Traffic and Highway Engineering - With Mindtap
Traffic and Highway Engineering - With Mindtap
5th Edition
ISBN: 9781305360990
Author: Garber
Publisher: CENGAGE L
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Chapter 5, Problem 23P
To determine

The expected reductions inthe number of crashes during the first three years after implementation of the countermeasures.

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Answer to Problem 23P

The expected reductions in number of crashes during the first three years after implementation of the countermeasures are 25crashes,26crashesand27crashes, respectively.

Explanation of Solution

Given:

The number of countermeasures is 4.

The countermeasure factors (CMFs) for the proposed four countermeasures are 0.25,0.30,0.17and0.28.

The number of crashes per year at the identified intersection during the past three years are 28,30and31.

The average annual daily traffic (AADT) at the intersection for the last three years respectively the number of crashes per yearsare 8450,9150and9850.

The average annual daily traffic (AADT) at the intersection during the first implementation is 10,850.

The estimated traffic growth rate per annum after implementation is 4%.

Formula used:

The crash reduction factor is given by,

  CR=[CR1+CR2(1CR1)+CR3(1CR1)(1CR2)+CR4(1CR1)(1CR2)(1CR3)] ...... (I)

Here, CR1 is the reduction factor for the first countermeasure and CR2 is the reduction factor for the second countermeasure, CR3 is the reduction factor for the third countermeasure and CR4 is the reduction factor for the fourth countermeasure,

The average number of crashes per year is given by,

  N=CrashrateforgivennumerofyearsTotalnumberofyears ...... (II)

The ADTbeforeimprovement is given by,

  N=AnnualcrashrateforgivennumerofyearsTotalnumberofyears ...... (III)

The crashes prevented first year is given by,

  Crashesprevented=N×CR×(ADTafterimprovementADTbeforeimprovement) ...... (IV)

Here, N is the expected number of crashes if countermeasure is implemented and the traffic volume remains the same, CR is the crash reduction factor and AADT is the average annual daily traffic.

The crashes prevented second year is given by,

  Crashesprevented=(1+0.04)N×CR×(ADTafterimprovementADTbeforeimprovement) ...... (V)

The crashes prevented third year is given by,

  Crashesprevented=(1+0.04)2N×CR×(ADTafterimprovementADTbeforeimprovement) ...... (VI)

Calculation:

Substitute 0.25 for CR1, 0.30 for CR2, 0.17 for CR3 and 0.28 for CR4 in equation (I).

  CR=[0.25+0.30(10.25)+0.17(10.25)(10.30)+0.28(10.25)(10.30)(10.17)]=0.6860.69

Substitute (28+30+31) for Crashrateforgivennumerofyears and 3 for Totalnumberofyears in equation (II).

  N=28+30+313=29.70

Substitute (8450+9150+9850) for Annualcrashrateforgivennumerofyears and 3 for Totalnumberofyears in equation (III).

  N=8450+9150+98503=9150

Substitute 29.70 for N, 0.69 for CR, 10,850 for ADTafterimprovement and 9,150 for ADTbeforeimprovement in equation (IV).

  Crashesprevented=(29.70)(0.69)(10,8509,150)=24.3025

Substitute 29.70 for N, 0.69 for CR, 10,850 for ADTafterimprovement and 9,150 for ADTbeforeimprovement in equation (V).

  Crashesprevented=(1+0.04)(29.70)(0.69)(10,8509,150)=(1+0.04)(24.30)=25.2726

Substitute 29.70 for N, 0.69 for CR, 10,850 for ADTafterimprovement and 9,150 for ADTbeforeimprovement in equation (VI).

  Crashesprevented=(1+0.04)2(29.70)(0.69)(10,8509,150)=(1+0.04)2(24.30)=26.2827

Conclusion:

Therefore, theexpected reductions in number of crashes during the first three years after implementation of the countermeasures are 25crashes,26crashesand27crashes, respectively.

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