Heelis, J. (n.d.). Horizontal Curve (Superelevation Calculation Sheet).xls. Retrieved from https://drive.google.com/file/d/1O3nIbiheKvvf5hjiq0uNra-LXdmTY07s A horizontal curve is a type of curved road that can be found on either two-lane or four-lane highways and roads with transit buses and cars sharing the same lane direction as opposed to separated lanes such as on most freeways or tollways with no intersections at grade level such as the tollway between Northern Virginia and Washington, D.C. The alignment of the lane is tangent to the curve with small radii compared to vertical curves. The angles used in this article are in degrees. The radius of a horizontal curve is measured from the tangent point to the centerline. This radius is rounded to the nearest tenth of a foot or meter for practical reasons, although it can be desirable specifically for design reasons for this value to be precise. Consider that one vehicle traveling at constant speed wants to cross another road with constant speed. The two points where they will meet are called "intersections", and are measured by drawing an imaginary line between them on their respective roads, which are both straight lines between these points horizontally and vertically since they are both at constant speeds. The point on the other road where they would meet is called the "intersection point". The "length" of this imaginary line is the horizontal distance (measured horizontally and vertically) between these two points, and is known as the "horizontal distance". The horizontal distance determines how far apart to draw their lanes. The easiest way to find it is to find where this imaginary line intersects each lane. The intersection point and the lane's midpoint (the halfway point between these two intersections) mark one side of a triangle, and any two points on another side of it – such as the starting and ending points – give its third corner. The angle between this third corner and the midpoint of the lane is the same as the angle between this imaginary line and the lane. A horizontal curve with a radius of "r" has an arc length of "L". (Assume no vertical curves for simplicity. Also, take the low-speed velocity to be constant over the whole curve.) The horizontal distance RA is found by finding where this line intersects the lane and finding where it intersects the horizontal: This product of units is known as "horizontal distance" or simply "length". Using these degrees can make calculation of horizontal distances easier. Suppose it is desired to measure a section of highway with a radius of 12 feet. Then find an imaginary line on this section with a midpoint for its intersection between two points on the same side of the road. The resulting angle is then equal to an angle equal to that between this line and that side of the road minus 90 degrees.
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