15.4.1. Mechanical widening

The reasons for the mechanical widening are: When a vehicle negotiates a horizontal curve, the rear wheels follow a path of shorter radius than the front wheels as shown in figure 15.5. This phenomenon is called off-tracking, and has the effect of increasing the effective width of a road space required by the vehicle.

Mechanical widening is necessary because during a turn, the rear wheels of a vehicle do not follow the exact same path as the front wheels. The rear wheels track a path with a smaller radius compared to the front wheels, which results in a need for extra width in the road. This phenomenon is known as off-tracking, meaning that vehicles require more space than what might be needed when traveling in a straight line. This effect can be significant, especially when large vehicles like trucks or trailers are involved.

Imagine riding a bicycle. When you turn right, the back wheel of the bike turns in a slightly tighter circle than the front wheel, causing you to need more space on the road than just your width. Similarly, vehicles, particularly large ones, need extra width on the road when they make turns to avoid collisions with other vehicles or road edges.

Therefore, to provide the same clearance between vehicles travelling in opposite direction on curved roads as is provided on straight sections, there must be extra width of carriageway available.

To ensure safety and proper spacing between vehicles navigating a curve, extra road width is essential. On straight roads, cars can maintain a safe distance easily. However, on curves, if the road is too narrow, vehicles risk colliding with each other, especially when larger trucks are involved. Extra carriageway width allows for more maneuvering space, ensuring that even if vehicles stray slightly from their intended path, they can do so safely without endangering other road users.

Consider an escalator moving in a curve at a mall. If too many people try to use it at once, they may bump into one another. However, if the escalator were wider, more people could fit comfortably, minimizing collisions and delays. Similarly, widening the road on curves reduces the risk of accidents caused by close quarters.

Trailer trucks also need extra carriageway, depending on the type of joint. In addition, speeds higher than the design speed causes transverse skidding which requires additional width for safety purpose.

Extra carriageway width is not just about vehicle size but also involves the dynamics of how vehicles behave at different speeds. For example, trailer trucks need more space because of their long bodies and the way they turn. Higher speeds lead to skidding, especially on curves where the traction is limited, hence requiring additional road width to ensure that vehicles can safely navigate turns without slipping.

Think about a bowling ball rolling down a tilted alley. If the ball gains speed, it may veer off to the side, particularly if the alley slopes sharply. In a similar way, vehicles traveling too fast on a curve are more likely to ‘skid’ off the intended path, which emphasizes the importance of having a wider turning space.

The expression for extra width can be derived from the simple geometry of a vehicle at a horizontal curve. Let R1 be the radius of the outer track line of the rear wheel, R2 be the radius of the outer track line of the front wheel, l be the distance between the front and rear wheel, n be the number of lanes, then the mechanical widening W is derived below.

To calculate the extra width required, geometrical principles are applied. As the vehicle goes around a curve, we can represent the positions of the front and rear wheels with variables based on their respective radii and the length between them. By using these variables in equations, we can achieve a formula for determining how much extra widening is necessary to accommodate the vehicle safely.

Imagine a racetrack with two lanes. The inner lane is a circle with a smaller radius, and the outer lane has a larger radius. A car on the inner lane has to follow a path that is closer to the center of the track, while a car on the outer lane has to cover more distance. Similar principles apply to how vehicles need more room on a curved road, and understanding these concepts helps engineers design safer roadways.

If the road has n lanes, the extra widening should be provided on each lane. Therefore, the extra widening of a road with n lanes is given by Wm = nl2/(2R).

When dealing with multi-lane roads, the concept of mechanical widening extends beyond just a single lane. Each lane must accommodate the additional width required due to off-tracking and thus the formula is adjusted to account for the number of lanes. This means that if two lanes face the same curvature as one lane, the total extra space needed will be double that for a single lane.

Think of a multi-lane highway where cars in one lane take a wider arc at turns compared to those in another lane adjoining it. If we need more room in one lane to accommodate turning vehicles, all other lanes must also adopt this additional space to maintain safety and consistency across the road design. The overall road design must account for the needs of all vehicles using all lanes.

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