26.6
トラバース角度の計算
トラバース角度の計算は測量の重要な構成要素であり、閉トラバース内の内角を計算するために使用されます。トラバースは、閉ループを形成する一連の接続された線で構成され、土地の境界の描写やマッピングによく使用されます。内角を計算することで、トラバースのジオメトリの精度が確保され、測量データの整合性を確認する…
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.
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Q1: How do you calculate internal angles in a closed traverse?
Internal angles at each vertex are calculated using the azimuths and bearings of adjacent sides. The process typically involves subtracting or adding these directional values from 180 degrees, depending on the orientation of the sides. For example, at vertex A, subtract the azimuth of one side and the bearing of the adjacent side from 180 degrees to find the internal angle.
Q2: What is the significance of the 360-degree angle sum in traverse computations?
For a closed traverse, the sum of all internal angles must equal 360 degrees. This verification confirms the traverse's geometric closure and validates the accuracy of angle measurements. If the sum deviates from 360 degrees, it indicates errors in the angle calculations or survey data that require correction.
Q3: Why are traverse angle computations essential in surveying?
Traverse angle computations ensure accuracy in traverse geometry and are critical for checking survey data integrity. They are widely applied in field surveying, construction layout, and geodetic projects to create precise maps, boundaries, and engineering designs. Accurate angle calculations guarantee the reliability of land boundary delineation and spatial measurements.
Q4: How do you verify the accuracy of computed internal angles?
After calculating individual internal angles at each vertex, sum all angles together. For a four-sided traverse, the total must equal 360 degrees. This check confirms the correctness of your calculations and the traverse's closure. If the sum differs from 360 degrees, recalculate the angles at each vertex.
Q5: What information is needed to begin traverse angle computations?
Traverse angle computations require known azimuths and bearings of the traverse sides. These directional values for each side of the closed traverse form the foundation for calculating internal angles at vertices. The combination of azimuth and bearing data allows surveyors to determine the geometric relationships between adjacent sides.
Q6: What is a closed traverse and how does it relate to angle calculations?
A closed traverse is a series of connected lines forming a closed loop, commonly used for land boundary delineation and mapping. The internal angles at each vertex must sum to 360 degrees, which is a fundamental property of closed polygons. This geometric constraint allows surveyors to verify the accuracy and closure of their traverse measurements.