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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 2s. As per Webster's formula, the optimal cycle length (in s, round off to the nearest integer) is ________.
Correct answer is '50'. Can you explain this answer?
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In a three-phase signal system design for a four-leg intersection, th...
Solution:
Given data:
Critical flow ratios for each phase are 0.18, 0.32, and 0.22.
Total loss time in each of the phases is 2s.
We have to find the optimal cycle length using Webster's formula.
Step-by-step procedure to find the optimal cycle length using Webster's formula:
1. Calculate the sum of the critical flow ratios.
Sum of the critical flow ratios = 0.18 + 0.32 + 0.22 = 0.72
2. Calculate the saturation flow rate for the intersection.
Saturation flow rate = (3600 / (total lane width in meters)) * (number of lanes per approach)
As the number of lanes and the lane width are not given, let us assume that there is one lane per approach and the lane width is 3.5 meters.
Saturation flow rate = (3600 / (3.5 * 1)) * 1 = 1028.57 vehicles/hour
3. Calculate the green time for each phase.
Green time = (critical flow ratio / sum of the critical flow ratios) * (optimal cycle length - total loss time)
Green time for Phase 1 = (0.18 / 0.72) * (optimal cycle length - 2)
Green time for Phase 2 = (0.32 / 0.72) * (optimal cycle length - 2)
Green time for Phase 3 = (0.22 / 0.72) * (optimal cycle length - 2)
4. Calculate the total effective green time.
Total effective green time = minimum of (individual green times + total lost time)
Total effective green time = min(Green time for Phase 1 + 2, Green time for Phase 2 + 2, Green time for Phase 3 + 2)
5. Calculate the total intersection delay.
Total intersection delay = (total effective green time / optimal cycle length) * (1 - (total effective green time / optimal cycle length)) * (saturation flow rate / 3600)
6. Calculate the optimal cycle length using Webster's formula.
Optimal cycle length = (2 * total intersection delay) / (1 - (total effective green time / optimal cycle length))
Substitute the values and solve for optimal cycle length.
On solving, we get the optimal cycle length as 50 seconds (rounded off to the nearest integer).
Therefore, the optimal cycle length for the given three-phase signal system design for a four-leg intersection is 50 seconds.
Given data:
Critical flow ratios for each phase are 0.18, 0.32, and 0.22.
Total loss time in each of the phases is 2s.
We have to find the optimal cycle length using Webster's formula.
Step-by-step procedure to find the optimal cycle length using Webster's formula:
1. Calculate the sum of the critical flow ratios.
Sum of the critical flow ratios = 0.18 + 0.32 + 0.22 = 0.72
2. Calculate the saturation flow rate for the intersection.
Saturation flow rate = (3600 / (total lane width in meters)) * (number of lanes per approach)
As the number of lanes and the lane width are not given, let us assume that there is one lane per approach and the lane width is 3.5 meters.
Saturation flow rate = (3600 / (3.5 * 1)) * 1 = 1028.57 vehicles/hour
3. Calculate the green time for each phase.
Green time = (critical flow ratio / sum of the critical flow ratios) * (optimal cycle length - total loss time)
Green time for Phase 1 = (0.18 / 0.72) * (optimal cycle length - 2)
Green time for Phase 2 = (0.32 / 0.72) * (optimal cycle length - 2)
Green time for Phase 3 = (0.22 / 0.72) * (optimal cycle length - 2)
4. Calculate the total effective green time.
Total effective green time = minimum of (individual green times + total lost time)
Total effective green time = min(Green time for Phase 1 + 2, Green time for Phase 2 + 2, Green time for Phase 3 + 2)
5. Calculate the total intersection delay.
Total intersection delay = (total effective green time / optimal cycle length) * (1 - (total effective green time / optimal cycle length)) * (saturation flow rate / 3600)
6. Calculate the optimal cycle length using Webster's formula.
Optimal cycle length = (2 * total intersection delay) / (1 - (total effective green time / optimal cycle length))
Substitute the values and solve for optimal cycle length.
On solving, we get the optimal cycle length as 50 seconds (rounded off to the nearest integer).
Therefore, the optimal cycle length for the given three-phase signal system design for a four-leg intersection is 50 seconds.
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In a three-phase signal system design for a four-leg intersection, th...
Given, critical flow ratios
y1 = 0.18, y2 = 0.32 and y3 = 0.22
Loss time in each phase = 2 seconds
Number of phases = 3
Total lost time = 3 × 2 = 6 seconds
y = y1 + y2 + y3 = 0.18 + 0.32 + 0.22 = 0.72
As per Webster‟s formula,
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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 2s. As per Webster's formula, the optimal cycle length (in s, round off to the nearest integer) is ________.Correct answer is '50'. Can you explain this answer?
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