Introduction to Transportation Engineering. Discussion of Stopping and Passing Distances

Transcription

1 Introduction to Transportation Engineering Discussion of Stopping and Passing Distances Dr. Antonio A. Trani Professor of Civil and Environmental Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Fall, Spring 2009 Virginia Tech 1

2 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 This text is the standard material used by transportation engineering to design highways and streets Virginia Tech 2

3 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 Virginia Tech 3

4 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 Virginia Tech 4

5 Sample Problem Driving behavioral models are perhaps the easiest to understand Driver Strategy: control, guidance, and navigation Virginia Tech 5

6 The Driver Transportation engineers deal with large numbers of drivers Elderly Middle age Young Handicapped, etc. Design standards cannot be predicated on the basis of the average driver In-class discussion Example of reaction time study Virginia Tech 6

7 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 concentration b) 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 Virginia Tech 7

8 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. Virginia Tech 8

9 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 guideway c) Consistent with the speed users are expect from the facility Virginia Tech 9

10 Highway Design Speed Equivalents (AASHTO 2004) Design Speed (km/hr) Design Speed (m.p.h.) Virginia Tech 10

11 Perception: Perception and Reaction a) Process of extracting information from the surrounding environment b) 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 seconds b) Accounts for the worse case scenario (a distracted driver) Virginia Tech 11

12 Perception and Reaction Times Car Obstacle Virginia Tech 12

13 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 distance b) passing sight distance Each technique applies in diverse conditions Virginia Tech 13

14 Stopping Sight Distance Two distance components are important to calculate Sight Stopping Distance (SSD): Reaction distance Distance traversed while the driver makes a decision to perceive, identify and react to an unexpected situation Braking distance Distance traversed in the physical activity of braking a vehicle Virginia Tech 14

15 Stopping Sight Distance Formulas Braking Distance d b = 2 V d 2a (1) V d where: is the design speed (m/s), is the vehicle d b acceleration (m/s 2 ) and is the braking distance (m). a Reaction Distance d r = V d t r (2) t r where: is the reaction time (s) and is the reaction distance (m). d r Virginia Tech 15

16 Stopping Distance Formulas Add two components to get, Sight Stopping Distance d SSD = 2 V d + V d t r 2a (3) This estimates the total sight stopping distance of the vehicle. Virginia Tech 16

17 Design Values In practical situations the following design values are recommended by ASHTO a = 3.4 m/s 2 (11.2 ft./s 2 ) t r = 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. Virginia Tech 17

18 Stopping Sight Distance Table source: Table 3.1 in A Policy on Geometric Design of Highways and Streets, AASHTO 2004, pp.112. Virginia Tech 18

19 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, d b = 2 V d a G 9.81 (4) Virginia Tech 19

20 G In this equation is the percent of grade divided by 100. Also, this equation requires V d be expressed in km/hr and the deceleration rate in m/s 2. a A table showing corrected braking distances by grade is shown in the table in the following page. Virginia Tech 20

21 Stopping Sight Distance on Grades (AASHTO Table) source: Table 3.1 in A Policy on Geometric Design of Highways and Streets, AASHTO 2004, pp.115. Virginia Tech 21

22 Exercise for Home Derive equation (4) using the following free body diagram. F f +/- mg sin(θ)= ma F f = mg cos(θ) f (V f ) 2 = (V o ) 2 +2 ad θ V f = final speed V o = initial speed W = mg F f = friction force (braking) f = equivalent coefficient of friction (dimensionless) a = vehicle acceleration/deceleration d= distance traveled F f Virginia Tech 22

23 Values of Equivalent Coefficients of Friction AASHTO Equivalent Coefficients of Friction (f) for Practical Stopping Distance Calculations. Speed (m.p.h.) Coefficient of Friction (f) Virginia Tech 23

24 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 speed b) Passing vehicle trails the overtaken vehicle c) Passing driver needs short period to perceive and react to the passing maneuver d) Delayed start and hurried to the opposing lane e) When the passing vehicle returns to its travel lane there is enough clearance between this vehicle and the oncoming vehicle Virginia Tech 24

25 Passing Sight Distance Diagram Virginia Tech 25

26 Assumptions in Passing Sight Distance source: Table 3.1 in A Policy on Geometric Design of Highways and Streets, AASHTO 2004, pp.120. Virginia Tech 26

27 Initial maneuver distance (d 1 ) d 1 = 0.278t i v m at i 2 (5) t i where: is the time of initial maneuver (s), 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). a Virginia Tech 27

28 Distance While Passing Vehicle Occupies Left Lane (d 2 ) d 2 = 0.278vt 2 (6) t 2 where: is the time the passing vehicle occupies the left v lane (s) and is the average speed of the passing vehicle (km/hr) Virginia Tech 28

29 Clearance Length (d 3 ) and Distance Traversed by Opposing Vehicle (d 4 ) Clearance distance d 3 = [ 30, 75] (7) This distance has been found by empirical observations to vary from 30 to 75 meters. Distance traveled by Opposing vehicle 2 d 4 = --d 2 3 (8) Somewhat optimistic assumption but used in practice. Virginia Tech 29

30 Passing Sight Distance (Design Values) source: Table 3.1 in A Policy on Geometric Design of Highways and Streets, AASHTO 2004, pp.124. Virginia Tech 30