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$1$ Intersection LOS and Design $(50$ points$)$

As part of this problem, you are asked to determine the overall intersection LOS score for a fictional intersection shown below Concidar the diacram of intareantion and turnine mnvamante

Following merimation is pioviueu:

Speed limit on all streets is $30$ mph

Lane width is $11$ ft on N$.$ Eolm St and $13$ ft on Pigah Church Rd$.$

No heavy vehicles on N$.$ Eolm St; $10\%$ of straight through volume on Pigah Church Rd consists of heavy vehicles

No buses on either street

N$.$ Eolm St$.$ is level, but Pigah Church Road has a $6\%$ grade $($uphill in the eastbound direction$)$

PIEV time is $1$ seconds

For the northbound and southbound direction, there are no heavy vehicles so the design vehicle is $12$ ft long and has a deceleration rate of $20f\frac{t}{s^2}$

For the eastbound and westbound directions, the design vehicle is $25$ ft long and has a deceleration rate of $10f\frac{t}{s^2}$

$1$

Answer the following questions and clearly report ALL values with the units:

a$)(8$ points$)$ Calculate the clearance time for each approach $($eastbound$,$ westbound, northbound, and southbound$),$ clearly indicating the value of each term used for the calculations.

b$)(12$ points$)$ For each of the two$-$lane groups $($left$-$turn lane group and through$-$right turn lane group$)$ for each approach $($that is$,$ a total of $8$ lane groups$),$ compute:

a$.$ Lane width correction factor

b$.$ Heavy$-$vehicle correction factor

c$.$ Grade factor

d$.$ Left turn factor.

e$.$ Right$-$turn factor

f$.$ Corrected Saturation flow rate.

c$)$ Design a four$-$phase signal using the phasing pattern below by calculating the following:

a$.(4$ points$)$ Critical Z ratio for all four phases using the Z$-$ratios for the involved lane groups

b$.(4$ points$)$ Optimal green time for all four phases

c$.(3$ points$)$ Cycle length

d$.(2$ points$)$ Effective green time

d$)$ Calculate the delay for:

a$.(8$ points$)$ each lane group,

b$.(4$ points$)$ each approach, and

c$.(3$ points$)$ the intersection as a whole.

e$)(2$ points$)$ Compute the overall intersection level of service.