Answer :
The degree of curvature, by the arc definition, for a circular curve with a radius of 3000 ft is 1 degree, 39 minutes, and 56 seconds.
In the field of surveying and civil engineering, the degree of curvature is a measure used to describe the curvature of a circular curve. It is important in road design and alignment. The degree of curvature is defined as the central angle subtended by an arc of a given length along the curve. In this case, we have a circular curve with a radius of 3000 ft.
To determine the degree of curvature, we can use the formula:
Degree of Curvature = (360 degrees) / (2πR / S),
where R is the radius of the curve and S is the length of the arc. Since we are given the radius as 3000 ft, we need to calculate the length of the arc.
The formula to calculate the length of an arc in degrees is:
Length of Arc = (Arc Angle / 360 degrees) × (2πR).
In this case, we want the length of the arc to be 1 degree. We can calculate the arc angle as follows:
Arc Angle = (Length of Arc / (2πR)) × 360 degrees.
By substituting the values, we find:
Arc Angle = (1 degree / (2π × 3000 ft)) × 360 degrees ≈ 0.0107 degrees.
To express this angle in degrees, minutes, and seconds, we multiply the decimal part by 60 to get the number of minutes and multiply the decimal part of the minutes by 60 to get the number of seconds. Therefore, the degree of curvature for a circular curve with a radius of 3000 ft is approximately 1 degree, 39 minutes, and 56 seconds.
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