- 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 4 - Equilateral Triangle
The fourth geocache in this series will use elements from Triangulation 2 (route creation) and Triangulation 3 (proximity alert creation).
In Triangulation 3 we learned how to find a destination where only the distances from multiple locations were known, but not the bearings. We are going to be given only two locations for this exercise, with no bearing or distance values provided other than to say that all locations are equidistant from all points given. This may initially seem a daunting task as it may appear the number of potential solutions are infinite, however, in reality only two possible solutions can exist.
To find coordinates forming an equilateral triangle from two known points:
Procedure
Before searching for this geocache, it is recommended to first solve Triangulation 3, the previous geocache in this series.
Configure your GPSr routing method to use Direct Routing.
Find the lamp post in this park marked with the number '3' and save waypoint 'T4A'.
Find the lamp post in this park marked with the number '9' and save waypoint 'T4B'.
Now we need to find the distance between these two waypoints.
Create route 'T4R' using sequence 'T4A' to 'T4B' and record route distance as 'T4RD'.
Create a proximity alert for waypoint 'T4A' on your Garmin GPSr using a radius value equal to 'T4RD'.
Adjust waypoint 'T4A' proximity alert value as required to obtain closest possible intersection with waypoint 'T4B'.
Create a proximity alert for waypoint 'T4B' on your Garmin GPSr using value identical to 'T4A' proximity alert.
Mark (and save) both proximity alert intersection points as waypoints 'T4X' and 'T4Y'.
Waypoints 'T4A', 'T4B' and 'T4X' form an equilateral triangle.
Waypoints 'T4A', 'T4B' and 'T4Y' also form an equilateral triangle.
Both waypoints 'T4X' and 'T4Y' are potential solutions.
You will need to explore the area around each waypoint using your 'geosense' to discover which is the correct solution. Those who are familiar with geocache placement guidelines should already know where to start looking first. A hint is available if you need it.
Upon finding the geocache log, rename the appropriate waypoint 'T4F'.
Once located, the container does not need to be removed in order to retrieve the log sheet.
When logging this 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.
You should now proceed to Triangulation 5, the next geocache in this series.