2 - Exercises for Practice

In this exercise, students are required to illustrate a simple circular curve. The elements of a simple circular curve include the radius of the curve, the center of curvature, and the tangents at both ends. To effectively show this, students can draw a circle representing the curve and label these key elements. The radius indicates how sharp or gradual the curve is, while the center of curvature is the central point from which all points of the curve are equidistant.

Understanding these terms is crucial in surveying and road design. Back tangents are the straight segments of road before the curve, while forward tangents are those straight segments that come after the curve. The point of intersection is where the two tangents meet. The deflection angle describes how much the road deviates from a straight line at a specific point on the curve. The degree of curve signifies how sharp the curve is, typically expressed in degrees per unit of length.

A compound curve consists of two or more circular curves of different radii that connect smoothly. The key elements to illustrate include the radii of each section, the centers, and the tangent points where each curve meets. Drawing these elements on the same sketch helps visualize how the curves interact and where one ends and the other begins.

A reverse curve consists of two curves that bend in opposite directions, typically used to connect two parallel straight lines. In this exercise, students should create a sketch showing both curves with labels for the points where the curves start and finish. This helps to visualize how the road transitions between two straight sections.

In this task, students are asked to create distinct sketches for each type of curve: simple, compound, and reverse. A simple curve is a single arc, a compound curve consists of multiple arcs, and a reverse curve connects two arcs bending in opposite directions. Clearly labeling each sketch enhances understanding of the different curve types.

Setting out a transition curve involves several requirements to ensure smooth vehicle movement when transitioning from a straight to a curved path. These include appropriate lengths for the transition curve, alignment with the main roadway, and ensuring it provides adequate sight distance for safety.

A transition curve is a gradual curve that connects a straight segment of a road to a circular curve. It is primarily used in highways and roads to smoothly transition vehicles from straight to curved paths, enhancing safety and comfort for drivers. The advantages of transition curves include reduced lateral acceleration on vehicles and increased sight distance for drivers.

Super-elevation is the banking of a roadway at a curve, allowing vehicles to counteract the effect of centrifugal force when turning. The amount of super-elevation usually depends on factors like the curve's radius and the expected speed of vehicles. By calculating these aspects, engineers ensure safer navigation through curves.

The general requirements of a transition curve include: 1) Adequate length based on design speed, 2) Proper alignment with adjacent curves or tangents, 3) Suitable super-elevation to facilitate smooth transitions, 4) Sufficient sight distance for drivers, and 5) Addressing drainage issues to avoid standing water. Each of these aspects contributes to the curve's effectiveness and safety.

When introducing a transition curve between a tangent and a circular curve, certain conditions must be met: It should gradually change the alignment from the tangent, ensure a smooth transition without abrupt changes in curvature, and provide suitable super-elevation that smoothly transitions to the circular curve's steepness.

Vertical curves can be classified into two main types: sag curves and crest curves. Sag curves have a low point in the middle, while crest curves peak at the center. Parabolic vertical curves are often preferred over circular ones because they provide better sight distances and smoother transitions, adapting better to changes in grades.

While parabolic curves offer smoother transitions, they are usually not used for horizontal highway curves due to practical challenges. Parabolic curves require more space and can complicate land acquisition or the cost of construction, making them less feasible for most highway applications.

The rate of change of grade refers to how quickly the slope of the road changes along a vertical curve. It's vital for maintaining vehicle stability and comfort; sudden changes can lead to discomfort or loss of control. A carefully designed rate of change of grade allows for smoother driving experiences.

In a parabolic curve, the elevation profile is consistent in the way it changes as you move along the curve. This characteristic results in equal second differences, which means that any change in elevation occurs uniformly throughout the curve, facilitating easier predictions for construction and maintenance.