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Publication Number:  FHWA-HRT-14-057    Date:  February 2018
Publication Number: FHWA-HRT-14-057
Date: February 2018

 

Safety Evaluation of Access Management Policies and Techniques

CHAPTER 9. SAMPLE PROBLEMS TO ILLUSTRATE THE USE OF THE MODELS

Six sample problems are presented in this chapter. For each sample problem, the four-step process presented in chapter 8 is referenced. The six sample problems apply to the following six scenarios:

SAMPLE PROBLEM 1

Estimate the effect of multiple variables that are all in the same model (scenario 1).

Problem Definition

A planned development is expected to increase existing traffic volumes by 50 percent and change the general characteristics of a residential corridor in an urbanizing area. The new development will increase the frontage from 30 to 100 percent. A new signalized intersection is proposed in the middle of the corridor to help accommodate the expected growth. A concern has been raised regarding the potential increase in right-angle crashes because these tend to be severe. It is desired to predict the number of right-angle crashes for both the existing and proposed conditions. The predicted crashes will be compared to estimate the relative impacts of the proposed changes.

Step 1: Select Land Use and Region

This is a residential corridor. After reviewing the summary statistics for residential land use in each of the four regions from which the models were developed and comparing them to the local data, it is determined that the corridor is most comparable to North Carolina.

Step 2: Select Crash Types and Variables of Interest

As noted in the problem definition, right-angle crashes are of interest. In this case, the variables of interest are PROPFULLDEV and SIGDENS.

Step 3: Select Analysis Type of Interest

It is desired to estimate the relative safety of two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, analysis option 1 (algorithm 1) is applicable because the objective is to compare the relative safety impacts.

Step 4: Select Applicable Model(s) and Perform Analysis

Table 26 presents the applicable models for right-angle crashes in a residential land use. The applicable model for PROPFULLDEV is residential right-angle model 2 (table 73). The applicable model for SIGDENS is residential right-angle model 2 (table 73). The applicable model is the same for the variables of interest, so multiple models and extrapolated variables are not required. Note that all variables are available to apply this model, so no default values are required.

The model coefficients from table 73 are as follows: intercept (–1.4079), region (0.8858 if North Carolina or Minnesota; 0 otherwise), AADT (0.1332), SIGDENS (0.2267), PROPLANE1
(–0.3633), and PROPFULLDEV (0.4295). The equation in figure 18 is applicable to this model.

Step 4.1.1: Data for Conditions of Interest

The data for the existing condition (do-nothing alternative A) are the following:

The data for the proposed condition (alternative B) are the following:

Step 4.1.2: Calculations for Nonextrapolated Variables

Case 1 applies when all variables of interest appear in only one model. Figure 23 and figure 24 predict right-angle crashes per year.

Figure 23. Equations. Calculation of predicted right-angle crashes/year (existing). Predicted right-angle crashes per year (existing) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.1332 power times exp to the open parenthesis 0.2267 times SIGDENS minus 0.3633 times PROPLANE1 plus 0.4295 times PROPFULLDEV close parenthesis power. Using the values from the existing condition, or do-nothing alternative A, this equation equals 2.5 times exp to the open parenthesis negative 1.4079 plus 0.8858 close parenthesis times 15,000 to the 0.1332 power times exp to the open parenthesis 0.2267 times 0.40 minus 0.3633 times 1.0 plus 0.4295 times 0.3 close parenthesis power. Solving this expression results in an answer of 4.22 right-angle crashes per year.

Figure 23. Equations. Calculation of predicted right-angle crashes/year (existing).

 

Figure 24. Equations. Calculation of predicted right-angle crashes/year (proposed). Predicted right-angle crashes per year (proposed) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.1332 power times exp to the open parenthesis 0.2267 times SIGDENS minus 0.3633 times PROPLANE1 plus 0.4295 times PROPFULLDEV close parenthesis power. Using the values from the proposed condition, or alternative B, this equation equals 2.5 times exp to the open parenthesis negative 1.4079 plus 0.8858 close parenthesis times 22,500 to the 0.1332 power times exp to the open parenthesis 0.2267 times 0.40 minus 0.3633 times 1.0 plus 0.4295 times 1.0 close parenthesis power. Solving this expression results in an answer of 6.59 right-angle crashes per year.

Figure 24. Equations. Calculation of predicted right-angle crashes/year (proposed).

 

Step 4.1.3: Calculations for Extrapolated Variables

There are no extrapolated variables, so this step is not applicable.

Step 4.1.4: Estimated Safety Impacts

Because this is case 1 in step 4.1.2, the difference in predicted crashes per year between the two alternatives is obtained directly from the model predictions obtained in step 4.1.2. The estimated effect of increasing development over the entire corridor, adding the signalized intersection, and the associated growth in mainline AADT is an increase of (6.59–4.22) = 2.37 right-angle crashes/yr. The proposed alternative is predicted to increase right-angle crashes by 56percent (i.e., 6.59/4.22).

In this sample problem, it was desired to compare the predicted right-angle crashes for existing and proposed conditions. The following computations are provided to illustrate the process for comparing the percent change in crashes related to the change in each individual variable:

SAMPLE PROBLEM 2

Estimate the effect of changes in two or more variables that are not all accommodated in the same model (scenario 2).

Problem Definition

On a mixed-use corridor, changes are being proposed that would eliminate existing roadside development while reducing the overall access density. This would involve the removal of several access points in parts of the corridor, which will reduce the corridor totals by 20 driveways and 10 unsignalized intersections. The proportion of the corridor with no development will increase from 0 to 15 percent. It is desired to estimate the relative effect of the proposed changes on total crashes. It is assumed that all other variables, including AADT on the mainline, will not change.

Step 1: Select Land Use and Region

This is a mixed-use corridor. After reviewing the summary statistics for mixed land use in each of the four regions from which the models were developed and comparing them with the local data, it is determined that the corridor is most comparable to Northern California.

Step 2: Select Crash Types and Variables of Interest

As noted in the problem definition, total crashes are of interest. In this case, the variables of interest are ACCDENS (i.e., density of driveways plus unsignalized intersections) and PROPNODEV.

Step 3: Select Analysis Type of Interest

It is desired to estimate the relative safety of two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, analysis option 1 (algorithm 1) is applicable because the objective is to compare the relative safety impacts.

Step 4: Select Applicable Model(s) and Perform Analysis

Table 24 presents the applicable models for total crashes in a mixed land use. The applicable model for ACCDENS is mixed/total model 1 (table 34). The applicable model for PROPNODEV is mixed/total model 3 (table 36). The applicable model is different for the variables of interest, so it is necessary to apply multiple models to estimate the effects. In this case, extrapolated variables are not required. Note that all variables are available to apply the models, so no default values are required.

The model coefficients for total crashes from table 34 are: intercept (–3.1845), region (1.1410 if North Carolina or Minnesota; 0 otherwise), AADT (0.5187), ACCDENS (0.0053), SIGDENS (0.1095), and PROPLANE1 (–0.5185). The equation in figure 18 is applicable to this model.

The model coefficients for total crashes from table 36 are intercept (–0.8926), region (0.6166 if North Carolina or Minnesota; 0 otherwise), AADT (0.3766), and PROPNODEV (–0.4252). The equation in figure 18 is applicable to this model.

Step 4.1.1: Data for Conditions of Interest

The data for the existing condition (do-nothing alternative A) are the following:

The data for the proposed condition (alternative B) are the following:

Step 4.1.2: Calculations for Nonextrapolated Variables

Case 2 applies when the two variables of interest (ACCDENS and PROPNODEV) appear in separate models. Therefore, it is necessary to consider the effects of each variable separately and then combine the effects to estimate the total impact of alternative B.

Effect of ACCDENS (Table 34)

Figure 25 and figure 26 predict ACCDENS for this situation.

Figure 25. Equations. Effect of ACCDENS: predicted total crashes/year (existing). Predicted total crashes per year (existing) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.5187 power times exp to the open parenthesis 0.0053 times ACCDENS plus 0.1095 times SIGDENS minus 0.5185 times PROPLANE1 close parenthesis power. Using the values from the existing condition, or do-nothing alternative A, this equation equals 8.0 times exp to the open parenthesis negative 3.1845 plus 0 close parenthesis power times 30,000 to the 0.5187 power times exp to the open parenthesis 0.0053 times 9.38 plus 0.1095 times 1.13 minus 0.5185 times 0.75 close parenthesis power. Solving this expression results in an answer of 56.08 total crashes per year.

Figure 25. Equations. Effect of ACCDENS: predicted total crashes/year (existing).

 

Figure 26. Equations. Effect of ACCDENS: predicted total crashes/year (proposed). Predicted total crashes per year (proposed) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.5187 power times exp to the open parenthesis 0.0053 times ACCDENS plus 0.1095 times SIGDENS minus 0.5185 times PROPLANE1 close parenthesis power. Using the values from the proposed condition, or alternative B, this equation equals 8.0 times exp to the open parenthesis negative 3.1845 plus 0 close parenthesis power times 30,000 to the 0.5187 power times exp to the open parenthesis 0.0053 times 5.63 plus 0.1095 times 1.13 minus 0.5185 times 0.75 close parenthesis power. Solving this expression results in an answer of 54.98 total crashes per year.

Figure 26. Equations. Effect of ACCDENS: predicted total crashes/year (proposed).

 

Effect of PROPNODEV (Table 36)

Figure 27 and figure 28 calculate the effect of PROPNODEV.

Figure 27. Equations. Effect of PROPNODEV: predicted total crashes/year (existing). Predicted total crashes per year (existing) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.3766 power times exp to the open parenthesis negative 0.4252 times PROPNODEV close parenthesis power. Using the values from the existing condition, or do-nothing alternative A, this equation equals 8.0 times exp to the open parenthesis negative 0.8926 plus 0 close parenthesis power times 30,000 to the 0.3766 power times exp to the open parenthesis negative 0.4252 times 0 close parenthesis power. Solving this expression results in an answer of 159.05 total crashes per year.

Figure 27. Equations. Effect of PROPNODEV: predicted total crashes/year (existing).

 

Figure 28. Equations. Effect of PROPNODEV: predicted total crashes/year (proposed). Predicted total crashes per year (proposed) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.3766 power times exp to the open parenthesis negative 0.4252 times PROPNODEV close parenthesis power. Using the values from the proposed condition, or alternative B, this equation equals 8.0 times exp to the open parenthesis negative 0.8926 plus 0 close parenthesis power times 30,000 to the 0.3766 power times exp to the open parenthesis negative 0.4252 times 0.15 close parenthesis power. Solving this expression results in an answer of 149.22 total crashes per year.

Figure 28. Equations. Effect of PROPNODEV: predicted total crashes/year (proposed).

 

Step 4.1.3: Calculations for Extrapolated Variables

There are no extrapolated variables, so this step is not applicable.

Step 4.1.4: Estimated Safety Impacts

The total change in safety is estimated as the sum of changes from the individual models. The change in total predicted crashes related to the change in ACCDENS is (56.08 – 54.98) = 1.10crashes/yr, and the change in total predicted crashes related to the change in PROPNODEV is (159.05 – 149.22) = 9.83 crashes/yr. The change in total predicted crashes from all modifications (alternative B as a whole) is a reduction of 10.93 total crashes per year (1.10 + 9.83). The proposed alternative is predicted to reduce total crashes by 5 percent: (54.98 + 149.22)/(56.08 + 159.05).

SAMPLE PROBLEM 3

Estimate the effect of a change in a single variable that is accommodated in models for different crash types (scenario 3).

Problem Definition

For a mixed-use corridor, a proposal has been made to increase the number of driveways by 10 and the number of unsignalized intersections by 5. It is desired to estimate the relative effect of the proposed changes on all available crash types. All other corridor characteristics, including the mainline AADT, are assumed to remain constant.

Step 1: Select Land Use and Region

This is a mixed-use corridor. After reviewing the summary statistics for mixed land use in each of the four regions from which the models were developed and comparing them with the local data, it is determined that the corridor is most comparable to Southern California.

Step 2: Select Crash Types and Variables of Interest

As noted in the problem definition, it is desired to estimate the relative effect of the proposed changes on all available crash types. In this case, the variable of interest is ACCDENS, which is the density of driveways plus unsignalized intersections.

Step 3: Select Analysis Type of Interest

It is desired to estimate the relative safety between two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, analysis option 1 (algorithm 1) is applicable because the objective is to compare the relative safety impacts.

Step 4: Select Applicable Model(s) and Perform Analysis

Table 24 presents the applicable models for various crash types in a mixed land use. For mixed land use, ACCDENS is directly available in models for total crashes, turning crashes, and right-angle crashes. ACCDENS is not included in any mixed land use models for injury or rear-end crashes without extrapolating from another land use type. (Note that the extrapolation is covered in sample problem 5.) The applicable models for ACCDENS include mixed/total model 1 (table 34), mixed/turning model 1 (table 39), and mixed/right-angle model 1 (table 44). The applicable models are for different crash types, so it is necessary to apply the models separately to estimate the effects by crash type. In this case, extrapolated variables are not considered. Note that all variables are available to apply the models, so no default values are required.

The model coefficients for total crashes are given in table 34 as intercept (–3.1845), region (1.1410 if North Carolina or Minnesota; 0 otherwise), AADT (0.5187), ACCDENS (0.0053), SIGDENS (0.1095), and PROPLANE1 (–0.5185). The equation in figure 18 is applicable to this model.

The model coefficients for turning crashes are given in table 39 as intercept (–2.1083), region (0.9647 if North Carolina or Minnesota; 0 otherwise), SIGDENS (0.1865), and ACCDENS (0.0088). The equation in figure 19 is applicable to this model. Note that the result is expressed as crashes per MVMT. The result is multiplied by MVMT to express it as crashes per mile per year.

The model coefficients for right-angle crashes are given in table 44 as intercept (–5.8048), region (1.8390 if North Carolina or Minnesota; 0 otherwise), AADT (0.4656), ACCDENS (0.0112), and SIGDENS (0.2284). The equation in figure 19 is applicable to this model.

Step 4.1.1: Data for Conditions of Interest

The data for the existing condition (do-nothing alternative A) are the following:

The data for the proposed condition (alternative B) are the following:

Step 4.1.2: Calculations for Nonextrapolated Variables

Case 1 applies because there is only one variable of interest (ACCDENS).

Total Crashes (Table 34)

Figure 29 and figure 30 predict the total crashes per year.

Figure 29. Equations. Total crashes: predicted total crashes/year (existing). Predicted total crashes per year (existing) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.5187 power times exp to the open parenthesis 0.0053 times ACCDENS plus 0.1095 times SIGDENS minus 0.5185 times PROPLANE1 close parenthesis power. Using the values from the existing condition, or do-nothing alternative A, this equation equals 2.5 times exp to the open parenthesis negative 3.1845 plus 0 close parenthesis power times 25,000 to the 0.5187 power times exp to the open parenthesis 0.0053 times 44.0 plus 0.1095 times 4.0 minus 0.5185 times 0.25 close parenthesis power. Solving this expression results in an answer of 33.99 total crashes per year.

Figure 29. Equations. Total crashes: predicted total crashes/year (existing).

 

Figure 30. Equations. Total crashes: predicted crashes/year (proposed). Predicted total crashes per year (proposed) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.5187 power times exp to the open parenthesis 0.0053 times ACCDENS plus 0.1095 times SIGDENS minus 0.5185 times PROPLANE1 close parenthesis power. Using the values from the proposed condition, or alternative B, this equation equals 2.5 times exp to the open parenthesis negative 3.1845 plus 0 close parenthesis power times 25,000 to the 0.5187 power times exp to the open parenthesis 0.0053 times 50.0 plus 0.1095 times 4.0 minus 0.5185 times 0.25 close parenthesis power. Solving this expression results in an answer of 35.09 total crashes per year.

Figure 30. Equations. Total crashes: predicted crashes/year (proposed).

 

Turning Crashes (Table 39)

Figure 31 and figure 32 predict the number of turning crashes per year.

Figure 31. Equations. Turning crashes: predicted turning crashes/year (existing). Predicted turning crashes per year (existing) equals open parenthesis MVMT close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times exp to the open parenthesis 0.0088 times ACCDENS plus 0.1865 times SIGDENS close parenthesis power. Using the values from the existing condition, or do-nothing alternative A, this equation equals open parenthesis 2.5 times 25,000 times 365 divided by 1,000,000 close parenthesis times exp to the open parenthesis negative 2.1083 plus 0 close parenthesis power times exp to the open parenthesis 0.0088 times 44.0 plus 0.1865 times 4.0 close parenthesis power. Solving this expression results in an answer of 8.60 turning crashes per year.

Figure 31. Equations. Turning crashes: predicted turning crashes/year (existing).

 

Figure 32. Equations. Turning crashes: predicted turning crashes/year (proposed). Predicted turning crashes per year (proposed) equals open parenthesis MVMT close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times exp to the open parenthesis 0.0088 times ACCDENS plus 0.1865 times SIGDENS close parenthesis power. Using the values from the proposed condition, or alternative B, this equation equals open parenthesis 2.5 times 25,000 times 365 divided by 1,000,000 close parenthesis times exp to the open parenthesis negative 2.1083 plus 0 close parenthesis power times exp to the open parenthesis 0.0088 times 50.0 plus 0.1865 times 4.0 close parenthesis power. Solving this expression results in an answer of 9.07 turning crashes per year.

Figure 32. Equations. Turning crashes: predicted turning crashes/year (proposed).

 

Right-Angle Crashes (Table 44)

Figure 33 and figure 34 predict the number of right-angle crashes per year.

Figure 33. Equations. Right-angle crashes: predicted right-angle crashes/year (existing). Predicted right-angle crashes per year (existing) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.4656 power times exp to the open parenthesis 0.0112 times ACCDENS plus 0.2284 times SIGDENS close parenthesis power. Using the values from the existing condition, or do-nothing alternative A, this equation equals 2.5 times exp to the open parenthesis negative 5.8048 plus 0 close parenthesis power times 25,000 to the 0.4656 power times exp to the open parenthesis 0.0112 times 44.0 plus 0.2284 times 4.0 close parenthesis power. Solving this expression results in an answer of 3.43 right-angle crashes per year.

Figure 33. Equations. Right-angle crashes: predicted right-angle crashes/year (existing).

 

Figure 34. Equations. Right-angle crashes: predicted right-angle crashes/year (proposed). Predicted right-angle crashes per year (proposed) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.4656 power times exp to the open parenthesis 0.0112 times ACCDENS plus 0.2284 times SIGDENS close parenthesis power. Using the values from the proposed condition, or alternative B, this equation equals 2.5 times exp to the open parenthesis negative 5.8048 plus 0 close parenthesis power times 25,000 to the 0.4656 power times exp to the open parenthesis 0.0112 times 50.0 plus 0.2284 times 4.0 close parenthesis power. Solving this expression results in an answer of 3.67 right-angle crashes per year.

Figure 34. Equations. Right-angle crashes: predicted right-angle crashes/year (proposed).

 

Step 4.1.3: Calculations for Extrapolated Variables

There are no extrapolated variables, so this step is not applicable.

Step 4.1.4: Estimated Safety Impacts

The estimated effect of increasing the number of driveways from 80 to 90 and the number of unsignalized intersections from 30 to 35 is as follows:

SAMPLE PROBLEM 4

Compare the expected crashes for two alternatives to select the most appropriate alternative (scenario 4).

Problem Definition

For a mixed-use corridor, a proposal has been made to increase the number of driveways by 10 and the number of unsignalized intersections by 5. An alternate proposal will increase the number of driveways by eight and the number of unsignalized intersections by four. It is desired to estimate the impact of each proposed alternative in terms of the project cost and expected number of right-angle crashes per year. All other corridor characteristics, including the mainline AADT, are assumed to remain constant. Note that this problem uses the same situation as sample problem 3 but incorporates the observed crash history.

Step 1: Select Land Use and Region

This is a mixed-use corridor. After reviewing the summary statistics for mixed land use in each of the four regions from which the models were developed and comparing them with the local data, it is determined that the corridor is most comparable to Southern California.

Step 2: Select Crash Types and Variables of Interest

As noted in the problem definition, it is desired to estimate the effect of the proposed changes on the expected number of right-angle crashes. In this case, the variable of interest is ACCDENS, which is the density of driveways plus unsignalized intersections.

Step 3: Select Analysis Type of Interest

It is desired to estimate the impact of each proposed alternative in terms of the project cost and expected number of right-angle crashes per year. A more precise estimate is required because the difference in expected crashes is to be compared with the difference in costs of the two alternatives. In this case, analysis option 2 (algorithm 2) is applicable because the objective is to estimate the expected crashes for the given alternatives.

Step 4: Select Applicable Model(s) and Perform Analysis

Table 24 presents the applicable models for right-angle crashes in a mixed land use. The applicable model for ACCDENS is mixed/right-angle model 1 (table 44). Because the EB method is to be applied as part of algorithm 2, it is necessary to select a base model from the last column of table 24. The applicable base model for applying the EB method is mixed/right-angle model 1 (table 24). In this case, the base model and the model for ACCDENS are the same. Note that extrapolated variables are not considered, and all variables are available to apply the models, so no default values are required.

The model coefficients for right-angle crashes are given in table 44 as intercept (–5.8048), region (1.8390 if North Carolina or Minnesota; 0 otherwise), AADT (0.4656), ACCDENS (0.0112), and SIGDENS (0.2284). The equation in figure 18 is applicable to this model.

Step 4.2.1: Data for Conditions of Interest

The data for the existing condition (do-nothing alternative A) are the following:

The data for proposed condition 1 (alternative B) are the following:

The data for proposed condition 2 (alternative C) are the following:

Step 4.2.2: Prediction for Existing Condition

Step 4.2.2a Baseline Predicted Right-Angle Crashes/Year (Existing Alternative A)

Use the base model (table 44) with the values from alternative A to estimate the baseline predicted crashes for the existing condition as shown in figure 35.

Figure 35. Equations. Baseline predicted right-angle crashes/year (existing alternative A). Baseline predicted right-angle crashes per year (existing) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.4656 power times exp to the open parenthesis 0.0112 times ACCDENS plus 0.2284 times SIGDENS close parenthesis power. Using the values from the existing condition, or do-nothing alternative A, this equation equals 2.5 times exp to the open parenthesis negative 5.8048 plus 0 close parenthesis power times 25,000 to the 0.4656 power times exp to the open parenthesis 0.0112 times 44.0 plus 0.2284 times 4.0 close parenthesis power. Solving this expression results in an answer of 3.43 right-angle crashes per year.

Figure 35. Equations. Baseline predicted right-angle crashes/year (existing alternative A).

 

Step 4.2.2b Estimated EB Weight

w is estimated using the equation in figure 36.

Figure 36. Equations. Estimate of w. w equals 1 divided by open bracket 1 plus open parenthesis k times years times step 4.2.2a estimate close parenthesis close bracket. Using the values from the existing condition, or alternative A, w equals 1 divided by open parenthesis 1 plus 0.5585 times 1 times 3.43 close parenthesis. This expression simplifies to 0.3430.

Figure 36. Equations. Estimate of w.

 

Note that the k is given for each specific model in appendix C. For the base model for mixed-use, right-angle crashes (table 44), the value of k = 0.5585.

Step 4.2.2c Expected Right-Angle Crashes/Year (Existing Alternative A)

The annual expected crash frequency (EB estimate) for existing conditions is calculated using the equation in figure 37.

Figure 37. Equations. Expected right-angle crashes/year (existing alternative A).  EB Estimate equals open bracket w times open parenthesis step 4.2.2a estimate close parenthesis close bracket plus open bracket open parenthesis 1 minus w close parenthesis times open parenthesis observed crashes divided by years of data close parenthesis close bracket. Using the values of w in figure 41 and the existing alternative A in figure 40, the EB estimate equals 0.3430 times 3.43 plus open parenthesis 1 minus 0.3430 close parenthesis times open parenthesis 17 divided by 4 close parenthesis. This simplifies to 3.97 right-angle crashes per year.

Figure 37. Equations. Expected right-angle crashes/year (existing alternative A).

 

Step 4.2.2d Estimated EB Correction Factor

The EB correction factor is calculated as the expected crashes for the existing condition (step 4.2.2c) divided by the baseline predicted crashes for the existing condition (step 4.2.2a). Figure 38 calculates the EB correction factor:

Figure 38. Equation. Estimate EB correction factor. EB correction factor equals expected crashes (existing) divided by baseline crashes (existing). Using the values from figure 40 and figure 42, the EB correction factor equals 3.97 divided by 3.43, which also equals 1.16.

Figure 38. Equation. Estimate EB correction factor.

 

This factor is used to adjust predictions for alternative scenarios and helps to account for several sources of potential bias, including variables that are omitted from the model.

Step 4.2.3: Prediction for Proposed Condition

Step 4.2.3a Difference in Predicted Right-Angle Crashes/Year for Existing and Proposed Condition

Apply steps 4.1.2 through 4.1.4 from algorithm 1 using the existing and proposed conditions as inputs. The result is an estimate of the difference in predicted crash frequency for the existing and proposed conditions.

Step 4.1.2: Calculations for Nonextrapolated Variables

Figure 39 through figure 41 predict the number of right-angle crashes per year.

Figure 39. Equations. Predicted right-angle crashes/year (existing alternative A). Predicted right-angle crashes per year (existing alternative A) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.4656 power times exp to the open parenthesis 0.0112 times ACCDENS plus 0.2284 times SIGDENS close parenthesis power. Using the values from the existing condition, or do-nothing alternative A, this equation equals 2.5 times exp to the open parenthesis negative 5.8048 plus 0 close parenthesis power times 25,000 to the 0.4656 power times exp to the open parenthesis 0.0112 times 44.0 plus 0.2284 times 4.0 close parenthesis power. Solving this expression results in an answer of 3.43 right-angle crashes per year.

Figure 39. Equations. Predicted right-angle crashes/year (existing alternative A).

 

Figure 40. Equations. Predicted right-angle crashes/year (proposed alternative B). Predicted right-angle crashes per year (proposed alternative B) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.4656 power times exp to the open parenthesis 0.0112 times ACCDENS plus 0.2284 times SIGDENS close parenthesis power. Using the values from the proposed alternative B, this equation equals 2.5 times exp to the open parenthesis negative 5.8048 plus 0 close parenthesis power times 25,000 to the 0.4656 power times exp to the open parenthesis 0.0112 times 50.0 plus 0.2284 times 4.0 close parenthesis power. Solving this expression results in an answer of 3.67 right-angle crashes per year.

Figure 40. Equations. Predicted right-angle crashes/year (proposed alternative B).

 

Figure 41. Equations. Predicted right-angle crashes/year (proposed alternative C). Predicted right-angle crashes per year (proposed alternative C) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.4656 power times exp to the open parenthesis 0.0112 times ACCDENS plus 0.2284 times SIGDENS close parenthesis power. Using the values from the proposed alternative C, this equation equals 2.5 times exp to the open parenthesis negative 5.8048 plus 0 close parenthesis power times 25,000 to the 0.4656 power times exp to the open parenthesis 0.0112 times 48.8 plus 0.2284 times 4.0 close parenthesis power. Solving this expression results in an answer of 3.62 right-angle crashes per year.

Figure 41. Equations. Predicted right-angle crashes/year (proposed alternative C).

 

Step 4.1.3: Calculations for Extrapolated Variables

There are no extrapolated variables, so this step is not applicable.

Step 4.1.4: Estimated Difference in Crashes/Year for Different Alternatives

Comparing alternative A and alternative B (i.e., an increase in the number of driveways by 10 and an increase in the number of unsignalized intersections by 5 for a mixed-use corridor), the predicted change in right-angle crashes is an increase of (3.67 – 3.43) = 0.24 right-angle crash/yr.

Comparing alternative A and alternative C (i.e., an increase in the number of driveways by 8 and an increase in the number unsignalized intersections by 4 for a mixed-use corridor), the predicted change in right-angle crashes is an increase of (3.62 – 3.43) = 0.19 right-angle crash/yr.

Step 4.2.3b Adjusted Predicted Right-Angle Crashes/Year for Existing Condition

Add the difference in predicted crashes for existing and proposed conditions from step 4.2.3a to the baseline predicted crashes for existing conditions from step 4.2.2a, as shown in figure 42.

Figure 42. Equations. Adjusted predicted right-angle crashes/year for existing condition. For alternative B, 0.24 plus 3.43 equals 3.67 right-angle crashes. For alternative C, 0.19 plus 3.43 equals 3.62 right-angle crashes.

Figure 42. Equations. Adjusted predicted right-angle crashes/year for existing condition.

 

Step 4.2.3c Expected Right-Angle Crashes/Year for Proposed Condition

Multiply the adjusted predicted crashes for the existing condition from step 4.2.3b by the EB correction factor from step 4.2.2d, as shown in figure 43.

Figure 43. Equations. Expected right-angle crashes/year for proposed condition. For alternative B, 3.67 times 1.16 equals 4.26 right-angle crashes per year. For alternative C, 3.62 times 1.16 equals 4.20 right-angle crashes per year.

Figure 43. Equations. Expected right-angle crashes/year for proposed condition.

 

Step 4.2.4: Estimated Safety Impacts

The results are provided as the expected crash frequencies per year for the crash types selected under both alternatives. The estimates for the existing conditions are from step 4.2.2c, and the estimates for the following proposed conditions are from step 4.2.3c:

This sample problem included calculations for right-angle crashes only. A similar method would be applied to compute the EB correction factor for other crash types using the crash history for those specific crash types. The applicable correction factor would then be applied to the model predictions for alternative scenarios to estimate the expected crashes for other crash types of interest. Recall that the results from individual crash type models should not be summed to estimate total crashes.

SAMPLE PROBLEM 5

Estimate the safety impact of variables that are available for a given crash type but not for the land use type of interest (scenario 5). In this case, it is necessary to use extrapolation. The extrapolation method first requires the use of a model from the land use and crash type of interest to predict crashes for existing conditions. Then, a model is selected from another land use to estimate the impacts of the variables of interest.

Problem Definition

For a commercial corridor, a proposal has been made to install a divided median for the entire length of the corridor. Presently, the corridor is partially divided. In the segment that is to be divided (currently undivided), a single median opening would be provided. It is desired to estimate the relative safety impact of the proposed changes on right-angle crashes. All other corridor characteristics, including the AADT, are assumed to remain constant.

Step 1: Select Land Use and Region

This is a commercial corridor. After reviewing the summary statistics for commercial use in each of the four regions from which the models were developed and comparing them to the local data, it is determined that the corridor is most comparable to Minnesota.

Step 2: Select Crash Types and Variables of Interest

As noted in the problem definition, it is desired to estimate the relative effect of the proposed changes on right-angle crashes. In this case, the variables of interest include the proportion of corridor with divided median (PROPDIV) and density of median openings (MEDOPDENS).

Step 3: Select Analysis Type of Interest

It is desired to estimate the relative safety of two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, analysis option 1 (algorithm 1) is applicable because the objective is to compare the relative safety impacts.

Step 4: Select Applicable Model(s) and Perform Analysis

Table 25 presents the applicable models for right-angle crashes in a commercial land use. There are no directly applicable models for PROPDIV or MEDOPDENS, but column 4 indicates that these variables may be considered through extrapolation. The applicable model for PROPDIV is mixed/right-angle model 2 (table 45). The applicable model for MEDOPDENS is mixed/right-angle model 2 (table 45). In this case, the applicable models are the same for the two variables of interest. It is also necessary to select a base model from the last column of table 25 for use in the extrapolation process. The applicable base model for extrapolation is commercial/right-angle model 1 (table 57). Note that default values are required from appendix D for use in the extrapolation process.

The model coefficients to estimate the impact of the variables of interest on right-angle crashes are given in table 45 as PROPDIV (–0.4710) and MEDOPDENS (0.1901). Note that only the coefficients for the variables of interest are required from this model.

The model coefficients for the base model are given in table 57 as intercept (–1.6746), region (1.4756 if North Carolina or Minnesota; 0 otherwise), AADT (0.1238), ACCDENS (0.0165), and SIGDENS (0.1532). The equation in figure 18 is applicable to this model.

Step 4.1.1: Data for Conditions of Interest

The data for the existing condition (alternative A) are the following:

The data for the proposed condition (alternative B) are the following:

Step 4.1.2: Calculations for Nonextrapolated Variables

The effects are extrapolated from a model for a different land use, so this step is not applicable.

Step 4.1.3: Calculations for Extrapolated Variables

For each of the two variables to be considered through extrapolation, the following steps are taken.

Step 4.1.3a Baseline Predicted Right-Angle Crashes/Year (Existing)

Use the base model (table 57) with the values from the existing condition (alternative A) to estimate the baseline predicted crashes for the existing condition as shown in figure 44.

Figure 44. Equations. Baseline predicted right-angle crashes/year (existing). Baseline predicted right-angle crashes per year (existing alternative A) equals open parenthesis length close parenthesis times exp to the open parenthesis intercept plus region close parenthesis power times open parenthesis AADT close parenthesis to the 0.1238 power times exp to the open parenthesis 0.0165 times ACCDENS plus 0.1532 times SIGDENS close parenthesis power. Using the values from the existing condition, or alternative A, this equation equals 5.0 times exp to the open parenthesis negative 1.6746 plus 1.4756 close parenthesis power times 46,000 to the 0.1238 power times exp to the open parenthesis 0.0165 times 52.6 plus 0.1532 times 3.6 close parenthesis power. Solving this expression results in an answer of 64.01 right-angle crashes per year.

Figure 44. Equations. Baseline predicted right-angle crashes/year (existing).

 

Step 4.1.3b Estimate the Impacts of the Variables of Interest for Existing Conditions

The effects of the variables of interest for the existing conditions are estimated using the equation in figure 45 along with the coefficients in table 45 and the values from alternative A:

Figure 45. Equation. Estimate of the impacts of the variables of interest for existing conditions. Multiplier equals exp to the open parenthesis coefficient close parenthesis times open parenthesis Variable Actual Value minus Variable Default Value close parenthesis power.

Figure 45. Equation. Estimate of the impacts of the variables of interest for existing conditions.

 

The coefficients for PROPDIV and MEDOPDENS are -0.4710 and 0.1901. The mean value of PROPDIV and MEDOPDENS are obtained from appendix D for the land use and region from which the model was developed. In this example, the corridor of interest is similar to Minnesota, and the model is based on data for a mixed land use. From appendix D, the mean values for PROPDIV and MEDOPDENS from mixed-use corridors in Minnesota are 0.61 and 1.47, respectively (table 76), and the multipliers are calculated as shown in figure 46.

Figure 46. Equations. Estimation of multipliers. This figure shows two equations. First, the multiplier for PROPDIV equals exp to the negative 0.4710 times open parenthesis PROPDIV existing minus PROPDIV mean close parenthesis power. Using the values for PROPDIV, this expression equals exp to the negative 0.4710 times open parenthesis 0.60 minus 0.61 close parenthesis power. This simplifies to 1.00. The second equation is: multiplier for MEDOPDENS equals exp to the 0.1901 times open parenthesis MEDOPDENS existing minus MEDOPDENS mean close parenthesis power. Using the values for MEDOPDENS, this expression equals exp to the 0.1901 times open parenthesis 1.60 minus 1.47 close parenthesis power. This simplifies to 1.03.

Figure 46. Equations. Estimation of multipliers.

 

Step 4.1.3c Adjusted Predicted Right-Angle Crashes/Year (Existing Alternative A)

The estimate from step 4.1.3b is then multiplied by the estimate from step 4.1.3a, as shown in figure 47.

Figure 47. Equations. Adjusted predicted right-angle crashes/year (existing alternative A). Adjusted predicted right-angle crashes per year (existing alternative A) equals multiplier for PROPDIV times multiplier for MEDOPDENS times existing predicted right-angle crashes per year. Using the previously calculated values, this equals 1.00 times 1.03 times 64.01 right-angle crashes per year, which simplifies to 65.93 right-angle crashes per year.

Figure 47. Equations. Adjusted predicted right-angle crashes/year (existing alternative A).

 

Step 4.1.3d Baseline Predicted Right-Angle Crashes/Year (Proposed)

Use the base model (table 57) with the values from the proposed condition (alternative B) to estimate the baseline predicted crashes for the proposed condition. In this case, there are no anticipated changes in the variables included in the base model; therefore, the estimate remains the same as the baseline predicted crashes for the existing conditions (64.01 right-angle crashes per year).

Step 4.1.3e Estimate the Impacts of the Variables of Interest for Proposed Conditions

The effects of the variables of interest for the proposed conditions are estimated using the equation in figure 20 along with the coefficients in table 45 and the values from alternative B.

The coefficients for PROPDIV and MEDOPDENS are –0.4710 and 0.1901. The mean value of PROPDIV and MEDOPDENS are obtained from appendix D for the land use and region from which the model was developed. In this example, the corridor of interest is similar to Minnesota, and the model is based on data for a mixed land use. From appendix D, the mean values for PROPDIV and MEDOPDENS from mixed-use corridors in Minnesota are 0.61 and 1.47, respectively (table 76), and the multipliers are calculated as shown in figure 48.

Figure 48. Equations. Estimation of multipliers. This figure shows two equations. First, the multiplier for PROPDIV equals exp to the negative 0.4710 times open parenthesis PROPDIV proposed minus PROPDIV mean close parenthesis power. Using the values for PROPDIV, this expression equals exp to the negative 0.4710 times open parenthesis 1.00 minus 0.61 close parenthesis power. This simplifies to 0.83. The second equation is: multiplier for MEDOPDENS equals exp to the 0.1901 times open parenthesis MEDOPDENS proposed minus MEDOPDENS mean close parenthesis power. Using the values for MEDOPDENS, this expression equals exp to the 0.1901 times open parenthesis 1.80 minus 1.47 close parenthesis power. This simplifies to 1.06.

Figure 48. Equations. Estimation of multipliers.

 

Step 4.1.3f Adjusted Predicted Right-Angle Crashes/Year (Proposed Alternative B)

The estimate from step 4.1.3e is then multiplied by the estimate from step 4.1.3d. as shown in figure 49.

Figure 49. Equations. Adjusted predicted right-angle crashes/year (proposed alternative B). Adjusted predicted right-angle crashes per year (proposed alternative B) equals multiplier for PROPDIV times multiplier for MEDOPDENS times proposed predicted right-angle crashes per year. Using the previously calculated values, this equals 0.83 times 1.06 times 64.01 right-angle crashes per year, which simplifies to 56.32 right-angle crashes per year.

Figure 49. Equations. Adjusted predicted right-angle crashes/year (proposed alternative B).

 

Step 4.1.4: Estimated Safety Impacts

The adjusted predicted crash frequency for proposed conditions (step 4.1.3f) is subtracted from the adjusted predicted crash frequency for existing conditions (step 4.1.3c). The result is the difference in the predicted crash frequency for alternative B compared with alternative A. The impact of the proposed conditions (i.e., installing a median along the remainder of the corridor with a single median opening) is a reduction of (65.93 – 56.32) = 9.61 right-angle crashes/yr.

SAMPLE PROBLEM 6

Estimate effects when one or more variables of interest do not appear in any models for any crash type of interest or land use (scenario 6).

When a variable is not included in any of the models, it is not possible to quantify the effects of those variables in the manner shown in the previous sample problems. Instead, qualitative assessments could be made based on relationships identified from basic summary statistics. To facilitate such an assessment, appendix E provides the correlation coefficients between the variables of interest that do not appear in any models and the various crash types by land use.

Correlation coefficients range between –1.0 and 1.0. A positive coefficient indicates that higher values of a variable are correlated with a higher crash frequency. A negative coefficient indicates that higher values of a variable are correlated with a lower crash frequency. The closer the coefficient is to –1.0 or 1.0, the stronger the correlation.

It is critical to employ caution and judgment when using correlation coefficients to assess the potential impact of a variable. Specifically, it must be noted that no other variables, including traffic volume, are accounted for in the correlation coefficients, which can result in completely erroneous relationships.

To provide a point of reference, the parameter estimates and p-values are also provided with the correlation coefficients. The parameter estimates are based on a restricted model in which only traffic volume and the variable of interest are included. Where the correlation coefficient and the parameter estimate differ (i.e., opposite signs), it may be an indication that other factors are confounding the results or that the association is not statistically significant.

Example of Logical Effects

Several of the variables in appendix E are related to the spacing of intersections and access points such as the minimum spacing of signalized intersections (MINSPCSIG). For all crash types in all three land use scenarios, the correlation coefficient is negative for MINSPCSIG as shown in table 27. This indicates that greater minimum signal spacing is correlated with fewer crashes. It should be noted that traffic volume is not considered in the estimation of correlation coefficients.

The model coefficients and associated p-values are also provided in table 27 (shown in parentheses below the respective correlation coefficients). The only other variable considered in the estimation of the model coefficients is AADT, so the results should be interpreted with caution because other important factors may be omitted. All of the model coefficients are negative, indicating that greater minimum signal spacing may reduce crashes for these crash types. This is consistent with the correlation coefficients. Further, many of the p-values are less than 0.10, particularly for commercial and residential land use, indicating that the effects are statistically significant.

Table 27. Correlation coefficients for MINSPCSIG (model coefficient, p-value).

Land Use Total Injury Turning Rear-End Right-Angle
Mixed-use –0.1800
(–0.0001, 0.2200)
–0.2100
(–0.0001, 0.2600)
–0.1600
(–0.0001, 0.3600)
–0.2000
(–0.0002, 0.1100)
–0.2100
(–0.0002, 0.0700)
Commercial –0.2100
(–0.0002, 0.0000)
–0.2200
(–0.0002, 0.0000)
–0.1600
(–0.0001, 0.0300)
–0.2200
(–0.0003, 0.0000)
–0.2300
(–0.0002, 0.0000)
Residential –0.3400
(–0.0002, 0.0100)
–0.3300
(–0.0002, 0.0000)
–0.2200
(–0.0001, 0.1100)
–0.3300
(–0.0003, 0.0000)
–0.3100
(–0.0001, 0.3400)

 

Example of Illogical Effects

Several of the variables in appendix E are related to the presence of left-turn lanes, such as the number of signalized intersections with a left-turn lane on the mainline (NOLTLSIG). For all crash types in all three land use scenarios, the correlation coefficient is positive for NOLTLSIG as shown in table 28. This indicates that left-turn lanes are correlated with higher numbers of crashes. What is not considered is that left-turn lanes are often installed along corridors with higher traffic volumes, which typically experience more crashes because of the higher volumes.

The model coefficients and associated p-values are also provided in table 28 (shown in parentheses below the respective correlation coefficients). The only other variable considered in the estimation of the model coefficients is AADT, so the results should be interpreted with caution because other important factors may be omitted. Some of the coefficients are negative, indicating that left-turn lanes may reduce crashes for these crash types. This is counterintuitive to the correlation coefficients and should indicate to the user that the results may be unreliable, and there may be other factors that should be considered. In addition, all p-values are much greater than 0.10, indicating that the effects are not statistically significant.

Table 28. Correlation coefficients for NOLTLSIG (model coefficient, p-value).

Land Use Total Injury Turning Rear-End Right-Angle
Mixed-use 0.790
(0.009, 0.282)
0.860
(0.011, 0.192)
0.740
(0.010, 0.328)
0.590
(0.004, 0.690)
0.860
(0.014, 0.168)
Commercial 0.730
(0.011, 0.259)
0.800
(0.010, 0.282)
0.650
(0.006, 0.583)
0.460
(0.013, 0.355)
0.810
(0.017, 0.173)
Residential 0.620
(–0.003, 0.911)
0.670
(0.005, 0.811)
0.590
(0.008, 0.765)
0.500
(0.017, 0.604)
0.390
(–0.027, 0.351)

 

 

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