Question

In a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are 0.18, 0.32, and 0.22. The total loss time in each of the phases is 2 s. As per Webster's formula, the optimal cycle length (in s, round off to the nearest integer) is \(\underline{\hspace{1cm}}\).

Hint:

Webster's formula is used to calculate the optimal cycle length for traffic signal systems based on the critical flow ratios.

Answer 1

Correct Answer: 48 - 52

To determine the optimal cycle length for a traffic signal system using Webster's formula, follow these steps:

1. The formula for the optimal cycle length \(C_0\) is given by:
   \(C_0 = \dfrac{1.5 \cdot L + 5}{1 - Y}\), where:
   • \(L\) is the total loss time per cycle. Given that each phase has a loss time of 2 s and there are three phases, \(L = 3 \times 2 = 6\) s.
   • \(Y\) is the sum of the critical flow ratios: \(Y = 0.18 + 0.32 + 0.22 = 0.72\).
2. Substitute the known values into Webster's formula:
   \(C_0 = \dfrac{1.5 \times 6 + 5}{1 - 0.72} = \dfrac{9 + 5}{0.28} = \dfrac{14}{0.28} = 50.\)

The optimal cycle length is 50 seconds.