40.7. Problems

1. The width of approaches for a rotary intersection is 12 m. The entry and exit width at the rotary is 10 m. Table below gives the trac from the four approaches, traversing the intersection. Find the capacity of the rotary.

This statement provides essential details necessary for calculating the capacity of the rotary intersection. It gives the width of the approaches leading to the rotary, specifies the widths of entry and exit, and outlines the configuration of traffic from the four directions approaching the rotary. To find the rotary's capacity, we will analyze the traffic flow and apply specific formulas related to rotary design.

Imagine a roundabout where different roads lead into it, like water flowing into a pool from different streams. Just as you might need to calculate how much water can gather in the pool based on the size of each stream’s width, we calculate traffic flow in the same way for safety and efficiency.

Approach Left turn Straight Right turn North 400 700 300 South 350 370 420 East 200 450 550 West 350 500 520

The table provides the distribution of traffic from four different approaches to the rotary: North, South, East, and West. Each direction has specified numbers for left turns, straight movements, and right turns, which are critical for understanding how vehicles are expected to maneuver within the rotary. This distribution helps in determining which traffic movements will create the highest demand on the rotary's capacity.

Think of a busy airport terminal with different gates. Each gate represents a direction of approach in a rotary. If one gate has three flights landing at the same time, it becomes congested, just as traffic does in a rotary when too many vehicles turn or go straight from one direction.

Weaving width is calculated as, w = [e1+e2]+3.5 = 13.5m

The weaving width is crucial for determining how much space is needed for the vehicles to navigate safely within the rotary. It is calculated using the formula that involves the entry and exit widths. Here, 'e1' and 'e2' represent the widths of the entry and exit, respectively, and the additional 3.5 meters accounts for a safety and operational buffer.

Imagine a wide river where multiple boats (vehicles) need to navigate towards an island (the rotary). If the boats are too close together, they may collide. Thus, calculating the weaving width is like ensuring there’s enough space for boats to maneuver without bumping into each other.

Weaving length ,l = 4 w = 54m ×

The weaving length is defined by the amount of distance required for vehicles to safely merge and diverge after entering or exiting the rotary. This is calculated by multiplying the weaving width by 4, ensuring there is ample distance for traffic to adjust speed and position without excessive delay or danger.

Consider a road with bike paths leading into a roundabout. Just as cyclists need enough distance to adjust their speeds and enter safely into the roundabout, vehicles also need adequate weaving length to navigate effectively and safely.

The proportion of weaving trac to the non-weaving trac in all the four approaches is found out rst.

To assess the rotary's capacity, we need to calculate the proportion of weaving versus non-weaving traffic. This is done for each approach to gauge which direction has the highest volume of traffic transitioning through the rotary. Knowing this ratio helps identify and mitigate bottlenecks where traffic might slow down and cause congestion.

Picture a theme park entrance where people can either take a direct path or wander off into different areas (weaving). Some walk directly in while others explore, creating different levels of foot traffic. Understanding these patterns allows the park to manage crowds effectively, just as traffic ratios inform rotary design.

Therefore, the capacity also need to be found only for that section.

The final capacity of the rotary is determined primarily by the section with the highest proportion of weaving traffic. The average entry and exit widths, along with the weaving width and length, are combined in a formula to find how many vehicles can pass through this busiest section per hour. This calculation ensures the rotary can handle expected traffic volumes efficiently.

Think of a funnel that lets water flow into a bottle. The narrowest part of the funnel determines how fast water goes into the bottle. Similar to this, the section with the highest weaving traffic dictates how efficiently traffic flows through the rotary.

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