18.2. Valley curve

Valley curve or sag curves are vertical curves with convexity downwards. They are formed when two gradients meet as illustrated in figure 18:1 in any of the following four ways:

1. when a descending gradient meets another descending gradient.
2. when a descending gradient meets a flat gradient.
3. when a descending gradient meets an ascending gradient.
4. when an ascending gradient meets another ascending gradient.

A valley curve, also known as a sag curve, is shaped like a dip and is oriented downwards. This occurs when two different slopes or gradients intersect. There are four primary scenarios:

• When two descending slopes meet, creating a smoother transition downward.
• When a downward slope meets a flat road leading to a pull downward.
• When a downward slope intersects with an upward slope, providing a transition from down to up.
• When two upward slopes meet, creating a hill-like dip. Understanding these configurations is crucial for designing roadways and ensuring safe driving conditions.

Imagine driving on a rollercoaster. As you approach a dip, you feel the plunge downwards — that’s similar to what happens with a valley curve on a road where the gradient changes.

There is no restriction to sight distance at valley curves during daytime. But visibility is reduced during night. In the absence or inadequacy of street light, the only source for visibility is with the help of headlights. Hence, valley curves are designed taking into account of headlight distance. In valley curves, the centrifugal force will be acting downwards along with the weight of the vehicle, and hence impact to the vehicle will be more. This will result in jerking of the vehicle and cause discomfort to the passengers.

Designing valley curves involves several vital considerations. Unlike during the day when visibility is unobstructed, night conditions challenge visibility, particularly without sufficient street lighting. For this reason, roadway designs must account for how far a vehicle’s headlights can illuminate the road ahead, ensuring that drivers have enough sight distance under varying conditions. Additionally, due to the nature of how vehicles move on downhill slopes, the combined effect of gravity and centrifugal force can create a jolting experience, indicating the necessity for smooth transitions in curves to enhance passenger comfort.

Think of a speed bump: if it’s too steep or abrupt, it jolts your car and passengers. Valley curves similarly need to be designed smoothly to avoid discomfort and ensure safety.

The valley curve is made fully transitional by providing two similar transition curves of equal length. The transitional curve is set out by a cubic parabola. The length of the valley transition curve is designed based on two criteria: 1. comfort criteria; that is allowable rate of change of centrifugal acceleration is limited to a comfortable level of about 0.6m/sec³. 2. safety criteria; that is the driver should have adequate headlight sight distance at any part of the country.

Creating a fully transitional valley curve involves designing two arcs that are mirror images of each other, forming a smooth entrance and exit. This design typically uses cubic parabolas because they allow gradual changes in acceleration, which enhances driver comfort. There are two main criteria for determining the appropriate length:

1. Comfort, which involves ensuring that changes in force acting on the vehicle don't exceed what is comfortable for passengers (limited to 0.6 m/sec³).
2. Safety, which ensures that irrespective of location, drivers can see a safe distance ahead with their headlights at night.

Consider a ramp that leads into a building; if it were steep, it would be hard to ascend, similar to how abrupt grade changes can impact driving comfort on roads. Smooth transitions, like those in well-built ramps or driveways, provide a more pleasant experience.

The length of the valley curve for headlight distance may be determined for two conditions: (1) length of the valley curve greater than stopping sight distance and (2) length of the valley curve less than the stopping sight distance.

Determining the appropriate length of a valley curve involves assessing two scenarios based on how long the curve is in relation to the distance a vehicle can stop in time (stopping sight distance). In the first case, if the valley curve is longer than the stopping sight distance, the driver has adequate visibility under the curve's lowest point, where headlight effectiveness is least. The second case addresses the opposite scenario, where the length of the valley curve is shorter than what's required for a safe stopping distance, emphasizing the need for careful analysis and design to avoid potential hazards.

Imagine walking on a curvy path in a park at night with a flashlight. If the path curves too much, you might not be able to see far enough ahead to walk safely, similar to what happens on the road if curves are too short for visible driving distance. Properly designing the length of curves ensures that drivers can navigate safely at night.

--