15.4. Extra Widening

Extrawidening refers to the additionalwidth of carriageway that is required on a curved section of a road over and above that required on a straight alignment.

Extra widening is necessary on curves to ensure that vehicles have enough space to navigate safely. This is because the path that a vehicle takes on a curve isn't straightforward and can lead to a requirement for more width due to the dynamics of vehicle motion.

Imagine trying to ride a bicycle around a tight corner. If you don't lean into the turn and give yourself extra room, you might wobble or even fall off. Similarly, roads need extra width for vehicles to maneuver comfortably around curves.

This widening is done due to two reasons: the first and most important is the additional width required for a vehicle taking a horizontal curve and the second is due to the tendency of the drivers to ply away from the edge of the carriageway as they drive on a curve.

The first reason, mechanical widening, is related to how vehicles turn. When a vehicle goes around a curve, its rear wheels follow a tighter arc than its front wheels, creating a need for extra space. The second reason, psychological widening, comes from drivers feeling like they need more space away from edges when navigating curves, which also requires additional width.

Think of a car making a left turn at an intersection. The driver may instinctively steer wider than necessary to avoid feeling like they might hit something, thus necessitating extra road width for safety.

The mechanical widening is related to the off-tracking phenomenon, where the rear wheels follow a path of shorter radius than the front wheels, increasing the effective width of road space required.

Off-tracking occurs when vehicles are in motion on curves. This geometric characteristic means that to maintain proper spacing between vehicles, especially in opposing directions, roads must be wider on curves than on straight segments.

Imagine a train on a curved track. The front of the train might take an outward arc while the back stays closer to the inner edge, which necessitates additional space on the outer side of the curve to prevent accidents.

The expression for extra width can be derived from the simple geometry of a vehicle at a horizontal curve. The mechanical widening W for a single lane is given by: W = l^2 / (2R - W_m)

In the formula, W represents the extra width needed, l is the wheelbase of the vehicle, and R is the radius of the horizontal curve. When a road is designed, these lengths are crucial to ensure that vehicles have enough room to navigate curves safely.

Consider a large truck making a turn. If the turn is too tight—made with inadequate width—there's a real risk of the truck hitting obstacles or tipping over, which highlights the importance of this widening in design.

There is a tendency for the drivers to drive close to the edges of the pavement on curves. Some extra space is to be provided for more clearance for crossing and overtaking operations on curves.

Psychological widening accounts for driver behavior. Drivers often feel more secure when they have extra space rather than riding the edge of the pavement. This behavior informs road design, which must incorporate this need for perceived safety.

Think about how you might walk along a narrow ledge. You would instinctively walk towards the center rather than the edge, seeking more safety. Roads must consider this natural instinct when constructing curves.

The total widening needed at a horizontal curve W is W = W_m + W_ps.

This total includes both the mechanical and psychological widenings. By combining these two aspects, road designers can determine the overall width necessary to provide safety and comfort for all vehicles traveling along the curve.

It's like preparing a buffet; you need to account for both the plates (mechanical) and the people around each plate (psychological) to ensure everyone has enough room and access without feeling cramped.

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