Category Archives: FORT 140

Distance Measurements Analysis

Ten teams of students measured the perimeter of a seven-sided traverse using pacing and taping. Each leg was measured twice. The standard deviations of the measurements of the perimeter showed that pacing gave much more variable results. Pacing also had a much wider certainty range at different probabilities.
                                           Pacing       Taping

Average 1056.1 1065.0
Standard Deviation 49.3 7.5
Maximum 1172 1071.61
Minimum 995 1051.1
Difference 177 20.51

As can be seen in the table above the range of measurements is much greater. This is somewhat expected as it is the combined results of ten different groups. Also, greater practice would result in less variability in the measurements.

STDEV-Graph.jpgThe chart shows the standard deviations for the measurements of each leg and illustrates the difference in the results.

Develop an Elevation Profile

In surveying we have been making elevation profiles from differential leveling data for as long as I have been teaching the course. Recently, I came across a help page from the University of Georgia that uses ArcGIS to associate data points with elevation data from a DEM, which is then graphed in Excel, with an XY scatter chart. The data can come from GIS points or a line digitized on the map. The edit – divide tool sets the points along a line at any spacing desired. Spatial analyst will extract the elevation from the DEM at each point.

Here is a section of the pipeline that goes through the Waynesboro Watershed.
And here is the resulting profile.
This method can help reduce the error form field measurements. And it can be used for much longer spans. 

GPS Testing

During the GPS testing lab each team recorded the UTM coordinates 25 times at each of five points.We finished with 200 measurements for each of the test points. We combined all the measurements for each of the points and calculated descriptive statistics.

The difference of each point from the average coordinate was calculated using the Pythagorean theorem. Histograms of the differences show a big difference in the results. In point 1 there was a great deal of difference among the results of each team. The combined data shows the wide variation. It would probably be a good idea to remeasure this point. Since the teams all used the same model of GPS receiver and measured during the same time period, these results point to a likely user error.

Point1histogram.jpgFor point 5 the differences are much smaller overall. They are also much more concentrated, indicating that all the readings were concentrated around the average, a consistent fix on the coordinates.

point5histogram.jpgNote that these charts used all the data points.

GPS Testing

During the GPS testing lab each team recorded the UTM coordinates 25 times at each of five points. After combining the readings I wanted to see if the results were statistically compatible or if they shouldn’t be compared. Another way to put it: are each team’s results form the same population or are there other factors that make the results not comparable.

There are some statistical methods to do this analysis. However, a simple way is to take the average of the eastings and northings, calculate the difference of each coordinate pair from the average, and plot the differences. The results should look like a scatter shot from shooting a target.

At point 5, the results seem to be randomly scattered around the average, or bullseye. The size of the spread is not very great.

Point 5 differences-corrected.jpg

Click on the thumbnail to see a larger version.

Point 1, on the other hand, shows the readings divided into distinct groups. Also, the magnitude of the differences is much greater.


All of the teams worked in the same time period, which means that GPS reception conditions must have been similar. The differences could be due to the differences between the GPS receiver units. More likely there was some variation in the operators or human error. I would recommend remeasuring this point to rule out human error.

Test of GPS Receiver

The Garmin Model 60 GPS receivers were tested at five different points around the Mont Alto campus. At each point seven teams recorded 30 measurements. The measurements were combined for analysis. The true position was assumed to be the average easting and northing coordinates. The distance from the correct position, or error, was calculated. The mean, standard deviation, minimum, maximum and other descriptive statistics were calculated. The error data was separated into half meter classes in the following histogram.


This table from the first point, located next to the General Studies building, shows the result. The average error of 3.3 meters is within the parameters for this model of GPS receiver.