How to figure Triangulation???

[+BugsandMustang]

I am trying find a cache that utilizes triangulation. This cache has 3 coordinates given to you and then a distance that each cache is from the unknown cache. Given this info it seems that it would be relatively easy to figure out. Plot out the 3 coordinates and draw a circle around each spot with the given distance and where they all meet is where the cache is. Well a few things that I do not know how to do. Do I use the Lat/Long coordinates that are given and map to a Topological map, do I use UTM (if UTM is it the WGS or NAD?) Once these are mapped how do I convert miles into lat/long or UTM? Is there a good source on the web that expanins how to do this or better yet, is there a formula or even a page that I could plug in coordinates, the distance each is and then get a coordinate? Any help in understanding how I can figure this out would be helpful. Thanks

[+Dersu]

Please post a link to the cache page and let us look at it. Sounds a like a trig problem, probably a obtuse triangle. No problem to solve if some of the info is available.

 

I have flouted the wild, I have followed its lure, fearless. familar, alone; yet the wild must win, and a day will come when I shall be overthrown. By: Robert Service

[+BugsandMustang]

The cache page is http://www.geocaching.com/seek/cache_details.aspx?ID=20947 I believe it is a relatively simple equation but my math skills have gone down the tubes.

[OlyHippy]

Here's an idea along those same lines. You can have the cache hunter go out to a given point on some terrain give them a magnetic azimuth to a known point on the ground; say a hill or rock pile, etc and then plug in a scenario of a 2nd party located near your position. eg,

 

From my current location I see a rock pile at 130* magnetic at approximately 300 meters. From a second position another guy sees the same rock pile at a 150* magnetic at approximately 200 meters. Where is position number 2 located?

 

You would have to have a map and protractor to make this work, but it might be kind of fun.

 

Or you could give two distict terrain features, shoot a resection (a back azimuth from each point) and make that location your cache. I'm just throwing stuff out there. In fact, I may do my new cache this way...we'll see

[+Dersu]

Well, it is not a simple obtuse triangle problem!

Above my math skills, but there is a way to do it without math, I think.

I don't want to post a spoiler here, so I will email you and see how much you want to know.

 

I have flouted the wild, I have followed its lure, fearless. familar, alone; yet the wild must win, and a day will come when I shall be overthrown. By: Robert Service

[+Renegade Knight]

If you can draw a circle in one of your programs and figure out the point of intersection that's the easy way. Otherwise when you draw it out it's triangles and solveing for them.

 

By all means use UTM it's much simpler.

 

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Wherever you go there you are.

[+BugsandMustang]

Unfortunately I do not have any software or good maps (If you all have recommendations I'm all ears, but I may have to hold off till I get a new computer.) In the meantime how is it possible to solve with a mathmatical equation? I have a very powerful calculator yet unforunatel don't know the calculations. I have converted to 2 different UTM's. Once it is in what does 1 UTM = or better yet what does a Mile equal in UTM's so I can use a protractor to draw my circles. I have tried figuring out wiht my GPS (ETrex Vista) if that helps, but they are soo far apart I have to zoom out so far that it is not possible in my mind to get a good reading. Any and all help would be appreciated! Thanks for the help

 

-Paul

[+nincehelser]

I can think of at least two different ways to approach this problem.

 

One way that involves math, but not so much as to strain your brain, is to write a simple spreadsheet program.

 

Basically, find the formula for computing the distance between any two coordinates. Then for any lat-long input, calculate the distance it is to each of the three points. When the distances work out about right, there's your answer. It's not real elegant, but it works.

 

I actually worked this out twice. Once with pure math, but I couldn't find the sign. I thought there must be something wrong with my calculations, so I did it again with the spreadsheet approach. Same basic area...ugh!

 

Turned out that finding the sign itself was a little tricker than I expected. The clues are EVIL!!!!

 

George

[+dwmurphy]

Take a look at this page, it might help you a little.

 

http://www.geocaching.com/seek/cache_details.aspx?ID=54531

 

You must save the start position as a waypoint. then as you go to each waypoint in sequence, you will end up crossing 2 lines of your "bread crumb" trail which will indicate the final cache position.

 

I'm not Lost, my GPS says I'm right here....no over here......no over here.

[+Renegade Knight]

Draw a picture of the problem. If you can solve a triangle or figure out how to solve a triangle you can do the math by hand.

 

The problem has two parts.

 

1) Solving the Triangle's.

2) Using the Triangle information to deterine the UTM coordinates.

 

You can put the UTM into your GPS and then have the GPS convert that into or from your D MM.MMM that you are used too.

 

==============================

Wherever you go there you are.

[dave and jaime]

maybe im not reading the problem right, but couldnt you get a map image that contains the area where the three caches are, and then draw three circles to scale from the cache points and use the intersection as the point where the sign is located. i decrypted the hint and i doubt if there would be anyconfusion as to the sign in question...in looking at the problem i would think that being within a couple hundred meters would be sufficient.

 

if someone who has done this cache sees a flaw here, please explain.

[+nincehelser]

I think the circle method would work fine for this cache. I think the problem some have with that is lack of paper maps and a compass (the circle drawing kind).

 

You're right, from the hints you know the location isn't going to out in the wild. You just have to get "close enough" and look for the right sign.

 

But as I said, the clues are EVIL!!!

 

George

[+BugsandMustang]

George you nailed it on the head. The largest map I have of Austin is Austin proper, and it only has room for one coordinate to be plotted, so drawing a circle does not help out. I have even gone to terrasserver and a few other maps, but it shows up too much detail that if I could draw a circle, it would max out at less than a mile and or I would have to paste 100 maps together. :-( I don't have enough ink... HEHE. I was hoping to utilize math skills (which I lost) and have spent 3-4 days trying to figure it out. Yes a topological map would be very beneficial, but I have not found one on the web nor do the maps I own display a large enough area. All of your help has been very helpful and I will let each and every one of you know what is used ;-) Thanks for all of the support and help!!!

[dave and jaime]

well you wouldnt need to print the map image if you could print a grid with long and lat drawn to scale. when you drew the 3 circles on the grid you could then use an online map and make a pretty good estimate as to where the sign is.

 

ps

couldnt find "The Brambles at Old Settlers", what are the coordinates?

[dave and jaime]

double posting ooops!!

[dave and jaime]

oops!!

[+Bloencustoms]

If you're using mapsource, you could enter the three waypoints, the print the map out, and plot the position manually. Once you know where it is on paper, scroll your pointer to the corresponding point on your screen, and read the coords at the bottom of your map. The program even has a distance tool that might work with a little fiddling around.

 

"I'm not moving my car 'till you get my food right!"

[+Rich in NEPA]

quote:

---

Originally posted by Bugs and Mustang:

This cache has 3 coordinates given to you and then a distance that each cache is from the unknown cache. Given this info it seems that it would be relatively easy to figure out.

---

 

It's easy to solve this problem graphically, and you don't even need a map to determine the coordinates of the unknown waypoint. Simply use a sheet of grid paper and scale the X and Y axes to include all the points. In this example each UTM grid square is 1km by 1km with 100-meter subdivisions. You could also add 10-meter subdivisions if your scale is fine enough. Most GPS receivers will resolve UTM coordinates down to 1 meter. You could also solve this algebraically, but I think this is just as good considering the inherent inaccuracies. Hope this helps.

 

Cheers ...

 

~Rich in NEPA~

 

 

--- A man with a GPS receiver knows where he is; a man with two GPS receivers is never sure. ---

[+Huntnlady]

MATH!TOO MUCH MATH! Why do you think I got this contraption anyway? Now you expect me to do the math?!

 

How would I figure in dead reckoning?

[Kerry.]

It's really not a triangulation problem at all but trileration or best described as Resection by distance and very similar to what GPS does.

 

It's relative easy to do but harder to actually (try to) explain but it's basically the (over determined solution of) intersection of circles. The centres are the given coords and the distances become the respective circle radius.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[BigMike]

Howdy Howdy Howdy. Pretty cool that one of my caches has made it to the discussion formus. I saw a cache like this when I was in Colorado for a trip. I spent a while trying to figure out how to do it with a spreadsheet, but I decided to use a powerful map that i had....my GPS. I plotted the coordinates for the first waypoint. THen I made another waypoint from that point by scrolling up x amount of miles, down, left, and right. SO when I was done, I had 5 waypoints. One in the center, then 4 that formed the qaudrant parts of the circle. I did the same with a second waypoint. After zooming out a bit, I could visually see the approximate intersection of the two circles. So i zoomed into that area and began plotting waypoints along the arc of both circles until they intersected. THen I used the third waypoint to figure out which circle intersection was the correct one. This should get you to within a hundred feet or so. Good luck!

[Duaut]

Now you know why your teachers and parents told that you needed math to live in the real world.

[+BugsandMustang]

Wooho!!! I finally did it! After a week of trying I did it! Help goes out to many. Lets just say that it can be done without paper. There are a number of resources on the net (http://www.jdmcox.com/) Is a beautiful piece of software that Really, REALLY helped out. Plus the help from all that replied helped me sleep last night ;-0. This is such a wonderful community. Note to self, try to learn how to do this with math next time ;-)

[+Zaboombafoo33]

thanks dave kbussiere@telus.net

quote:

---

Originally posted by Rich in NEPA:

quote:

---

Originally posted by Bugs and Mustang:

This cache has 3 coordinates given to you and then a distance that each cache is from the unknown cache. Given this info it seems that it would be relatively easy to figure out.

---

http://img.Groundspeak.com/user/1132_3700.jpg

 

It's easy to solve this problem graphically, and you don't even need a map to determine the coordinates of the unknown waypoint. Simply use a sheet of grid paper and scale the X and Y axes to include all the points. In this example each UTM grid square is _1km by 1km_ with _100-meter subdivisions_. You could also add 10-meter subdivisions if your scale is fine enough. Most GPS receivers will resolve UTM coordinates down to 1 meter. You could also solve this algebraically, but I think this is just as good considering the inherent inaccuracies. Hope this helps.

 

Cheers ...

 

_~Rich in NEPA~_

 

http://img.Groundspeak.com/user/1132_1200.jpg

 

__--- A man with a GPS receiver knows where he is; a man with two GPS receivers is never sure. ---__

---

 

Hard in Easy Out

 

[This message was edited by Zaboombafoo33 on April 16, 2003 at 02:57 PM.]

[+GEO*Trailblazer 1]

Wrong link and double post

[+GEO*Trailblazer 1]

The GPS uses the Spherical Triangle here is a link http://mathworld.wolfram.com/SphericalTriangle.html

 

WHEN ALL ELSE FAILS *GEOTRYAGAIN* http://www.msnusers.com/MissouriTrails