Elementary Surveying, Global Edition
Elementary Surveying, Global Edition
14th Edition
ISBN: 9781292060491
Author: Charles D. Ghilani, Paul Wolf
Publisher: PEARSON
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Chapter 16, Problem 16.24P
To determine

Develop the observation equations for the given baseline vectors

   The observation equations for baseline components are:XBR= 1,164,499.387+ v1YBR= 4,660,600.879+ v2ZBR= 4,182,158.213+ v3XTH= 1,168,947.841+ v4YTH= 4,650,766.249+ v5ZTH= 4,191,851.263+ v6

Given that

Baseline vector are given as

Elementary Surveying, Global Edition, Chapter 16, Problem 16.24P , additional homework tip  1

Elementary Surveying, Global Edition, Chapter 16, Problem 16.24P , additional homework tip  2

Explanation:

Writing observation equation for X coordinate for jim to troy:

   XBR= XB+ ΔXBR+v1

WHERE

XB= X coordinate of the station bonnie = 1,161,121.599m

∆XB-R= X component in baseline vector = 3.377.788m

1= residual

   XBR=1,161,121.599+3.377.788+v1          = 1,164,499.387+ v1

Writing observation equation for Y coordinate for Bonnie to Ray:

   YBR= YB+ ΔYBR+v2

WHERE

YB= Y coordinate of the station BONNIE = 4,655,872.977

ΔYB-R = Y component in baseline vector = 4,727.902

2= residual

    YBR=4,655,872.977+4,727.902+v2          = 4,660,600.879+ v2

Writing observation equation for Y coordinate for Bonnie to Ray:

   ZBR= ZB+ ΔZBR+v3

WHERE

ZB= Z coordinate of the station bonnie = 4,188,330.232m

∆ZB-R= Z component in baseline vector = 6,172.019m

3= residual

   ZBR=4,188,330.232+6,172.019+v3          = 4,182,158.213+ v3

Writing observation equation for X coordinate for tom to herb:

   XTH= XT+ ΔXTH+v4

WHERE

XT= X coordinate of the station Tom = 1,176,398.558m

∆XT-H= X component in baseline vector = 7,450.717m

4= residual

    XTH=1,176,398.558 7,450.717+v4          = 1,168,947.841+ v4

Writing observation equation for y coordinate for tom to herb:

   YTH= YT+ ΔYTH+v5

WHERE

YT= Y coordinate of the station tom = -4,653,039.613m

∆YT-H= Y component in baseline vector = 2,273.364m

5= residual

   YTH=4,653,039.613+2,273.364+ v5          = 4,650,766.249+ v5

Writing observation equation for Z coordinate for tom to herb

   ZTH= ZT+ ΔZTH+v6

WHERE

ZT= Z coordinate of the station tom = 4,187,198.360m

∆ZT-H= Z component in baseline vector = 4652.903m

6= residual

   ZTH=4,187,198.360m +4652.903+v6          = 4,191,851.263+ v6

Conclusion:

Hence, the observation equations for baseline components are:

   XBR= 1,164,499.387+ v1YBR= 4,660,600.879+ v2ZBR= 4,182,158.213+ v3XTH= 1,168,947.841+ v4YTH= 4,650,766.249+ v5ZTH= 4,191,851.263+ v6

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