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The length of a summit curve needed to provide s stopping sight distance when the deviation angle N=1/20 is?
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Length of Summit Curve for Stopping Sight Distance


Introduction


Summit curves are designed to provide adequate stopping sight distance for drivers on a road with a steep incline. The stopping sight distance is the distance required for a driver to see an obstacle and bring the vehicle to a stop safely. This calculation is based on the deviation angle N, which is the ratio of the vertical rise to the horizontal distance.


Calculating the Length of a Summit Curve


To calculate the length of a summit curve needed to provide stopping sight distance, the following steps should be taken:



  • Determine the design speed of the road.

  • Calculate the stopping sight distance based on the design speed and other factors such as vehicle reaction time and braking distance.

  • Calculate the minimum length of the summit curve based on the deviation angle N and the stopping sight distance.

  • Verify that the length of the summit curve is adequate for the design speed of the road.



Example Calculation


For example, let's assume that the design speed of a road is 40 mph and the stopping sight distance is 300 feet. If the deviation angle N is 1/20, the minimum length of the summit curve can be calculated as follows:



  • Stopping sight distance = 300 feet

  • Deviation angle N = 1/20

  • Horizontal distance = Stopping sight distance / (1 + N) = 300 / (1 + 1/20) = 272.73 feet

  • Vertical rise = Horizontal distance * N = 272.73 * 1/20 = 13.64 feet

  • Minimum length of summit curve = 2 * sqrt((Vertical rise * Horizontal distance) / 30) = 2 * sqrt((13.64 * 272.73) / 30) = 52.87 feet



In this example, the minimum length of the summit curve is 52.87 feet. This length should be verified to ensure that it is adequate for the design speed of the road.
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The length of a summit curve needed to provide s stopping sight distance when the deviation angle N=1/20 is?
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