A six-lane divided multilane highway (three lanes in each direction) has a measured free-flow speed of 50 mi/h. It is on mountainous terrain with a traffic stream consisting of 7% large trucks and buses and 3% recreational vehicles. The driver population adjustment in 0.92. One direction of the highway currently operates at maximum LOS C conditions and it is known that the highway has PHF = 0.90. Required:
How many vehicles can be added to this highway before capacity is reached, assuming the proportion of vehicle types remains the same but the peak-hour factor increases to 0.95?

2901 vehicles

Explanation:

We are given;

Percentage of large trucks & buses; p_t = 7% = 0.07

Percentage of recreational vehicles; p_r = 3% = 0.03

PHF = 0.90

Driver population adjustment; f_p = 0.92

First of all, let's Calculate the heavy vehicle factor from the formula;

f_hv = 1/[1 + p_t(e_t - 1) + p_r(e_r - 1)]

Where;

e_t = passenger car equivalents for trucks and buses

e_r = passenger car equivalents for recreational vehicles

From the table attached, for a mountainous terrain, e_t = 6 and e_r = 4. Thus;

f_hv = 1/[1 + 0.07(6 - 1) + 0.03(4 - 1)]

f_hv = 1.44

Let's now calculate the initial hourly volume from the formula;

v_p = V1/(PHF × N × f_hv × f_p)

Where;

v_p = 15-minute passenger-car equivalent flow rate

V1 = hourly volume

N = number of lanes in each direction

From online tables of LOS criteria for multilane freeway segments, v_p = 1300 pc/hr/ln

Thus;

1300 = V1/(0.9 × 3 × 1.44 × 0.92)

V1 = 1300 × (0.9 × 3 × 1.44 × 0.92)

V1 = 4650 veh/hr

Now, let's Calculate the final hourly volume;

From online sources, the maximum capacity of a 6 lane highway with free-flow speed of 50 mi/h is 2000 pc/hr/ln.

We are told the online peak-hour factor increases to 0.95 and so PHF = 0.95.

Thus;

2000 = V2/(0.95 × 3 × 1.44 × 0.92)

V2 = 2000(0.95 × 3 × 1.44 × 0.92)

V2 = 7551 veh/hr

Number of vehicles added to the highway = V2 - V1 = 7551 - 4650 = 2901 vehicles

it was a fall down when it happens

explanation: