Chapter 7, Problem 1P

To determine

The sum of the flow ratios for the critical lane group.

Answer to Problem 1P

The sum of the flow ratios for the critical lane group is $0.707$ .

Explanation of Solution

Formula Used:

Write the expression for the flow ratio.

  $\text{Flow}\text{ratio}=\frac{v}{s}$
.......... (I)

Here, $v$ is the flow rate and $s$ is the saturation flow rate.

Write the expression to for the sum of flow ratio in the critical lane group.

  $Y_{\text{C}}=F_{{\text{C}}_1}+F_{{\text{C}}_2}+F_{{\text{C}}_3}$ ........... (II)

Here, $Y_{\text{C}}$ is the sum of flow ratios in the critical lane group and $F_{{\text{C}}_{\text{1}}}$ is the flow ratio for critical lane group in phase $1$ , $F_{{\text{C}}_2}$ is the flow ratio for critical lane group in phase $2$ and $F_{{\text{C}}_3}$ is the flow ratio for critical lane group in phase $3$

Calculation:

Consider Phase $1$ .

Calculate the flow ratio for Northbound Left(NBL).

Substitute $\text{330}\text{veh}/\text{hr}$ for $v$ and $\text{1700}\text{veh}/\text{hr}$ in equation (I).

  $\begin{array}{c}\text{Flow}\text{ratio}=\frac{\text{330}\text{veh}/\text{hr}}{1700\text{veh}/\text{hr}}\\ =0.194\end{array}$

Calculate the flow ratio for Southbound Left(SBL).

Substitute $\text{365}\text{veh}/\text{hr}$ for $v$ and $\text{1750}\text{veh}/\text{hr}$ in equation (I).

  $\begin{array}{c}\text{Flow}\text{ratio}=\frac{\text{365}\text{veh}/\text{hr}}{1750\text{veh}/\text{hr}}\\ =0.208\end{array}$

Maximum ratio of each phase is called as a critical lane group.

The critical lane group flow ratio for phase $1$ is $0.208$ .

Consider Phase $2$ .

Calculate the flow ratio for Northbound Right Turn (NBL T/R).

Substitute $\text{1125}\text{veh}/\text{hr}$ for $v$ and $\text{3400}\text{veh}/\text{hr}$ in equation (I).

  $\begin{array}{c}\text{Flow}\text{ratio}=\frac{\text{1125}\text{veh}/\text{hr}}{3400\text{veh}/\text{hr}}\\ =0.3301\end{array}$

Calculate the flow ratio for Southbound Right Turn (SBL T/R).

Substitute $\text{1075}\text{veh}/\text{hr}$ for $v$ and $\text{3300}\text{veh}/\text{hr}$ in equation (I).

  $\begin{array}{c}\text{Flow}\text{ratio}=\frac{\text{1075}\text{veh}/\text{hr}}{3300\text{veh}/\text{hr}}\\ =0.325\end{array}$

The critical lane group flow ratio for phase $2$ is $0.330$ .

Consider Phase $3$ .

Calculate the flow ratio for Eastbound Left (EBL).

Substitute $\text{110}\text{veh}/\text{hr}$ for $v$ and $\text{650}\text{veh}/\text{hr}$ in equation (I).

  $\begin{array}{c}\text{Flow}\text{ratio}=\frac{\text{110}\text{veh}/\text{hr}}{650\text{veh}/\text{hr}}\\ =0.169\end{array}$

Calculate the flow ratio for Westbound Left (WBL).

Substitute $\text{80}\text{veh}/\text{hr}$ for $v$ and $\text{600}\text{veh}/\text{hr}$ in equation (I).

  $\begin{array}{c}\text{Flow}\text{ratio}=\frac{\text{80}\text{veh}/\text{hr}}{600\text{veh}/\text{hr}}\\ =0.133\end{array}$

Calculate the flow ratio for Eastbound Right Turn (EB T/R).

Substitute $\text{250}\text{veh}/\text{hr}$ for $v$ and $\text{1750}\text{veh}/\text{hr}$ in equation (I).

  $\begin{array}{c}\text{Flow}\text{ratio}=\frac{\text{250}\text{veh}/\text{hr}}{1750\text{veh}/\text{hr}}\\ =0.142\end{array}$

Calculate the flow ratio for Westbound Right Turn (WB T/R).

Substitute $\text{285}\text{veh}/\text{hr}$ for $v$ and $\text{1800}\text{veh}/\text{hr}$ in equation (I).

  $\begin{array}{c}\text{Flow}\text{ratio}=\frac{\text{285}\text{veh}/\text{hr}}{1800\text{veh}/\text{hr}}\\ =0.158\end{array}$

The critical lane group flow ratio for phase $3$ is $0.169$ .

Substitute $0.208$ for $F_{C{L}_1}$ , $0.330$ for $F_{C{L}_2}$ and $0.169$ for $F_{C{L}_3}$ in equation (II).

  $\begin{array}{c}{Y}_{\text{C}}=0.208+0.330+0.169\\ =0.707\end{array}$

Conclusion:

The sum of the flow ratios for the critical lane group is $0.707$ .