26.6
Design Example: Traverse Angle Computations
Consider a closed traverse with four vertices. The azimuths of the two sides and the bearings of the other two sides are given. The objective is to find the internal angle at each vertex of the traverse.
Firstly, the angle at A is calculated by subtracting 50 degrees, the azimuth of AB, and 75 degrees, the bearing angle of DA, from 180 degrees, resulting in 55 degrees.
Next, the angle at B is calculated by subtracting 120 degrees, the azimuth of BC, from 180 degrees and adding 50 degrees, the azimuth of AB, resulting in 110 degrees.
At C, the angle is calculated by subtracting 20 degrees, the bearing angle of CD, from 120 degrees, the azimuth of BC, resulting in 100 degrees.
Lastly, the angle at D is calculated by adding 75 degrees, the bearing angle of DA, to 20 degrees, the bearing angle of CD, resulting in 95 degrees.
To check the accuracy, the sum of all the internal angles is calculated, which turns out to be 360 degrees, indicating the correctness of the internal angles.
Traverse angle computations are a critical component of surveying, used to compute the internal angles within a closed traverse. A traverse consists of a series of connected lines forming a closed loop, often used for land boundary delineation or mapping. Calculating the internal angles ensures accuracy in the traverse geometry and is essential for checking survey data integrity.
The process begins with known azimuths and bearings of the traverse sides. Internal angles at each vertex are calculated by applying basic relationships in geometry, typically using subtraction or addition of given angles from 180 degrees, depending on the orientation of the sides. For example, the internal angle at a vertex is determined by the difference between the azimuth or bearing of two adjacent sides.
After computing individual angles, their sum is verified against the expected total for a closed traverse. For a four-sided traverse, the sum of the internal angles must equal 360 degrees. This check confirms the traverse’s closure and the accuracy of angle measurements.
Traverse angle computations are widely applied in field surveying, construction layout, and geodetic projects, ensuring precision in creating maps, boundaries, and engineering designs.
Consider a closed traverse with four vertices. The azimuths of the two sides and the bearings of the other two sides are given. The objective is to find the internal angle at each vertex of the traverse.
Firstly, the angle at A is calculated by subtracting 50 degrees, the azimuth of AB, and 75 degrees, the bearing angle of DA, from 180 degrees, resulting in 55 degrees.
Next, the angle at B is calculated by subtracting 120 degrees, the azimuth of BC, from 180 degrees and adding 50 degrees, the azimuth of AB, resulting in 110 degrees.
At C, the angle is calculated by subtracting 20 degrees, the bearing angle of CD, from 120 degrees, the azimuth of BC, resulting in 100 degrees.
Lastly, the angle at D is calculated by adding 75 degrees, the bearing angle of DA, to 20 degrees, the bearing angle of CD, resulting in 95 degrees.
To check the accuracy, the sum of all the internal angles is calculated, which turns out to be 360 degrees, indicating the correctness of the internal angles.
From Chapter 26:
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26.6 : Design Example: Traverse Angle Computations
Angles and Directions
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26.1 : Meridians
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26.2 : Azimuths and Bearings
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26.3 : Compass
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26.4 : Magnetic Declination
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26.5 : Local Attraction
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