Field Survey Notes

You just come back from the field and you want to establish how good your measurements were. There are two easy ways to do that.

The first step is to establish the angular error

The second step is to plot the traverse. Easiest way to calculate the coordinates from latitudes and departure calculations, see below.

Most likely, when you plot your traverse, it will “not close” back on your starting point. That distance is referred to as your CLOSING ERROR. The ratio of that distance over the total, horizontal distance is the PRECISION of your traverse, a measure of how good your fieldwork was

A worked example. Here are the field notes. Note that skipping a line makes it easier to discern which measures are taken between which stations.

The first step is to transcribe the field notes into Excel or whatever tabular data manipulation environment you will be using. Note we have used sta.from and sta.to in order to keep things straight.

raw data




 sta.from sta.to fs bs slope sd




1 1 2 130 310  -4 79.7




2 2 3 205 27 -2 202.2




3 3 4 345 165 0 72.8




4 4 1 20 200 2 173.8

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The declination of 17° is added to each fs measurement to create fs.dec. Why is the declination added? Imagine if you obtained a magnetic measurement of 0°, that translates to 17° east of true north.

Declination correction




 sta.from sta.to fs bs slope sd fs.dec




1 1 2 130 310 -4 79.7 147




2 2 3 205 27 -2 202.2 222




3 3 4 345 165 0 72.8 2




4 4 1 20 200 2 173.8 37

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Correct horizontal distance for slope :

HD = SD * cos(slope° * pi / 180)

Note that the differences between slope and horizontal distances are small because there was not much elevation change over the surveyed area.

Horizontal distance




 sta.from sta.to fs bs slope sd fs.dec hd




1 1 2 130 310 -4 79.7 147 79.50585




2 2 3 205 27 -2 202.2 222 202.07683




3 3 4 345 165 0 72.8 2 72.80000




4 4 1 20 200 2 173.8 37 173.69413

We should also obtain the sum of horizontal distance, which will be needed in the latitudes and departures corrections:

Sum of HD: 528.08 

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Calculate interior angles. This is done by using foreshots and backshots. For example, angle 4-1-2 is calculated:

200 - 130 = 70

Interior Angles




 sta.from sta.to fs bs slope sd fs.dec hd ia




1 1 2 130 310 -4 79.7 147 79.50585 70




2 2 3 205 27 -2 202.2 222 202.07683 105




3 3 4 345 165 0 72.8  2 72.80000 42




4 4 1 20 200 2 173.8 37 173.69413 145
 

Looks like we got fairly close with the sum of interior angles.

Sum of interior angles: 362 

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Correct the azimuths based on the interior angle error. In this case the error was +2, and the number of angles was 2. To make the corrected interior angles sum to 360, it is necessary to subtract 0.5 from each measured azimuth.

Corrected azimuths




 sta.from sta.to fs bs slope sd fs.dec hd ia fs.cor




1 1 2 130 310 -4 79.7 147 79.50585 70 146.5




2 2 3 205 27 -2 202.2 222 202.07683 105 221.5




3 3 4 345 165 0 72.8 2 72.80000 42 1.5




4 4 1 20 200 2 173.8 37 173.69413 145 36.5

To calculate corrected interior angles, add or subtract the correction factor to each interior angle (not shown, because we don't need the corrected interior angles for further calculation).

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Calculate latitudes and departures. For example, look at station 2:

latitude = hd * cos(azimuth) = 202.07 * cos(222 * pi / 180) = 150.17

Latitudes and Departures




 sta.from sta.to fs bs slope sd fs.dec hd ia fs.cor lat dep




1 1 2 130 310 -4 79.7 147 79.50585 70 146.5 -66.29881 43.882222




2 2 3 205 27 -2 202.2 222 202.07683 105 221.5 -151.34659 -133.900156




3 3 4 345 165 0 72.8 2 72.80000 42 1.5 72.77505 1.905682




4 4 1 20 200 2 173.8 37 173.69413 145 36.5 139.62521 103.317224

Calculate the sums of latitudes and departures.

Sums of L&D: -5.25 15.2

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Under perfect conditions these should sum to 0. Because they don't, determine the correction. For example, station 1:

-(-5.25 / 528.08 * 79.51) = 0.79

Latitude and Departure correction factors




 sta.from sta.to fs bs slope sd fs.dec hd ia fs.cor lat dep lat.cor dep.cor




1 1 2 130 310 -4 79.7 147 79.50585 70 146.5 -66.29881 43.882222 0.7896932 -2.289221




2 2 3 205 27 -2 202.2 222 202.07683 105 221.5 -151.34659 -133.900156 2.0071314 -5.818420




3 3 4 345 165 0  72.8 2 72.80000 42 1.5 72.77505 1.905682 0.7230872 -2.096138




4 4 1 20 200 2 173.8 37 173.69413 145 36.5 139.62521 103.317224 1.7252197 -5.001194

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Balance the latitudes and departures by adding the correction factors to the originally calculated latitudes and departures. For example, station 1:

-66.3 + 0.8 = -65.5

Balanced Latitude and Departure




 sta.from sta.to fs bs slope sd fs.dec hd ia fs.cor lat dep lat.cor dep.cor lat.bal dep.bal




1 1 2 130 310 -4 79.7 147 79.50585 70 146.5 -66.29881 43.882222 0.7896932 -2.289221 -65.50911 41.5930012




2 2 3 205 27 -2 202.2 222 202.07683 105 221.5 -151.34659 -133.900156 2.0071314 -5.818420 -149.33946 -139.7185753




3 3 4 345 165 0 72.8 2 72.80000 42 1.5 72.77505 1.905682 0.7230872 -2.096138 73.49814 -0.1904563




4 4 1 20 200 2 173.8 37 173.69413 145 36.5 139.62521 103.317224 1.7252197 -5.001194 141.35043 98.3160304
Sums of balanced lat & dep: 0 0 

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Calculate X and Y coordinates by starting at a known point (station1 in this example), and then sequentially adding the latitudes and departures of subsequent points.

X and Y




 sta.from sta.to fs bs slope sd fs.dec hd ia fs.cor lat dep lat.cor dep.cor  lat.bal dep.bal x y




1 1 2 130 310 -4 79.7 147 79.50585 70 146.5 -66.29881 43.882222 0.7896932 -2.289221 -65.50911 41.5930012 1277180 241854.7




2 2 3 205 27 -2 202.2 222 202.07683 105 221.5 -151.34659 -133.900156 2.0071314 -5.818420 -149.33946 -139.7185753 1277221 241789.2




3 3 4 345 165 0 72.8 2 72.80000 42 1.5 72.77505 1.905682 0.7230872 -2.096138 73.49814 -0.1904563 1277082 241639.9




4 4 1 20 200 2 173.8 37 173.69413 145 36.5 139.62521 103.317224 1.7252197 -5.001194 141.35043 98.3160304 1277082 241713.3

It is possible to double-check the calculated X and Y coordinates by adding the latitudes and departures for the last station. They should result in the coordinates for the first station:

1277082 + 98 = 1277180

241713.3 + 141.3 = 241854.7

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Another check can be done by calculating the distances between stations (using the Pythagorean theorem) and comparing them with the measured distances. For example, line 3-4 (note the XY coordinates shown in the table are displayed in a truncated form):

sqrt((1277081.77 - 1277081.58)^2 + (241639.85 - 241713.35)^2) = 73.5

Distance




 sta.from sta.to fs bs slope sd fs.dec hd ia fs.cor lat dep lat.cor dep.cor lat.bal dep.bal x y dist




1 1 2 130 310 -4 79.7 147 79.50585 70 146.5 -66.29881 43.882222 0.7896932 -2.289221 -65.50911 41.5930012 1277180 241854.7 77.59782




2 2 3 205 27 -2 202.2 222 202.07683 105 221.5 -151.34659 -133.900156 2.0071314 -5.818420 -149.33946 -139.7185753 1277221 241789.2 204.50808




3 3 4 345 165 0 72.8 2 72.80000 42 1.5 72.77505 1.905682 0.7230872 -2.096138 73.49814 -0.1904563 1277082 241639.9 73.49839




4 4 1 20 200 2 173.8 37 173.69413 145 36.5 139.62521 103.317224 1.7252197 -5.001194 141.35043 98.3160304 1277082 241713.3 172.18010

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The last calculations are:

• Area, which can be calculated from the XY coordinates.

Area: 11308.6 ft² = 0.26 ac

• Linear error of closure

EOC = sqrt((-5.25 ft)² + (15.2 ft)²) = 16 ft

• Precision

Precision = EOC / perimeter = 16 / 528 = 1:33

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Finally, a few maps can be made using ArcGIS (click for full-sized versions):

source code