Chapter 6, Problem 1P

To determine

The hourly volume.

Answer to Problem 1P

The hourly volume is $3904\text{veh/h}$ .

Explanation of Solution

Given:

The width of lane is $11\text{ft}$ .

The width of right side shoulderis $4\text{ft}$ .

The heavy vehicle on the rolling terrainis $10\%$ .

The peak hour factoris $0.90$ .

Formula Used:

Write the expression for free flow speed.

  $FFS=75.4-f_{\text{LW}}-f_{\text{RLC}}-3.22TR{D}^{0.84}$ …… (I)

Here, $FFS$ is the free flow speed, $f_{\text{LW}}$ is the adjustment for free lane width, $f_{\text{RLC}}$ is the adjustment for lateral clearance, $3.22TR{D}^{0.84}$ is the adjustment for total ramp density.

Write the expression for the analysis flow rate.

  $v_{\text{p}}=\frac{V}{PHF\times N\times f_{\text{HV}}}$ …… (II)

Here, $v_p$ is the flow rate, $V$ is the hourly volume, $PHF$ is the peak hour factor, $N$ is the number of lanes and $f_{\text{HV}}$ is the heavy vehicle adjustment factor.

Write the expression for the heavy vehicle adjustment factor.

  $f_{\text{HV}}=\frac{1}{1+P_{\text{T}}\left(E_{\text{T}}-1\right)}$ …… (III)

Here, $P_{\text{T}}$ is the proportion of the heavy vehicles and $E_{\text{T}}$ is the passenger car equivalent for heavy vehicles.

Calculation:

Refer Table $6.3$ “Adjustment of the lane width” of the book “Principles of Highway Engineering and traffic, $6^{\text{th}}$ Edition.

The $f_{\text{LW}}$ for lane width $11\text{ft}$ is $1.9$

Refer Table $6.4$ “Adjustment of the right shoulder lateral clearance” of the book “Principles of Highway Engineering and traffic, $6^{\text{th}}$ Edition.

The $f_{\text{RLC}}$ for right shoulder lateral clearance width $4\text{ft}$ for $3$ lanes is $0.8$ .

The $TRD$ is calculated as,

  $\begin{array}{c}TRD=\frac{3}{6}\\ =0.5\text{ramps/mi}\end{array}$

Substitute $0.5\text{ramps/mi}$ for $TRD$ , $1.9$ for $f_{\text{LW}}$ and $0.8$ for $f_{\text{RLC}}$ in equation (I).

  $\begin{array}{c}FFS=75.4-1.9-0.8-3.22{\left(0.5\right)}^{0.84}\\ =70.9\text{mi/h}\end{array}$

Refer Table $6.5$ “Passenger car equivalent for extended freeway segments” of the book “Principles of Highway Engineering and traffic, $6^{\text{th}}$ Edition.

The $E_{\text{T}}$ for rolling terrain is $3.0$ .

Substitute $3.0$ for $E_{\text{T}}$ and $0.10$ for $P_{\text{T}}$ in equation (III).

  $\begin{array}{c}{f}_{\text{HV}}=\frac{1}{1+0.1\left(3.0-1\right)}\\ =0.833\end{array}$

Refer Table $6.2$ “LOS criteria for basic freeway segments “Principles of Highway Engineering and traffic, $6^{\text{th}}$ Edition”.

The value of maximum flow ratefor maximum LOS C condition of $FFS\approx 70\text{mi/h}$ is $1735$ .

Substitute $1735$ for $v_{\text{P}}$ , $3$ for $N$ , $0.833$ for $f_{\text{HV}}$ and $0.90$ for $PHF$ in equation (II).

  $\begin{array}{c}1735=\frac{V}{0.90\times 3\times 0.833}\\ V\simeq 3904\text{veh/h}\end{array}$

Conclusion:

Thus, the hourly volumeis $3904\text{veh/h}$ .