CE351 Transportation Systems: Planning and Design

Transcription

1 CE351 Transportation Systems: Planning and Design TOPIC: HIGHWAY USERS PERFORMANCE (Part III) 1

2 ANOUNCEMENT Updated d Schedule on: 351

3 Course Outline Introduction ti to Transportation ti Highway Users and their Performance Geometric Design Pavement Design Traffic and Queuing Level of Service in Highways and Intersections 3

4 LAST CLASS Vehicle Performance (part II) Acceleration Braking Force THIS CLASS Stopping Sight Distance (SSD) Practical vs. theoretical formulas Geometric design Vertical Curves 4

5 Forces Acting on a Vehicle while Braking 5

6 Braking Force Ratio BFR = l + h μ + l r f h ( μ + f ) rl front = ( μ + f ) rear rl Efficiency η b = gmax μ 6

7 Theoretical Stopping Distance I With b = mass factor accounting for moments of inertia during braking (1.04 for automobiles) from physics stopping distance is: S = V V 1 γ b m F b VdV + R (.35) With resistances: S = γ b V VdV m F + R + f W ± V 1 b a rl W sinθ g (.36) 7

8 Theoretical Stopping Distance II Solving the equation: sin (.39) γ 1 ± bw μw + K av + f rlw W θ g S = ln gk a μw + K av + f rlw ± W sin θ g Ignoring air resistance (why?) S = g γ ( ) b V1 V ( η μ + f ± sin θ ) b (.43) rl g 8

9 Problem.1 A small truck is to be driven down a 4% grade at 75 mi/h. The coefficient of road adhesion is and it is known that the braking efficiency is 80% when the truck is empty and it decreases eases by one percentage point for every 100 lb of cargo added. Ignoring aerodynamic resistance, if the driver wants the truck to be able to achieve a minimum theoretical stopping distance of 300 ft from the point of brake application, what is the maximum amount of cargo (in pounds) that can be carried? 9

10 Practical Stopping Distance Basic physics 101 equation 1 V = V + ad (.44) Where: d = deceleration distance (practical stopping distance) in ft (m), a = acceleration (negative for deceleration) in ft/s (m/s), V1 = initial vehicle speed in ft/s (m/s), and V = final vehicle speed in ft/s (m/s). 10

11 Practical Stopping Distance AASHTO [001] recommends a deceleration rate of 11. ft/s (3.4 m/s), so with grade and V = 0: V 1 d = (.47) a g ± G Where: g g = gravitational constant, 3. ft/s (9.807 m/s), G = roadway grade (+ for uphill and for downhill) in percent/100, and Other terms as defined previously. 11

12 Braking Distance Deceleration used by AASHTO a = 11. ft/sec is the assumption Deceleration used by most drivers (Frambro et al. 1997) a = 18.4 ft/sec Is a=18.4 high or low? What do you think? 1

13 Anti-Lock Braking Systems ABS can get close to 100% efficiency and avoid wheels locking EBD Electronic brake distribution Performance example: NISSAN 350Z 0-60 acceleration: 5.5 seconds acceleration: 14.0 seconds Peak acceleration g's: 0.66 Peak braking g's: 1.1(g=3 3. ft/s) 13

14 Relationship Model and Breaking Distance User Vehicle Environment 14

15 Stopping Sight Distance (SSD) Worst-case conditions Poor driver skills Low braking efficiency Wet pavement Perception-reaction time =.5 seconds (AASHTO) AVERAGE DRIVERS = 1 to 1.5 seconds Equation V 1 SSD = + V1t a g ± G g r 15

16 QUESTION? What would you guess the perception/reaction time of an average racer? s. 0.0s s s s 16

17 Braking Distance ( γ ) b V1 V Theoretical S = ( ) ignoring air resistance g η μ + ± sinθ b f rl g Practical d = F or grade = 0 V1 V V1 V a d = g ± G a g Perception d p = V1 t p Total d = d + s d p 17

18 Stopping Sight Distance (SSD) from ASSHTO A Policy on Geometric Design of Highways and Streets, 001 Note: this table assumes level grade (G = 0) 18

19 SSD Quick and Dirty 1. Acceleration due to gravity, g = 3. ft/sec. There are 1.47 ft/sec per mph 3. Assume G = 0 (flat grade) ( 1.47 V ) ( 0) V V V V 1 d = 1 = = V = = 1. g a g ± G ( ) ( ) a d p = 1.47 V1 t p = 1. 47Vt p V ds = Vt p V = V 1 in mph a = deceleration, 11. ft/s in U S customary units = Conservative perception / reaction time =.5 seconds t p 19 a

20 Problem.8 An engineering student claims that a country road can be safely negotiated at 70 mi/h in rainy weather. Because of the winding nature of the road, one stretch of level e pavement e has a sight sg distance of only 590 ft. Assuming practical stopping distance, comment on the student s claim (is it safe? why or why not? 0

21 RECAP 1

22 Relationship Model and Breaking Distance User Vehicle Environment

23 Why is vehicle performance important? Determines all highway design and traffic operations Defines how transportation engineers must react to advancing vehicle technologies The single most important factor in defining the tradeoff between mobility (speed) and safety 3

24 Why is vehicle performance important? Understand basic tradeoff: SAFETY vs. COST Cookbook rules for Frequently found design problems Know Basic Principles for Special or custom based problems 4

25 Other users and vehicles 5

26 Speeds Walking Speed Ranges from.5 to 6.5 ft/sec (typical 4 ft/sec) Conduct walking studies when large number faster or slower than 4 ft/sec Bicycle Speed 8-1mph (very large variations) MORE TO FOLLOW ABOUT SPEED STUDIES 6