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From page 73... ... B-1 Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) A P P E N D I X B The work presented in this appendix represents a significant enrichment to the understanding of the lateral extent of errant vehicle trajectories during an encroachment. Read the entire page →
From page 74... ... B-2 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers CHAPTER 1 INTRODUCTION One objective of this research was to determine the probability of an errant vehicle's trajectory laterally extending to a location of interest (e.g., across the median, to the barrier) Read the entire page →
From page 75... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-3 CHAPTER 2 BACKGROUND The outcome under assessment in epidemiological studies is often the time to an event of interest such as relapse of cancer or relief from disease. Read the entire page →
From page 76... ... B-4 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers CHAPTER 3 AVAILABLE DATA The NCHRP Project 17-22 data contains 787 reconstructed trajectories from run-off-road crashes. Read the entire page →
From page 77... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-5 Table B-1 Factor Level Summary Statistics and Variable Names Covariate Variable Name Levels Number of Trajectories 16-05 17-55 Foreslope (1V:xH) Read the entire page →
From page 78... ... B-6 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Table B-2 shows that in both data sets, the maximum recorded lateral extent in feet (MaxLatF) is above 100 ft by a few decimal places, but the study design included the censoring of data at 100 ft. Read the entire page →
From page 80... ... Table B-3 Correlation Matrix for Data Elements in the Combined Projects 16-05 and 17-55 Data Sets Pearson's Correlation MaxLatF Veh Outcome DriverInput EncAng Spd BtW BS BSW FS FSW MaxLatF 1.0000 -0.0377 -0.5024 -0.5041 0.5051 0.2727 0.0180 0.0063 -0.0497 -0.0513 0.1541 Veh 1.0000 -0.0557 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Outcome 1.0000 0.1693 -0.3482 -0.3103 0.0167 -0.0412 -0.0052 -0.0499 -0.0962 DriverInput 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 EncAng 1.0000 0.0489 0.0877 0.1259 0.0805 0.0000 -0.0711 Spd 1.0000 0.1986 0.2852 0.1824 0.0000 -0.1610 BtW 1.0000 0.5110 0.3268 0.0000 -0.2885 BS 1.0000 0.4692 0.0000 -0.4143 BSW 1.0000 0.0000 -0.2649 FS 1.0000 0.0000 FSW 1.0000 Spearman's Correlation MaxLatF Veh Outcome DriverInput EncAng Spd BtW BS BSW FS FSW MaxLatF 1.0000 -0.0320 -0.5026 -0.5029 0.5557 0.2779 0.0293 0.0202 -0.0320 -0.0343 0.1304 Veh 1.0000 -0.0600 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Outcome 1.0000 0.2067 -0.3530 -0.3202 0.0116 -0.0479 -0.0107 -0.0779 -0.0438 DriverInput 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 EncAng 1.0000 0.0477 0.0970 0.1321 0.0805 0.0000 -0.0673 Spd 1.0000 0.2144 0.2919 0.1779 0.0000 -0.1487 BtW 1.0000 0.5934 0.3617 0.0000 -0.3023 BS 1.0000 0.4922 0.0000 -0.4115 BSW 1.0000 0.0000 -0.2508 FS 1.0000 0.0000 FSW 1.0000 Read the entire page →
From page 81... ... Table B-4 Correlation Matrix for Data Elements Limited to the Project 17-55 Data set Pearson's Correlation MaxLatF Veh Outcome DriverInput EncAng Spd FS FSW MaxLatF 1.0000 -0.0333 -0.5713 -0.5018 0.5245 0.4036 0.0371 0.1794 Veh 1.0000 -0.0366 0.0000 0.0000 0.0000 0.0000 0.0000 Outcome 1.0000 0.1994 -0.2898 -0.3636 -0.0447 -0.1830 DriverInput 1.0000 0.0000 0.0000 0.0000 0.0000 EncAng 1.0000 0.0000 0.0000 0.0000 Spd 1.0000 0.0000 0.0000 FS 1.0000 0.0000 FSW 1.0000 Spearman's Correlation MaxLatF Veh Outcome DriverInput EncAng Spd FS FSW MaxLatF 1.0000 -0.0298 -0.5315 -0.5149 0.5513 0.4111 0.0410 0.1663 Veh 1.0000 -0.0431 0.0000 0.0000 0.0000 0.0000 0.0000 Outcome 1.0000 0.1995 -0.2574 -0.3643 -0.0543 -0.1509 DriverInput 1.0000 0.0000 0.0000 0.0000 0.0000 EncAng 1.0000 0.0000 0.0000 0.0000 Spd 1.0000 0.0000 0.0000 FS 1.0000 0.0000 FSW 1.0000 Read the entire page →
From page 82... ... B-10 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers CHAPTER 4 DATA ANALYSIS Time, as measured in feet to the trajectory terminus, is the response variable (T) Read the entire page →
From page 83... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-11 The Kaplan-Meier survival curves essentially provide a visual representation of the collected trajectory data, as shown in Figure B-2a for the combined Projects 16-05 and 17-55 data sets and Figure B-2b for only the Project 17-55 data set. Read the entire page →
From page 85... ... Figure B-3 Survival probability by vehicle type and trajectory outcome for the combined Projects 16-05 and 17-55 data sets. Read the entire page →
From page 86... ... Figure B-4 Survival probability by vehicle type and trajectory outcome limited to only the Project 17-55 data set. Read the entire page →
From page 87... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-15 Table B-5 Log-Rank Test of Each Covariate. Read the entire page →
From page 91... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-19 Competing Risks It was found with the Kaplan-Meier (K-M) Read the entire page →
From page 93... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-21 Comparing the CIFs considers each type of event and does not assume independence between the time to the different types of events. Read the entire page →
From page 94... ... B-22 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers The consideration of various statistical models for (1) competing risks and (2) Read the entire page →
From page 95... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-23 xj = Covariates collected during data collection (e.g., slope, vehicle type) Read the entire page →
From page 96... ... B-24 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Survival Event of interest is the maximum lateral extent when the vehicle stops or returns to the road. Overturning is treated as a competing risk event that eliminates the chance of either stopping or returning to the road. Read the entire page →
From page 97... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-25 Figure B-9 Estimated survival function. Read the entire page →
From page 98... ... B-26 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Figure B-10 Estimated competing risk of overturn. Read the entire page →
From page 99... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-27 CHAPTER 5 FIELD COLLECTED TRAJECTORIES NCHRP Project 17-11: Determination of Safe/Cost Effective Roadside Slopes and Associated Clear Distances was completed in 2004 by TTI at Texas A&M. Read the entire page →
From page 100... ... B-28 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Table B-7 Comparison of Departure Speed and Angle for Specific Field-Collected Crash Databases Reference Number of Cases 50th Percentile of Data Set Departure Speed Departure Angle NCHRP Project 17-11 485 19.9° NCHRP Project 17-11* 485 48.9 mph 16.9° NCHRP Project 17-22 392 49.7 mph 17.2° NCHRP Report 665 877† 49.3 mph 16.9° NCHRP Project 17-43 1124 48.6 mph 13.8° * Read the entire page →
From page 101... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-29 CHAPTER 6 RESULTS The mean encroachment speed of the data simulated in the Project 17-55 data set was 50 mph and the mean encroachment angle was 17.5 degrees. Read the entire page →
From page 102... ... B-30 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Figure B-11 Estimated survival function (solid) and scale maximum lateral extent model (dashed) Read the entire page →
From page 103... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-31 CHAPTER 7 IMPLEMENTING THE RESULTS NCHRP Project 15-65 defines "PY j [a] Read the entire page →
From page 104... ... B-32 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Yj (ft) Read the entire page →
From page 105... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-33 Table B-8 Recommended representation of passing THR terrain (THRTERRAIN) Read the entire page →
From page 106... ... B-34 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers REFERENCES Bligh, Roger P and Shaw-Pin Miaou, "Determination of Safe/Cost Effective Roadside Slopes and Associated Clear Distances [Completed Project] Read the entire page →
From page 107... ... Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) B-35 Sheikh, Nauman, Roger P Read the entire page →

From page 73...

... B-1 Probability of Reaching the Lateral Offset of Feature j -- PY(Yj) A P P E N D I X B The work presented in this appendix represents a significant enrichment to the understanding of the lateral extent of errant vehicle trajectories during an encroachment.