外文翻译跨越式精确三角高程测量.docx

1、外文翻译跨越式精确三角高程测量附录A 外文翻译Precise Height Determination Using Leap-FrogTrigonometric LevelingAyhan Ceylan1 and Orhan Baykal2Abstract: Precise leveling has been used for the determination of accurate heights for many years. The application of this technique is difficult, time consuming, and expensive, es

2、pecially in rough terrain. These difficulties have forced researchers to examine alternative methods of height determination. As a result of modern high-tech instrument developments, research has again been focused on precision trigonometric leveling. In this study, a leap-frog trigonometric levelin

3、g (LFTL) is applied with different sight distances on a sample test network at the Selcuk University Campus in Konya, Turkey, in order to determine the optimum sight distances. The results were compared with precise geometric leveling in terms of precision, cost, and feasibility. Leap-frog trigonome

4、tric leveling for the sight distance S=150 m resulted in a standard deviation of 1.87 mm/ and with a production speed of 5.6 km/ day.CE Database subject headings: Leveling; Height; Surveys.Introduction The development of total stations has led to an investigation of precise trigonometric leveling as

5、 an alternate technique to conventional geometric leveling (Kratzsch 1978; Rueger and Brunner 1981, 1982; Kuntz and Schmitt 1986; Hirsch et al. 1990; Whalen 1984; Chrzanowski et al. 1985; Kellie and Young 1987; Young et al. 1987; Haojian 1990; Aksoy et al. 1993). Most of these papers give more pract

6、ical results, rather than theoretical. In this study, we treat the subject more theoretically, with current instruments. We also discuss theoretical aspects such as limits of the techniques, errors, and accuracies in leap-frog trigonometric leveling. Slope distances and zenith angles are measured us

7、ing either a unidirectional or a reciprocal or leap-frog method of field operation in trigonometric leveling. Both of the targets in leap-frog trigonometric leveling can always be placed at the same height above the ground. Thus, sight lengths are not limited by the inclination of the terrain, and s

8、ystematic refraction errors are expected to become random because the back- and foresight lines pass through the same or similar layers of air. The number of setups per kilometer can be minimized by extending the sightlengths to a few hundred meters. This reduces the accumulation of errors due to in

9、strument settlement that is another significant source of systematic error.1 Assistant Professor, Engineering and Architecture Faculty, Konya Selcuk Univ., 42031 Konya, Turkey. E-mail: aceylanselcuk.edu.tr2 Professor, Civil Engineering Faculty, Istanbul Technical Univ., 80626 Istanbul, Turkey. Note.

10、 Discussion open until January 1, 2007. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possiblepublication on August 6, 20

11、03; approved on August 25, 2005.Principle of Unidirectional Trigonometric Leveling Trigonometric leveling is the determination of height differences by means of the measured zenith angles and the slope distance. Similar to geometric leveling, the height difference between two turning points (benchma

12、rks) is computed as the sum of several single height differences obtained from each settlement. The measurement model of the unidirectional trigonometric leveling (UDTL) is illustrated in Fig. 1. The total station is set up at only one point and the observations are performed only in one direction.

13、In Fig. 1, =geodetic (ellipsoidal) zenith angle from to; =observed zenith angle from to; =model error due to the refraction effect; ij=model error due to the deviation of the plumb line; Sij=slope distance between Pi and Pj; hi and hj=ellipsoidal heights of Pi and Pj, respectively; Rm=mean radius of

14、 the earth (6,370 km)and hij=height difference from Pi to Pj.The height difference hij is formulated as (1) where the first term is the nominal height difference, the second term is the spherical effect of the earth, and the third term is the total effect due to the deviation of the plumb line and t

15、he vertical refraction (Coskun and Baykal 2002).The coefficient of refraction, kij, is defined as the ratio between the refraction angle dZri and half of the center angle (Rueger and Brunner 1982); i.e. (2)and (3) The center angle, , can be computed as (4) If is introduced into Eq. (3), the model er

16、ror due to the refraction effect, dZri, is obtained as follows: (5) The height difference between the station points Pi and Pj via unidirectional zenith angle observation is obtained from Eqs. (1) and (5) (6) In practice, the effect of deviation of plumb line is very small because the zenith angles

17、observed along the sight lengths are not longer than 500 m. Thus, the second term in Eq. (6) can be ignored (Rueger and Brunner 1982). As a result, the height difference between the station points, Pi and Pj, is computed from UDTL observations asPrinciple of Leap-Frog Trigonometric Leveling Observat

18、ion of leap-frog trigonometric leveling (LFTL) was performed in back and foresight reading at one setup of the total station between two turning points, the same method used in geometric leveling. The measurement model of the LFTL is shown in Fig. 2.Fig. 2. Measurement model of LFTL According to Fig

19、. 2 and Eq. （7）, the height difference between the station points, Pi and Pj, is obtained from LFTL observations asConsidering where the first term is the nominal height difference, the second term is the spherical effect of the earth, the third term is the effect due to the vertical refraction, and

20、 the fourth term is the total influence of all other random errors, namely, sinking of target rods, verticality and calibration of rods, and uncertainties in the deviations of plumb lines. If we use the following assumptions:the second term in Eq. (9) will be zero. As a result, the height difference

21、 between the station points, Pi and Pj, is computed as It is obvious that the height difference obtained from Eq. (11) is affected by the difference in the actual refraction coefficients and other random errors in the leap-frog trigonometric leveling (LFTL). The refraction term requires further inve

22、stigation. The uncertainty in the refraction term of Eq. (11)can be minimized by making the lengths of the back- and foresights equal. However, inequalities often exist between the refraction coefficients of the backsight and foresight, even if these distances are equal. In any case, the method of L

23、FTL will make the difference in the coefficients of refraction tolerably small. For a special case, the mean coefficient of refraction k of a length can be computed from reciprocal zenith angle observations The accuracy of LFTL can be obtained by applying the law of variance propagation to Eq. (11)

24、under the following assumptions:After propagating errors, an expression for the variance in height difference between Pi and Pj can be derived asStandard deviations of the distances, the zenith angles, the refraction coefficients, and other random errors are denoted by, , , respectively. The varianc

25、e of a 1 km level line is computed asThe computed standard deviations of a 1 km LFTL line, based on standard deviations of 1.0, 2.0, and 3.5 mm for zenith angles and slope distances, respectively, are summarized in Table1. The uncertainty in the coefficient of refraction is taken as 0.05 and 0.10 fo

26、r (nonsimultaneous) reciprocal zenith angle observations. The value of has been arbitrarily accepted as 0.30 mm for total influence of all other random errors.Table 1. Standard Deviations _in mm_ of a 1 km LFTL Line with Sight Distances of 100, 150, 200, and 300 m and Average Zenith Angles of 80, 85

27、,and 90ApplicationsThe precise leveling (PL) and LFTL measurements were performed on a leveling network with eight points established on hilly terrain at the Campus Area of Selcuk University in Konya, Turkey (Fig. 3).Design and Calibration of Surveying InstrumentsPL measurements were carried out by

28、a measurement team of six people (one observer, one recorder, two rodmen, and two auxiliary)using a precise leveling instrument(Wild N3) equippedwith a parallel glass micrometer and a pair of 3 m invar rods(Wild). LFTL measurements were performed by a team of four people using a pair of target rods

29、and a total station. The accuracy of zenith angle measurement with six series is 1 using the total station Sokkia SET2 telescope magnification: 30x; minimum reading: 1; accuracy of horizontal and zenith angle measurement: 2; accuracy of distance measurement: (3 mm +2 ppmS). Target rods were formed b

30、y two parts, a bottom one, which was an invar rod of 2 m, and a top one, which was an iron bar 1 m in length and 2 cm in diameter. These two parts were attached together. A reflector was mounted on target rod at a height of 1.70 m from the bottom in order to implement distance measurements and two t

31、arget plates for vertical angle observations at levels of 2.20 and 3.00 m, respectively. A circular spirit bubble (with 10 precision) and a tripod were used to plumb the target rod (Fig. 4). Several target plates with different patterns of various dimensions were investigated for targeting accuracy

32、of sight distances of 200 and 300 m. A red and white colored circle target was preferred for LFTL. It has been proven that the accuracy of single targeting is better than 30 /M (M=telescope magnification) in average atmospheric conditions (Chrzanowski 1989). Consequently, the target plate in Fig. 5 is preferred. Because a pair of target rods is used commonly in LFTL, the height differences between the target plates on backward and forward rods should be determined with the highes