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-f_{LW}-f_{LC}-f_{M}-f_{A}

f_{LW} = 0.0 (from Table 6-3 [Trans I Class lecture note] for 12 ft lane width)

f_{LC} = 0.0 (assuming no lateral obstruction, 0.0 for TLC of 12 ft in Table 6.11 [Trans I Class lecture note])

f_{M} = 0.0 (from Table 6.12 [Trans I Class lecture note] for divided highways)

f_{A} = 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 + P_{T}(E_{T} – 1)] =1 / [ 1 + 0.08(1.5 – 1)] = 0.96 (E_{T} =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.