[Solution]Transportation Engineering Assignment

A new 6 miles segment of a multi-lane divided highway is proposed for design and construction in a rural area. The following facts apply to…

A new 6 miles segment of a multi-lane divided highway is proposed for design and construction in a rural area. The following facts apply to this project:

AADT (two-way) = 40,000
Speed limit = 45 mph
K = 15%
D = 55/45 directional split
Level terrain
8 percent trucks
7 access points per mile
PHF = 0.80
Assume Base Free-flow Speed (BFFS) is 7 mph greater than posted speed limit

What is the number of lanes in each direction of the typical section required to meet the design criteria of LOS D?
 
Solution
Referring to Transportation Engineering I class lecture note “TTE+4004+L13+Intro+to+Freeway+LOS+2018+Wed.pdf” pages 126-170 (Trans I Class lecture note) and HCM 2010 Chapter 14.
 
Since this is a new highway, use of desirable design criteria are recommended to obtain longer service life of the project. As such, 12 feet lane, 0 lateral obstructions are to be assumed:
 
BFFS= 45 + 7 =52 mph
FFS = BFFS-fLW-fLC-fM-fA
fLW = 0.0 (from Table 6-3 [Trans I Class lecture note] for 12 ft lane width)
fLC = 0.0 (assuming no lateral obstruction, 0.0 for TLC of 12 ft in Table 6.11 [Trans I Class lecture note])
fM = 0.0 (from Table 6.12 [Trans I Class lecture note] for divided highways)
fA = 1.75 (from Table 6.13 [Trans I Class lecture note] for 7 access points per mile [by interpolation])
FFS=52 – 0 – 0 – 0 – 1.75 = 50.25 mph, rounded to 50 mph
 
From Table 6.10 and Fig. 6.4 [Trans I Class lecture note], for LOS D and FFS = 50 mph, maximum flow rate is 1680 pcphpl.
 
Based on Equation 6.7 [Trans I Class lecture note Slide #88], the 15-min passenger-car equivalent flow rate (i.e., demand flow rate under equivalent base conditions) vp is
vp = V / ( PHF x N x fhv  x fp )
in which,
V = DDHV = AADT x K x D = 40,000 x 0.15 x 0.55 = 3300 vph
PHF = 0.80 (given)
N = number of lanes (unknown)
fhv = 1 / [ 1 + PT(ET – 1)] =1 / [ 1 + 0.08(1.5 – 1)] =  0.96  (ET =1.5 from Exhibit 14-12 in HCM 2010 for level terrain)
fp = 1 (assumed for familiar users)
 
let vp = maximum flow rate = 1680 pcphpl, we have
1680 = (3300) / (0.80 x N x 0.96 x 1)
N = 3300/(0.8 x 0.96 x 1 x 1680)=2.56 lanes, say N = 3 in each direction.
 
There should be 3 lanes in each direction of the typical section required to meet the design criteria of LOS D.

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