Measurement over a Short Distance. Tom Mathew

Transcription

1 Measurement over a Short Distance Tom Mathew

2 Outline Introduction Data Collection Methods Data Analysis Conclusion

3 Introduction Determine Fundamental Traffic Parameter Data Collection and Interpretation Determine Speed Trends Driver Behaviour Safety Aspects

4 Methods of Measurement Manual Pavement Markings Enoscope Automatic Road Detectors Doppler-Principle Meters Electronic-Principle Detectors

5 Manual Method Two observer required Easy use and low cost of equipments Higher Error Time consuming

6 Manual Method: Enoscope

7 Recommended Study Lengths Average Traffic Stream Speed Study Length (Kmph) (meters) below above 25 90

8 Automated Methods Road Detectors Pneumatic Road Tubes Induction Loops Radar Guns Work based on the Doppler principle Give directly speed of vehicle Video Image Processing

9 Manual method Data Collection Sheet

10 Manual method Data Collection Sheet

11 Data Analysis Presentation Frequency Distribution Table Frequency Histogram Frequency Distribution Curve Cumulative Frequency Distribution Curve

12 Data Analysis Frequency Distribution Table Individual speeds collected from the field are used Shows total number of vehicles observed in each speed group Speed groups of more than 10 kmph are not recommended No Range Frequency

13 Frequency Histogram Data Analysis

14 Data Analysis Frequency Distribution curve

15 Data Analysis Cumulative Frequency Distribution curve

16 Data Analysis Central Tendency Mean Speed Median Speed Pace & Pace Interval Dispersion Standard Deviation Percentile Speeds Quartile speed

17 Data Analysis: Central Tendency Mean Speed Average speed (Time mean speed) Median Speed Speed that divides the distribution in to equal parts Pace and Pace interval The 10 Kmph interval speed in which highest percentage of drivers is observed and Pace Interval is defined as total traffic percent present in the pace

18 Data Analysis: Dispersion Standard Deviation Most common measure of spread of data Measure of deviation of individual from the average

19 Data Analysis: Dispersion N th Percentile Speed Speed corresponding to N percentage of vehicles have lesser or equal speed Commons percentiles 15 th percentile: Reasonable lower speed observed 85 th percentile: Reasonable higher speed observed 98 th percentile: Speed used for safety and geometric design

20 Data Analysis: Dispersion N th Percentile Speed

21 Data Analysis: Dispersion Quartile Speeds 0 th Percentile (or Minimum Speed) 25 th Percentile Speed 50 th Percentile Speed (or Median speed) 75 th Percentile Speed 100 th Percentile (or Maximum Speed)

22 Data Analysis: Dispersion Quartile Speeds Maximum Speed 85 percentile Mean speed 15 percentile Minimum Speed

23 E.g. Data Analysis: Dispersion

24 Conclusion Data Collection Methods Data Analysis Presentation Central tendency Dispersion Sample size

25 Thank You Questions?

26 The rest of the slides are temporary ones and are draft

27 Problem 1 Consider the following spot speed data, collected from a freeway site operating under free-flow conditions: a. Plot the frequency and cumulative frequency curves for these data. b. Find and identify on the curves: median speed, modal speed, pace, and percent vehicles in pace.

28 Problem 1 Speed Range (Kmph) Frequency

29 Solution Frequency Distribution Table Speed Range Mid speed Frequency Km/h Vi(Km/h) fi (in no.) % Frequency Cumulative % Frequency % 2% % 6% % 20% % 39% % 54% % 67% % 79% % 88% % 94% % 97% % 99% % 100% Total %

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32 b) From the curves, Solution Median speed, v 50 = 42 Kmph Modal speed, = 38 Kmph Pace = Kmph Percent vehicles in pace = 54-20= 34%

33 Standard Error of Mean The means of different sample taken from the same population are distributed normally about the true mean of population with a standard deviation, is known as standard error(e).

34 Precision and Confidence Intervals The confidence interval (µ) for the estimated true mean speed is given by µ = v m ± Z σ s where, v m = True mean speed σ s = Standard deviation Z = Value calculated from Standard Normal distribution Table for a particular confidence level. for 95% confidence, Z = 1.96 for 99.7% confidence, Z = 3.00

35 Sample Size Minimum no. of Sample required. Confidence of observed data analysis. Required sample size is given by n r = Z2 σ s 2 e 2 where, n r = required sample size e = permissible error Z = confidence value from ND table

36 Problem 2 Consider the spot speed data of numerical 1, and a. Compute the mean, standard deviation and standard error of the speed distribution. b. Determine different percentile speeds. c. What are the confidence bounds on the estimate of the true mean speed of the underlying distribution with 95% confidence? With 99.7% confidence? d. Based on the results of this study, a second is to be conducted to achieve a tolerance of ±1.5 km/h with 95% confidence. What sample size is needed?

37 Solution Speed Range Mid speed Frequency Km/h Vi(Km/h) fi (in no.) fi*vi fi*(vi-vm)^ Total

38 a) Mean speed of distribution v m = 45.77Kmph v m = f i v i n v m = Standard Deviation of the Speed

39 b) From the Cumulative Frequency Curve 85 th percentile Speed = V 85 V 85 = 58 Kmph 15 th percentile Speed = V 15 V 15 = 32 Kmph 98 th percentile Speed = V 98 V 98 = 72 Kmph

40 c) Confidence interval for True mean speed µ = v m ± Z σ s For 95% confidence, Z= 1.96 (from ND Table) = ± 1.96 x 11.7 = ± Kmph For 99.7% confidence, Z= 3.0 (from ND Table) = ± 3.0 x 11.7 = ± 35.1 Kmph

41 d)sample size required for 95% confidence with acceptable error of 1.5 Kmph n r = Z2 σ s 2 S e 2 n r = n r = 234 So, we have less sample size, to achieve that confidence with given error.

42 Location of Studies Conform to the intended purpose of the study. Vehicle moves with free flow speed Before vehicle starts decelerate Before or after the curve Road is unaffected by traffic congestion.

43 Conclusion Studied importance of speed in pavement design. Studied various types of speeds. Studied how to collect and analyse the data regarding speed. Studied the various measurement methods to calculate speed. Studied various percentile speeds, their importance in highway design and their formulation.

44 References Hobbs, F.D., Traffic planning and Engineering, Pergamon Press, in Matson, T.M., Smith, W.S., Hurd, F.W., Traffic Engineering, McGraw Hill Book Company, in Roess, R.P., Prassas, S.E., McShane, W.R., Traffic Engineering, Pearson Education International, in 2005.