How To...

Triangulation

• 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.
• Apply the following techniques to find the location of unknown points using only a Garmin GPSr and a creative interpretation of the above methods.

1. Intersection by Bearing

1.1. Find the point of intersection between two bearings from two points

1.1.1. Find the coordinates for a distant landmark within visual range    Landmark (X) in visual range Save current locationas Waypoint (B) Project a waypoint beyondLandmark (X) Save Waypoint (A)    Move to a new location and save Waypoint (C) Project a waypoint beyondLandmark (X) Save Waypoint (D) Create new route on GPSr...    ...from Waypoint (A) to (B)... ...add Waypoint (B) to (C)... ...finish Waypoint (C) to (D) Mark Waypoint (X) atroute intersection

1.1.2. Find the coordinates for an unknown waypoint where two locations and bearings are known    Move to first locationand save as Waypoint (B) Project a waypoint atspecified Bearing Save Waypoint (A) Move to second location...    Save second locationas waypoint (C) Project a waypoint atspecified Bearing Save Waypoint (D) Create new route on GPSr...    ...from Waypoint (A) to (B)... ...add Waypoint (B) to (C)... ...finish Waypoint (C) to (D) Mark Waypoint (X) atroute intersection

1.2. Find the point of intersection between two bearings to two points

• Modify each bearing between 001° and 180° by adding 180°
• Modify each bearing between 181° and 360° by subtracting 180°    Move to first locationand save as Waypoint (B) Project a waypoint atspecified Bearing Save Waypoint (A) Move to second location...    Save second locationas waypoint (C) Project a waypoint atspecified Bearing Save Waypoint (D) Create new route on GPSr...    ...from Waypoint (A) to (B)... ...add Waypoint (B) to (C)... ...finish Waypoint (C) to (D) Mark Waypoint (X) atroute intersection

2. Intersection by Distance

2.1. Find the point of intersection between multiple points with known distances

• Find the coordinates for an unknown waypoint where two locations and distances are known (Bilateration)
• Find the coordinates for an unknown waypoint where three locations and distances are known (Trilateration)    Two known locations,points (A) and (B) Create Proximity Alert atspecified distance for point (A) Create Proximity Alert atspecified distance for point (B) Two solutions exist whereProximity (A) and (B) intersect    Three known locations,points (A), (B) and (C) Two solutions exist whereProximity (A) and (B) intersect Create Proximity Alert atspecified distance for point (C) Mark Waypoint (X) whereProximity (A)(B)(C) intersect

3. Intersection of Circle

3.1. Find the points of intersection on a circle with a line by bearing    Save 'Circle' location as Waypoint (A) Move to 'Bearing' locationand save as Waypoint (B) Create Proximity Alert atspecified distance for point (A) Project a waypoint atspecified Bearing    Save Waypoint (C) Create new route on GPSr... ...from Waypoint (B) to (C) Two solutions exist where (B)(C) intersects (A)

4. Midpoint

4.1. Find the midpoint between two known points    Two known locations,points (A) and (B) Create new route on GPSr from waypoint (A) to (B) Create Proximity Alert (A) at ½ distance of Route (A)(B) Create Proximity Alert (B) equal to Proximity Alert (A)    Adjust both Proximity Alerts in equal increments if they do not overlap precisely Proximity Alerts (A) and (B) exhibit correct overlap Mark location where Proximity Alerts (A) and (B) intersect Route (A)(B) Saved Waypoint (X) is (A)(B) midpoint

4.2. Find the midpoint between three known points    Three known locations,points (A), (B) and (C) Create new route on GPSr from waypoint (A) to (B) and record route distance Create new route on GPSr from waypoint (B) to (C) and record route distance Create new route on GPSr from waypoint (C) to (A) and record route distance    Solution will be between longest route (A)(B) and shortest route (C)(A) Create Proximity Alert for any point using a value between (A)(B) and (C)(A) Create Proximity Alerts for remaining points using the same value If Proximity Alerts do not all overlap, increase the value and repeat process    Create a Proximity Alert for any point using new value Create Proximity Alerts for remaining points using the same value If all Proximity Alerts overlap but do not intersect at same point, reduce value and repeat Create a Proximity Alert for any point using new value    Create Proximity Alerts for remaining points using the same value Mark Waypoint (X) where all Proximity Alerts intersect at same point Saved Waypoint (X) is (A)(B)(C) midpoint Create Proximity Alert (X) using final (A)(B)(C) value to verify solution

5. Equilateral Triangle

5.1. Find coordinates to form an equilateral triangle from two known points    Two known locations,points (A) and (B) Create new route on GPSr from waypoint (A) to (B) Find total distance for Route (A)(B) Create Proximity Alert (A) using distance (A)(B)    Adjust Proximity Alert (A) distance as required for precise intersection with point (B) Create Proximity Alert (B) equal to Proximity Alert (A) Mark Waypoints (X) and (Y) where Proximity Alerts (A) and (B) intersect (A)(X)(B) and (A)(Y)(B) form Equilateral Triangles  