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How do you triangulate a position from multiple Benchmarks?


RubyHunter
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I recently came across a Mystery Geocache that uses benchmarks to find the cache location. The description gives the PID number and the distance from the disk. And I can't for the life of me figure out how to make the end points meet. Needless to say I need a little help. This type of hunt looks like it would be a lot of fun if you had the right tools. The cache I'm looking at is http://www.geocaching.com/seek/cache_detai...3d-6c2e58155bc5 if you'd like to take a look.

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I recently came across a Mystery Geocache that uses benchmarks to find the cache location. The description gives the PID number and the distance from the disk. And I can't for the life of me figure out how to make the end points meet. Needless to say I need a little help. This type of hunt looks like it would be a lot of fun if you had the right tools. The cache I'm looking at is http://www.geocaching.com/seek/cache_detai...3d-6c2e58155bc5 if you'd like to take a look.

 

Plot the positions of the benchmarks on a map (or Google Earth) and then use the measure tool to measure the required distances. Where the lines meet is where the cache will be. Get a reading of the coordinates for that point. Some trial and error will be needed unless you wish to track down some software that will do it for you.

 

Don't forget to find the benchmarks and log them! Have fun,

 

 

John

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Some thoughts on finding the Cache.

 

1. Plot 3 or 4 of the points on a map as suggested by 2oldfarts and obtain an approximate position for the unknown point “C”. You mainly just need to know where “C” is with respect to the other points, north or south, east or west.

 

2. Pick two of the survey marks that have adjusted horizontal positions. Call them points “A” and “B”. Do an “inverse” between them using NGS’ on-line software (need to enter the lat. and long. of each point). The inverse will give you the distance between points “A” and “B” (called AB), and the azimuths each way between “A” and “B”.

 

3. You now have the three sides of a triangle, AB from the inverse, AC from the list of given distances, and BC also from the list of given distances.

 

4. Use the Cosine Law to find the angle at point “A” of the triangle.

 

5. From the inverse done in step #2, find the azimuth from “A” to “B”.

 

6. From the map (step 1) determine if you need to add the angle at “A” to the azimuth from “A” to “B”, or subtract it (is point “C” to the left or right of the line AB?) The result of this arithmetic will then give you the azimuth to “C”. (Remember, azimuths increase clockwise.)

 

7. Using NGS’ on-line “forward” software, enter the lat. and long. of “A”, the azimuth to “C”, and the distance AC, and the result will be the lat. and long. of “C”.

 

To check the results, select two different points for “A” and “B”. The result should be very close.

 

Note, “inverse” and “forward” are in the “Geodetic Tool Kit” under “Tools” on the NGS Home Page.

 

GeorgeL

NGS

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Law of cosines, law of sines, spherical trigonometry, yeah I think you can find all of these in some book.

 

You can also download the software COMPSYS21 here: COMPSYS21 It uses Vincenty's method so expect accuracy. No elevation correction but where you’re looking this shouldn't matter

With 3 of those marks having adjusted coordinates you should have no problem. Use the "Circle-Circle" intersection i.e. "distance-distance", there will be 2 results with any 2 stations but if you use the 3rd you should easily find the right one.

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That Compsys21 looks like a very good utility that I'll have to try out. Thanks!

 

The contrary may be proven, but I'd start out with the assumptions that the creator of the cache used some form of Vincenty equations to get his distances, and that for scaled locations he used the lat-lon given, as if it were precise

 

However, a friend of mine did cache GCHQT8 that depended on finding 4 other locations spread over 10 miles or so, and calculating the coordinates of the cache at the intersection of the diagonals. He just assumed that he could interpolate lat-lon values and computed the intersection by ratios. The geodetic solution is 23 feet north of the flat world solution.

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I created a similar cache about two years ago nearby in Southern California:

"Can You Help ME Find My Cache" GC1B73V

 

It was fun to create (including the upfront "fiction" part), but other than a few locals with the math / computer skills (and a good friend of mine), it doesn't get much attention. I suspect it's on a lot of the locals "Ignore" list. Oh yeah, a couple folks on the forum solved it also.

 

You really only need three of the four benchmarks (I made it easier than I had to), and the key is the Tienstra Method.

(top of the list is Mesa Mike, a forum regular - wasn't there when I created the cache!)

 

Drawing lines on a map might work (if you're very accurate), and did for several of the finders, but the proper way is the Tienstra method (formula). It was a challenge I enjoyed to implement the Tienstra method in an Excel spreadsheet, and have it work!

 

If anyone wants the challenge, I'll be happy to "grade" your solutions. Extra credit for doing your own math, rather than using Mike's Website. Drop me an email with your coords for the cache:

lklem "at" roadrunner.com

 

Klemmer

Edited by Klemmer & TeddyBearMama
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I recently came across a Mystery Geocache that uses benchmarks to find the cache location. The description gives the PID number and the distance from the disk. And I can't for the life of me figure out how to make the end points meet. Needless to say I need a little help. This type of hunt looks like it would be a lot of fun if you had the right tools. The cache I'm looking at is http://www.geocaching.com/seek/cache_detai...3d-6c2e58155bc5 if you'd like to take a look.

 

It would seem you need to "pin" the given benchmarks on a map. Scale out the distances on the edge of a piece of paper. Rotate the paper so one length mark is on the pin and the other end joins with another leg. They should all lead to a common point the degree of accuracy prooven by the number of reference points. Checking one PID, I know it is in NY.

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Some comments on COMPSYS21.

 

-It is the only program I have used that gives me some of the capabilities, which is great.

 

It has some minor problems:

 

-The menu offers "accuracy to 1/1000 second" and other choices, but these are really fractions of a degree not second.

 

-If you set up 4 points for calculations and pick any one for forward, or any pair for inverse, the results box still says 12 and 21, not whatever you selected. This program would be much nicer if it kept track of the point numbers/names and let you store the result of a Forward as a new point number for successive calculations.

 

-The results box floats always on top of everything on the desktop, which is often not what you want.

 

-The installation wasn't quite clear enough and I wasn't paying enough attention so I overwrote some DLLs with older versions and now my computer has some problems.

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Thanks for all the info. At least I now have a starting point to work with, and that was all I was looking for. I've downloaded the programs listed in the posts and will work with them today. But first I'll hunt down the benchmarks to verify coords. I read somewhere that there are differences between the WGS84, which most recreational GPSr's use, and NAD83 Datums. From what I've seen on the mapping program I currently use they seem to be pretty close. But I'll make no assumptions in that respect.

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WGS84 and NAD83 differ by something on the order of a meter or a yard, and thus the choice isn't too important for use with a handheld. If you want to get into the fine points, look up the HTDP program on NGS site, but I don't think it is worthwhile for this project. I'll bet the guy who put this cache together didn't consider the difference.

 

All GPS units work in WGS84 and convert to whatever display datum you have selected. All the handhelds I'm familiar with actually make zero adjustment for NAD83.

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Law of cosines, law of sines, spherical trigonometry, yeah I think you can find all of these in some book.

 

You can also download the software COMPSYS21 here: COMPSYS21 It uses Vincenty's method so expect accuracy. No elevation correction but where you’re looking this shouldn't matter

With 3 of those marks having adjusted coordinates you should have no problem. Use the "Circle-Circle" intersection i.e. "distance-distance", there will be 2 results with any 2 stations but if you use the 3rd you should easily find the right one.

Bingo. easy-peazy. I have yet to have a complete understanding of all of the math. I fumbled with GE trying to plot this out. I tried this application after I thought I understanded the circle-circle function. Couple that with the parking coords and I had it. I was 80' off with GE but I wasn't done yet. I am questioning if it would be close enough though.

 

Thanks! I'm thinking of developing my own BM caches.

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