Highway Engineering

The Design of Highway Intersections 147

Example 5.9 – Calculation of time-and-distance diagram
Three two-phase signalised intersections are spaced 400 m apart. The main
axis of flow is in the north/south direction. Details of the actual and satura-
tion flows at each of the junctions are given in Table 5.9. The starting delays
are taken as 2 seconds per green period, the amber period is 3 seconds in all
cases and the period during which all lights show red during a change of
phase is 2 seconds.
Locate the critical intersection, calculate the minimum and maximum
actual green times and outline the construction of the time-distance diagram
indicating how vehicles will progress along the main axis of flow.
The junction is illustrated diagrammatically in Fig. 5.33.

Solution

Intergreen period =10 seconds (5 seconds per phase, 3 s amber +2s red)
Lost time =8 seconds in total per cycle (4 seconds per phase, 2 s starting and
2s during intergreen)
Firstly the optimum cycle time for each intersection must be calculated
applying Equation 5.34 to the three sets of data in Table 5.9:

Co=(1.5L+5) ∏(1 -Sycrit)

Values ofycritfor each intersection in the network are indicated in Table 5.9.

Intersection Approach Actual flow Saturation flow yycrit

(vehicles/hour) (vehicles/hour)

A1 North 800 3200 0.250

South 1200 3200 0.375 0.375

East 800 1800 0.444

West 500 1550 0.323 0.444

A2 North 1100 3200 0.344

South 1160 3200 0.363 0.363

East 1020 2150 0.474

West 525 1800 0.291 0.474

A3 North 800 3200 0.250

South 1000 3200 0.313 0.313

East 800 1800 0.444

West 400 1800 0.222 0.444

Table 5.9Critical ratios for each intersection in the network

Based on the critical ratios in Table 5.9, the optimum cycle time for each

intersection can be computed as:

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