Definition of closed and open polygons in geometry

Soil surveying is the study of how to measure soil properly which produces accurate and fast measurement results. measurement techniques can use  closed or open polygons  depending on the terrain and field situations. But before discussing the two. We need to know what the meaning of the polygon is. 

Polygon is a method for determining the horizontal position of points in the field in the form of a polygon by measuring angles and distances. the goal is to get field data in the form of horizontal coordinates (x,y). Why do you have to form a polygon? because it is used as a basic framework for mapping an area.

The equipment that is often used for this work is the theodolite and measuring rods which I have discussed in the previous article. In addition to the above tools, there are other equipment such as statives, measuring forms, stationery and umbrellas. For now, there is a more sophisticated tool, namely the Total Station. You can read the article on understanding the total station for a more complete explanation. 

The difference is in the theodolite we have to write down all the measurement data such as ba, bt, bb, angle and so on. While at the Total Station data recording is done automatically by the tool.

Back to the previous topic as in the first paragraph, polygons consist of three kinds, namely  closed polygons and open polygons. We will discuss one by one.

Closed Polygon

Closed polygons are the basic framework of measurements that form a closed polygon. What is meant by closing is if starting from point 1 then to point 2 and so on, it will return to point 1 again. So it will form a polygon. The function of returning to the starting point is used to correct the angles for each polygon. 

In the picture above, it can be seen that all angles are regular but in field measurements all angles have different magnitudes.  then how to apply in the field? In principle, what needs to be remembered is that the determination of the number of polygon points is adjusted to field conditions. For example, if a very large area is measured, it requires many polygon points. Try to use as few points as the most important polygons close. The more polygon points, the higher the angle error rate.

The image above has a hexagon, meaning that if we calculate the total number of interior angles, we can use the formula (n-2)x180.
Sum of angles in total = (6-2)x180 = 720 degrees. The result of the calculation is the angle if the polygon is completely closed. but did you know that measurements in the field can not be like that. Usually there is a slight error in the number of interior angles due to several factors in the field. For example, if I compare the measurement results from the field before being corrected, I get the number of interior angles of 720d54'43" (720 degrees 54 minutes 43 seconds). So my measurement results have an error or excess angle of 54'43". 

So what must be corrected is 54'43" so that the inner angle matches the results of the formula above. In addition to correcting the inner angle, the function of this closed polygon is to correct the elevation. For example, when we start measuring from the starting point or point 1 with the initial elevation 100 m from sea level. So when we return to the starting point again after passing through polygon points 2,3,4,5, and 6, the final elevation should be 100 m as well. If it is more or less than that, it must be corrected.

Open Polygon

Open polygon measurements are commonly used to measure roads, rivers, and irrigation. but in fact it can be used to measure the area of ​​open land. but it is still recommended to use closed polygons when measuring land area. What is meant by open here is that the polygon has no interior angles as in closed. so the measurement starts from the starting point but does not return to the starting point as in the image below. 

Open polygons are divided into 2, namely perfectly bound and not perfectly bound. It is said to be perfectly bound if we have coordinate data at  the starting point and ending point in the  form of coordinates and elevation data (x, y, z). While imperfectly bound is only having coordinates and elevation data at the starting point. Coordinate data can be obtained from benchmarks. what are benchmarks? please read my previous article. 

This perfectly unbound polygon cannot be corrected so that only reliable and experienced surveyors can use this because they are sure that the accuracy and angle error is only small. The level of error in the measurement is very dependent on the measurer himself how accurately he can do it.

This is an article that discusses the meaning of closed and open polygons in soil surveying. Actually, in theory, I have forgotten a bit, but the application in the field I still understand very well. Of course, to overcome all of that, I was reading the geometry book again and I synchronized it with my experience in the field. Hope it is useful. 
then how to carry out measurements in the field? You can read the article entitled How to measure land area using the closed polygon method.              

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