- The intent of this series of geocaches is to help us learn how to apply triangulation techniques to find the location of unknown points using a handheld GPSr.
- While these geocaches were created and tested using a Garmin GPSr, they can also be found using a smartphone or other device with the appropriate software.
- It is recommended to find this series of geocaches in numerical order (1-6) as each geocache builds on techniques and information learned in previous finds.
The Oxford dictionary defines Triangulation as "(in surveying) the tracing and measurement of a series or network of triangles in order to determine the distances and relative positions of points spread over a territory or region, especially by measuring the length of one side of each triangle and deducing its angles and the length of the other two sides by observation from this baseline."
In practice, 'Triangulation' is actually a generic term commonly used when referring to several surveying terms:
- Triangulation refers to the process of determining the location of a point by forming triangles to it from known points, using only angle measurements.
- Trilateration (True Range Multilateration) is a method of determining the location of a point using multiple known distance measurements from known points.
- Triangulateration involves the use of both angle and distance measurements to determine the location of a point.
To find the final location of each geocache in this series, we will actually be using Triangulateration, which is a combination of both Triangulation and Trilateration.
Additional information can be found at GPSrChive > How To... > Triangulation.
While the procedures provided in this geocache series are not mutually exclusive, and exploring additional techniques to solve each problem is encouraged, please be mindful of accuracy limitations imposed when using consumer grade equipment to perform these exercises.
Triangulation 6 - Midpoint of Three Locations
The sixth (and final) geocache in this series will use elements from Triangulation 1 (waypoint projection) , Triangulation 2 (route creation), and Triangulation 3 (proximity alert creation).
In Triangulation 3, we were provided with three known locations and distances to an unknown waypoint, and we only needed to determine where those three distances intersected to find the destination location. While this exercise is similar, it will be more difficult and time consuming.
Here we will again be given three known locations, but no distance values, other than to say that the distance between each waypoint and the destination is identical. We only need to determine the coordinates for a single point that is equidistant from the waypoints provided.
To accomplish this, we will first measure the distances between each of the waypoints provided. We can surmise that the solution will be a value greater than the shortest distance recorded yet smaller than the largest distance recorded. Armed with this information, we can apply the techniques learned in Triangulation 3 with some trial and error to find the solution.
To find the midpoint (equidistant) between three known points:
Procedure
Before searching for this geocache, it is recommended to first solve Triangulation 5, the previous geocache in this series.
Configure your GPSr heading to use True North.
Configure your GPSr routing method to use Direct Routing.
From the posted coordinates:
Project and save waypoint 'T6A' using a bearing of 41 degrees and a distance of 1093 feet.
Project and save waypoint 'T6B' using a bearing of 62 degrees and a distance of 624 feet.
Project and save waypoint 'T6C' using a bearing of 307 degrees and a distance of 592 feet.
Now we need to find the distances between each set of waypoints.
Create route 'T6R1' using sequence 'T6A' to 'T6B' and record route distance as 'T6R1D'.
Create route 'T6R2' using sequence 'T6B' to 'T6C' and record route distance as 'T6R2D'.
Create route 'T6R3' using sequence 'T6C' to 'T6A' and record route distance as 'T6R3D'.
Compare 'T6R1D', 'T6R2D' and 'T6R3D', recording longest route value as 'T6RL' and the shortest route value as 'T6RS'.
The solution will be shorter than the longest route recorded ('T6RL'), and longer than shortest route recorded ('T6RS').
Finding the correct value will require some trial and error.
Create identical proximity alerts for waypoints 'T6A', 'T6B' and 'T6C' on your Garmin GPSr using a radius value between 'T6RS' and 'T6RL'.
If any one proximity alert ring does not overlap both remaining proximity alert rings, increase the radius value and repeat.
If all proximity alert rings overlap each other but do not all intersect at a common location, decrease the radius value and repeat.
When all proximity alert rings intersect each other near a single common location, mark (and save) the location as waypoint 'T6F'.
Waypoint 'T6F' is the midpoint for waypoints 'T6A', 'T6B' and 'T6C'.
To verify our solution, we can create a proximity alert for 'T6F' using the final radius value from waypoints 'T6A', 'T6B' and 'T6C'.
The proximity alert for 'T6F' will intersect waypoints 'T6A', 'T6B' and 'T6C' if your solution is correct.
Upon arrival at waypoint 'T6F', put down the GPSr and use your 'geosense' to find the geocache container.
Once located, the container does not need to be removed in order to retrieve the log sheet.
While signing the log, be certain to reflect on the triangulation terms, techniques and skills you have learned from this series.
When logging your find online, please include the brand and model of the equipment used to find this geocache.
Please exercise special care when retrieving and replacing the log to prevent muggles from unintentionally discovering and potentially vandalizing the container.
Do you feel the navigation skills experienced here may benefit you in your future endeavors?
Would you like to see more geocaches similar to these published?