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 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 Virginia Tech 2 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 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 Sample Problem • Driving behavioral models are perhaps the easiest to understand Driver Strategy: control, guidance, and navigation Virginia Tech 5 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 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 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 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 Highway Design Speed Equivalents (AASHTO 2004) 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 Virginia Tech 10 Perception and Reaction • Perception: 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 Perception and Reaction Times Car Obstacle Virginia Tech 12 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 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 Stopping Sight Distance Formulas Braking Distance 2 Vd d =----- - (1) b 2a where: Vd is the design speed (m/s), a is the vehicle 2 acceleration (m/s ) and db is the braking distance (m). Reaction Distance dr = Vd tr (2) where: tr is the reaction time (s) and dr is the reaction distance (m). Virginia Tech 15 Stopping Distance Formulas Add two components to get, Sight Stopping Distance 2 Vd d =------ + V t (3) SSD 2a d r This estimates the total sight stopping distance of the vehicle. Virginia Tech 16 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. Virginia Tech 17 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 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, 2 Vd db = ----------------------------------------- (4) a 254⎛⎞---------- +− G ⎝⎠9.81 Virginia Tech 19 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. Virginia Tech 20 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 Fundamental Forces Acting on the Vehicle Derive equation (4) using the following free body diagram. Ff +/- mg sin(θ)= ma Ff = mg f 2 2 (Vf) = (Vo) +2 ad Ff θ Vf = final speed Vo = initial speed W = mg Ff = friction force (braking) f = equivalent coefficient of friction (dimensionless) a = vehicle acceleration/deceleration d= distance traveled Virginia Tech 22 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 Virginia Tech 23 Fundamental Equation Using basic principles of kinematics, we find the basic formula to estimate braking distance, 2 2 Vd Vd d ==------ -------- (5) b 2a 2gf 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) Virginia Tech 24 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), V2 22.22 d ==-------d- ----------------------------- = 8 3 . 7 meters b 2gf 29.81()0.30 This is equivalent to 274 feet. Note that this value is slightly higher than that reported in Exhibit 3-1. Virginia Tech 25 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, 2 Vd d = ----------------------- (6) b 2gf()+− G Note that in this equation positive grades (uphill) reduce the braking distance needed. Virginia Tech 26 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 ==tr Vd 2.5() 22.2 =55.5 meters The braking distance accounting for grade is, V2 22.22 d ==-----------------------d ------------------------------------------------ = 76.1 b 2gf()+− G 29.81()()0.3+ 0.03 meters. The stopping distance is then the sum of braking and reaction distances, Virginia Tech 27 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%). Virginia Tech 28 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 29 Passing Sight Distance Diagram Virginia Tech 30 Assumptions in Passing Sight Distance source: Table 3.1 in A Policy on Geometric Design of Highways and Streets, AASHTO 2004, pp.120.