Question

I've answered the first half, but im stuck on the second half with multilanes and i need help with it .

Highway Capacity and Level-of-Service Analysis

Freeways

A new segment of freeway is being built to connect two existing parallel freeway facilities, in an urban area. The following traffic and roadway characteristics are expected:

Traffic Characteristics

• AADT = 92000 veh/day

• K = 13%

• D = 50%

• PHF = 0.92

• 8% trucks and buses

• 3% RVs

• Primarily commuters

Roadway Characteristics

• Grade in peak direction: 1.42 miles, 3.25% upgrade

• Interchange density = 1.8 per mile

• Lane widths = 12 ft

• Shoulder widths = 4 ft

1. Determine the number of lanes necessary to ensure that this new freeway segment will operate at no worse than LOS D during the peak hour in the peak direction.

2. How much additional traffic, in the peak direction, can be accommodated before the freeway reaches capacity?

Multilanes

A section of a multilane highway is to be reconstructed to improve the level of service. The section being considered is on a 5.0% upgrade that is 3/4 mile long. The highway currently has 4-lanes (2 in each direction – all are 12-ft lanes) with a two-way left-turn lane in the middle and 4 foot shoulders on the right side. It is to be reconstructed into a 6-lane facility (3-lanes in each direction) undivided facility but, due to commercial development surrounding the highway, must remain in the current 72 foot right of way. There are currently 35 access points per mile and the free flow speed is determined to be 50 mi/h. It is known that the road currently operates at capacity with 420 trucks/buses (no recreational vehicles) during the peak hour, a peak hour factor of 0.95 and all-commuter traffic.

The redesign is to reduce the number of access points per mile to 10 and to reduce the grade to 4.0% for 3/4 mile. It is estimated that the new design will increase traffic by 13%.

1. Determine the lane width and shoulder width combination that will maximize capacity given that the 3 lanes (each direction) must fit within 36ft?

2. For the maximum-capacity lane/shoulder combination chosen above, determine the new design's level of service and density.

Answer 1

Answering the 2nd half i.e multilanes part- based on your request

Multi lane Highway

AADT = 92000 veh/day in both directions

K factor = DHV/AADT = 13% = 0.13

DHV = design hourly volume. Therefore DHV = .13 * AADT = .13 *92000 = 11960 veh/hr

DDHV = directional design hourly volume = D * DHV = D * K * AADT

= 50% of DHV = .5 *.13 * 92000 = 5980 veh/hr

currently N = number or lanes in each direction = 2

currently lane width = 12 foot lanes + two way left-turn lane + 4 ft shoulders on right side

Currently ROW =72 feet, and you have 4 travel lanes (toal in both direction) plus two way left-turn lane + 4 ft shoulders on right side

So your current cross section is like this - if you calculate it out based on lane widths and clearance

For the above section we know that

PHF = 0.95

Assume that the peak hourly flow rate = V veh/hr

So it is given that trucks/buses = 420. So Percentage of trucks/buses = 420/V * 100

% of RV's =0

upgrade = 5% over a segment which is 0.75mile long. So assume ET = 4.0

so we need to calculate heavy vehicle factor using the formula

Heavy vehicle factor = fHV and it is calculated using the formula

So fHV = 1/(1+ 420/V *3 + 0) = 1/(1+1260/V)

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Calculate vp

vp is calculated by the formula

where

vp = 15 mt passenger car equivalent flow rate in pc/h

So peak hour volume = V veh/hr

fp = driver population factor. Assume equal to 1 because all are familiar drivers

Peak Hour Factor PHF = 0.95 as given

N = Number of lanes in one direction = 2 for the unmodified road

fHV = heavy vehicle factor calculated earlier to be equal to 1/(1+1260V)

fp = driver familiarity factor - assume it to be 1 and that most are familiar drivers

So vp = V/(0.95 * 2 * 1/(1+1260/V) * 1) = V*(1+1260/V)/1.9

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FFS = 50 mi/h

So density = vp/FFS = vp/50 pc/mi/ln = vp/80.467 pc/km/ln

Since it is given that it is at at capacity= assume LOS =E,

So based on guideline table below, maximum density at LOS E = 28 pc/km/ln

so equate density to 28, we have vp/80.467 = 28. Therefore vp = 2253.076 pc/hr

so V*(1+1260/V)/1.9 = 2253.076 - so solve for V as as quadratic equation

and you will get V = 3021 veh/hr - use this V in testing the modified options

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After improvement

N = 3 lanes in each direction = but we are also told we have to work within the 72ft ROW

So in the new design you can have lane widths of 10ft, or 11 ft or 12 feet. In each possibility you must calculate the different possibilities of right-shoulder lateral clearance .We are told it has become a 6 lanes (3 in each direction) undivided facility.

We need to determine density for both combinations to then check which one gives lower density and hence better LOS. This will all depend on the deductions from free flow speed which are inturn dependent on lane widths and rightside later clearance etc

So there are three possibilities for re-design labelled as Modified-1, Modified-2 and Modified-3. These can be shown as

Calculate the density for each modified option.

For modified option we know that vp increases by 13%

V for improved section = 3021*1.13 =3414 veh/hr

So Truck% = 420/3414 = 12.3% - so PT = .123

PR is still zero

We know that the modified highway has 4% updgrade over 3/4mile and has 12.3% trucks. So based on HCM tables, assume that the ET value = 3

So calculate the new heavy vehicle factor

Heavy vehicle factor = fHV and it is calculated using the formula

So fHV = 1/(1+ .123*2 +0) =1/1.246 = 0.8025

So calculate vp for the modified section

vp for modifeid section is calculated by the formula

where

vp = 15 mt passenger car equivalent flow rate in pc/h

So peak hour volume = V veh/hr = 3414 veh/r

fp = driver population factor. Assume equal to 1 because all are familiar drivers

Peak Hour Factor PHF = 0.95 as given

N = Number of lanes in one direction = 3 for the modified road

fHV = heavy vehicle factor calculated earlier to be .8025

fp = driver familiarity factor - assume it to be 1 and that most are familiar drivers

So vp = V/(0.95 * 3 * .8025 * 1) = 3414/2.2871 = 1492.72 pc/hr

So density of modified road (in pc/km/ln= vp/FFS of modified road = 1492.72/1.60934 *FFS (in mph)

= 927.53/FFS (mph) - EQUATION 2

So for maximum capacity configutation, density should be lowest.

Obviously density will be lowest when the denominator of equation 2 is highest.

So FFS has to be maximized.

WE know that FFS = BFFS - fLW - fLC -fN -fID

FFS for old section = 50mph

So we can calculate BFFS for old secton which is 63.2 mph.

So no we have to set up a comparative table to evaluate the FFS for the three modified options given the conditions.

We know that Number of lanes =3 so fN has to be same for all options i.e 3 mph

also number of interchanges/mile = 10 in all three options so fID for all options is the same i.e 7.5mph

So we have the following comparitive table. Asssume that the BFFS for the facility does not change from before and remains at 63.2. So for each modified option combination we must calculate the FFS based on BFFS - fLW - fLC -fN -fID

So clearly the FFS is highest in option 3 i.e when you have 12ft lanes and zero lateral clearance on right side.

So the option which will give maximum capacity and lowest density is shown below

Calculate the density for this option using the equation

Density (pc/km/ln) = 927.53/FFS (mph) = 927.53/50.3 = 18.4399 pc/km/lm

Therefore LOS for modified highway = LOS D