测量学：求导线各点坐标

编程语言 2024-11-06 21:58:52 阅读次数: 0

题目：

已知如下条件，试求导线各点坐标:

$\alpha_{AB}= 224^°20^′18^″$

$\beta_{0}= 301^°42^′30^″$

$x_{b} = 1647.76m$

$y_{b} =1428.55m$

1	89 30 06
2	81 43 20
3	98 16 30
B	90 29 54
12	163.35
23	120.75
3B	144.96
B1	119.50

答案：

$\Sigma_{测}=\angle{1}+\angle{2}+\angle{3}=359^°59^′50^″$

$f_{\beta}=\Sigma_{测}-\Sigma_{理}=-10^″$

$\frac{f_{\beta}}{4}=-2.5^″$

$\angle{B^{'}}=\angle{B}+3^{"}=90^°29^′57^″$

$\angle{1^{'}}=\angle{1}+3^{"}=89^°30^′09^″$

$\angle2^{'}=\angle{2}+\angle{2}^{"}=81^°43^′22^″$

$\angle3^{'}=\angle{3}+\angle{2}^{"}=98^°16^′32^″$

$\alpha_{AB}=224^°20^′18^″$

$\alpha_{B1}=\alpha_{AB}-180^{\circ}+\beta_0=346^{\circ}2^{′}48{″}$

$\alpha_{12}=\alpha_{B1}-180^{\circ}+\angle1^{′}=255^{\circ}32^{′}57{″}$

$\alpha_{23}=\alpha_{12}-180^{\circ}+\angle2^{′}=157^{\circ}16^{′}19{″}$

$\alpha_{3B}=\alpha_{23}-180^{\circ}+\angle3^{′}=75^{\circ}32^{′}51{″}$

$\alpha_{B1}=\alpha_{3B}+180^{\circ}+\angle{B}^{′}=346^{\circ}2^{′}48{″}$

$\Delta{x}_{B1}=L_{B1}\cdot cos\alpha_{B1}=115.974$

$\Delta{x}_{12}=L_{12}\cdot cos\alpha_{12}=-40.764$

$\Delta{x}_{23}=L_{23}\cdot cos\alpha_{23}=-111.374$

$\Delta{x}_{3B}=L_{3B}\cdot cos\alpha_{3B}=36.179$

$\Delta{y}_{B1}=L_{B1}\cdot sin\alpha_{B1}=-28.815$

$\Delta{y}_{12}=L_{12}\cdot sin\alpha_{12}=-158.182$

$\Delta{y}_{23}=L_{23}\cdot sin\alpha_{23}=46.653$

$\Delta{y}_{3B}=L_{3B}\cdot sin\alpha_{3B}=140.373$

$f_x=\Sigma_{\Delta{}x}-0=0.015$

$f_y=\Sigma_{\Delta{}y}-0=0.029$

$D=548.56$

$\frac{\sqrt{f_{x}^{2}+f_{x}^{2}}}{\Sigma_{D}}=5.95\times10^{-5}<\frac{1}{2000}$

$V_{x_{B1}}=\frac{-f_x}{\Sigma_{D}}\cdot{D_{B1}}=-0.003$

$V_{y_{B1}}=\frac{-f_y}{\Sigma_{D}}\cdot{D_{B1}}=-0.006$

$V_{x_{12}}=\frac{-f_x}{\Sigma_{D}}\cdot{D_{12}}=-0.004$

$V_{y_{12}}=\frac{-f_y}{\Sigma_{D}}\cdot{D_{12}}=-0.009$

$V_{x_{23}}=\frac{-f_x}{\Sigma_{D}}\cdot{D_{23}}=-0.003$

$V_{y_{23}}=\frac{-f_y}{\Sigma_{D}}\cdot{D_{23}}=-0.006$

$V_{x_{3B}}=-f_{x}-V_{x_{B1}}-V_{x_{12}}-V_{x_{23}}=-0.005$

$V_{y_{3B}}=-f_{x}-V_{y_{B1}}-V_{y_{12}}-V_{y_{23}}=-0.008$

$\begin{cases} \Delta{x_{B1}^{'}}= \Delta{x_{B1}}+V_{x_{B1}}=115.971\\ \Delta{y_{B1}^{'}}= \Delta{y_{B1}}+V_{y_{B1}}=-28.821 \end{cases} \Rightarrow \begin{cases} x_{1}=\Delta{x_{B1}}^{'}+x_{B}=1763.731\\ y_{1}=\Delta{y_{B1}}^{'}+y_{B}=1399.729 \end{cases}$

$\begin{cases} \Delta{x_{12}^{'}}= \Delta{x_{12}}+V_{x_{12}}=-40.768\\ \Delta{y_{12}^{'}}= \Delta{y_{12}}+V_{y_{12}}=-158.191 \end{cases} \Rightarrow \begin{cases} x_{2}=\Delta{x_{12}}^{'}+x_{1}=1722.963\\ y_{2}=\Delta{y_{12}}^{'}+y_{1}=1241.538 \end{cases}$

$\begin{cases} \Delta{x_{23}^{'}}= \Delta{x_{23}}+V_{x_{23}}=-111.377\\ \Delta{y_{23}^{'}}= \Delta{y_{23}}+V_{y_{23}}=46.647 \end{cases} \Rightarrow \begin{cases} x_{3}=\Delta{x_{23}}^{'}+x_{2}=1611.586\\ y_{3}=\Delta{y_{23}}^{'}+y_{2}=1288.185 \end{cases}$

$\begin{cases} \Delta{x_{3B}^{'}}= \Delta{x_{3B}}+V_{x_{3B}}=36.174\\ \Delta{y_{3B}^{'}}= \Delta{y_{3B}}+V_{y_{3B}}=140.365 \end{cases} \Rightarrow \begin{cases} x_{B}=\Delta{x_{3B}}^{'}+x_{3}=1647.76\\ y_{B}=\Delta{y_{3B}}^{'}+y_{3}=1428.55 \end{cases}$