Introduction to Transportation Engineering

Discussion of Stopping and Passing Distances

Dr. Antonio A. TraniProfessor of Civil and Environmental EngineeringVirginia Polytechnic Institute and State University

Blacksburg, VirginiaFall, Spring 2009

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Introductory Remarks

• The presentation of the materials that follow are taken from the American Association of State and Highway Officials (AASHTO):

• “A Policy on Geometric Design of Highways and Streets - 2004”

• This text is the standard material used by transportation engineering to design highways and streets

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Driver Performance

• The human-machine system

• The driver

• Perception and reaction

• Vehicle kinematic equations

• Acceleration and deceleration problems

• Stopping distance criteria

• Passing sight distance criteria

• Examples

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Human Machine Systems

• Complex human-machine behavior in transportation engineering

• Some examples:• Air traffic controllers interacting with pilots who in turn

control aircraft• Highway drivers maneuvering at high speeds in moderate

congestion and bad weather• A train engineer following train control signals at a busy

train depot

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Sample Problem

• Driving behavioral models are perhaps the easiest to understand

Driver Strategy: control, guidance, and navigation

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The Driver

• Transportation engineers deal with large numbers of driversElderlyMiddle ageYoung Handicapped, etc.

• Design standards cannot be predicated on the basis of the “average driver”

• In-class discussion

• Example of reaction time study

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Anecdotal Experience About Drivers

• Drivers do not like more than 0.3 g of lateral acceleration at low speeds (< 30 m.p.h.)

• No more than 0.1 g at 60 m.p.h.

• Human factor issues in highway design:a) As speed increases so does visual concentrationb) As speed increases, the focus of visual concentration

changes (600 ft. at 25 m.p.h., 2000 ft. at 65 m.p.h.)c) As speed increases, peripheral vision is reduced (100 deg.

At 25 m.p.h., 40 at 60 m.p.h.)d) As speed increases, foreground details fade (large shapes

meaningful at high speeds)e) As speed increases, space perception is impaired

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Visual Acuity

• Ability to distinguish details clearly

• Varies from person to person

• Affected by the speed of the objects passing by

• Affected by weather and environmental conditions (i.e., day acuity is better than nighttime acuity)

• A person with 20/20 vision can read letters one inch in height at 60 ft. (or 1/3 inch at 20 ft.)

• A person with 20/40 vision can read the same one inch letters at only 30 ft.

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Design Speed

• While designing highways and other transportation systems we use the concept of design speed

• Design speed is the speed used to establish the geometric features of the roadway or guideway (in case of trains)

• Design speed features:a) As high as practically possible (except for local streets)b) Should be higher than the typical operating speeds of the

roadway or guidewayc) Consistent with the speed users are expect from the facility

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Highway Design Speed Equivalents

Design Speed (km/hr) Design Speed (m.p.h.)

20 15

30 20

40 25

50 30

60 40

70 45

80 50

90 55

100 60

110 70

120 75

130 80

(AASHTO 2004)

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Perception and Reaction

• Perception:a) Process of extracting information from the surrounding

environmentb) Too much information can easily overload a human

controller (driver, pilot, controller)c) Drivers and pilots can only perceive small amounts of bits/

second of information

• Secondary tasks or activities are very dangerous and distracting (driving and using a cell phone)a) Value for perception time used in highway design is 2.5

secondsb) Accounts for the worse case scenario (a distracted driver)

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Perception and Reaction Times

CarCar

ObstacleObstacle

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Sight Distance Considerations

• The ability of an operator to see ahead

• Critical in the design of transportation facilities (highways, railways, etc.)

• For highways two types of analyses are critical:a) stopping sight distanceb) passing sight distance

• Each technique applies in diverse conditions

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Stopping Sight Distance

Two distance components are important to calculate Sight Stopping Distance (SSD):

• Reaction distanceDistance traversed while the driver makes a decision to

perceive, identify and react to an unexpected situation

• Braking distanceDistance traversed in the physical activity of braking a

vehicle

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Stopping Sight Distance Formulas

Braking Distance

db

Vd2

2a------= (1)

where: Vd is the design speed (m/s), a is the vehicle acceleration (m/s2) and db is the braking distance (m).

Reaction Distance

dr Vdtr= (2)

where: tr is the reaction time (s) and dr is the reaction distance (m).

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Stopping Distance Formulas

Add two components to get,

Sight Stopping Distance

dSSD

Vd2

2a------ Vdtr+= (3)

This estimates the total sight stopping distance of the vehicle.

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Design Values

In practical situations the following design values are recommended by ASHTO

• a = 3.4 m/s2 (11.2 ft./s2)

• tr = 2.5 seconds

• Driver’s eye position = 1,080 mm (3.5 ft.)

• Height of the critical object = 600 mm (2.0 ft.)

A table showing the recommended AASHTO stopping distances is shown in the following page.

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Stopping Sight Distance Table

and Streets, AASHTO 2004, pp.112. source: Table 3.1 in A Policy on Geometric Design of Highways

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Stopping Sight Distance on Grades

Grades affect stopping distance due to the gravitational force acting in favor (downhill) or opposing (uphill) the motion of a vehicle.

ASSHTO recommends the following formula to adjust the braking distance for grade conditions,

db

Vd2

254 a9.81---------- G+−⎝ ⎠

⎛ ⎞-----------------------------------------= (4)

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In this equation G is the percent of grade divided by 100. Also, this equation requires Vd be expressed in km/hr and the deceleration rate a in m/s2. In equation (4) the braking distance is calculated in meters.

A table showing corrected braking distances by grade is shown in the table in the following page.

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Stopping Sight Distance on Grades (AASHTO Table)

and Streets, AASHTO 2004, pp.115. source: Table 3.1 in A Policy on Geometric Design of Highways

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Fundamental Forces Acting on the Vehicle

Derive equation (4) using the following free body diagram.

Ff

W = mg

Ff +/- mg sin(θ)= maFf = mg f

f = equivalent coefficient of friction (dimensionless)

θ(Vf)2 = (Vo)2 +2 adVf = final speedVo = initial speedFf = friction force (braking)

a = vehicle acceleration/deceleration d= distance traveled

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Values of Equivalent Coefficients of Friction

AASHTO Equivalent Coefficients of Friction (f) for Practical Braking Distance Calculations.

Speed (m.p.h.) Coefficient of Friction (f)

20 0.40

30 0.35

40 0.32

50 0.30

60 0.29

70 0.28

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Fundamental Equation

Using basic principles of kinematics, we find the basic formula to estimate braking distance,

db

Vd2

2a------ Vd2

2gf--------= = (5)

where the value of a has been subtituted by the product of the gravity (g) and the equivalent friction factor (f).

This equation is dimensionally correct and can be used with consistent units (metric or English)

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Sample Problem # 1

Calculate the braking distance for a car traveling at 80 km/hr in flat terrain.

The 80 km/hr speed is equivalent to 22.2 m/s. According to the AASHTO table the value of equivalent friction coefficient (f) at 80 km/hr is 0.30. Using equation (5),

db

Vd2

2gf-------- 22.22

2 9.81( )0.30----------------------------- 83.7= = = meters

This is equivalent to 274 feet. Note that this value is slightly higher than that reported in Exhibit 3-1.

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Introducing Gradient in the Equation

Using the free body diagram in slide 22, we can show that if a grade G (G expressed as grade (%) divided by 100) is introduced to the problem, equation (5) becomes,

db

Vd2

2g f G+−( )-----------------------= (6)

Note that in this equation positive grades (uphill) reduce the braking distance needed.

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Example Problem

The car in problem # 1 now travels uphill at 80 km/hr. Find the stopping distance if the slope is 3% uphill.

The reaction distance is:

dr trVd 2.5 22.2( ) 55.5= = = meters

The braking distance accounting for grade is,

db

Vd2

2g f G+−( )----------------------- 22.22

2 9.81( ) 0.3 0.03+( )------------------------------------------------ 76.1= = =

meters. The stopping distance is then the sum of braking and reaction distances,

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Problem # 2 (cont.)

dssd dr db+ 76.1 55.5+ 131.6= = = meters

For flat terrain the stopping distance is 139.2 meters (83.7 + 55.5 meters).

Conclusion:

A 3% grade reduces the stopping distance by 5.4%. Note that the reduction of braking distance is ~9%.

Examine the AASHTO tables in Exhibits 3-1 and 3-2 and see that at 50 mph, the reduction in stopping distance is 20 feet (4.7%).

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Passing Sight Distance

• Applicable for two-lane roads and two-way highways

• Major source of concern from a design viewpoint

• Many assumptions in the analysis (AASHTO, 2004):a) Overtaken vehicle travels at uniform speedb) Passing vehicle trails the overtaken vehiclec) Passing driver needs short period to perceive and react to

the passing maneuverd) Delayed start and “hurried” to the opposing lanee) When the passing vehicle returns to its travel lane there is

enough clearance between this vehicle and the oncoming vehicle

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Passing Sight Distance Diagram

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Assumptions in Passing Sight Distance

and Streets, AASHTO 2004, pp.120. source: Table 3.1 in A Policy on Geometric Design of Highways

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Initial maneuver distance (d1)

d1 0.278ti v m– ati

2-----+⎝ ⎠⎛ ⎞= (7)

where: ti is the time of initial maneuver (s), a is the average vehicle acceleration (km/hr/s), v is the average speed of the passing vehicle (km/hr), and m is the difference in speeds of the overtaken vehicle and the passing vehicle (km/hr). For most calculations AASHTO assumes the value of m to be 15 km/hr.

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Distance While Passing Vehicle Occupies Left Lane (d2)

d2 0.278vt2= (8)

where: t2 is the time the passing vehicle occupies the left lane (s) and v is the average speed of the passing vehicle (km/hr)

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Clearance Length (d3) and Distance Traversed by Opposing Vehicle (d4)

Clearance distance

d3 30 75,[ ]= (9)

This distance has been found by empirical observations to vary from 30 to 75 meters. Note that the table on page 31 of the handout shows the appropriate clearance distance.

Distance traveled by Opposing vehicle

d4

23---d2= (10)

Somewhat optimistic assumption but used in practice.

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Passing Sight Distance (Design Values)

and Streets, AASHTO 2004, pp.124. source: Table 3.1 in A Policy on Geometric Design of Highways

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