Highway design
Highway design is a critical aspect of civil engineering that focuses on creating safe, efficient, and sustainable road systems. The process involves a variety of considerations, including government specifications, geographical features, water drainage, and land use, particularly concerning environmentally sensitive areas. Engineers conduct thorough traffic analyses, estimating expected vehicle volumes and types, while also factoring in driver visibility and safety. Mathematical modeling plays a key role in designing both the horizontal and vertical alignments of highways.
Modern highway designers utilize computer software to create three-dimensional visual models, aiding in the calculation of grade, which determines the slope of the highway sections. Proper grade design is essential for ensuring smooth traffic flow, effective drainage, and minimizing fuel consumption. Vertical curves, defined as either sag or crest curves depending on their grades, also play a significant role in maintaining the safety and functionality of highways. Ultimately, highway design aims to maximize the lifespan of roadways while accommodating diverse traffic needs and environmental considerations.
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Highway design
Summary: Highway design requires an adequate model of anticipated traffic and a determination of the grade.
In the early twentieth century, a series of Federal Aid Highway Acts aimed to create a national highway system. Considerations for a highway design include government design specifications and speed limits, the planned route’s geographical and geological features, water drainage requirements, land use issues such as environmentally sensitive areas, driver comfort and safety, and maximization of the highway’s life span. Planners and engineers also gather data and determine the minimum and maximum expected traffic volumes based on number of standard axles, vehicle types, expected uses, driver visibility requirements, and the minimum radius of bends and curves. The mathematics used in designing the combination of horizontal and vertical, and straight and curved, sections of a proposed highway results in a design plan that construction crews follow as they build and maintain the highway. Mathematicians also investigate questions related to highways such as mileage, distance, and traffic issues. Mathematician and physicist Louis Roberts served as director of energy and environment at the Transportation System Center in Massachusetts, a division of the U.S. Department of Transportation that researches and develops transportation-related energy conservation practices.
Modeling Highways
Highway designers utilize mathematics to create a three-dimensional layout when planning the horizontal and vertical sections that comprise a highway. The plan view (x and z coordinates) shows the proposed highway’s horizontal alignment, which is comprised of straight sections known as “tangents” and the horizontal curves that connect them. The profile view (y axis) shows the proposed highway’s vertical alignment, which is comprised of the various slopes known as “grades” at points along the highway. Computer software programs enable modern engineers to create visual models of the plan route and aid in the mathematic calculations involved.
One of the key calculations of highway design and construction is the determination of the necessary grade along the various sections that comprise the highway, defined as the measure of the highway’s slope. The grade of a section of highway is calculated using the equation grade = (rise ÷ run) × 100. This equation divides the highway’s height increase along that section, known as the “rise,” by the horizontal distance a vehicle on a level highway section travels, known as the “run.” Designers express distance as stations, whereby one station is 100 feet of highway alignment distance.
The resulting decimal calculation gives the ratio of rise-to-run, which is the grade of that particular section of highway. The decimal grade is then converted to and expressed as a percentage through multiplication by 100. Grade calculations are used to ensure smooth traffic flow along the highway and along the intersections between highways and other roadways as well as to ensure proper water drainage. Designing the proper grade can also help reduce fuel consumption and prevent accidents. During construction, crews move and level the dirt along the right-of-way to create the desired grades.
Vertical Curves
There are two types of vertical curves used in highway design: sag vertical curves and crest vertical curves. The difference between the two is the measurement between the tangent grades at the starting and ending points of the curve, expressed as a percentage. An ending tangent grade that is higher than the beginning tangent grade defines a sag vertical curve, while an ending tangent grade that is lower than the beginning tangent grade defines a crest vertical curve. Thus, a sag vertical curve has a negative value and a crest vertical curve has a positive value. These measurements and calculations combine to create the completed highway design plan.
Bibliography
Clevenson, Larry, Mark F. Schilling, Ann E. Watkins, and William Watkins. “The Average Speed on the Highway.” College Mathematics Journal 32, no. 3 (2001).
Fwa, T. F. The Handbook of Highway Engineering. Oxfordshire, England: Taylor & Francis, 2006.
O’Flaherty, C. A. Highways: The Location, Design, Construction and Maintenance of Road Pavements. Oxford, England: Butterworth-Heinemann, 2002.
Schoon, John G. Geometric Design Projects for Highways: An Introduction. Reston, VA: ASCE Press, 1999.