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Publication Number: FHWA-HRT-06-033
Date: August 2006

Task Analysis of Intersection Driving Scenarios: Information Processing Bottlenecks

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APPENDIX A. SCENARIO TIMING AND KINEMATICS

This appendix provides details about how the scenario timing information and milestones used to make decisions about task allocation and timing were derived. More specifically, each scenario has an approximate timeline showing the key temporal milestones that represent key events that can be pinpointed in time based on scenario dynamics and assumptions. These milestones were used to make judgments about the pacing of tasks within scenario segments (e.g., forced-paced versus self-paced), as well as to provide a basis for the overall sequencing of certain sets of tasks. Where possible, milestones were calculated based on vehicle kinematics. This appendix provides details about the underlying equations, variables, results, and assumptions used to calculate timing values for each milestone. The resulting milestones were then incorporated into scenario timelines to provide an overview of the general timing of the scenario events.

Note that the timelines are not based on the absolute timing of events. They could not be done on this basis because most scenarios contained segments with undetermined durations (e.g., waiting for a safe gap in traffic), which make a time zero reference point impossible to determine. Consequently, the timeline is limited to showing the time interval between successive milestones or the duration of key tasks. The intervals between milestones that are presented in the timelines are always shown in bold in the milestone calculation tables. Also note that the timelines differentiate between normal driving-related milestones and hazard-related milestones (pictured in red). The hazard milestones provide information about approximately when the subject driver should have completed tasks associated with checking for specific hazards. Although these hazard milestones may be temporally interspersed with the other milestones, they are presented separately at the end of each set of scenario milestone descriptions. Moreover, they are displayed in the timelines without reference to other landmarks, with the implicit assumption that they represent some fixed time duration before the hazard (e.g., red-light-running vehicle) would be encountered in the roadway.

The kinematic features of each scenario, which determined the temporal and physical placement of the milestones, included acceleration and deceleration levels, RT, sight distances to the intersection, vehicle gap distances, and braking distances. The scenario dynamics and any associated assumptions were based on established values and guidelines described in the human factors literature and standard roadway design reference materials, such as the AASHTO Green Book(3) and the MUTCD.(4) Also, distances traveled and times of travel were calculated using standard motion equations found in any general physics text. (See Halliday, Resnick, and Walker,(5) page 20, to obtain these equations.)

General Assumptions

To determine the key temporal milestones associated with the scenario events, several assumptions were made regarding roadway geometry and design, RT, acceleration/deceleration levels, vehicle dimensions, and other elements in each of the scenarios. Table 92 lists the most commonly applied assumptions for determining the vehicle kinematics along with references to the information sources that provide a justification for the assumptions. These general assumptions apply to all milestones in the scenarios except in special cases; deviations from these assumed values are noted in the discussions of the scenario milestone calculations. Note that Green Book references refer to the 2004 AASHTO edition.(3)

Another general assumption that applies to the Approach segments of all scenarios is that although the scenario task analyses all specify that the subject vehicle decelerates slightly at the start of the Approach segment, it is assumed that the subject vehicle is traveling faster than 50 km/h at the start of the segment and that this initial deceleration reduces travel speed to a constant 50 km/h.

Table 92. Commonly applied assumptions with corresponding justification.

Assumption

Value

Reference

Motor reaction time (used for braking and accelerating and other tasks under normal conditions).

0.4 sec

Green 2000 (30)

Perceptual-motor reaction time for emergency/evasive actions.

0.70 sec

Green 2000 ††(30)

Roadway design speed.

50 km/h

Green Book, p. 7(3)

Vehicle length.

5.8 m

Green Book, p. 16(3)

Vehicle minimum centerline turn radius.

6.4 m

Green Book, p. 19(3)

Comfortable deceleration level.

−3.4 meters per second squared (m/sec2)

Green Book, p. 111(3)

Hard (emergency) deceleration level.

−4.5 m/sec2

Green Book, p. 111(3)

Acceleration level.

2.0 m/sec2

Akçelik and Besley (2002) †††(31)

Many calculations involving a driver response used a motor response time instead of a perceptual-motor response time. The reason for this was that the perceptual, cognitive, and decisionmaking components of these activities are already represented in the task analysis, and including them in the RT would artificially reduce the time available for conducting those tasks. Also, the value of 0.4 sec for the motor RT was selected–even though it is on the upper end of the range of observed motor times(30) because it better generalizes both the time-critical and more leisurely situations in which the motor RT is applied in this analysis. At a practical level, however, the short time difference between the 0.4 sec motor RT and the observed lower bound of 0.2 sec for motor RTs would have negligible effect on the time available to conduct scenario tasks.

†† Calculations involving emergency or evasive maneuvers used a 0.70 perceptual-motor RT. This represents a best-case average RT for an expected event.(30) In this case, an expected event is assumed rather than an unexpected event, because if the drivers are performing the tasks listed in the task analysis, the subject driver should be led to expect the hazard in most instances. Note that in contrast to elsewhere in this analysis–where just a motor RT is used–this RT represents both motor and perceptual components of the response. Both components were combined because detecting and reacting to a hazard in this manner seems to be an automatic or self-contained action (Groeger, 2000).(11)

††† To simplify the calculations, we used a constant acceleration level interpolated from acceleration tables and models.(3,31) The value that we used (2.0 m/sec2) ended up being on the high end of the interpolation, but this was necessary because lower values did not provide sufficient clearance when the subject vehicle was accelerating through gaps in oncoming traffic.

Scenario Kinematics

The following sections describe the calculations used to determine the key temporal milestones based on vehicle kinematics for each scenario. Each description contains the following elements:

  • A timeline summarizing the timing of the milestones in relation to the scenario segments. The timeline is based on the results of the milestone calculations presented in this appendix.
  • A table of key temporal milestones.
  • A description of each milestone.
  • A textual description of the milestone.
  • A table listing the equations used to calculate the timing and distances associated with the milestone and the assumptions made for the calculation.
  • Additional information regarding assumptions where applicable.

Note that the units used in all equations conform to the International System of Units (SI) meter-second-kilogram (MSK) standard. Therefore, distance is calculated in m, speed is calculated in meters per second (m/sec), acceleration is calculated in m/sec2, and time is calculated in sec. For the convenience of the reader, some variables discussed in the assumptions are described in other units (e.g., speeds measured in km/h); however, the calculations were made using MSK units.

Scenario 1–Left turn on green light

Figure 62 provides the timeline and calculated vehicle speed information for Scenario 1. The key temporal milestones are described in table 93. Some milestones that are shown in figure 62 (e.g., intersection becomes visible) are not described in table 93 and do not have corresponding timestamps computed. These milestones either do not affect the scenario timing in a meaningful way, or they cannot be computed because of insufficient information. They are included only to provide additional contextual information for understanding the timeline.

View Alternative Text

Figure 62. Scenario 1–Left Turn on Green Light

timeline depicting key temporal milestones.

Table 93. Scenario 1–Left Turn on Green Light

description of key temporal milestones.

Key Milestones

Description

A

Street sign becomes readable.

This milestone provides the earliest point at which the driver can begin determining if the intersection is the correct turn intersection (task 1.1.7) and, in conjunction with the braking distance (next milestone), indicates the time available to perform tasks 1.1.7 and 1.1.8.

B

Comfortable braking distance.

This milestone provides the latest point at which the driver can begin decelerating and maintain a comfortable deceleration level. It also represents the time point before which the driver should have completed tasks 1.1.7 and 1.1.8.

C

Vehicle stops.

This milestone is the point where the vehicle comes to a complete stop at the stop line and marks the endpoint of segment 2 (Deceleration).

D

Turn completed.

This milestone represents the end of the interval in which the subject vehicle is actively engaged in turning (tasks 1.5.1 through 1.5.3) and is directly in the path of oncoming traffic (after the acceleration RT).

Milestone A–Street sign becomes readable

This milestone provides the earliest point at which the driver can begin reading the street signs to determine if the intersection is the correct turn intersection (task 1.1.7). It also indicates the time available to perform tasks 1.1.7 and 1.1.8 in conjunction with the braking distance (next milestone). Table 94 lists the equations and assumptions in Scenario 1–Left Turn on Green Light, Milestone A.

Table 94. Scenario 1–Left Turn on Green Light

equations and assumptions for Milestone A.

Description

Equations

Eq. No.

Result

Assumptions

Distance from intersection that street sign becomes readable.

dread = 0.48 m x height of text in mm

1

73 m

  • Street sign letter height of 152.4 millimeters (mm).
  • Typical symbol reading distance of 12.2 m/(25.4 mm of text height).† †

Distance traveled to braking distance.

dcutoff = dread - ddecel

2

39 m

  • ddecel taken from Milestone B
  • Vehicle is traveling at a constant speed of 50 km/h.

Time available to read the sign.

t subscript sign. t subscript sign equals the d subscript cutoff divided by v subscript 0

3

2.8 sec

  • Vehicle is traveling at a constant speed of 50 km/h.

MUTCD reference for letter height: p. 2D-17.(4)

† † MUTCD reference for sign distance relative to letter height: p. 2A-7. (4)

Milestone B–Comfortable braking distance

Milestone B provides the latest point at which the driver can begin decelerating and maintain a comfortable (nonemergency) deceleration level until coming to a full stop at the stop line. It also represents the time point before which the driver should have completed tasks 1.1.7 and 1.1.8. Table 95 lists equations and assumptions for Scenario 1–Left Turn on Green Light, Milestone B.

Table 95. Scenario 1–Left Turn on Green Light, Milestone B,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Braking reaction time (tBRT).

Assumed value

_

0.4 sec

  • General motor RT.

Deceleration interval (excludes braking RT).

t subscript decel. t subscript decel equals negative v subscript 0 divided by A

4

4.1 sec

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −3.4 m/sec2 (a).

Distance traveled during deceleration (includes braking RT).

ddecel = 0.5at2decel + v0 (tdecel + tBRT )

5

34 m

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −3.4 m/sec2 (a).

Milestone C–Vehicle stops

This is the point where the vehicle comes to a complete stop at the stop line and marks the endpoint of segment 2 (Deceleration). Table 96 lists equations and assumptions for Scenario 1–Left Turn on Green Light, Milestone C.

Table 96. Scenario 1–Left Turn on Green Light, Milestone C,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Time to stop line once decision is made to stop.

tstop = tBRT + tdecel

6

4.5 sec

  • Vehicle comes to a complete stop at the stop line.
  • tBRT (0.4 s) and tdecel (4.1 sec) taken from Milestone B.

Milestone D–Turn completed

Milestone D represents the interval from the onset of the turn (including the motor RT) up until the turn is complete (tasks 1.5.1 through 1.5.3), and it represents the time that the subject vehicle is directly in the path of oncoming traffic (after the acceleration motor RT). Table 97 lists equations and assumptions for Scenario 1–Left Turn on Green Light, Milestone D.

Table 97. Scenario 1–Left Turn on Green Light, Milestone D,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Acceleration reaction time (tART).

Assumed value

 

-

0.4 sec

  • General motor RT.

Time to complete turn.

t subscript turn. t subscript turn equals the sum of the following: the square root of the product 2 times d subscript turn, end of product, that product divided by A, end of square root, to that square root add t subscript A R T

7

4.7 sec

  • Distance from turn location to completion point is 22 m (dturn) including vehicle length.
  • Vehicle accelerates at a constant level of 2.0 m/sec2 (a).

The cognitive/perceptual elements of this action are defined as being part of the preceding tasks. More specifically, the decision to turn is the culmination of tasks 2.4.5 through 2.4.8 of the preceding segment; thus, this RT simply represents the time needed to press the accelerator and start turning the steering wheel following this decision.

Scenario 2–Left turn on yellow light

Figure 63 provides the timeline and calculated vehicle speed information for Scenario 2. The key temporal milestones are described in table 98. Some milestones shown in figure 63 (e.g., intersection becomes visible) are not described in table 98 and do not have corresponding timestamps computed. These milestones either do not affect the scenario timing in a meaningful way, or they cannot be computed because of insufficient information. They are included only to provide additional contextual information for understanding the timeline.

View Alternative Text

Figure 63. Scenario 2–Left Turn on Yellow Light

timeline depicting key temporal milestones.

Table 98. Scenario 2–Left Turn on Yellow Light

description of key temporal milestones.

Key Milestones

Description

A

Comfortable braking distance.

Provides the latest point at which the driver can begin decelerating and maintain a comfortable deceleration level. It also specifies the endpoint of the Approach segment.

B

Traffic signal turns yellow.

Marks the beginning of segment 3 (Decision to Proceed) and determines how much time the driver has to complete the following segments (3 through 5).

C

Vehicle reaches turning speed.

The point at which the subject vehicle reaches the turning speed and then continues towards the turn location at a constant speed.

D

Initiate turn.

The point at which the subject vehicle arrives at the location where it is necessary to begin the left turn. It also marks the end of the Intersection Entry segment.

E

Turn completed.

Represents the interval in which the subject vehicle is actively engaged in turning (tasks 2.5.1 through 2.5.3).

Hazard Milestones

Description

F

Braking distance for stopping in the intersection.

This is the last point in time that the subject vehicle can still come to a stop in the intersection before starting the turn trajectory. It represents the point by which the driver must have determined that it is safe to proceed (e.g., there are no oncoming vehicles–task 2.4.6–or hazards in the turn path–task 2.4.7).

G

Last point for emergency maneuver in reaction to red-light runners.

This represents the latest time by which the subject driver can detect and respond to the hazard in order to initiate at least a minimal evasive action (task 2.5.3).

Milestone A–Comfortable braking distance

Milestone A is the latest point at which the driver can begin decelerating and maintain a comfortable deceleration level. It also specifies the endpoint of the Approach segment. Table 99 lists the equations and assumptions for Scenario 2–Left Turn on Yellow Light, Milestone A.

Table 99. Scenario 2–Left Turn on Yellow Light, Milestone A,

equations and assumptions.

Description

Equation

Eq.

Result

Assumptions

Braking reaction time (tBRT).

Assumed value

_

0.4 sec

  • General motor RT

Deceleration interval (excludes braking RT).

t subscript decel. t subscript decel equals negative v subscript 0 divided by A

8

4.1 sec

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of−3.4 m/sec2(a).
  • Projected deceleration endpoint (0 km/sec) is the stop line.

Deceleration distance (excludes braking RT).

ddecel = 0.5at2decel + v0 (tdecel + tBRT)

9

28 m

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −3.4 m/sec2 (a).

An endpoint of 0 km/h at the stop line was used to calculate the starting point for braking, with the assumption that the vehicle continues at a constant speed after reaching 16 km/h. This endpoint was selected instead of the turn location because it is more conservative (drivers can stop more easily for hazards at the crosswalk). At a practical level, however, the difference between this endpoint and an endpoint of 16 km/h at the turn location is negligible.

Milestone B–Traffic signal turns yellow

This milestone marks the beginning of Decision to Proceed, segment 3, and it determines how much time the driver has to complete the following segments 3 through 5 (table 100). One point to note is that the yellow light onset time is arbitrary, but nevertheless important, because it affects the allocation of tasks within segments and the time available to perform some of those tasks. A primary objective in setting the yellow onset time was to have the light change when it was not safe for the subject vehicle to stop (which works out to be just after the braking distance in this scenario). Another consideration was that the light should not change to red until after the turn was initiated (start of Execute Turn segment), so that the subject driver would still be required to check for–and need to able to stop in response to–oncoming traffic crossing on a late yellow light. Thus, a yellow onset time of 2.5 sec after the start of the Deceleration segment (and exactly 4 sec before the Execute Turn segment) was chosen because it maximizes the time available to perform the tasks that need to be completed before the start of the Execute Turn segment, while still meeting the other requirements.

Table 100. Scenario 2–Left Turn on Yellow Light, Milestone B,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Yellow light detection time (tDRT).

Assumed value

-

0.4 sec

  • Light detection time.

Time to make decision to proceed.

Assumed value

-

1.0 sec

  • Arbitrary time interval representing the time required to make decision to proceed.

Yellow phase duration.

Assumed value

-

4.0 sec

  • Yellow light duration time of 4 sec.† †

The detection time is based on the perception RT reported in studies in which drivers respond to a light-based event, such as the change in traffic light or the onset of brake lights. The value chosen (0.4 sec) is on the high end of observed values reported in Green (2000).(30)

† † A yellow phase duration of 4 sec represents the upper bound of recommended phase durations.(23) This value was chosen in order to remain consistent with the yellow phase duration used in Scenario 3 (see the Segment 3 timeline discussion above for an explanation of the basis of this assumption). An advantage of using this interval duration was that it allowed the yellow onset to occur relatively far back in the intersection, which permitted the use of a more complicated scenario because the subject driver would still have time to complete a larger set of tasks before turning.

Milestone C–Vehicle reaches turning speed

Milestone C represents the point at which the subject vehicle reaches the turning speed and then continues toward the turn location at a constant speed. Table 101 lists equations and assumptions for Scenario 2–Left Turn on Yellow Light, Milestone C.

Table 101. Scenario 2–Left Turn on Yellow Light, Milestone C,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Time required to decelerate to turning speed (ttv).

t subscript tv. t subscript tv equals the following quotient: the sum of v subscript f minus v subscript 0, end of sum, that sum divided by A

10

2.8 sec

  • Vehicle decelerates at a constant level of −3.4 m/sec2 (a) from 50 km/h (v0) to 16 km/h (vf).

Distance traveled until turn speed reached.

dtv = 0.5at2tv + v0ttv

11

25 m

Milestone D–Initiate turn

Milestone D represents the point at which the subject vehicle arrives at the location where it is necessary to begin the left turn. It also marks the end of the Intersection Entry segment. Table 102 lists equations and assumptions for Scenario 2–Left Turn on Yellow Light, Milestone D.

Table 102. Scenario 2–Left Turn on Yellow Light, Milestone D,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Time required to travel from point at which turning speed reached until stop line reached.

t subscript stopline. t subscript stopline equals the quotient of the following: the sum of d subscript decel minus d subscript tv, end of sum, that sum divided by v

12

0.7 sec

  • ddecel (28 m) from Milestone A.
  • dtv (25 m) from Milestone C.
  • Vehicle traveling at constant speed of 16 km/h (v).

Distance to turn point from stop line (dTP).

Assumed value

-

7.6 m

  • Value determined from roadway geometry.

Time required to travel from stop line to turn point at constant speed.

t subscript TP equals d subscript TP divided by v

13

1.7 sec

  • Vehicle traveling at constant speed of 16 km/h (v).

Milestone E–Turn completed

Milestone E represents the interval in which the subject vehicle is actively engaged in turning (tasks 2.5.1 through 2.5.3). Table 103 lists equations and assumptions for Scenario 2–Left Turn on Yellow Light, Milestone E.

Table 103. Scenario 2–Left Turn on Yellow Light, Milestone E,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Acceleration/steering reaction time (tART).

Assumed value

-

0.4 sec

  • General motor RT.

Distance traveled during motor reaction time.

dART = v0tART

14

1.8 m

  • Vehicle traveling at constant speed of 16 km/h (v0).

Distance through turn.

dturn = dpath - dART

15

16.7 m

  • Total path distance through the intersection of 18.5 m including vehicle length (dpath).

Time required to accelerate through turn.

t subscript turn. t subscript turn equals negative v subscript 0 plus the square root of v subscript 0 squared plus 2 times A times d subscript turn, end of square root, all divided by A

16

2.4 sec

  • Vehicle accelerates at a constant level of 2.0 m/sec2 (a).

† The cognitive/perceptual elements of this action are defined as being part of the preceding tasks. More specifically, the decision to turn is the culmination of tasks 2.4.5 through 2.4.8 of the Intersection Entry Segment. Thus, this RT simply represents the time needed to press the accelerator and start turning the steering wheel following this decision.

Milestone F–Braking distance for stopping in the intersection

Milestone F is the last point in time that the subject vehicle can still come to a stop in the intersection before starting the turn trajectory. It represents the point by which the driver must have determined that it is safe to proceed (e.g., there are no oncoming vehicles–task 2.4.6–or hazards in the turn path–task 2.4.7). Table 104 lists equations and assumptions for Scenario 2–Left Turn on Yellow Light, Milestone F.

Table 104. Scenario 2–Left Turn on Yellow Light, Milestone F,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Emergency perceptual-motor reaction time (tERT).

Assumed value

-

0.70 sec

  • Emergency RT.

Deceleration time.

t subscript decel. t subscript decel equals negative v subscript 0 divided by A

17

1.1 sec

  • Vehicle traveling at
    16 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −4.0 m/sec2 (a).

Latest time to initiate braking for stopping at turn location.*

tstop = tERT + tdecel

18

1.8 sec

  • No additional assumptions.

* Measured from a turn point that is 7.6 m from the stop line.

Milestone G–Last point for emergency maneuver in reaction to red-light runners

Milestone G represents the latest point at which it is possible to initiate at least a minimal evasive action in response to a potential collision with a red-light-running vehicle (task 2.5.3). Note that this duration is not intended to allow the subject vehicle to come to a stop or even to necessarily avoid the collision. It simply represents a minimal interval for the driver to see the potential problem and initiate a last=minute emergency maneuver that will have at least a minimal effect on the impending collision. The actual duration is an arbitrary value that is large enough to contain an emergency RT (0.7 sec) and a minimal amount of time for the vehicle to respond to the braking (1.3 sec). Table 105 lists equations and assumptions for Scenario 2–Left Turn on Yellow Light, Milestone G.

Table 105. Scenario 2–Left Turn on Yellow Light, Milestone G,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Emergency perceptual-motor reaction time (tERT).

Assumed value

-

0.70 sec

  • Emergency RT.

Time for minimal response (tresponse).

Assumed value

-

1.3 sec

  • See text above.

Latest time to respond to hazard.*

thazard = tERT + tresponse

19

2.0 sec

  • No additional assumptions.

* Measured from hypothetical collision point of 0.8 m before the turn point.

Scenario 3–Straight on yellow light

Figure 64 provides the timeline and calculated vehicle speed information for Scenario 3. The key temporal milestones are described in table 106. Some milestones that are shown in figure 64 (e.g., intersection becomes visible) are not described in table 106 and do not have corresponding timestamps computed. These milestones either do not affect the scenario timing in a meaningful way or they cannot be computed because of insufficient information. They are included only to provide additional contextual information for understanding the timeline.

View Alternative Text

Figure 64. Scenario 3–Straight on Yellow Light timeline

depicting key temporal milestones.

Table 106. Scenario 3–Straight on Yellow Light description of key temporal milestones.

Key Milestones

Description

A

Farthest distance to legally proceed.

This is the farthest distance away from the intersection that the driver can be and still make it into the intersection before the light turns red. It represents the start of the option zone in which drivers have the option to either proceed or to stop. Note that the light is assumed to turn yellow when the subject vehicle reaches this point.

B

Aggressive braking distance.

This provides the latest point at which the driver can begin decelerating and still maintain a moderately aggressive, nonemergency deceleration level for coming to a stop at the stop line. It represents the end of the option zone in which drivers have the option to either proceed or stop.

Hazard Milestones

Description

C

Last point for emergency maneuver in reaction to red-light runners.

This represents the latest time by which the subject driver can detect and respond to the hazard in order to initiate at least a minimal evasive action (task 3.3.4).

D

Last point for emergency maneuver in reaction to oncoming traffic turning left at the last minute.

This represents the latest time by which the subject driver can detect and respond to oncoming traffic turning left at the last minute and make at least a minimal evasive action (task 3.3.5).

Milestone A–Farthest distance to legally proceed

Milestone A addresses the farthest distance away from the intersection that the driver can be and still make it into the intersection before the light turns red. It represents the start of the option zone in which drivers have the option to either proceed or to stop. Note that the light is assumed to turn yellow when the subject vehicle reaches this point. Also, note that the subject vehicle cannot begin the process of deciding whether to go until the yellow light onset has been detected. Table 107 lists equations and assumptions for Scenario 3–Straight on Yellow Light, Milestone A.

Table 107. Scenario 3–Straight on Yellow Light, Milestone A,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Yellow light detection time (tDRT).

Assumed value

-

0.4 sec

  • Light detection time.

Distance traveled during yellow phase.

dyellow = v0tyellow

20

56 m

  • Yellow phase duration of 4 sec (tyellow).
  • Vehicle traveling at constant speed of 50 km/h (v0).

Latest distance from stop line to be able to proceed legally.

dproceed = dyellow - dint

21

50 m

  • Signal turns red when vehicle is 1 m into the intersection (dint).

Time available for tasks 3.2.4 through 3.2.8 (option zone).

t subscript task. t subscript task equals the sum of the following: the quotient of the sum d subscript minus d subscript stop, end sum, that sum divided by v subscript 0, from that quotient subtract t subscript DRT

22

1.0 sec

  • Vehicle traveling at constant speed of 50 km/h (v0).
  • dstop (3.9 sec) from Milestone B.

The detection time is based on the perception RT reported in studies in which drivers respond to a light-based event, such as the change in traffic light or the onset of brake lights. The value chosen (0.4 sec) is on the high end of observed values reported in Green (2000).(30)

Milestone B–Aggressive braking distance

Milestone B indicates the latest point by which the driver can begin decelerating and still maintain a moderately aggressive, nonemergency deceleration level for coming to a stop at the stop line. It represents the end of the option zone in which drivers have the option to either proceed or stop; however, whether the driver stops or continues through the intersection depends on the outcome of segment 2 (Decision to Proceed). Thus, it is also the point by which tasks 3.2.5, 3.2.7, and 3.2.8 should be completed.

Table 108 lists equations and assumptions for Scenario 3–Straight on Yellow Light, Milestone B.

Table 108. Scenario 3–Straight on Yellow Light, Milestone B,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Braking reaction time (tBRT).

Assumed value

-

0.4 sec

  • General motor RT.

Distance traveled during braking RT (dBRT).

dRT = v0tBRT

23

6 m

  • Vehicle traveling at constant speed of 50 km/h (v0).

Braking time.

t subscript BR. t subscript BR equals negative v subscript 0 divided by A

24

3.5 sec

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −4.0 m/sec2 (a).
  • Vehicle comes to a complete stop at the stop line.

Braking distance.

dBR = 0.5 at2BR + v0tBR

25

24 m

Latest time to brake.

tstop = tBRT + tBR

26

3.9 sec

Latest distance to stop point for braking.

dstop = dBRT + dBR

27

30 m

Vehicle enters the intersection.

t subscript int. t subscript int equals d subscript int divided by v subscript 0

28

2.5 sec

  • Vehicle traveling at constant speed of 50 km/h (v0).
  • Intersection entry occurs 6 m past the stop line (dint.).

Due to the time-critical nature of stopping before the light turns red, a more aggressive deceleration was used. The Green Book (p. 111)(3) defines hard (emergency) braking to be 4.5 m/sec2 and comfortable braking to be 3.4 m/sec2. A level of 4.0 m/sec2 is roughly in between these values and likely reflects an aggressive level of deceleration.

Milestone C–Last point for emergency maneuver in reaction to red-light runners

Milestone C represents the latest point at which it is possible to initiate at least a minimal evasive action in response to a potential collision with a red-light-running vehicle (task 3.3.4). How it works is that an arbitrary cutoff point for responding to a potential hazard was selected (0.7 sec RT + 1.3 sec maneuver (table 109). This 2-sec interval allows a vehicle traveling at 50 km/h to slow to just more than 30 km/h and provides some time to alter the vehicle's trajectory. Note that this interval may not allow the drivers to avoid a collision, but it will reduce the consequences of that collision. Also, an implicit assumption in this approach is that once the vehicle is within 2 sec of the potential collision point, it is no longer worthwhile to continue to systematically search for that hazard because any subsequent response will have little or no effect in mitigating the crash impact.

Table 109. Scenario 3–Straight on Yellow Light, Milestone C,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Emergency perceptual-motor reaction time (tERT).

Assumed value

-

0.70 sec

  • Emergency RT.

Time for minimal response (tresponse).

Assumed value

-

1.3 sec

  • See text above.

Latest time to respond to hazard.*

thazard = tERT + tresponse

29

2.0 sec

  • No additional assumptions.

* Measured from hypothetical collision point of 1.8 m into the intersection.

Milestone D–Last point for emergency maneuver in reaction to oncoming traffic turning left at the last minute

Milestone D represents the latest point at which it is possible to initiate at least a minimal evasive action in response to a potential collision with a red-light-running vehicle (task 3.3.5). How it works is that an arbitrary cutoff point for responding to a potential hazard (0.7 sec RT + 1.3 sec) maneuver; was selected (table 110). This 2-sec interval allows a vehicle traveling at 50 km/h to slow to just more than 30 km/h and provides some time to alter the vehicle's trajectory. Note that this interval may not allow the drivers to avoid a collision, but it will reduce the consequences of that collision. Also, an implicit assumption in this approach is that once the vehicle is within 2 sec of the potential collision point, it is no longer worthwhile to continue to systematically search for that hazard because any subsequent response will have little or no effect in mitigating the crash impact.

Table 110. Scenario 3–Straight on Yellow Light, Milestone D,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Emergency perceptual-motor reaction time (tERT).

Assumed value

-

0.70 sec

  • Emergency RT.

Time for minimal response (tresponse).

Assumed value

-

1.3 sec

  • See text above.

Latest time to respond to hazard.*

thazard = tERT + tresponse

30

2.0 sec

  • No additional assumptions.

Measured from hypothetical collision point of 5.4 m into the intersection.

Scenario 4–Straight on green light

Figure 65 provides the timeline and calculated vehicle speed information for Scenario 4. The key temporal milestones are described in table 111. Some milestones shown in figure 65 (e.g., intersection becomes visible) are not described in table 111 and do not have corresponding timestamps computed. These milestones either do not affect the scenario timing in a meaningful way, or they cannot be computed because of insufficient information. They are included only to provide additional contextual information for understanding the timeline.

View Alternative Text

Figure 65. Scenario 4–Straight on Green Light timeline

depicting key temporal milestones.

One noteworthy point is that most key milestones in this scenario are arbitrarily set in time. This is because the lead vehicle braking event (which triggers the need to change lanes) can happen at any point in time, which means that essentially any amount of time can be allotted to complete the scenario tasks; however, our goal was to maintain a challenging and rapid task pacing. This was done by first determining the time intervals and scenario assumptions that would achieve this objective, and then working backwards from there to set the overall scenario timing. In particular, we started with a 2.5 sec time-to-collision (TTC) between the subject vehicle and the turning vehicle in the originating lane as the endpoint to the lane change, then went backward in the timeline to accommodate additional intervals for the "executing lane changing" (2.0 sec), "preparing for lane changing" (2.5 sec), and "detect brake lights" (0.4 sec) events in order to set the lead vehicle braking milestone. Note that the time interval durations are explained below in the individual milestone discussions. In addition, two scenario assumptions were made in order to promote rapid pacing of the lane change: that the lead vehicle does not brake until the subject vehicle is close enough to the intersection so that the lane change must be completed quickly and that there is another vehicle behind the subject vehicle in the destination lane, which requires the subject vehicle to keep traveling at speed to make the lane change possible.

Note that for the remainder of the Scenario 4 milestone calculation discussion, the term "lead vehicle" refers to the vehicle in front of the subject vehicle in the originating lane.

Table 111. Scenario 4–Straight on Green Light description of key temporal milestones.

Key Milestones

Description

A

Driver detects lead vehicle braking.

This milestone is the last task conducted as part of the Approach Segment, and it prompts the subject driver to determine if it is possible to change lanes in the next segment (Prepare for Lane Change).

B

Complete preparation for lane change.

This marks the end/duration of the Prepare for Lane Change Segment.

C

Complete lane change.

This marks the end/duration of the Execute Lane Change Segment. It also corresponds with the point at which the subject vehicle is no longer in potential conflict with the turning vehicle in the original lane.

Hazard Milestones

Description

D

Last point for emergency maneuver in reaction to red-light runners.

This represents the latest time by which the subject driver can detect and respond to the hazard in order to initiate at least a minimal evasive action (task 4.4.5).

E

Last point for emergency maneuver in reaction to oncoming traffic turning left at the last minute.

This represents the latest time by which the subject driver can detect and respond to oncoming traffic turning left at the last minute and make at least a minimal evasive action (task 4.4.6).

Milestone A–Driver detects lead vehicle braking

Milestone A is the last task conducted as part of the Approach segment, and it prompts the subject driver to determine if it is possible to change lanes in the next segment (Prepare for Lane Change) (table 112).

Table 112. Scenario 4–Straight on Green Light, Milestone A,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Time required for lead vehicle to decelerate to a stop (tdecelL).

t subscript decel capital L. t subscript decel capital L equals negative v subscript 0 divided by A

31

4.1 sec

  • Lead vehicle traveling at constant speed of 50 km/h at onset of braking (v0).
  • Lead vehicle decelerates at a level of −3.4 m/sec2 (a).

Detect brake lights (detection RT tDRT).

Assumed value

-

0.4 sec

  • Light detection time.† †

Lead vehicle deceleration distance.

d subscript decel capital L. d subscript decel capital L equals negative v subscript 0 squared divided by the product 2 times A

32

28 m

  • Lead vehicle traveling at constant speed of 50 km/h at onset of braking (v0).
  • Lead vehicle decelerates at a level of −3.4 m/sec2 (a).

The lead vehicle deceleration trajectory is required for the calculation of the 2.5-sec TTC separation between the lead and subject vehicles at the completion of the lane change.

† † The detection time is based on the perception RT reported in studies in which drivers respond to a light-based event, such as the change in traffic light or the onset of brake lights. The value chosen (0.4 sec) is on the high end of observed values reported in Green (2001).(30)

Milestone B–Complete preparation for lane change

Milestone B marks the end/duration of the Prepare for Lane Change segment (table 113).

Table 113. Scenario 4–Straight on Green Light, Milestone B,

equations and assumptions.

Description

Equation

Result

Assumptions

Duration of activities related to preparing for the lane change (tprepLC).

Assumed value

2.5 sec

  • The lane change is hurried.

† This value is based on research by Mourant and Donohue,(32) which was conducted on novice drivers making left-side lane changes and found that drivers took an average of 2.4 sec to complete the visual scanning that precedes a lane change. Also, more recent research indicates that most glances related to prelane scanning behavior can be captured in an analysis window encompassing the 3 sec just before the lane-change onset.(24)

Milestone C–Complete lane change

Milestone C marks the end/duration of the activities related to maneuvering the subject vehicle from the originating lane to the destination lane. It also corresponds with the point at which the subject vehicle is no longer in potential conflict with the lead vehicle in the originating lane. A key assumption is that the lane change is completed by the point in time where there is a 2.5-sec TTC between these vehicles (table 114).

Table 114. Scenario 4–Straight on Green Light, Milestone C,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Duration of the lane change (texecLC).

Assumed value

-

3.0 sec

  • The lane change is hurried.

Time to stop line at completion of lane change (tstopline).

t subscript stopline. t subscript stopline equals t subscript TTC minus the quotient 5.8 divided by v subscript 0

33

2.1 sec

  • Lane change completed when TTC with lead vehicle is 2.5 sec (tTTC).
  • Rear bumper of lead vehicle 5.8 m from stop line.
  • Vehicle traveling at constant speed of 50 km/h.

This value is slightly faster than the low end of the range for observed lane change durations in city environments, which have 3.5 to 3.4 sec as a lower bound and a mean/modal duration of around 6 sec.(33,34) The reason why a shorter duration was assumed was to reflect the hurried pacing of the lane change because the subject vehicle must get out of the way of the stopping lead vehicle in the originating lane. Also, we conducted informal pilot testing in a driving simulator with three experienced drivers and found that they were consistently able to complete a comparable lane-change maneuver in around 2.5 to 3 sec. As a practical matter, the duration of this segment has little effect on the scenario because lengthening this interval would just mean that the lane change has to start farther back from the intersection.

Milestone D–Last point for emergency maneuver in reaction to red-light-runners

Milestone D represents the latest point at which it is possible to initiate at least a minimal evasive action in response to a potential collision with a red-light-running vehicle (task 4.4.5). It works with an arbitrary cutoff point for responding to a potential hazard (0.7 sec RT + 1.3 sec maneuver). This 2-sec interval allows a vehicle traveling at 50 km/h to slow to just more than 30 km/h and provides some time to alter the vehicle's trajectory. Note that this interval may not allow the drivers to avoid a collision, but it will reduce the consequences of that collision. Also, an implicit assumption in this approach is that once the vehicle is within 2 sec of the potential collision point, it is no longer worthwhile to continue to search systematically for that hazard because any subsequent response will have little or no effect in mitigating the crash impact. Table 115 lists equations and assumptions for Scenario 4–Straight on Green Light, Milestone D.

Table 115. Scenario 4–Straight on Green Light, Milestone D, equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Emergency perceptual-motor reaction time (tERT).

Assumed value

-

0.70 sec

  • Emergency RT

Time for minimal response (tresponse).

Assumed value

-

1.3 sec

  • See text above

Latest time to respond to hazard.*

thazard = tERT + tresponse

34

2.0 sec

  • No additional assumptions.

* Measured from the hypothetical collision point of 1.8 m into the intersection.

Milestone E–Last point for emergency maneuver in reaction to oncoming traffic turning left at the last minute

Milestone E represents the latest point at which it is possible to initiate at least a minimal evasive action in response to a potential collision with a red-light-running vehicle (task 4.4.6). It works with an arbitrary cutoff point (0.7 sec RT + 1.3 sec) for responding to a potential hazard maneuver. This 2-sec interval allows a vehicle traveling at 50 km/h to slow to just more than 30 km/h and provides some time to alter the vehicle's trajectory. Note that this interval may not allow the drivers to avoid a collision, but it will reduce the consequences of that collision. Also, an implicit assumption in this approach is that when the vehicle is within 2 sec of the potential collision point, it is no longer worthwhile to continue to search systematically for that hazard because any subsequent response will have little or no effect in mitigating the crash impact. Table 116 lists equations and assumptions for Scenario 4–Straight on Green Light, Milestone E.

Table 116. Scenario 4–Straight on Green Light, Milestone E,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Emergency perceptual-motor reaction time (tERT).

Assumed value

-

0.70 sec

  • Emergency RT.

Time for minimal response (tresponse).

Assumed value

-

1.3 sec

  • See text above.

Latest time to respond to hazard.*

thazard = tERT + tresponse

35

2.0 sec

  • No additional assumptions.

* Measured from the hypothetical collision point of 5.4 m into the intersection.

Scenario 5–Right turn on green

Figure 66 provides the timeline and calculated vehicle speed information for Scenario 5. The key temporal milestones are described in table 117. Some milestones that are shown in figure 66 (e.g., intersection becomes visible) are not described in table 117 and do not have corresponding timestamps computed. These milestones either do not affect the scenario timing in a meaningful way or they cannot be computed because of insufficient information. They are included only to provide additional contextual information for understanding the timeline.

View Alternative Text

Figure 66. Scenario 5–Right Turn on Green Light timeline

depicting key temporal milestones.

Table 117. Scenario 5–Right Turn on Green Light description of key temporal milestones.

Key Milestones

Description

A

Street sign becomes readable.

This provides the earliest point at which the driver can begin determining if the intersection is the correct turn intersection (task 5.1.7). In conjunction with the braking distance (next milestone), this milestone indicates the time available to perform tasks 5.1.7 and 5.1.8.

B

Comfortable braking distance.

This provides the latest point at which the driver can begin decelerating and maintain a comfortable deceleration level. It also represents the time point before which the driver should have completed tasks 5.1.5 through 5.1.8.

C

Vehicle reaches turning speed.

This is the point at which the subject vehicle reaches the turning speed and then continues towards the turn location at a constant speed.

D

Initiate turn.

This is the point at which the subject vehicle arrives at the location where it is necessary to begin the right turn. It also marks the end of the Intersection Entry Segment.

E

Turn completed.

This represents the interval in which the subject vehicle is actively engaged in turning (tasks 5.4.1 through 5.4.4).

F

Braking distance for stopping in the intersection.

This is the last point in time that the subject vehicle can still come to a stop in the intersection before starting the turn trajectory. It represents the point by which the driver must have determined that it is safe to proceed (e.g., there are no conflicts with red-light-running traffic–task 5.3.6, oncoming left-turning vehicles–task 5.3.7, or hazards in the turn path–task 5.3.8).

Milestone A–Street sign becomes readable

Milestone A provides the earliest point at which the driver can begin determining if the intersection is the correct turn intersection (task 5.1.7) and, in conjunction with the deceleration cutoff point (next milestone), it indicates the time available to perform tasks 5.1.5 through 5.1.8. Table 118 lists equations and assumptions for Scenario 5–Right Turn on Green Light, Milestone A.

Table 118. Scenario 5–Right Turn on Green Light, Milestone A,

equations and assumptions.

Description

Equations

Eq. No.

Result

Assumptions

Distance from intersection in which street sign becomes readable.

dread = 0.48 m x height of text in mm

36

73 m

  • Street sign letter height of 152.4 mm (6inches).
  • Symbol legibility distance of 12.2 m per 25.4 mm (40 ft per in) of text height.††

Distance traveled to braking distance.

dcutoff = dread - ddecel

37

39 m

  • Vehicle is traveling at a constant speed of 50 km/h.
  • ddecel(34 m) from Milestone B.

Time of travel to braking distance.

t subscript cutoff. t subscript cutoff equals the d subscript cutoff divided by v subscript 0

38

2.8 sec

  • Vehicle is traveling at a constant speed of 50 km/h.

MUTCD reference for letter height: p. 2D-17.(4) ††MUTCD reference for sign distance relative to letter height: p. 2A-7.(4)

Milestone B–Comfortable braking distance

Milestone B provides the latest point at which the driver can begin decelerating and maintain a comfortable deceleration level. It also represents the time the subject driver has to complete tasks 5.1.7 and 5.1.8 when the street signs become readable. Table 119 lists equations and assumptions for Scenario 5–Right Turn on Green Light, Milestone B.

Table 119. Scenario 5–Right Turn on Green Light, Milestone B,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Braking reaction time (tBRT).

Assumed value

-

0.4 sec

  • General motor RT.

Deceleration Interval (excludes Braking RT).

t subscript decel. t subscript decel equals negative v subscript 0 divided by A

39

4.1 sec

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −3.4 m/sec2(a).
  • Projected deceleration endpoint (0 km/sec) is the stop line.

Deceleration distance (excludes Braking RT).

ddecel = 0.5at2decel + v0tdecel

40

28 m

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −3.4 m/sec2(a).

An endpoint of 0 km/h at the stop line was used to calculate the starting point for braking, with the assumption that the vehicle continues at a constant speed after reaching 16 km/h. This endpoint was selected instead of the turn location because it is more conservative (drivers can stop more easily for hazards at the crosswalk). At a practical level, however, the difference between this endpoint and an endpoint of 16 km/h at the turn location is negligible.

Milestone C–Vehicle reaches turning speed

Milestone C represents the point at which the subject vehicle reaches the turning speed and then continues towards the turn location at a constant speed. Table 120 lists equations and assumptions for Scenario 5–Right Turn on Green Light, Milestone C.

Table 120. Scenario 5–Right Turn on Green Light, Milestone C,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Time required to decelerate to turning speed (ttv).

t subscript tv. t subscript tv equals the quotient of the following: the sum of v subscript f minus v subscript 0, end of sum, that sum divided by A

 

41

2.8 sec

  • Vehicle decelerates at a constant level of −3.4 m/sec2 (a) from 50 km/h (v0) to 16 km/h (vf).

Distance traveled until turn speed reached.

dtv = 0.5attv2 + v0ttv

 

42

25 m

Milestone D–Initiate turn

Milestone D is the point at which the subject vehicle arrives at the location where it is necessary to begin the right turn. It also marks the end of the Intersection Entry segment. Table 121 lists equations and assumptions for Scenario 5–Right Turn on Green Light, Milestone D.

Table 121. Scenario 5–Right Turn on Green Light, Milestone D,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Time required to travel from point at which turning speed reached until stop line reached.

t subscript stopline. t subscript stopline equals the quotient of the following: the sum of d subscript decel minus d subscript tv, end of sum, that sum divided by v

43

0.7 sec

  • ddecel (28 m) from Milestone B.
  • dtv (25 m) from Milestone C.
  • Vehicle traveling at constant speed of 16 km/h (v).

Distance to turn point from stop line (dTP).

Assumed value

-

0.4 m

  • Value determined from roadway geometry.

Time required to travel from stop line to turn point at constant speed.

dturn = dpath - dART

44

0.1 sec

  • Vehicle traveling at constant speed of 16 km/h (v).

Milestone E–Turn completed

Milestone E represents the interval in which the subject vehicle is actively engaged in turning (tasks 5.4.1 through 5.4.4). Table 122 lists equations and assumptions for Scenario 5–Right Turn on Green Light, Milestone E.

Table 122. Scenario 5–Right Turn on Green Light, Milestone E,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Acceleration reaction time (tART).

Assumed value

-

0.4 sec

  • General motor RT.

Distance traveled during acceleration reaction time.

dART = v0tART

45

1.8 m

  • Vehicle traveling at constant speed of 16 km/h (v0).

Distance through turn.

dturn = dpath - dART

46

14 m

  • Total path distance through the intersection of 16.3 m including vehicle length (dpath).

Time required to accelerate through turn.

t subscript turn. t subscript turn equals negative v subscript 0 plus the square root of v subscript 0 squared plus 2 times A times d subscript turn, end of square root, all divided by A

47

2.2 sec

  • Vehicle accelerates at a constant level of 2.0 m/sec2 (a).

The cognitive/perceptual elements of this action are defined as being part of the preceding tasks. More specifically, the decision to turn is the culmination of tasks 2.4.5 through 2.4.8 of the preceding segment; thus, this RT simply represents the time needed to press the accelerator and start turning the steering wheel following this decision.

Milestone F–Braking distance for stopping in the intersection

Milestone F is the last point in time that the subject vehicle can still come to a stop in the intersection before starting the turn trajectory. It represents the point by which the driver must have determined that it is safe to proceed (e.g., there are no conflicts with red-light-running traffic–task 5.3.6, oncoming left-turning vehicles–task 5.3.7, or hazards in the turn path–task 5.3.8). Table 123 lists equations and assumptions for Scenario 5–Right Turn on Green, Milestone F.

Table 123. Scenario 5–Right Turn on Green Light, Milestone F,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Emergency perceptual-motor reaction time (tERT).

Assumed value

-

0.70 sec

  • Emergency RT.

Deceleration time.

t subscript decel. t subscript decel equals negative v subscript 0 divided by A

48

1.0 sec

  • Vehicle traveling at 16 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −4.0 m/sec2 (a).

Latest time to initiate braking for stopping at intersection entry.*

tstop = tERT + tdecel

49

1.7 sec

  • No additional assumptions.

* Measured from an intersection entry point that is 5 m from the stop line.

Scenario 6–Right turn on red light

Figure 67 provides the timeline and calculated vehicle speed information for Scenario 6. The key temporal milestones are described in table 124. Some milestones shown in figure 67 (e.g., intersection becomes visible) are not described in table 124 and do not have corresponding timestamps computed. These milestones either do not affect the scenario timing in a meaningful way, or they cannot be computed because of insufficient information. They are included only to provide additional contextual information for understanding the timeline.

View Alternative Text

Figure 67. Scenario 6–Right Turn on Red Light timeline depicting

key temporal milestones.

 

Table 124. Scenario 6–Right Turn on Red Light description of key temporal milestones.

Key Milestones

Description

A

Complete preparation for lane change.

This marks the end/duration of the Prepare for Lane Change segment.

B

Complete lane change.

This marks the end/duration of the Execute Lane Change segment.

C

Braking distance.

This provides the latest point at which the driver can begin decelerating based on an aggressive deceleration level.

D

Vehicle stops.

This is the point where the vehicle comes to a complete stop at the stop line and marks the endpoint of segment 4 (Stop).

E

Turn completed.

This represents the interval in which the subject vehicle is actively engaged in turning (tasks 6.6.1 through 6.6.4), following the motor RT.

Milestone A–Complete preparation for lane change

Milestone A marks the end/duration of the Prepare for Lane Change segment. Table 125 lists equations and assumptions for Scenario 6–Right Turn on Red Light.

Table 125. Scenario 6–Right Turn on Red Light, Milestone A,

equations and assumptions.

Description

Equation

Result

Assumptions

Duration of activities related to preparing for the lane change.

Assumed value

2.5 sec

  • The lane change is hurried.

This value is based on research by Mourant and Donohue,(32) which was conducted on novice drivers making left-side lane changes and found that drivers took an average of 2.4 sec to complete the visual scanning that precedes a lane change. More recent research indicates that most glances related to prelane scanning behavior can be captured in an analysis window encompassing the 3 sec just before the lane-change onset.(24)

Milestone B–Complete lane change

Milestone B marks the end/duration of the activities related to maneuvering the subject vehicle from the originating lane to the destination lane. Table 126 lists equations and assumptions for Scenario 6–Right Turn on Red Light.

It is noteworthy that the driver is not assumed to begin decelerating until after the lane change is complete. This assumption is based partly on the fact that there is a following vehicle in the destination lane that is traveling at full speed and the subject vehicle must stay ahead of it. At a more practical level, keeping these components separate simplifies the allocation of tasks among the scenario segments.

Table 126. Scenario 6–Right Turn on Red Light, Milestone B,

equations and assumptions.

Description

Equation

Result

Assumptions

Duration of the lane change.

Assumed value

3.0 sec

  • The lane change is hurried.

This value is slightly faster than the low end of the range for observed lane change durations in city environments, which have 3.5 to 3.4 sec as a lower bound and a mean/modal duration of around 6 sec.(33, 34) The reason why a shorter duration was assumed was to reflect the hurried pacing of the lane change because the subject vehicle must get out of the way of the slowing/stopping lead vehicle in the originating lane. Also, the researchers conducted informal pilot testing in a driving simulator with three experienced drivers and found that they were consistently able to complete a comparable lane-change maneuver in around 2.5 to 3 sec. As a practical matter, the duration of this segment has little effect on the scenario because lengthening this interval would just mean that the lane change has to start farther back from the intersection.

Milestone C–Braking distance

Milestone C provides the latest point at which the driver can begin decelerating based on an aggressive deceleration level. Table 127 lists equations and assumptions for Scenario 6–Right Turn on Red Light, Milestone C.

Table 127. Scenario 6–Right Turn on Red Light, Milestone C,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Braking reaction time (tBRT).

Assumed value

-

0.75 sec

  • Perceptual/cognitive and motor RT.

Deceleration interval (excludes the Braking RT).

t subscript decel. t subscript decel equals negative v subscript 0 divided by A

50

3.5 sec

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −4.0 m/sec2 (a).† †
  • Vehicle comes to a complete stop at the stop line.

A response time that includes both a perceptual/cognitive and motor component was used for this milestone because these elements are not completed in the previous segment as is the case in other instances in which just the motor RT is used. Because there are no data on comparable situations (i.e., recognize that the vehicle is close enough to the intersection and initiate braking), this value is based on a 0.75 sec RT that represents RTs for common expected events,(30) which at least share some features in common with the current situation. In particular, the subject driver's task is relatively simple (recognizing that the vehicle is close enough to stop; see Scenario 6, task analysis table), and the upcoming intersection is also expected.

† † A deceleration level that is more aggressive than the comfortable deceleration level used in most of the other stopping/deceleration tasks was used. This is because the driver's preoccupation with the preceding lane-change maneuver is assumed to delay the driver's ability to identify and respond to the onset of the comfortable braking distance.

Milestone D–Vehicle stops

Milestone D represents the point where the vehicle comes to a complete stop at the stop line and marks the endpoint of segment 4 (Stop). Table 128 lists equations and assumptions for Scenario 6–Right Turn on Red Light, Milestone D.

Table 128. Scenario 6–Right Turn on Red Light, Milestone D,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Time to stop line once decision is made to stop.

tstop = tBRT + tdecel

51

4.2 sec

  • Vehicle comes to a complete stop at the stop line.
  • tBRT and tdecel from Milestone C.

Milestone E–Turn completed

Milestone E represents the interval in which the subject vehicle is actively engaged in turning (tasks 6.6.1 through 6.6.4), following the motor RT. Table 129 lists equations and assumptions for Scenario 6–Right Turn on Red Light, Milestone E.

Table 129. Scenario 6–Right Turn on Red Light, Milestone E,

equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Acceleration reaction time (tART).

Assumed value

-

0.4 sec

  • General motor RT.

Time to complete turn.

t subscript turn. t subscript turn equals the sum of the following: the square root of the product 2 times d subscript turn, end of product, that product divided by A, end of square root, to that square root add t subscript A R T

52

 

3.8 sec

  • Distance from turn location to completion point is 11.3 m (dturn) including vehicle length
  • Vehicle accelerates at a constant level of 2.0 m/sec2 (a).

Scenario 7–Stop on red light

Figure 68 provides the timeline and calculated vehicle speed information for Scenario 7. The key temporal milestones are described in table 130. Some milestones shown in figure 68 (e.g., intersection becomes visible) are not described in table 130 and do not have corresponding timestamps computed. These milestones either do not affect the scenario timing in a meaningful way or they cannot be computed because of insufficient information. They are included only to provide additional contextual information for understanding the timeline.

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Figure 68. Scenario 7–Stop on Red Light timeline depicting key temporal milestones.

 

Table 130. Scenario 7–Stop on Red Light description of key temporal milestones.

Key Milestones

Description

A

Driver detects and responds to lead vehicle braking.

This occurs when the subject driver detects/confirms that the lead vehicle has begun stopping for the red light and begins decelerating in response.

B

Vehicle stops.

This is the point where the vehicle comes to a complete stop at the stop line and marks the endpoint of segment 2 (Stop).

Milestone A–Driver detects and responds to lead vehicle braking

Milestone A occurs when the subject driver detects/confirms that the lead vehicle has begun stopping for the red light and begins decelerating in response. Note that the lead vehicle braking distance does not include an RT component because the brake lights (which indicate the need to respond to the lead vehicle) do not illuminate until after the RT occurs. Table 131 lists equations and assumptions for Scenario 6–Stop on Red Light, Milestone A.

Table 131. Scenario 7–Stop on Red Light, Milestone A, equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Lead vehicle comfortable braking distance.

t subscript BRL. t subscript BRL equals negative v subscript 0 divided by A

53

4.1 sec

  • Lead vehicle traveling at constant speed of 50 km/h at onset of braking (v0).
  • Lead vehicle decelerates at a level of −3.4 m/sec2 (a).

Yellow light detection time (tDRT).

Assumed value

-

0.4 sec

  • Light detection time.

Braking reaction time (tBRT).

Assumed value

-

0.4 sec

  • General motor RT.

Distance between the lead vehicle and subject vehicle at time of lead-vehicle braking.

dsubscript delta = v0tgap

54

28 m

  • Vehicles traveling at constant speed of 50 km/h at onset of lead vehicle braking (v0).
  • 2-sec gap between vehicles (tgap) is assumed.

The detection time is based on the perception RT reported in studies in which drivers respond to a light-based event, such as the change in traffic light or the onset of brake lights. The value chosen (0.4 sec) is on the high end of observed values reported in Green (2000).(30)

Milestone B–Vehicle stops

Milestone B represents the point where the vehicle comes to a complete stop at the stop line and marks the endpoint of segment 2, Stop. Table 132 lists equations and assumptions for Scenario 7–Stop on Red Light, Milestone B.

Table 132. Scenario 7–Stop on Red Light, Milestone B, equations and assumptions.

Description

Equation

Eq. No.

Result

Assumptions

Deceleration time (tdecel).

t subscript decel. t subscript decel equals negative v subscript 0 divided by A

55

4.1 sec

  • Vehicle traveling at 50 km/h at onset of braking (v0).
  • Vehicle decelerates at a constant level of −3.4 m/sec2 (a).

Time to stop line once decision is made to stop.

tstop = tBRT + tDRT + tdecel

56

4.9 sec

  • Vehicle comes to a complete stop 1 m from the rear bumper of the lead vehicle (6.8 m from the stop line).
  • tBRT (0.4 sec) and tDRT (0.4 sec) from Milestone A.

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