How to Calculate Traverse Angle Closure

The use of lengths and directions of lines between points, to determine the positions of those points, is called traversing. The method is normally used in surveying. A traverse that begins and ends at the same point is called a closed traverse. These are useful to surveyors because they provide a means of checking the survey measurements that might not be possible for an open traverse. The directions between points of the traverse are called the azimuths. The distances between points are given in terms of latitude, or difference along the north-south meridian, and departure, or difference along the east-west meridian.

Things You'll Need

  • Calculator with trig functions
  • Compass or theodolite
  • Measuring wheel or other distance-measuring device
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Instructions

    • 1

      Find the azimuths from each point to the next, by measuring the angle between the direction to the next point and true north. Record the measure of each azimuth. Depending upon the desired precision, the azimuths may be given in degrees, minutes and seconds.

    • 2

      Measure and record the direct distance between consecutive points along the traverse. Compute the latitude change between consecutive points by multiplying the direct distance by the cosine of the azimuth. Compute the departure change between consecutive points by multiplying the direct distance by the sine of the azimuth. Record all latitudes and departures.

    • 3

      Add all the latitudes together. Add all the departures together. Ideally, the sum of all the latitudes will equal zero and the sum of all the departures will equal zero, but often there is a slight error.

    • 4

      Compute the linear misclosure of the traverse. First, square the final latitude and departure, if different from zero. Add the two squares, and calculate the square root of that sum.

    • 5

      Adjust for possible errors if the linear misclosure is acceptably small. For each line between points, divide the latitude error by the total traverse perimeter distance, and multiply that by the distance between the two points. Add that value to the measured latitude value. Repeat the process for the departure values.

    • 6

      Repeat the measurement of angles and distances if the linear misclosure is too large. Typically, the misclosure is considered acceptable if the error is less than the smallest distance that can be shown on a map at a particular scale.

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