Balancing Consecutive Co-ordinates using axis method | Survey | Traverse Computation
Balancing the consecutive coordinate is one of the important tasks in Traverse Computation. While doing the survey using theodolite or any other instruments, the algebraic sum of latitudes and departures must be zero. A traverse is balanced by applying a correction to latitudes and departures. This is called balancing a traverse. The closing error can occur due to the error in instrument or error due to the surveyor. To remove such error, the balancing of the consecutive coordinate is necessary.
We follow different methods for balancing the closing error. They are
Here in this made-up example, abcdea` is the traverse. If there was no closing error, a` and a would have been at the same point but due to the closing error a and a`do not lie at the same point and because of this reason balancing of consecutive coordinate is necessary and different methods are adopted. And here I will be explaining about axis method.
Once traverse is plotted we do some geometry on the figure and balance the error in the traverse.
Since a and a` are not at the same point we need to compute some techniques to eliminate the error.
Here in this figure, we can see the dotted line passing through a` and a and stretched up to the line cd. This dotted line is the axis. The axis should be in such a way that it divides the traverse at almost half. Once the axis is plotted we get the point on the line cd where it is intersected. We can give any random arbitrary point name at that point but I haven't given any name to that point.
After the point is obtained, we plot other dotted lines to the vertex of the traverse. And now after plotting the vertex we might want to extend it a bit further. So, here we have extended the line from the arbitrary intersected point to the vertices e and b. We might as well draw the lines at c and d but as it is already a dark line, the dotted line could not be seen properly. However, it would be better to plot the line as sometime it might be necessary.
This is exactly the point where people might get confused. Now, I will try to explain this figure as best I can. Once the dotted lines are produced at e and b, now we will proceed further for obtaining the traverse after the elimination of the error.
First, we bisect the line aa` and obtain the point A as you can see in the figure. Now, from point A we will draw the line parallel to ea` and the point that intersects at the dotted line plotted to e from the ar point is our required point E.
Again from point E, we will draw the line parallel to the line ed up to the point that intersects at the dotted line from the arbitrary point to d (the line does not look parallel in the figure because it is not plotted by the drafter) but in this case, the dotted line is covered by a dark line. The required intersected point is D.
Similarly, from the point, A we can draw the line parallel to ab the point where the parallel line intersects with the dotted line from the arbitrary point is our point B.
Again from point B, we can draw the line parallel to bc and the intersection of the parallel line to the dotted line from the arbitrary point is our required point C.
So, like this, we can get the required traverse ABCDEA.
I could have done it in AutoCAD with the addition of different layers but due to some technical problem, it cannot be done but if it is possible I will try to do it and write another blog with AutoCAD drawing.
Also, there are some conditions in which axis will not divide traverse into almost 2 halves and I will write about it in the next blog explaining how can we balance the consecutive coordinate. And I will also, mention why is it necessary to divide it into almost 2 halves.
I don't know if someone will ever read this blog or not but if you have some queries then please do comment, I will try to solve the problem if I can.
We follow different methods for balancing the closing error. They are
- Bowditch Method
- Transit Method
- Graphical Method
- Axis Method
I am explaining about Axis method.
This method is not used widely but in some cases, this method is quite helpful. This method is applied when angles are measured very accurately as compared to linear measurement. In this method, we can visualize the traverse while balancing it. Unlike Bowditch and Transit method we don't need to compute theoretical calculation. The theoretical calculation is not required and we can observe the traverse.
I find some people had difficulty in understanding the axis method for balancing consecutive coordinates. So, I decided to explain as much as I know. It could be a little confusing to visualize if all the computation is watched at a single diagram but if we watch it step by step it is not that difficult to understand. And it is not inexplicable too. With a simple diagram and some plotting with visualization is enough to explain and understand this method. Here I will make a handmade drawing of a made-up traverse.
In the axis method first, we make the traverse and spot the closing error.
In the axis method first, we make the traverse and spot the closing error.
Here in this made-up example, abcdea` is the traverse. If there was no closing error, a` and a would have been at the same point but due to the closing error a and a`do not lie at the same point and because of this reason balancing of consecutive coordinate is necessary and different methods are adopted. And here I will be explaining about axis method.
Once traverse is plotted we do some geometry on the figure and balance the error in the traverse.
Since a and a` are not at the same point we need to compute some techniques to eliminate the error.
Here in this figure, we can see the dotted line passing through a` and a and stretched up to the line cd. This dotted line is the axis. The axis should be in such a way that it divides the traverse at almost half. Once the axis is plotted we get the point on the line cd where it is intersected. We can give any random arbitrary point name at that point but I haven't given any name to that point.
After the point is obtained, we plot other dotted lines to the vertex of the traverse. And now after plotting the vertex we might want to extend it a bit further. So, here we have extended the line from the arbitrary intersected point to the vertices e and b. We might as well draw the lines at c and d but as it is already a dark line, the dotted line could not be seen properly. However, it would be better to plot the line as sometime it might be necessary.
First, we bisect the line aa` and obtain the point A as you can see in the figure. Now, from point A we will draw the line parallel to ea` and the point that intersects at the dotted line plotted to e from the ar point is our required point E.
Again from point E, we will draw the line parallel to the line ed up to the point that intersects at the dotted line from the arbitrary point to d (the line does not look parallel in the figure because it is not plotted by the drafter) but in this case, the dotted line is covered by a dark line. The required intersected point is D.
Similarly, from the point, A we can draw the line parallel to ab the point where the parallel line intersects with the dotted line from the arbitrary point is our point B.
Again from point B, we can draw the line parallel to bc and the intersection of the parallel line to the dotted line from the arbitrary point is our required point C.
So, like this, we can get the required traverse ABCDEA.
I could have done it in AutoCAD with the addition of different layers but due to some technical problem, it cannot be done but if it is possible I will try to do it and write another blog with AutoCAD drawing.
Also, there are some conditions in which axis will not divide traverse into almost 2 halves and I will write about it in the next blog explaining how can we balance the consecutive coordinate. And I will also, mention why is it necessary to divide it into almost 2 halves.
I don't know if someone will ever read this blog or not but if you have some queries then please do comment, I will try to solve the problem if I can.
i read.
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