2.7.1. Types of vertical curves

Vertical curves are usually parabolic, primarily because its shape provides a transition and also computationally efficient. The characteristic of a parabolic curve is that the gradient changes from point to point but the rate of change in grade remains constant. Hence, for finding the length of the vertical curve, the rate of change of grade should be an essential consideration as this factor remains constant throughout the length of the vertical curve.

Vertical curves are designed to create a smooth transition between different grades or slopes on a road or railway. A parabolic curve is preferred because as you move along the curve, the steepness (gradient) changes gradually, making it easier for vehicles to navigate. The 'rate of change of grade' will tell you how much the gradient is altered per unit distance, and a consistent rate ensures that drivers experience a comfortable and safe driving condition as they move from one slope to another.

Imagine riding a roller coaster that has steep drops and sharp turns versus one that has smooth, gradual slopes. The second roller coaster provides a more pleasant experience because changes in height (or gradient) happen slowly, preventing any sudden jarring movements.

Summit curve: When two grades meet at the summit and the curve will have convexity upwards, the curve is simply referred as summit curve.

A summit curve occurs when two upward slopes come together to form an elevated point. The shape of the curve is 'convex upward,' meaning it bulges outwards. This type of curve is essential for safe driving because it allows vehicles to transition from going uphill to downhill smoothly, reducing the risk of accidents caused by sudden shifts in elevation. It is important to ensure that vehicles can see ahead while approaching and descending the summit, facilitating safety.

Think of a hill where you can drive up to the top and then gradually descend. If you were to suddenly encounter a steep drop instead, it could startle you. The summit curve is like the smooth crest of that hill, making the experience manageable and comfortable.

Valley (Sag) curve: When two grades meet at the valley (sag) and the curve will have convexity downwards, the curve is simply referred as the valley (sag) curve.

A valley or sag curve is the opposite of a summit curve; it forms where two downward slopes intersect, creating a dip. This type of curve has a 'concave' shape, meaning it dips inward. When vehicles travel over a sag curve, the forces acting on them can create discomfort due to the combined effects of gravity and the curved shape of the road. Safety is a vital consideration, especially at night when visibility is reduced, as headlights may not reach as far into the valley.

Consider driving through a tunnel that dips downwards. As you approach the lowest point, you might feel a sense of gravity pulling you down. The valley curve helps manage this feeling by ensuring a smooth transition, much like how safety features in a car provide a more comfortable ride.

Summit curves are usually provided: (i) when an upgrade is followed by a downgrade, (ii) when a steeper upgrade is followed by a milder upgrade, and (iii) when a milder downgrade is followed by a steeper upgrade.

Summit curves are specifically designed based on how slopes interact with each other. When transitioning from an upward grade to a downward one, or when varying degrees of gradients occur (like steeper to milder), careful planning is needed to ensure drivers do not experience sudden changes that could lead to loss of control. The design must also consider the comfort and visibility of drivers to optimize their experience.

This is similar to a ski slope where skiers might transition from a steep incline to a gentler slope. A well-designed gradient allows skiers to maintain speed while feeling secure, whereas unexpected changes can create a risk of falls or crashes.

A valley (sag) curve is usually provided; (i) when a downgrade is followed by an upgrade, (ii) when a steeper downgrade is followed by a milder upgrade, and (iii) when a milder upgrade is followed by a steeper upgrade.

Similar to summit curves, valley curves require strategic placement depending on how grades transition from downward to upward slopes. Ensuring that there is proper support for visibility during day and night is essential, particularly since headlights are the primary source of light in low visibility conditions. The goal is to minimize discomfort and maximize safety as vehicles navigate through these downsloping curves.

Imagine driving down a steep hill where the curve at the bottom requires you to quickly adjust to climbing again. If that curve is ill-designed, you might feel your car struggling to maintain traction. A valley curve ensures a smoother change from downhill to uphill, akin to ramps in parking garages that make the change in elevation easier for vehicles.

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