Webster's Method | Transportation Engineering - Civil Engineering (CE) PDF Download

Introduction

Webster's method stands as a rational and straightforward approach used in traffic signal design. It relies on formulae developed by Webster to establish signal timings and optimize traffic flow at intersections. This method provides a systematic and practical framework for designing traffic signals based on Webster's formulas.

Cycle Length

Traffic signals operate on the principle of time-sharing. The cycle length represents the duration required to complete an entire sequence of signal phases at an intersection. For instance, it encompasses the time taken for a signal to transition through its phases, typically from red to yellow, then green, and eventually back to the red signal again, completing one full cycle.

Green and Red Interval

The green interval denotes the duration when the traffic signal displays the green signal, allowing vehicles to proceed through the intersection. Conversely, the red interval refers to the period when the signal displays the red light, signifying a halt for vehicles at the intersection.

Change Interval

The change interval typically represents the duration of the yellow signal phase. The yellow signal, also known as the amber signal, serves as a transition period between the green and red signals, cautioning drivers to prepare for the impending change in signal status.

The calculation of the amber time can be done using a straightforward formula, often derived from specific guidelines or principles related to traffic engineering and signal design. This calculation helps determine the optimal duration for the amber signal based on various factors such as intersection geometry, traffic flow characteristics, and safety considerations.

The amber signal, visible within the stopping sight distance of the vehicle, provides a crucial warning period. It allows drivers enough time to decelerate safely and come to a complete stop before the signal switches to red. This proactive measure enhances safety by enabling drivers to react appropriately and smoothly transition from the green to the red signal without abrupt braking or potential hazards.

In this scenario, when the vehicle reaches the point beyond its stopping sight distance before the amber signal, it's crucial to allocate enough time for the vehicle to traverse the intersection without abrupt halts.

The required travel distance for the vehicle includes the stopping sight distance (SSD), the length of the carriageway (W), and the length of the vehicle (L). Therefore, the determination of the amber time involves...

Amber time = (SSD + W + L) / v,
where, v is the velocity of the vehicle (or design speed)

Clearance Interval

The clearance interval represents the duration allocated for pedestrians to cross the intersection safely and for additional time to ensure vehicles have completely cleared the intersection.

Phase:
A phase refers to the count of paths or movements intersecting at a junction. For instance, in a four-armed intersection, there are typically four phases. It's also calculated as the total of the green interval, change interval, and clearance interval.

Lost Time:
At a traffic signal, when the signal turns green, the first vehicle in line requires a certain amount of time to react and begin moving. Subsequent vehicles follow with slightly reduced reaction times, gradually decreasing until they reach a consistent time known as the headway.

The additional time that vehicles ahead of the queue take beyond the consistent headway is termed as lost time. Every phase incorporates this lost time, which is crucial to consider when calculating the most effective cycle length for the signal.

Saturation Flow (s):
Saturation flow represents the maximum vehicular flow achievable and is the reciprocal of the headway. When the headway is measured in seconds, the saturation flow is calculated as:

Saturation flow = 3600/headway in vehicles per hour.

Observed Volume (v):
Observed volume refers to the real-time traffic flow observed at an intersection, often quantified as the number of vehicles passing through within a specific timeframe. It is essentially represented as vehicles per unit time, offering a direct measure of the actual traffic volume.

Critical Flow Ratio:
The critical flow ratio for a phase signifies the ratio between the observed traffic flow volume and the saturation flow across all phases at an intersection. This ratio is calculated as.

Critical flow ratio at i_th phase = observed volume / saturation flow = v/s at i_th phase

Optimum Cycle Length By Webster Method

Based on those parameters, Webster devised a straightforward equation to compute the most efficient cycle length for an intersection. This cycle length is also considered as the overall cycle time for a signal system. Webster's formula is expressed as:

Optimum cycle length (Co) = (1.5*L + 5) / (1 - y),
where,
L - total lost time including all red time,
L = (n * Lost time at a phase) + All red time
n - number of phases
All red time is usually taken as zero
Lost time at a phase is usually taken as 2 seconds
y - is the summation of the critical flow ratio at all the phases

Green Time by Webster Method:
Green time for a road 'a' by Webster's method is given as,
Ga = (ya/y) * (Co - L),
where,
ya - critical flow ratio for road 'a'
y - summation of all critical flow ratio
Co - Optimum cycle length
L - lost time including all red time