Article Index

4. Example

A crew surveyed the exterior of the parcel shown. They assumed the coordinates of the southernmost corner (1001) and used the record bearing for the southwesterly line (1001-1002).

 

img126

Point

North

East

1001

3684.22

2208.05

1002

4030.04

1940.56

1003

4244.27

2366.04

1004

3802.06

2607.77

Figure H-20
Parcel Survey
 

 

Later, a second survey crew was sent out to locate the existing drainfield. They did not have the first crew's coordinates so they occupied the northernmost corner (NE), for which they assumed coordinates, and backsighted the westernmost corner (NW), for which they assumed a direction. They then shot the drainfield corners. As a check, they also shot the distance from NE to NW.  

img127

Point

North

East

NE

5000.00

3000.00

501

4914.03

2776.03

502

4814.98

2786.38

503

4829.01

2911.57

504

4934.06

2895.69

Figure H-21
Drainfield Survey
 

 

When the coordinates were brought together and plotted the results were as shwon in Figure H-22:

 

img125
Figure H-22
Parcel and Drainfield Combined

 

Using the boundary survey as the reference system, translate the drainfield data.

Determine transformation parameters

 

Step (1) Rotation angle

Line NE-NW coincides with line 1003-1002; line NE-NW must be rotated into line 1003-1002.

img133

Convert the bearings to azimuths and compute the rotation angle.

 

Line NE-NW       img134
Line 1000-1002       img135

 

From Equation H-1: 

img136

 

Step (2) Scale

Length of line NE-NW is 476.41', line 1003-1002 is 476.37'.

From Equation H-2:

img137

This represents a distortion of 1/(1-0.999916) = 1/11,900. If this is within tolerance, then the scale factor can be ignored. We will apply it in this example.

 

Step (3) Translations

Use the coordinates of points 1003 and NE in Equation H-3:

img138

img139

 

Step (4) Math check

For a parameters math check, convert NW to see if it matches the coordinates of 1002.

In the From system, NW's coordinates are:

img150

Transform and check:

img151

img152

 

Step (5) Transform points 501-504

 Use Equation H-14 with the parameters computed in Steps (1)-(3)

Point 501

img140

img141

Point 502

img142

img143

Point 503

img144

img145

Point 504

img146

img147

 

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