仪器对中误差对测角精度的影响及公式推证

仪器对中误差对测角精度的影响及公式推证 1 .1 第期矿 山 测 量? 20023 年月 MINE SURVEYING Mar.2002 仪器对中误差对测角精度的影响及公式推 证 210098周西振 (河海大学测量工程系 南京 ) 摘要 文中针对隧道工程及地铁工程中导线测量仪器的对中误差对测角精度的影响,进行了简单的公式推导及精度方面的。 关键词 对中误差 导线测量 推证 ""1 概 述 ρβ,ωρω ? ?esin()esin εε =, =随着我国经济建设的快速发展，隧道工程、地铁工程 2 1 a b 等大型在建工程项目也越来越多，而贯通测量经常是在宽 总的仪器对中误差对测角的影响为:ρ?β,ωρω ?"esin() "esin只数米的竖井或平巷中进行，在那里光线不足，通视条件 εε " = + =+ 2 a b 不好，观测条件受地形限制较多，导线测量更要认真仔 β,ωω sin() sin细，特别是在仪器的对中方面，仪器的对中误差对测角精 ρ + (1) = "ea b 度的影响不可忽视，下面就这一问进行简单的讨论。 ?ρe" 如令则 εωβ,ωa=b=S," = [sin+sin( )](2) s 由此可知ε及ω成函数关系。ω之值有所变化，则ε仪器对中误差对测角精度的影响及公式推证 2 之值亦将发生变化。现在来求ε″为最大及ε″为最小时 的ω的角度。 A B 所谓ε为最小，即 ρ? "e ε ωβ,ω " =[sin+sin()] = 0s ωβ,ω sin+sin() = 0 a b 即ωβω,β?ω sin+sincoscossin) = 0 cos 以 ω除各项则得: β0ωβ,β?ωtg+sincostg) = 0 ω,β,βtg(1cos) = sin, ε1C ε2 E β β ω sin + F2 2β sin β ω , ,故tg= = ,ββ1cos 2 2sin2 D ββ ? 2sin cos β2 2 附图,, = ctg , = β2 2 ABCD 在附图中、、为三个导线点。为由于仪器不对中 2sin2 1β β CD? ACB=所产生的偏心的点。为偏心距即对中误差。0 ω ?β?= +90也可写成 ω 所以tg=tg(90+ ), 2 2 ADB= 为正确的角度。而?β，则为仪器偏心后所测得的1 这说明当偏心距与之间的角度为 β?时，CDBD +90ε 度。而及 εAB 角即因仪器不对中所产生的对及两方1 2 2 向的角度误差。 也就是当偏心距CD垂直于β角的二等分线时，ε″的数值 ββ εε= + +最小。 求ε″的最大值时，由微积分可知，须先求出对ω 即 0 12 的 CCECF AD BD 由作垂线及分别垂直及。 第一次导数的值，使之为零，然后解算出ω的值，该值即 CDF=EDC=令?ω ， 则?(β,ω) CF CE 示最大。 e CD = ?ρ e" sin sin( þ ) ε ωβ,ω求对的第 ss ω从函数 " =[sin+sin()] s CECF 一次导数， 而ε ε = = sin, sin1 2 a b ε ρ"e d 因ε 及 ε 均很小，因此可得ω,β,ω = [coscos()] ,1 2 ω dsρ× ρ× CECF" " ρ "e ε=ε , = 令ω,β,ω [coscos()] = 0,2 1 a b s CECF ω 代入及则得即 β,ω cos= cos() 200231 `1 年月第期矿 山测量 3 结 语 β ω β,ωω 所以 也就是 = () ,=2 80 m 由以上分析可知，在边长为的情况下，欲使对中β ω 即 ，=CD 在β的二平分线上时ε″值为最大。51 mm误差所引起的测角误差不大于″，对中误差应小于; 2 102 mm由上面的计算，可知在井下巷道内测量时，必须注意如测角误差不大于″，对中误差应小于。对于地下 使仪器对中误差的方向不要在夹角的平分角线的方向上， 工程，其控制点间间距一般都比较短，因此在高精度重要 应是它在平分角线的垂直方向上。 1mm坑道的贯通测量中，对中误差不应大于。一般的贯通 β2 mm测量也不宜大于。在对隧道工程及地铁工程的导线测 ω 2,的值代入，在式()中如以ε″值为最大时的 = 2 量中，仪器对中要尽量仔细、认真，使对中误差小于 β β β ρρ"e 2"e εβ,则得" = [sin +sin()] = sin ,1mm，尽量使用光学对中器，因光学对中比垂球对中精度 s 2 2 s 2 要高，以此来减小对测角精度的影响。在高精度全站仪普 ε ?"s 故e = (3) TC2003 遍被使用的今天，如全站仪等就设置有激光对中功 β ρ2"sin 0.5 mm能，可使对中误差在以内。 2 由上式可以求得当β为一定值时，要用什么样的对中 3误差才能保证ε″的值在一定限度内。今按照式()计算 =180510Se 出当β?，ε″分别为″及″，在各个不同值时 作者简介 周西振 ,1963生, 男,河南人,河海大学测量系工程 的最大值参见附表。 师。主要从事教学、实验以及大坝监测等方面的科研工作。在相关 Se=180附表 β ?，ε″及为以下值时的值 刊物上发表“变形监测网基准点与工作基点的稳定性分析”等 S(m) 多篇。 e(mm) 10 30 50 80 100 120 "ε 0.12 0.36 0.60 0.97 1.21 1.45 5 ε″,″ 10ε″,″ 0.24 0.73 1.21 1.94 2.42 2.91 :收稿日期:2001年5月29日: 12 100t(上接第页)5.1.2 由于韩桥煤矿五采区的多万煤炭的采出，延长 4.2 地表移动变形量小 根据了矿井的服务年限，解决了众多职工的工作、生活等重大 实测资料计算得出: 最大倾社会问题，稳定了当地的经济发展。 0.9 mm/m斜为; 最大曲率5.2 社会效益 0.0310-10/m为; 最大水平5.2.1 采用条带开采，既采出了煤炭资源，又减少了对农 0.6 mm/m变形为; 最大下田耕地的破坏，保护了原有的地表生态环境，节省征迁占 3 20.2 mm/d沉速度为。 m40010。 用地× 由于采用条带法开采，地表移动变形和下沉速度都很 5.2.2 根据韩桥煤矿五采区条带开采经验，我们在义安煤 小，所以对保护地表建筑物极为有利。 矿大西三采区、新河煤矿工业广场以及张集煤矿西一采区 4.3 地表无明显活跃期 等进行了推广应用，在减少地表沉陷和变形值、保护地表 根据地表移动观测得知，五采区条带工作面回采推进 建筑物方面都取得了良好的效果。 190 m2/3H到时，地表开始下沉，起动距为，在整个地表移 6160 mm 动期(年时间)内，地表最大下沉量为，由于下 沉量小，下沉速度缓慢，地表无明显活跃期。 参考文献 5 经济效益评估 [1] 何国清等.矿山开采沉陷学徐州:中国矿业大学出版社,. 1991 5.1 矿井经济效益 5.1.1 韩桥煤矿在五采区采用条带法开采至今，共采出煤 第一作者简介 张荣亮,男,1952年生。1976年毕业于南京地 100t炭多万，通过观测，地表各种变形值均很小，地面的 质学校,现今为东南大学技术学院，。测绘高级工程师。现在 建(构)筑物基本完好无损，不但节约了大量的搬迁赔偿 徐州矿务集团公司生产技术部测绘科从事矿区测绘管理与研究 工作。发表论文10篇。科研课题12项并都获奖。 :收稿日期:2001年10月31日: Calculation of the Frequency of PENTAX PM-SI Photoelectric Analysis on the characteristic of Surfacc-moving Basin Resulted Distance Meter--Elaboration is made in the paper, of the method for from combined Coal Mlng with Roof caving at Yanzhou Mine Area calculating the frequency of PENTAX PM-SI photoelectric distance Through comprehensive analysis on some information obtained meter, thereby providing standard data for frequency examination from observation of ground surface movement caused by combined conducted later on (Gao Wenguang). coal Ming at Yanzhou Mine Area. the research works are carried out Computer Simulation of Mining-Related Subsidence on the characteristic and mechanism of Surface-Moving caused by Transmission in Soil--A set of computer software are developed. To combined coal Ming and from this, experiential formulas have been simulate the law governing the deformation of soil subsidence caused derived for calculation of displacement angle and maximum by coal mining, by means of taking the law of the subsidence subsidence angle and suitable angle parameters have been transmission in soil as a theoretical model and using visual software obtaincd( Zhang Liangui et al). for developing environment Visual Basic 6.0. The paper also presents Research on the Technology of Monitoring the Subsidence of the main function of the program and the key points in 111gb Building and Its Application--The paper describes the reason programming( Dai Ziqiang Ct al). and mechanism causing subsidence of a high building and the means to Analysis on Spatial Data Storage by Use of Oracle Spatial Object determining observation precision. The calculation method of stable Model In GISAjialysis is given in the paper on the limitation of standard for subsidence monitoring are given in the paper. Detailed relational DBMS or object-oriented DBMS to Spatial storage data to discussions are made on some problems concerning operation be stored. It describes some advantages fund in case of using special technology in combination of Engineering practice and some useful component Oracle Spatial of object-related database Oracle 81 to consideration and some euggestions are also put forward in this paper make spatial data storage and management. Analysis is also made in the (Hun Xianghong etal) paper on the geometry of spatial data in Oracle Spatial and oti object An Approach to coal Pillar Design for Protection Buildings on storing model (Zhou Xinzhong et al). Ground Surface at Mountain Area-Analysis is given in the paper, on Experiment on Horizontally Controlled Short Baseline Surveying Design parameters of coal pillars left for protection at Mine area Carried by Quick Static Positioning with GPS"With improvement of through simulation experiment of subsidence resulted from coal relative positioning precision and stability of GPS. the minimum mining under mountain mine area, combined with some information distance between adiacent points and the minimum observation time from observation of movement of ground surface at the area. The which the current GPS surveying criterion requires in control survey at author has also made his own point of view on still partially imperfect each order are unreasonable. In the paper the author makes suggestions points in the current regulations in relation to the design of coal pillar for revision of some related stipulations listed in the current GPS under the mountain areas (Hu ,linshan). surveying criterion based on many observations and experiments (Hu A Method of Calculation of Stake Coordinates on Transition Youjian et al). Curves Small in Radius-Easy calculation can be carried out on central Research on the Method of General Design of Digital City stake coordinate at each point on a gentle transition curve by means of Construction - - Digital city is a systematic engineering and the establishing a symmetrical coordinate system and appropriate construction of it must be carried out from general design. Taking the coordinate transition. The method described in the paper is simple and digital Changsha city as an example, the paper makes a brief discussion practicable. Less input information are needed in programming and It on the method of general design of digital city including systematic is very easy to make a program in pocket computer or programmable structure design of the digital city as well as design of network calculator. It is not only suitable for curves with large radius but also topology structure(Zhou Xiaoguang et al). overcomes the disadvantages found in original calculation method (He Development and Utilization of Resource Environ.nt at Mine Area Pingzong). Based on GIS - By use of information system of resource environment A Practical Algorithm of Triangulation Set up at Arbitrary set up at mining area on the basis of GIS. some research work can be Terrains-A simple and practical algorithm of triangulation terrain is carried out on utilization of information of mine area space, the elaborated in the paper. This algorithm is theoretically based on information of the resource environment, the information of land Triangulation in planar set of points of Greedy Heuristic. It can be used reclamation and the balance of ecology etc. An optimum strategic to treat arbitrary sample polygonal domains. it is easy for the decision can be made on reasonable development and utilization of algorithm to be extensively applied to complexly nested domains resource at mine area, assessment of environment ecology, regional ( Zhang Liang et al). planning and sustainable development by means of making in-depth The Influence of Instrument Centering Error on Angle Measure processing collected data of information and utilization of a series of ment Precision and Formular Proving--Description is made in the technical measures such t~s simulation emulation and virtual reality in paper of the influence of centering error of surveying instrument on the information system. The discussion is made in combination of angle measurement precision in case of traverse surveying in tunnel application of GIS system in resource environment at mine area (Liu and subway Engineering. Formular derivation precision analysis is also Wenlong). given in the paper (Zhou Xizlien). Design of Information System for House Registration Superficial Analysis on Examination and Approval of Design Management Based on GIS - Brief description is made in the paper of the important significance of development of GIS related information Drawing in Coal Mine Surveying ''Drawing examination and system for House Registration management and the way to realization approval is an important link in coal mine surveying. However, for of this. it mainly comprises design principle, system function, ' some reasons, many problems existed in that. In the paper, the author development environment, database setting up and associated theory sums up those problems found in the examination and approval of (Wang Yuhong et al). design drawing so as to draw attention to those problems, consequently, to ensure safe mine production and gaining higher economic profit (Cheng Zheng et