Research on Trigonometric Leveling
Freedu
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
E-mail:*****************
Abstract —As the total station trigonometric leveling can survey without the restrictions of topography. So, we can use it to survey the third & fourth order level survey in some special areas. In this article, we propose a new total station measuring method from combining the defect of traditional measurement methods. The advantages of this method is that it can improve the precision without measuring height of device and prism, and it can replace the third and fourth level of measurement under certain conditions. This method can greatly improve efficiency and shorten the project duration in the construction survey ． Keywords- trigonometric leveling ；total station ；error analysis
I. I NTRODUCTION
Engineering construction often relates to height measurement. The traditional measurement methods are leveling surveying and trigonometry trigonometric leveling. Although the two methods have their own characteristics, but there are shortcomings. With the widespread use of the Total Station and using the track rod with the total station method to measure the elevation of the increasingly popular, traditional trigonometric leveling method has shown its limitations. After a long journey, a new trigonometric leveling method has been summed up. This approach combines the advantages of two traditional approaches to further improve the accuracy of the trigonometric leveling and to survey faster.
This article systematically expounds the principle of traditional trigonometric leveling methods and the new methods, compares their advantages and disadvantages, and analyses the main errors and measurement accuracy in the process of trigonometric leveling.
II.
P RINCIPLE OF T RADITIONAL T RIGONOMETRIC L EVELING AND THE N EW M ETHOD
The basic formula of the traditional trigonometric leveling: tan B A H H D i t α=++- (1) where A H is the elevation of a known point, B H is the elevation of the unknown point, D is the horizontal distance between the two points, α is the vertical angle when observe from point A to point B, i is instrument height, t is the height of the prism.
For traditional methods, total station must be set up in the known elevation point. At the same time, you must measure out the height of both the instrument and the prism if you want to measure the elevation of the unknown points.
If we can measure the elevation of the measured point while set point of total station arbitrarily like leveling surveying, instead of set it on a known elevation point, and do not measure out instrument and prism, speed of measurement
will be faster. As shown in the figure 1, assuming that the elevation of the point A is known, the elevation of the point B is unknown, here we measure the elevation of other points by total station.
Figure 1. Diagram for trigonometric leveling
Firstly, seen by trigonometric leveling principle:
(tan )
B A H H D i t α=-+- (2)
where i, t is unknown, but one thing is sure that once the instrument set, value of i will remain unchanged. At the same time choose tracking lever as a reflecting prism, assume that the value of t is also fixed. Seen from formula (2),
tan B A H i t H D W α+-=-= (3) By formula (3), the value of W will remain unchanged in any station. And while both A H and tan D αare known, it is possible to calculate the value of W .
Operation of this new method is as follows:
Shown in Figure 2, elevation of point A is known, elevation of point B is unknown, and the instrument is set up at point C between A and B. The instruments sight point A to get the
reading 1V . That 1V =1D
1tan α, and calculate the value of W, W = A H +1D 1tan α. At this time related constants such as elevation of station, instrument height and prism height can be of any value, not necessary to set before measuring.
And then set elevation of point C to W , set the instrument height and prism height to 0. Then elevation of point C is known. Finally sight the target point B and measured its elevation, that is
22tan B H W D α=+ (4) Therefore, using the new method, elevation of point B is 1122tan tan B A H H D D αα=-+
(5)
