Trigonometry, Triangles and Treachery

The containers     So... how did this one come about? Well I guess it all started at the event organised in conjuction with the Hampshire County Council. Details of the event can be found on other websites so I'm not going in to that here. Suffice it to say that I came away from the event with two screw top, waterproof, aluminium pots and a vague idea for a new cache. I'd been wanting to place a 'difficult' cache for some time and the germ of an idea had gradually grown and taken shape in my mind during the time I spent at the HCC event and the day I spent afterwards on the Isle of Wight with Omally, Merman and Keith of the Motley Crew. (Collectively, we later gained notoriety as 'The Grockles').
     It all boiled down to finding suitable locations for three caches. I started with the Ordnance Survey Explorer map for my home area, Sheet 193. Cache-1The grid reference for the bottom, left hand corner of the sheet is 'TL 00000 20000' while the grid reference for the top, right hand corner of the sheet is 'TL 30000 40000'. For anyone that doesn't know, the OS Grid Reference system is based on lines drawn 1 kilometre apart with a 'major' line every 10 kilometres. Each 100 kilometre square has a different letter designation. Very simply, the first group of five digits is the horizontal location. This is called the 'Easting'; the second group of five digits is the vertical location and is called the 'Northing'. Ordnance Survey explain this much better than I do so if you don't know what I'm on about, I suggest you have a look here. This particular map covers a rectangle of land 30 kilometres from west to east (00000 to 30000 metres) and 20 kilometres south to north (20000 to 40000 metres).
Cache-2     As the grid is based on an actual unit of distance and not some arbitary unit, it is very easy to calculate the distance from one known grid reference to another. Conversely, if you have two known reference points and the distance to a third from each of them, you can calculate the grid reference of the third. That is the basis for this cache. The two known reference points are the bottom left corner and top right corner of OS Explorer sheet 193. Originally, I was going to place the two aluminium pots (Cache 1 and Cache 2) anywhere that was a sensible cache location but I thought it would be a nice refinement if they were both the same distance from each of the two reference points. After a lot of work with MemoryMap software and a lot of time checking out possible cache locations, I eventually decided on the two that are currently being used. Cache 3 locationThe two pots are not exactly the same distance from the two reference points but they are very close, only a few meters away. To compensate for the small error between the calculated grid reference for each cache and the actual grid reference of each cache, I give the digits contained in the WGS84 latitude and longitude for each cache on the cache sheet. I don't propose to give a full explanation of the maths involved here but if you don't know how to calculate the cache locations from the information I've given, a full explanation can be found here. This is an absolute spoiler though, as it will give you the actual WGS84 co-ordinates for both caches. Please only look at this page if you really have no idea what I've been talking about.

     OK... so I had locations for the first two parts of this multi-cache. Now I needed a location for the third. Again I wanted it to be an equal distance from the first two caches. As the first two caches were placed symetrically on the map, it was obvious that a third cache, placed an equal distance from each of the first two caches would lie on a direct line between the reference points for the first two caches. That is to say; it would lie on the diagonal line between the bottom left corner and top right corner of the map sheet 193. There were numerous possible cache locations along this line but after checking them all out, only one was really suitable. This was some nine and a half kilometres from each of the first two caches. Having fixed the location of the third cache, I could now plant all three. The first two each contain a laminated card that gives their own grid reference and the direction and distance to the third cache. It also tells you to remember a number but not why; that comes later. All three containers are sprayed up black and dark green (see first photo) to make them a little less conspicuous.
The wood that contains the final cache     Cache 1 was placed in a hole at the base of a tree on a river bank. I think it's a willow tree but I'm not exactly sure. I do know that it's leaning over at quite an angle and it's just a few yards upstream from a small wooden footbridge over the river (see second photo).
     Cache 2 was also placed in a hole at the base of a tree. In this case, an ash tree standing alone beside a bridle path. The hole was quite deep so the cache is attached to a small, dead branch by a length of 'para-cord' (see third photo). This effectively stops the pot from falling out of reach (I hope).
     I've also left a notepad and pencil in each of the caches so that anyone who comes 'unprepared' can make a note of the information and won't be tempted to take the laminated card. The actual location of the third cache can be calculated in exactly the same way as the first two. For those that still don't understand, the solution can be found here. Using these solutions, effectively reduces the difficulty to 1 star per cache.
     Cache 3 is a rectangular plastic box with a 'locking' lid and is placed at the base of another ash tree beside a footpath. The fourth photo shows this location. It was taken from out in the field to the right of the footpath. It's not in a hole this time, just out of sight behind the tree and covered with grass and twigs.

Final cache location     OK... So far it's all been very straight forward. "Where does the 'treachery' bit come in?" I can hear you ask. Well it's here.... this isn't the final cache. This box just contains a Zip-Loc bag which in turn contains a number of envelopes. Take one and replace the cache. Printed on the envelope are the co-ordinates for the final cache. Don't open the envelope.... it contains two photographs which will help you to locate the final cache but you shouldn't really need them. It's not that difficult to find but it is just over 5km away as the cod swims so you need to get back to your car.
     The final and it really is the final cache is hidden in a wood. There is parking at the start of a bridle path (The Hertfordshire Way) at N51 57.737'  W000 09.872'. From there follow the bridle path north. You might be tempted to take a short cut by turning left and following the track along edge of the crop field (see photo number 5) but this isn't strictly a public right of way so you do so at your own risk. You will also come up against an almost impenetrable mass of brambles in the summer. Follow the bridle path until it runs alongside the north-eastern edge of the wood and then follow the track down the northwest edge of the wood. You will find the cache beneath the usual 'forest debis' at the base of a hazel bush with a distinctive, star shaped stump in front of it (sixth photo). It's a small ammunition box that is locked with a combination padlock... more treachery. You were told to remember a number; this is why.
     So... that's it, Trigonometry, Triangles and Treachery. I hope you enjoyed it. I certainly had a lot of fun setting it.


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Last updated 18.9.2004