical profiles in highway design . Further, the PRT also plays a significant role in the designing of the duration of yellow phase at signalized intersections . During the onset of yellow phase, either a driver stops safely before the stop line or proceeds through the intersection before the end of yellow phase are both highly related to the PRT. In reality, the safety of intersections is maintained by alleviating the dilemma zone which is calculated based on the estimation of the PRT. Accordingly, PRT is of significant importance in traffic safety. However, this important parameter is not considered into the crash mechanisms of most widely used surrogate indicators. The possible reason would be the time gap between the study of surrogate indicators and PRT. It is found that most of the well-recognized surrogate indicators were proposed in 70’s of 19th century, while most of the studies of PRT were carried out in this century. Before the distributions of PRT were obtained, the surrogate indicators have been proposed and widely used in safety evaluations. Hence seldom research has been done to establish the link between the PRT and surrogate indicators. Due to the ignorance of the PRT in most surrogate indicators, it is of great importance to take into account the PRT in safety evaluation due to its significance in crash mechanism. Wang and Stamatiadis [42–44] proposed a series of pioneering works to creatively incorporate the impact of the PRT in order to better evaluate intersection safety. Yet little research has been done for proactive motorway safety evaluation with the consideration of the PRT.
Three Modified Surrogate Indicators
Modified Deceleration Rate to Avoid a Crash (MDRAC)
This paper aims to examine whether the consideration of the PRT can improve the surrogate indicator’s performance or not. To this end, we reanalyse the crash mechanisms of selected surrogate indicators by considering the phase of the PRT.
Fig 1 shows the crash mechanism of DRAC by taking into account the PRT, where a critical situation is depicted when the following vehicle just adapts its speed to that of the leading vehicle in time. As can be seen in Fig 1, the distance travelled by the following vehicle should be equal to the available distance, mathematically: (5) by simplifying Eq 5, MDRAC can be represented as: (6)
Accordingly, MDRAC can be expressed by speeds, PRT and TTC as follows, (7) where V2 and V1 represent the speeds of the following and leading vehicles, respectively; R denotes the PRT; d2 is the deceleration rate of the following vehicle; and TTC represents the time to collision value for the initial state (t = 0). This finding is also derived by Wang and Stamatiadis [42–44].
By comparing with DRAC, MDRAC is able to reflect the severity on the basis of TTC. For the same car-following scenario, the MDRAC can be varied due to the different PRTs of distinct drivers. If TTC is less than PRT, the following driver would not have enough time to react, a collision is not avoidable. In this paper, 3.4 m/s2 is suggested as the threshold of MDRAC by AASHTO .
Modified Crash Potential Index (MCPI)
Since CPI describes the probability that a given vehicle DRAC exceeds its maximum available deceleration rate (MADR) or braking capacity, by using MDRAC instead of DRAC, the modified CPI (MCPI) can be represented as: (8) where MDRACi(t) is the MDRAC value for the ith car-following scenario at discrete time t, estimated by Eq 7, N and Δt are the total number and duration of time interval inspected; T is the total time duration investigated. According to the distribution of MADR, MCPI is measured based on the results of MDRAC. MCPI represents the crash potential index based on the consideration of the PRT, a higher MCPI indicates a more dangerous scenario.
Modified Proportion of Stopping Distance (MPSD)
By taking into account the PRT, we propose modified surrogate indicator PSD by updating the minimum acceptable stopping distance (MSD). In this conflict process, the modified MSD (MMSD) should contain two parts: 1) the distance travelled for the following vehicle during its PRT; 2) the braking distance travelled by the following vehicle its PRT till it stops, mathematically (9) where V2 is the speed of the following vehicle, R represents the PRT of the following driver, d2 denotes the maximum acceptable deceleration rate taken by the following vehicle. Then, the modified PSD (MPSD) can be expressed as: (10)
MPSD is believed to be more realistic compared to the traditional PSD. However, it is impossible to get the scenario-specific PRT during a survey. In this regard, the distribution of PRT is introduced. According to the previous research, the distribution of PRT is observed to be lognormally distributed [45–48]. Green  suggests the log-normal distributions as a mean of 1.3 seconds and a standard deviation of 0.6 second for the crossing and lane change situations. For rear-end situation, PRT is reported by Triggs and Harris  to follow a lognormal distribution with a mean of 0.92 second and a standard deviation of 0.28 second. Without loss of generality, we use the lognormal distribution with a mean of 0.92 second and a standard deviation of 0.28 second as the PRT distribution in this study for rear-end situation.
Validation of the Micro-Traffic Simulation Model
VISSIM is a useful micro-traffic simulation tool, which has been widely used in traffic simulation [40–44, 49]. In this research, VISSIM is applied to simulate the traffic of the investigated section on the Pacific Motorway. To ensure the accuracy of VISSIM on simulation, we validate our simulation model by comparing the speeds and volumes [50–53]. All field data are collected on the investigated section which is located between the exits #20 and #9 of the northbound of Pacific Motorway.
Based on previous studies [26, 37, 54], we use four error tests to assess the differences between the simulation results and the field data: (1) Theil’s inequality coefficient (U); (2) root mean square percentage error (RMSPE); (3) root mean square error (RMSE); (4) mean percentage error (MPE), mathematically, (11)(12)(13)(14) where represents the simulation value (speed) of the nth vehicle in the VISSIM model; denotes the field value of the nth vehicle; N0 is the number of observations. We randomly select 20 vehicles from the field data and record their times. Then these vehicles will be matched with those generated from our simulation model according to the recorded time. In this study, the four error tests are carried out for comparing the speeds of randomly selected vehicles. Five groups of field data are randomly extracted, each of which contains 20 vehicles. The average error tests are aggregated in Table 1. As can be seen in the table, the simulation model performs well.
We further use Geoffery E. Heavers (GEH) test to conduct volume validation. Geoffery E. Heavers (GEH), a modified chi-square statistics, has been widely employed to compare the fitness between simulation and field data [51–53]. Mathematically, GEH can be represented as (15) where S denotes simulated data, while F represents field data. GEH is regarded as a good statistical measure by considering both relative and absolute differences between simulated and field data. In this study, the field and simulated data of 20 randomly chosen time periods are compared. Each time period contains one hour. Table 2 shows the results on comparison of total flow per hour between field and simulated data. As suggested by Dowling et al.  and Holm et al. , a GEH value for sum volume of all links less than 4 is considered as a good fit. Therefore, Table 2 further demonstrates the effectiveness of the simulation model.
Performance Analysis of Modified Surrogate Indicators
In order to test the performances of the traditional and modified surrogate indicators, we carry out a case study on the Pacific Motorway. The Pacific Motorway (M1) in Queensland, Australia, is the major urban road corridor connecting Tugun to the Sunshine Coast hinterland via the Gold Coast and Brisbane. In this research, the investigated section is chosen between the exits #20 and #9 of the northbound Pacific Motorway. Based on the traffic data provided by the department of TMR in Queensland, the average traffic volume, speed and time headway for each 15-minute from 21st July 2014 (Monday) to 27th July 2014 (Sunday) are available for each lane, respectively. By setting these parameters in VISSIM, the traffic condition of the investigated section can be simulated. Thus the risk of the whole section can be evaluated by different surrogate indicators based on the trajectories generated by VISSIM. Furthermore, according to the historical crash data provided by TMR, all rear-end crashes for this section from 2005 to 2013 are considered into analysis.
A Comparative Study of Crash Surrogate Indicators
With the aim of testing the impact of the PRT, we compare the performances of traditional and modified surrogate indicators on the crash prediction. In this study, we use VISSIM to simulate the traffic situation of investigated section for 168 successive time periods (24 hours per day times 7 days) from Monday to Sunday. Based on the trajectory data, we exacted the traffic data such as the speed of leading (V1) and following vehicle (V2), the length of the leading vehicle (l1), the time headway of the following vehicle (h2) in any car-following scenario. Suggested by Vogel , the gap distance of this car following scenario (D1−2) can be estimated as (V2 × h2 − l1). According the definitions of surrogates, the risk can be represented by different surrogate indicators. By considering the randomness or heterogeneity of PRT and MADR, we use Monte-Carlo method to calculate the risk by applying different surrogates. For each car-following scenario, the risk is calculated based on 1000 seeds for both distributions. The concepts of individual and societal risk were proposed by Considine  and have been widely used in safety evaluation [26, 30, 57, 58]. Individual risk is defined as the crash risk or threat to an individual motorist, which is regarded as the likelihood of collision occurring to the individual traveler i. For each car-following scenario, the individual risk can be obtained by comparing the surrogate value and the surrogate threshold. In this study, the thresholds of DRAC (MDRAC), CPI (MCPI) and PSD (MPSD) are 3.4 m/s2, 0 and 1 respectively. Further, the societal risk is defined as the combined risk of all individual risks to all of the affected motorists during time period T measured by surrogate indicator j, mathematically represented by (16) where IRij(t) represents the individual risk of the discrete scenario i at discrete time t measured by surrogate j, τsc is the time-scan interval, there are a total of N time instances during time period T. In this study, the probabilistic properties of crashes during weekdays are found to be different with those during weekends. In this regard, we categorize all the data into weekdays and weekends for better representation.
Fig 2 shows the linear relationships between the crash counts and societal risks represented by different surrogate indicators (P values<0.05). The R square value indicates how well the societal risk fits crash counts in a linear model. The higher R square value indicates better performance of the surrogate indicator on predicting crash in a linear relationship. As can be seen in Fig 2, the R squares of modified surrogate indicators MDRAC (0.5847), MCPI (0.4989) and MPSD (0.5143) are higher than those of the traditional surrogates DRAC (0.4492), CPI (0.2201) and PSD (0.4433), respectively. Besides, it is found that the R square difference (0.2788) between MCPI and CPI is greater than that (0.0710) between MPSD and PSD and that (0.1355) between MDRAC and DRAC.
Findings and Discussions
According to our analysis, it is found that the modified surrogate indicators have higher R squares compared with traditional ones. There is no surprise that the crash prediction performance is improved by considering the PRT. Further, the impact on CPIs is much more significant than that on the other two indicators. The possible reason relies on their different methodology of crash mechanism. By considering the PRT in the crash mechanism, MDRAC will be measured by TTC, PRT and speed difference. For the cases in which PRT is greater than TTC, a collision will happen before the following driver reacts to stop, thus the MDRAC is infinity and the value of MCPI is 1. Accordingly, in those cases, the value of CPI can be greatly changed by taking into account the PRT. Consequently, PRT is a critical parameter to determine potential risk in the crash mechanism of MCPI. However, for those cases in which PRT is greater than TTC, the values of DRAC are likely to be greater than 3.4 m/s2 due to the small TTC. Then these scenarios are considered as dangerous. Thus the R square difference between DRAC and MDRAC is not as big as that of CPI and MCPI. In other words, the consideration of the PRT affects the performance of MCPI in a higher degree than that of MDRAC. Besides, in the crash mechanism of PSD, PRT is only adding to the MSD which can slightly change the ratio of RD and MSD, hence the consideration of the PRT would just slightly decrease MPSD.
It is of great importance to carry out more studies by considering the PRT into the surrogate modelling. Two further works can be done based on this study. Firstly, the PRT can be incorporated into the crash mechanisms of surrogate indicators which are designed for the crossing and lane changing situations. Secondly, another comparative study can be accomplished to examine the different impacts of PRT on surrogate indicators in terms of different speed limits.
We are grateful to the Department of TMR in Queensland on the data collection for this research.
Conceived and designed the experiments: XQ. Performed the experiments: YK XQ AE. Analyzed the data: YK JW. Contributed reagents/materials/analysis tools: YK XQ. Wrote the paper: YK XQ AE.
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This article should not be interpreted to mean that human perception-reaction time is 1.5 seconds. There is no such thing as the human perception-reaction time. Time to respond varies greatly across different tasks and even within the same task under different conditions. It can range from .15 second to many seconds. It is also highly variable. In many cases, the very concept of perception-reaction time simply doesn't apply2.
1. A "standard" or "generally accepted" PRT cannot and does not exist; 2. Exact PRT values are almost always impossible to determine due to lack of data, to the impossibility of knowing when to start timing and to the general difficulty of going from the simplified research world to the real-world; 3. A PRT cannot be determined by cookbook methods such as "Olson", AASHTO or a computer program; 4. Specifying PRT without specifying deceleration holds little value, since stopping depends on both. Drivers often trade them off. Braking at maximum possible deceleration cannot be assumed; and 5. PRT generally does not explain why a collision occurred. It is not a cause, but rather a symptom to be explained. The real cause lies in the answer to the question, "Why was the PRT insufficient?" By example, imagine that you car stops. Why? The gas gauge points to empty. Is that why the car stopped? No. Your car does not stop because the gas gauge needle points to empty. The guage is only an overt symptom and indicator, of being out of gas. The car stopped because it was out of gas, not because the gas gauge's needle position. PRT is like the gas gauge. The empty tank is like low visibility, misplaced action boundary, response conflict, violated expectation, driver impairment, etc.
Seminar Available on this topic.In many cases, the speed with which a person can respond, "reaction time," is the key to assigning liability. It is common practice for accident reconstructionists simply to use a standard reaction time number, such as 1.5 seconds, when analyzing a case. In fact, reaction time is a complicated behavior and is affected by a large number of variables. There can be no single number that applies universally. Reaction time is a surprisingly complex topic. Unfortunately, most "experts" used canned numbers without a good appreciation for where the numbers originate, how they were obtained or the variables that affect them. Moreover, there are several distinct classes of reaction time, each with somewhat different properties. In this article, I briefly describe some keys issues. The discussion focuses primarily on driver reaction time. Reaction Time Components
When a person responds to something s/he hears, sees or feels, the total reaction time can be decomposed into a sequence of components.
1 Mental Processing Time
This is the time it takes for the responder to perceive that a signal has occurred and to decide upon a response. For example, it is the time required for a driver to detect that a pedestrian is walking across the roadway directly ahead and to decide that the brakes should be applied. Mental processing time is itself a composite of four substages:
- Sensation: the time it takes to detect the sensory input from an object. ("There is a shape in the road.") All things being equal, reaction time decreases with greater signal intensity (brightness, contrast, size, loudness, etc.), foveal viewing, and better visibility conditions. Best reaction times are also faster for auditory signals than for visual ones. This stage likely does not result in conscious awareness.
- Perception/recognition: the time needed to recognize the meaning of the sensation. ("The shape is a person.") This requires the application of information from memory to interpret the sensory input. In some cases, "automatic response," this stage is very fast. In others, "controlled response," it may take considerable time. In general, novel input slows response, as does low signal probability, uncertainty (signal location, time or form), and surprise.
- Situational awareness: the time needed to recognize and interpret the scene, extract its meaning and possibly extrapolate into the future. For example, once a driver recognizes a pedestrian in the road, and combines that percept with knowledge of his own speed and distance, then he realizes what is happening and what will happen next - the car is heading toward the pedestrian and will possibly result in a collision unless action is taken. As with perception/recognition, novelty slows this mental processing stage. Selection of the wrong memory schema may result in misinterpretation.
- Response selection and programming: the time necessary to decide which if any response to make and to mentally program the movement. ("I should steer left instead of braking.") Response selection slows under choice reaction time when there are multiple possible signals. Conversely, practice decreases the required time. Lastly, electrophysiological studies show that most people exhibit preparatory muscle potentials prior to the actual movement. In other words, the decision to respond occurs appreciably faster than any recordable response can be observed or measured.
2. Movement Time
Once a response is selected, the responder must perform the required muscle movement. For example, it takes time to lift the foot off the accelerator pedal, move it laterally to the brake and then to depress the pedal.
Several factors affect movement times. In general, more complex movements require longer movement times while practice lowers movement times. Finally the Yerkes-Dodson Law says that high emotional arousal, which may be created by an emergency, speeds gross motor movements but impairs fine detailed movements.
3 Device Response Time
Mechanical devices take time to engage, even after the responder has acted. For example, a driver stepping on the brake pedal does not stop the car immediately. Instead, the stopping is a function of physical forces, gravity and friction.
Here's a simple example. Suppose a person is driving a car at 55 mph (80.67 feet/sec) during the day on a dry, level road. He sees a pedestrian and applies the brakes. What is the shortest stopping distance that can reasonably be expected? Total stopping distance consists of three components:
- Reaction Distance. First. Suppose the reaction time is 1.5 seconds. This means that the car will travel 1.5 x80.67 or 120.9 feet before the brakes are even applied.
- Brake Engagement Distance. Most reaction time studies consider the response completed at the moment the foot touches the brake pedal. However, brakes do not engage instantaneously. There is an additional time required for the pedal to depress and for the brakes to engage. This is variable and difficult to summarize in a single number because it depends on urgency and braking style. In an emergency, a reasonable estimate is .3 second, adding another 24.2 feet.
- Physical Force Distance. Once the brakes engage, the stopping distance is determined by physical forces (D=S�/(30*f) where S is mph) as 134.4 feet.
Almost half the distance is created by driver reaction time. This is one reason that it is vital to have a good estimate of speed of human response. Below, I give some values which I have derived from my own experience and from an extensive review of research results.
Response speed depends on several factors so there can be no single, universal reaction time value. Here is a list of factors which affect reaction time. In all cases, the times assume daylight and good visibility conditions.
Reaction times are greatly affected by whether the driver is alert to the need to brake. I've found it useful to divide alertness into three classes:
- Expected: the driver is alert and aware of the good possibility that braking will be necessary. This is the absolute best reaction time possible. The best estimate is 0.7 second. Of this, 0.5 is perception and 0.2 is movement, the time required to release the accelerator and to depress the brake pedal.
- Unexpected: the driver detects a common road signal such as a brake from the car ahead or from a traffic signal. Reaction time is somewhat slower, about 1.25 seconds. This is due to the increase in perception time to over a second with movement time still about 0.2 second.
- Surprise: the drive encounters a very unusual circumstance, such as a pedestrian or another car crossing the road in the near distance. There is extra time needed to interpret the event and to decide upon response. Reaction time depends to some extent on the distance to the obstacle and whether it is approaching from the side and is first seen in peripheral vision. The best estimate is 1.5 seconds for side incursions and perhaps a few tenths of a second faster for straight-ahead obstacles. Perception time is 1.2 seconds while movement time lengthens to 0.3 second.
People brake faster when there is great urgency, when the time to collision is briefer. The driver is travelling faster and/or the obstacle is near when first seen. While brake times generally fall with greater urgency, there are circumstances where reaction time becomes very long when time-to-collision is very short. The most common situation is that the driver has the option of steering into the oncoming lane into order to avoid the obstacle. The driver then must consider alternative responses, braking vs. steering, weigh the dangers of each response, check the left lane for traffic, etc.
When other driving or nondriving matters consume the driver's attention, then brake time becomes longer. For example, on a winding road, the driver must attend more to steering the car through the turns. Another major load on attention is the use of in-car displays and cell phones. There is no doubt that both cause delays in reaction times, with estimates ranging from 0.3 to as high a second or more, depending on the circumstances.
Humans have some highly built-in connections between percepts and responses. Pairings with high "stimulus-response compatibility" tend to be made very fast, with little need for thinking and with low error. Low stimulus-response incompatibility usually means slow response and high likelihood of error.
One source of many accidents is the human tendency to respond in the direction away from a negative stimulus, such as an obstacle on a collision course. If a driver sees a car approach from the right, for example, the overwhelming tendency will be to steer left, often resulting in the driver steering right into the path of the oncoming vehicle. The stimulus-response capability overrides and the driver simply cannot take the time to observe the oncoming car's trajectory and to mentally calculate itsimple, reflexive uture position. In short, the driver must respond to where the car is now, not where it will be at some point in the future.
Most people have experienced this phenomenon when going into a skid. The correct response is to turn the wheel in the direction of the skid, but it takes practice and mental concentration to avoid turning the wheel away from the skid, which is the high compatibility response.
Psychological Refractory PeriodFollowing a response, people exhibit a "psychological refractory period." During this period, new responses are made more slowly than if there had been no previous behavior. For example, suppose a driver suddenly steers left and then right. The steer-right response will occur more slowly because it immediately followed the steer-left. Age
Although most basic research finds that older people respond slower than younger ones, the data on older drivers' braking times are not entirely clear. One problem is that different studies have used different definitions of older; that is, sometimes "older means 50, sometimes it could mean 70. Moreover, some studies find no slowing of reaction time with age. Instead, they conclude that the older driver's greater experience and tendency to drive slower compensate all or in part for the decline in motor skills. [Note Added. Aging effects in PRT depend heavily on the task. For simple,reflexive responses, healthy older people show little slowing. For complex and/or low visibility tasks, however, they can be much slower.]
Although the data are not clear, it seems likely that females respond slightly slower than males.
Nature of the Signal
In the examples cited above, the driver detected a distinct signal such as a brake light, the appearance of a clear obstacle in the path, etc. Some braking cues are subtler and more difficult to detect, causing slower braking times.
One of the most difficult situations occurs when a driver must detect motion of the car immediately ahead, its acceleration or deceleration. Accidents frequently occur because the driver fails to notice that the car ahead has stopped and does not apply brakes until it is too late.
The general problem involves estimating time-to-collision (TTC). It is a tough problem for several reasons. One is that it is much more difficult to judge motion toward or away from you than it is to judge motion of something which cuts across your path. It's simply a matter of optics. Humans, in part, sense motion by registering the movement of an object image projected on the retina, the light-sensing portion of the eye. The movement of the object's image is much smaller with motion toward/away than with motion cutting across the frontal plane.
Second, it is more difficult to judge motion of the object ahead if we are moving as well. The visual system must then disentangle the retinal image motion caused by the movement of the object ahead from the retinal image motion caused by our own "egomotion." This is far more complex a problem than judging motion of an object when we are stationary.
Third, the normal expectation is that cars do not stop in the middle of the road. Reaction time, as explained above, is much slower when people encounter a low probability or unexpected event.
Reaction time increases in poor visibility. Low contrast, peripheral viewing, bad weather, etc. slow response. Moreover, virtually all reaction time studies have been performed in high light, photopic visibility conditions. At night in urban areas, vision operates in the mesopic range, so there is mixed rod-cone activation. The few existing data suggest that reaction time sharply increases as the rods become the primary photoreceptor.On the other hand, there are some situations in which response is faster in low light. For example, light emitting sources, such as rail-highway crossing signals or brake lights, produce better reaction times at night. With no sun or skylight to reflect off the fixture and with a darker background, the signal has higher contrast and greater visibility.
More complex muscular responses take longer. For example, braking requires lifting the foot from the accelerator, moving laterally to the brake pedal and then depressing. This is far more complex than turning the steering wheel. While there have been relatively few studies of steering reaction time, they find steering to be 0.15 to 0.3 second faster. Perception times are presumably the same, but assuming the hands are on the steering wheel, the movement required to turn a wheel is performed much faster than that required to move the foot from accelerator to brake pedal.Reaction Time At Night
The same factors affecting reaction in daylight conditions operate at night. Light level per se, has little effect on reaction time. For example, one study found that under scotopic vision, decreasing light levels by a factor of ten only slowed reaction time by 20-25 msec (1/40 to 1/50 second.)However, there are new variables at work. For example, a light which might have low contrast and low conspicuity during the day because the background is bright could become highly conspicuous at night and produce faster reaction times. Always remember that contrast is what matters: people see contrast, not light. Complex Reaction Times In his classic "On The Speed Of Mental Processes," Donders (1868) proposed a classification scheme that experts still use to distinguish among three different types of reaction time, simple (Type A) and more complex situations, choice (Type B) and recognition (Type C). While most of the variables affect simple and complex types in the same way, choice and recognition reaction times each add new factors that must also be considered. Choice reaction time (Type B) occurs when there are multiple possible signals, each requiring a different response. The responder must choose which signal was present, and then make the response appropriate for that light. This requires two processes not present in simple reaction time: 1) signal discrimination - decide which signal occurred and 2) response selection - choose the response based on which signal occurred. In the classic laboratory procedure, a person sits with his/her fingers on 2 different telegraph keys and waits for one of 2 different lights to flash. When a signal occurs, s/he releases the telegraph key assigned to that signal. Reaction time is again the time between light onset (signal) and release of the key (response.) With multiple signals, the responder cannot simply detect the signal but must also recognize which signal occurred and then mentally program the correct response. These extra mental operations slow reaction. Choice reaction times slow as the number of possible signals increases according to the equation, RT = a + b log2N where a and b are constants and N is the number of alternatives. The equation has two terms. The "a" constant is simply the "irreducible minimum" reaction time in the situation. (The variable part is called "the reducible margin.") The relationship between RT and the number of alternatives is nonlinear - doubling the number of alternatives does not increase RT by a factor of 2 but rather by the log of the number of possible signals. In Type C, or "recognition," reaction time, there are multiple possible signals but only one response. In this case, the responder makes the response when one stimulus occurs but withholds response when the other(s) appears. The standard lab version of this paradigm has a subject with his/her fingers on 1 telegraph key and waits for one of x different lights to flash. When the signal light occurs, s/he releases the telegraph. If one of the nonsignal lights occurs, then the subject should make no response. This is sometimes called the "go, no-go" paradigm. Reaction times are invariably longer than for simple reaction time. A good example would occur when a police officer confronts a "suspect." The officer sees something in the suspect's hand and must make a go (shoot) or no-go (don't shoot) decision. Final Comments This article has focused on driver reaction times. While the basic principles generalize to estimating other reaction times, the exact numbers do not. Each type of reaction time has its own peculiarities that must be examined. For example, reaction time for a shooter who is tracking a target might be 0.3 second. but even this would be a function of trigger pull weight. 1This is a brief summary/elaboration of the article, "'How Long Does It Take To Stop?' Methodological Analysis of Driver Perception-Brake Times" Transportation Human Factors, 2, pp 195-216, 2000. 2See Green, M. (2009). Perception-Reaction Time: Is Olson (& Sivak) All You Need To Know?," Collision, 4, 88-95. 3See Green, M. (2017). Roadway Human Factors: From Science To Application. Tucson: Lawyers & Judges Publishig.