How to Figure a Delta Angle

Transportation engineers use delta angles to optimize traffic flow designs.
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A delta angle is the angle made when two straight lines intersect while each line also tangentially intersects the same curve shaped configuration on opposite ends. The word tangentially means the straight line "just touches" the curve. For example, if you have a curved shaped configuration and you draw a straight line that intersects the curve on the right side and draw another line that intersects the curve on the left side, the delta angle is the angle made when the two lines intersect. Transportation engineers use delta angles along with horizon curve calculations to optimize traffic system designs.

    Refer to Figure 1 from the horizontal curves resource document located at http://www.iowadot.gov/design/dmanual/02a-01.pdf to get a visual representation of how to determine or measure L or LC. L is the total length in feet of the circular curve from the point of curvature, or "PC", to the point of tangency, or "PT" measured along its arc. Determine or measure L of the curved shape configuration from which you are looking to calculate the delta angle. As an example, assume L is 25 feet.

    Refer to Figure 1 from the horizontal curves resource document located at http://www.iowadot.gov/design/dmanual/02a-01.pdf to get a visual representation of how to determine or measure R. R is the radius of the circular curve measured in feet. Determine or measure R of the curved shaped configuration from which you are looking to calculate the delta angle. As an example, assume R is 25 feet.

    Calculate the delta angle using the formula: Delta = (180L)/(3.1415R). Using the above examples, the delta angle will be 52.3 ((180 x 25ft)/(3.1415 x 25ft)) degrees.

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