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Trilateration Mystery Cache

Hidden : 4/26/2007
Difficulty:
2.5 out of 5
Terrain:
1.5 out of 5

Size: Size:   regular (regular)

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How Geocaching Works

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Geocache Description:

The co-ordinates at the top of this page are not those of the cache. A multi-element puzzle cache, involving visits to several locations in the Dunmurry / Lambeg area. Skill in GPS-handling, map reading, and mathematics are all required to find the final cache.

The first in a series of caches intended to illustrate the principles of satellite-based global positioning. May take more than an hour to find the intermediate caches, and some desk-work thereafter to calculate the final hiding place.


In order to complete this cache, you will need: (a) A car. (b) A compass and Ordnance Survey Sheet 15 (Belfast) 1:50000 Map (c) Paper & pencil. It would also be useful to have plenty of time, good skill in handling a GPS receiver, and some knowledge of applied co-ordinate geometry.

Each waypoint will give you a "range" in metres which is its distance from the final cache.

Visit the four supplied waypoints (in any order). Note the information at Wp1. The other three waypoints are small 4x3 cm tab-lock boxes hidden as regular caches. Each box contains cards with the range. (Please do NOT remove a card if you have something to write on, instead.) After gathering all the data, use whatever means you wish to establish the final co-ordinates.

"Trilateration" is the use of geometry to find the positions of objects by their relative distances, rather than using angles as in trigonometry. To help those taking this mathematical approach, I have given the Irish Grid references (square "J") to 10 centimetre resolution. These figures are much more accurate than the transformations supplied by most handheld GPSr's and their use is strongly recommended.

Children should NOT be allowed to search for the final cache on their own, for reasons which will become apparent.

Please do not contact me for help or co-ordinate confirmation unless you have logged at least one DNF on the cache page. Find logs must be worded in such a way that the final location is not pointed to. Good luck -Wlw.


"How GPS Works"

The civilian GPS units familiar to all geocachers are really just a radio receiver with a computer attached, and having some kind of output display.

To find our location in 3D (Latitude, Longitude and Altitude), we need at least four radio signals with the following characteristics: they must be (a) from a known location, and (b) have known timings.

GPS navigation satellites carry very (very!) accurate atomic clocks. Their position is also predictable: your GPSr has a table of orbital data for the satellites, called an "almanac", and this is updated with minor corrections for each spacecraft (the "ephemeris") which are continually broadcast.

As it receives the GPS navigation signal from each satellite, your GPSr performs a series of calculations to establish its own distance from each transmitter. The results of this are called "pseudoranges". For any given location, we can imagine that each satellite is surrounded by an invisible sphere whose radius is the range to that location. Where the spheres intersect is your approximate position.

As the calculations proceed, other mathematical filters and corrections are applied to refine the position - and the more satellites in view, the more accurate this position becomes.

The cache: A tab-lock box 18x18x11cm is hidden at ground level. When replacing the container, please make sure that it is properly hidden from view. This cache is not suitable for Travel Bugs/Geocoins, as it may not receive many visits in the course of a year.

Additional Hints (No hints available.)