1、 附录 A 外文翻译 Precise Height Determination Using Leap-Frog Trigonometric Leveling Ayhan Ceylan1 and Orhan Baykal2 Abstract: Precise leveling has been used for the determination of accurate heights for many years. The application of this technique isdifficult, time consuming, and expensive, especially i
2、n rough terrain. These difficulties have forced researchers to examine alternativemethods of height determination. As a result of modern high-tech instrument developments, research has again been focused on precisiontrigonometric leveling. In this study, a leap-frog trigonometric leveling (LFTL) is
3、applied with different sight distances on a sample testnetwork at the Selcuk University Campus in Konya, Turkey, in order to determine the optimum sight distances. The results were comparedwith precise geometric leveling in terms of precision, cost, and feasibility. Leap-frog trigonometric leveling
4、for the sight distanceS=150 m resulted in a standard deviation of 1.87 mm/km 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 ofprecise trigonometric leveling as an alternat
5、e technique to conventionalgeometric leveling (Kratzsch 1978； Rueger and Brunner1981, 1982； Kuntz and Schmitt 1986； Hirsch et al. 1990； Whalen1984； Chrzanowski et al. 1985； Kellie and Young 1987； Younget al. 1987； Haojian 1990； Aksoy et al. 1993). Most of thesepapers give more practical results, rat
6、her than theoretical. In this study, we treat the subject more theoretically, with currentinstruments. We also discuss theoretical aspects such aslimits of the techniques, errors, and accuracies in leap-frog trigonometricleveling. Slope distances and zenith angles are measured using either aunidirec
7、tional or a reciprocal or leap-frog method of field operationin trigonometric leveling. Both of the targets in leap-frogtrigonometric leveling can always be placed at the same heightabove the ground. Thus, sight lengths are not limited by the inclinationof the terrain, and systematic refraction erro
8、rs are expectedto become random because the back- and foresight linespass through the same or similar layers of air. The number ofsetups per kilometer can be minimized by extending the sight lengths to a few hundred meters. This reduces the accumulationof errors due to instrument settlement that is
9、another significantsource of systematic error. 1Assistant Professor, Engineering and Architecture Faculty, KonyaSelcuk Univ., 42031 Konya, Turkey. E-mail: aceylanselcuk.edu.tr 2Professor, Civil Engineering Faculty, Istanbul Technical Univ., 80626Istanbul, Turkey. Note. Discussion open until January
10、1, 2007. Separate discussionsmust be submitted for individual papers. To extend the closing date byone month, a written request must be filed with the ASCE ManagingEditor. The manuscript for this paper was submitted for review and possible publication on August 6, 2003； approved on August 25, 2005.
11、Principle of Unidirectional Trigonometric Leveling Trigonometric leveling is the determination of height differencesby means of the measured zenith angles and the slope distance.Similar to geometric leveling, the height difference between twoturning points (benchmarks) is computed as the sum of seve
12、ralsingle height differences obtained from each settlement. The measurement model of the unidirectional trigonometricleveling (UDTL) is illustrated in Fig. 1. The total station is set upat only one point and the observations are performed only in onedirection. In Fig. 1, Zij=geodetic (ellipsoidal) z
13、enith angle from pito pj；Zij=observed zenith angle from pito pj； dZr=model error dueto the refraction effect； ij=model error due to the deviation ofthe plumb line； Sij=slope distance between Pi and Pj； hi andhj=ellipsoidal heights of Pi and Pj, respectively； Rm=mean radiusof the earth (6,370 km)and
14、hij=height difference from Pito Pj. The height differencehij is formulated as hij = Sij cosZij + Sij22Rm sin2Zij Sij ij + dZr (sinZij ) (1) where the first term is the nominal height difference, the secondterm is the spherical effect of the earth, and the third term is thetotal effect due to the dev
15、iation of the plumb line and the verticalrefraction (Coskun and Baykal 2002). The coefficient of refraction, kij, is defined as the ratio betweenthe refraction angle dZri and half of the center angle ij(Ruegerand Brunner 1982)； i.e. kij = dZriij2 (2) and dZri = ij2 kij (3) The center angle,ij, can b
16、e computed as ij Sij sin Zij2Rm (4) If ijis introduced into Eq. (3), the model error due to therefraction effect, dZri , is obtained as follows: dZij = Sij sin Zij2Rm kij (5) The height difference between the station points Pi and Pj viaunidirectional zenith angle observation is obtained from Eqs. (
17、1) and (5) hij=SijcosZij-SijsinZijij+ SijsinZij 22 (1 ) (6) In practice, the effect of deviation of plumb line is very smallbecause the zenith angles observed along the sight lengths are notlonger than 500 m. Thus, the second term in Eq. (6) can be ignored (Rueger and Brunner 1982). As a result, the height differencebetween the station points, Pi and Pj, is computed fromUDTL observations as Principle of Leap-Frog Trigonometric Leveling Observation of leap-frog trigonometric leveling (LFTL) was performedin back and foresight reading at one setup of the totalstation between two turning points,
