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The grade of a highway is a measure of its incline or slope. The amount of grade indicates how much the highway is inclined from the horizontal. For example, if a section of road is perfectly flat and level, then its grade along that section is zero. However, if the section is very steep, then the grade along that section will be expressed as a number, usually a percentage, such as 10 percent.

The illustration below shows a highway in profile (from the side). Notice that a right triangle has been constructed in the diagram. The elevation, or height, of the highway increases in the sketch when moving from left to right. The bottom of the triangle is the horizontal distance this section of highway covers. This horizontal distance, sometimes called the "run" of the highway, indicates how far a vehicle would travel on the road if it were level. However, it is apparent that the road is not level but rises from left to right. This "rise" is a measure of how much higher a vehicle is after driving from left to right along the road.

To calculate the grade of a section of highway, divide the rise (height increase) by the run (horizontal distance). This equation, used to calculate the ratio of rise-to-run for highway grades, is the same ratio as the slope "y /x " encountered in a Cartesian coordinate system . In the example above, the rise of the highway section is 100 feet, while the run is 1,000 feet. The resulting grade is thus 100 feet divided by 1,000 feet, or 0.1.

Highway grades are usually expressed as a percentage. Any number represented in decimal form can be converted to a percentage by multiplying

that number by 100. Consequently, a highway grade of 0.1 is referred to as a "10 percent grade" because 0.1 times 100 equals 10 percent. The highway grade for a section of highway that has a rise of 1 kilometer and a run of 8 kilometers is , or 0.125. To convert the highway grade into a percentage, multiply 0.125 by 100, which results in a grade of 12.5 percent.

When a new highway or road is being planned, its grade over its various sections is one of the key aspects that must be determined in advance. The grade of the road is very important for the safety of the motorists who will be using it. Most of us have experienced how a rolling bicycle has a tendency to pick up speed as it goes downhill, and how when going uphill the bicycle will slow down unless the cyclist pedals harder. The same situation must be considered when constructing modern highways.

If a grade is too steep, vehicle operators must use excessive braking when going downhill. In contrast, vehicle operators going uphill will have to slow down severely, possibly affecting traffic flow adversely. Grades are of great concern for vehicles carrying or pulling heavy loads, like semi-tractor trailers, or a family car pulling a camper or boat. To avoid these problems the highway engineers who plan and design highways pay close attention to road grades, and design into the highway's construction smaller grades rather than larger ones.

The concept of highway grades can also be applied to other types of pathways that are used by people or vehicles. For instance, residential roads are constructed to have a slight grade from the curb to the center of the road. A grade of 1 percent is considered the minimum required for proper drainage during a rainstorm. For a run of 10 feet, a 1 percent grade means one-tenth of a foot rise from the curb to the middle of the road.

Another situation where grade is an important consideration is in the construction of ramps for the disabled. Wheelchair ramps must have a fairly low grade, because if a ramp is too steep, people may be unable to use it. Nationwide, a generally accepted maximum grade for wheelchair ramps is8.3 percent, or a ratio of 1:12.

Philip Edward Koth with

William Arthur Atkins

## lnternet Resources

Grade or Super Elevation Calculations. Raleigh, North Carolina: Departments of Math and Physics, Wake Technical Community College. <http://www.wake.tec.nc.us/math/Projects/HighwayPatrol/grade.htm>.

## WHAT DEFINES A HIGHWAY?

A highway is a road with a hard surface, such as asphalt or concrete, that is open for the general public to drive upon. Highways connect towns, cities and industrial areas to one another. Most highways follow the "lay of the land." In other words, highways must rise and fall as hills and valleys are encountered.