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My $600 Gps Just Got A $60 Helper...


HIPS-meister
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... in the form of a Brunton 8099 compass. $60-odd(USD) at the local map store.

 

The advantage of a compass of this type is that it allows measurements to be accurately taken "from 500 feet away with 1-degree accuracy," which is exactly what I need to do.

 

As a simple example of how I use this tool, I located a cache in Camelback Mountain Park (Phoenix, AZ) then used my compass to check the location as I proceeded to the next cache. From 500 feet away the compass not only told me which boulder concealed the first cache, but which side it was on. Now I turned my attention to the next cache I was searching for. Using the compass once again, I learned exactly where to look for the cache I was about to find, from about 120 feet away. I walked directly to it.

 

The key to my technique, as I have already discussed here in other threads, is distance to the target. If you simply "follow the pointer until you get close" to a cache, you'll soon discover that below a certain distance the GPS can no longer tell you which way to go. You may also have noticed that the bearing changes more and more the closer you get; conversely, the bearing changes very little if you are still far away. So, seeking to use that very fact to my advantage, this is what I do:

  • When the expected location of the cache is in-sight, I stop near a prominent landmark that I expect to be able to see from there, and let my GPS settle for about a minute.
  • Next, I take the bearing from my GPS and dial it in to the compass. I now sight along this bearing to see where I want to go.
  • If the range-to-target is uncertain, I repeat the procedure from one or two locations to either side, triangulating on the target.
  • I walk to the location and take back-bearings (using the south-seeking end of the needle) on the landmarks previously chosen to confirm my exact position. (You can be a few feet off and not know it, and "a few feet" makes a difference.)
  • I now search, within the expected area of uncertainty that the GPS owner would have seen, being confident that I am very close to the spot where he or she once stood.
  • I do not use my GPS at all once I have established the search bearing, except as a guess-timator of distance-traveled if I chose to take only one bearing. (e.g. when I'm pretty sure where the cache will be along the line, but of course don't want to be "surprised.") Next Toy: a bowhunter's optical rangefinder...

This technique not only works; it works very well. When you work from a distance, the "combined uncertainty" that comes from not knowing where the cache is nor where you are .. the combination that leaves you walking in circles .. begins to "cancel out" so that you're left with not much more uncertainty than the original cache-owner had. If you take your time to let your GPS settle, and you take your time with the compass-work, you can (it has happened to me) discover the cache literally by stepping on it.

 

The features of a compass of this type are important: the compass has one free-floating pointer, with a circle, and a separate fixed dial with a slightly wider circle. You sight on the target, then with the mirror turn the dial until the circles coincide, then read your bearing. (Red and blue lines extending across the two dials facilitate back-bearings.) It's a two-step process. And, if you take your time doing it and re-check your work, you'll get 1-degree precision. (Set the magnetic declination to zero degrees since you are working throughout in magnetic bearings.) From a 500-foot distance, I find that the bearing is usually spot-on, or +/- 1-degree or maybe 2. Thus the need for precision.

 

Happy caching! Hope This Helps!

Edited by HIPS-meister
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Your procedure makes a lot of sense. As a small boat navigator who has logged many hours sailing off the Southern New England coast I've often used a similar method to find ATONs (Aids to Navigation, or bouys) in heavy fog. When I get within roughly 200' of the waypoint I watch the distance on my GPS (Garmin 48) but steer with the ship's compass and ignore the GPS bearing. I've found the distance reading stays pretty accurate to within about 50' and at that point it's eyes and ears. And for you who have never experienced New England fog it's about like finding a cache in dense underbrush. Visibility at times can be less than 30'. Of course, caches don't usually have bells or horns on them like some of our ATONs.....

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The key to my technique is to use the GPS pointer. It points at this rock or that tree and if it's a big enough rock it will tell me which side it's on.

 

Of course the pointer doesn't help much when you get close but that's when you are supposed to be looking.

 

I really, need to see someone who uses a compass to see what the heck they are doing with it, because I have a hard time figuring out why one is needed at all to find a cache.

 

There seems to be two kinds of cachers. Those who use a compass and those who don't and they don't really seem to see how the other functions. Yet both find caches. :ph34r:

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A compass can be useful, especially if you're in an area with poor reception, but a short distance away you're got a clear view of the sky.

 

But if you can get good reception the whole time, you can skip the time-consuming actions of sighting and triangulation. How? Ignore the swinging arrow, and look at the actual coordinates. With a little bit of practice, you'll learn to walk in the proper direction to make the numbers change the way you want them to. Once you make your GPS coordinates agree with the cache coordinates, start searching with the knowledge that this is more accurate than sighting with a compass from 50 feet away (think about for a second, and you'll see why).

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No, I don't intend to resurrect that other discussion, but I can .. very briefly .. recap why this technique works.

 

The key to understanding this improvement is to carefully consider all of the implications of the fact that there are two, not just one, things that you do not know:

  • You do not know exactly where the cache is (of course), nor the error experienced by the cache-owner, and...
  • You do not know exactly where you are.

Both of these figures may be presented to you as "exact" numbers, but in fact there is a region of "possible points on earth" that could produce the same result. The size of this region varies according to the usual factors... sattelite position, clouds, tree cover, and so-on. It's what gives us a sport, of course. (Most graphic GPSes will show it to you with a circle drawn on the screen.) But that's only one of the regions: there are two. Not one... two! Two! Two! Two! :cry:

 

Given that you cannot know either of these two locations with certainty, even though the GPS may pretend that you do, when you are close to the cache those two sources of error tend to combine into a larger region. Maybe a much larger region: an eighteen-foot circle could be 3 x 18 = 54 feet wide. Furthermore, when the two circles overlap, your bearing-to-target could be any number at all, and you have no way to know which one is right. That "little pointer" you're relying on, literally does not know which way to go, so it may lead you around in circles. (Or it may not: it may be perfectly accurate. Such is the nature of probability problems. The trick is, you don't know for sure until you find the cache. :huh: )

 

When the two regions are hundreds of feet apart, there is one thing that you can know with great certainty: the bearing shown on your GPS screen will be very close to "the (unknowable) 'right' answer." If you imagine a box that's eighteen feet wide and four hundred feet long, there's one thing you can say about that box: it's very narrow! If you were to shine a flashlight down the length of it, you couldn't twist your hand too far to the left or to the right or the beam of light wouldn't come out the other end (without bouncing off the walls a time or two).

 

At the yonder end of that box, yep, there's still a region and it's still eighteen feet wide. (You can't ever do anything about that, unless you are a surveyor.) But it's not "eighteen plus eighteen plus another eighteen" feet wide. And this can be a really, really big, really helpful difference out in the field.

 

[Note: GPSes are very smart. If they've had time to collect hundreds of data points and they see that you are walking in a straight-line bearing, they're smart enough to assume .. at least for a while .. that you're probably still doing so. Therefore a "current position" value that's close to that expected location is more likely to be correct than an outlier, and it's given more weight in the computer's calculations. You can even see your GPS continuing to plot your location when you've driven into a tunnel... pure guesswork since the data-stream has been cut off. If you walk straight toward your target, that plays to your advantage. But if you get stumped and start to wander around... so does your GPS.]

 

All that I can say is... it does work. It does make a difference, and I simply encourage you to try it. There may be plenty of situations where it isn't necessary and a few evil ones where it perhaps-deliberately is made difficult-to-apply, :ph34r:(Who, me?) but when you need it, remember it and try it. 'Nuff said.

Edited by HIPS-meister
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All well and good, if  all the coords are dead on, or close. But there is a well known error in the handhelds we use.  and that could throw you off by quite a bit at times.  :lol:

"A well known error in the handhelds <you> use?" :huh: Well, you've certainly picqued my curiosity, and I daresay I'm not the only one. Care to elaborate?

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All well and good, if  all the coords are dead on, or close. But there is a well known error in the handhelds we use.  and that could throw you off by quite a bit at times.  :lol:

"A well known error in the handhelds <you> use?" :huh: Well, you've certainly picqued my curiosity, and I daresay I'm not the only one. Care to elaborate?

On a good day, with PERFECT reception, a consumer GPS is only accurate to 9-12ft. Most likely it will be closer to 15ft or more. The accuracy reading your GPS gives you is only an estimate of how accurate it thinks it might be; since it has no other reference point to compare to, your GPS cant even be sure. So even if your display shows 15ft accuracy you COULD really be 30ft off.

Now.... take that inaccuracy of the hider's GPS, and factor in the inaccuracy of the seeker's GPS. Say the hider's GPS was 15ft off to the south when he hid it. When you go looking for the cache, your GPS is reading 20ft off to the north (this isn't a fixed error either, it changes with your view of the satellites). This means *IF* you can even actually zero your GPS, you're still going to actually be 35ft away from the cache.

Even if your had a $10,000 centimeter accuracy GPS; the cache coords you are seeking were still posted with a consumer GPS, so you might STILL be 10-20ft off.

A compass can help a lot in finding the general area of a cache, especially with a GPS that doesn't have a built in compass; but being able to pinpoint what side of a boulder the cache is hidden on is just pure luck.

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The supplier of Chrysler original parts and accessories pretty much hit the nail on the head. The fallacy is that your GPSr is somehow more accurate when you're at a distance from the cache, just because the bearing reading is nice and steady. But that's only do to the rounding that comes into play the further away you are from the cache.

 

The main flaw is this: "When the two regions are hundreds of feet apart, there is one thing that you can know with great certainty: the bearing shown on your GPS screen will be very close to "the (unknowable) 'right' answer." This isn't true, because the further apart the two points are, the less precise the displayed bearing reading becomes, due to rounding.

Edited by Prime Suspect
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Amen, Vagabond, well said. :rolleyes: I admit i am relatively new to this delightful sport, but i find great pleasure in the hunt. if i could go directly to the cache with no trouble time after time it would take away from the sport and the thrill of finding the darn thing after some pleasureable work. my gps gets me close enough to find it time after time and as far as dnf's, most of them were stolen or removed by the owner and not reported as such.

 

love this thing we do.

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Let's assume for a minute that we can get incredibly accurate readings down to a few feet. Why don't we just put a tracking beacon on the cache and a little strobe so you don't miss it when you get close? Isn't the "hunt" the most interesting part of the find? If the GPS gets me in a 30' circle, I am happy. I will do the rest from there.

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I agree with the use of the compass. Being an EXPERT with a paper map and compass may not help find the cache sooner, but it may well help you find yourself and your way out if need be. Having spend many years in SAR, I've often looked for the "experienced woodsman" whose batteries had died on his GPS and cell phone. The type of compass you choose is also important, if it is designed to clip onto your zipper, it is a zipper pull not a compass. Buy a proper compass, spend $60 to $100, and then learn to use it. Check out local SAR groups, orienteering clubs or your local college and take a night course. Think of it as life insurance.

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No, I don't intend to resurrect that other discussion, but I can .. very briefly .. recap why this technique works.

It doesn't work. There are so many things wrong with the argument I wouldn't even know where to begin.

 

So I won't. I will simply make the following observation:

 

The math is wrong.

 

Math is not something where everyone's opinion is equal; there are right and wrong answers. In this case, HIPSMeister is wrong. Period.

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We never leave home without our IRIS 50:

Irrespective of how well that works as a compass, It's way cool looking! Looks like a found UFO artifact. Does it have a "stun" setting?

It's not only cool-looking, but also perfect for our outdoor (mainly yachting) needs. Precise, rugged, and readable in the dark 'cause it's sort of luminiscent...

 

BS/2

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Like I said, I'm not going to resurrect the topic from the other thread, and I see no particular reason to belabor that point despite the abundance of gauntlets that are being thrown down here. Get out there in the field, away from all those silly light-posts, and try it for yourself.

Edited by HIPS-meister
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I won't debate the math either.

 

Having not seen the last thread, I thought I would share my hightly modified version of this that also happens to be quicker too.

 

At the 500 ft point (or basically when my distances shift from .1mi to ft) I start taking bearings off the pointer with the idea to focus in on some distant point which I estimate to be that distance (takes some practice getting this about right and also assumes you can even see that far in proper direction). I'll then as I walk off-axis (or remain on a trail or some other means of avoiding the straight on bushwack), but still in the general direction of the cache (depending on the terrain of course) and take another look at the pointer at perhaps the ~250-200 ft point and see if my focus point is still the same. Conditions permitting, I try to use as close to a straight line approach for the last ~150 ft and really only monitor the distance. When I hit ~30 ft I stop and put the GPS down to settle and start looking around in the immediate vicinity at likely hiding spots. If this doesn't seem to be working I'll go back and look at the GPS again and note the distance reading and factor that into the equation.

 

This methodology accomplishes a quick running fix of sorts on the cache without getting bogged down in taking sightings. It also gets your brain engaged somewhat into figuring out where the cache might be without blindly following the needle. Finally, it takes into account the reality noted above that in many situations the cache is not going to be where your GPS says it should be.

 

Btw, the 30ft stop and drop figure is what just works for me. I think it's a reflection of the fact that the GPS is always catching up to some degree if you are on the move.

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Hmm,, If that works for you fine.. Me? I rely on dead reckoning. When I get close to a cache, the compass in the GPSr starts rotating every which way. When that starts happening, I back up until the needle stabilizes. Then I get my bearing and distance to the target and direction while standing still. The human mind is a wonderful thing... I can estimate pretty accurately.. or, if I have to step off the distance in a straight line to the target, where the cache is likely located. The thrill of discovery is a good feeling of accomplishment, when I start looking for the cache after stepping off the remaining distance, I find it by my own presence of mind.

 

Seems to me that you are taking your mind out of the equation and relying on machinery to do the whole job. What would happen if you were up in the woods, lost, hurt, and needed to move to get rescued. Would all that machinery do you any good if it were lost, broken or the batteries dead?

 

I will rely on my own facilities, with the exception of the GPS as the only piece of machinery I use. To make geocaching any more technically sanitary is to take the fun out of it in my humble opinion. :huh:

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I have found that near-constant reception helps me more than anything.

 

I lucked into this solution due to my handicap - I have one leg and geocache on crutches, thus both hands are occupied when walking, and often when just standing, if on uneven terrain.

 

This led me to purchase a Magellan Dashboard Mount, a $19 mount that has a clamp for my Meridian Platinum and a suction cup.

 

I took a couple of straightened and twisted coat-hangers and made a stiff necklace that attaches to either side of the mount and loops around my neck, alowing the suction cup to sit flat and centered on my chest.

 

I wrapped the coat hangers with tape, I will use heat-shrink tubing next time for zero-maintenance.

 

The dash mount base swivels, allowing me to fold it down against my belly when not in use, and building in some flexibility for when I fall (often!).

 

This gives me a hands-free GPS that is always on plane with the horizon and always pointed dead ahead of me.

 

It works in the car or out, works in woodland or urban areas where signal is intermittent, and more often than not allows me to go directly to the cache area.

 

I can see the screen with a quick downward glance and can work the GPS keys with either hand without moving the GPS.

 

A geocacher saw this lashup in Pennsylvania when I was caching up there a couple of years ago, copied it and started selling them on the internet - don't know how well he's doing with it, but you might run a search for him if you don't want to build one yourself.

 

While my caching buddies are moving their GPS in and out of pockets, bags, etc. and walking this way and that, turning their bodies in circles, I do things in straight lines with near-constant signal and am regularly able to be the first in a group to either make the find or get within a few feet.

 

And oh yeah - dead-reckoning is always part of it - I watch my electronic compass (wouldn't own a GPS without one) and look ahead to where it's pointing as I approach - then, when the GPS goes nuts I have an object to focus on that more often than not will be close - geoaching friends are always surprised when I say from 200' away that "It's by that fencepost" or "It's in those rocks", and it is.

 

Good luck,

Ed

Edited by TheAlabamaRambler
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I lucked into this solution due to my handicap - I have one leg and geocache on crutches, thus both hands are occupied when walking, and often when just standing, if on uneven terrain.

Wow ! Next time I feel like complaining about coordinates 15 feet off, I shall silently take my hat off to you !

 

I'm trying to visualise your solution. Sounds a bit like what a musician who plays guitar and harmonica would use, to keep the harmonica in place. My main problem would be finding space for the magnifying glass - unless the GPSr was down by my stomach, my aging eyes wouldn't be able to focus on it !

 

Nick

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UGH not this again. HERE IT IS AGAIN. Your GPSr will only point to where it caclulates the waypoint coordinates is if it is off by 50 feet then your bearing will be off by 50 feet NO MATTER HOW FAR AWAY YOU ARE. I guess you feel you have come up with a clever method but it is not. Just like WORDSTAR let it die. But I am glad you feel it works for you. Just wait till your looking in a tree or rock pile that is 50 feet from where the actual cache is. We do not put down this method because we hate you but because you are promoting a FALSE premise.

cheers

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I am glad to learn I have been doing it wrong all this time. Now by using this method I will be able to find some caches

 

Gawd, me too! After 1100 LOGGED caches and at least 200 I didn't log it's comforting to know I don't have to follow that darn GPS any more!

 

Wish I had known this long ago!

 

Ya'll got any tips on how to get rich quick from home with no investment or work? That'd help me a lot too.

 

Ed

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I virtually always take a couple compasses with me when I head out into the outdoors, and if it’s very far off the beaten path I generally have a “quad” map with me as well. For caching, I love the ones on mountainsides, or that are otherwise hard to get to. I often use a sighting compass to triangulate and get a general idea of where I’m trying to get to so I can pick a route that looks like it might work. (We won’t discuss my skills a picking a good route from a distance) I also use it sometimes near the cache if it’s in an area where GPS reception is bad enough to make it worthwhile to seek out good reception. As for being more accurate, everything I’ve seen when trying the concept in the field would indicate to me that it induces even more error if anything. (Provided you have reasonable GPS reception near the cache of course). I’ve found it’s pretty rare when the GPS doesn’t guide me right up to ground zero with little if any effort. I must admit I got a bit of a kick out of the other thread on this subject where it was implied you could triangulate with a 1:24,000 scale map and a compass and identify the location of the cache to within a meter. Now that, would be a navigational feat.

 

Regarding my compass preference, I’ve found the multifunction units a little awkward to use for both map work and sighting use, hence, I prefer a dedicated sighting compass and separate base plate unit for my map work. The sighting compass I take most of the time is my Sunnuto KB20 vista, as I find it very light, quick, easy to use, and precise.

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UGH not this again. HERE IT IS AGAIN. Your GPSr will only point to where it caclulates the waypoint coordinates is if it is off by 50 feet then your bearing will be off by 50 feet NO MATTER HOW FAR AWAY YOU ARE. I guess you feel you have come up with a clever method but it is not. Just like WORDSTAR let it die. But I am glad you feel it works for you. Just wait till your looking in a tree or rock pile that is 50 feet from where the actual cache is. We do not put down this method because we hate you but because you are promoting a FALSE premise.

cheers

 

Cheers is right.. Applause also.. :)

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Sounds a bit like what a musician who plays guitar and harmonica would use, to keep the harmonica in place.

that's exactly what i was thinking! a harmonica "bracket" or something similar. kudos to The AR for finding a cool solution. (and ditto on the electronic compass! :) )

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You want to hear something incredibly counter-intuitive?

 

Let's say that the GPS does calculate the cache position to be "off by 50 feet." It's perfectly possible for that to happen, say with an accuracy circle of 25 feet and a DOP of 2.0. There are things that you can do to improve this (like continuous reception, otherwise known as letting your GPS "settle down," but it's perfectly possible for the position fix to be "off by 50 feet."

 

The counter-intuitive thing is that ... the farther away you are from the cache, the less that 50-foot discrepancy matters. No, it won't get you closer than the accuracy of the original reading (which, if really off by 50 feet, ought to be reported to and adjusted by the owner), but it will reduce the effective impact of that discrepancy upon your search time.

 

By and large, though, cache owners are very careful in their work, and after a few successful finds, the odds of the coordinates "still" being seriously off are pretty darned small. Real geocachers don't blame the cache-owner nor their equipment. :D

 

I didn't open up this thread over here to repeat the other one, which is now closed. The technique works, period. The mathematical reasons behind it may not be obvious (probability problems usually aren't), but they are quite sound.

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...The counter-intuitive thing is that ... the farther away you are from the cache, the less that 50-foot discrepancy matters...

 

Except for one thing. When you read the bearing, a 1/2 degree error at 500 feet magnifies the eror at the other end so an error of 2% at 100 feet from the cache is more accurate at the cache location. It's a simple geometry (but don't ask me to do the numbers).

 

One variation of your method that I came up with that could help is to project a waypoint let's say 5000 meters past the cache location when you are let's say 100 meters from the cache., Then when you walk down the 100 meters, you'll be at the cache location at 5000 meters to go without the "dancing bee" arrow movements since the GPS is still looking 5000 meters further on for the wayppoint.

 

Try that and see how it works.

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...And oh yeah - dead-reckoning is always part of it - I watch my electronic compass (wouldn't own a GPS without one) and look ahead to where it's pointing as I approach - then, when the GPS goes nuts I have an object to focus on that more often than not will be close - geoaching friends are always surprised when I say from 200' away that "It's by that fencepost" or "It's in those rocks", and it is....

We make a betting game out of that aspect. Who's right from the farthest away. It can be hard at half a mile but by the time we hit a quarter mile someone usually gets it. That is if we can see that far in the terrain.

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Here we go again. Mopar makes an excellent argument why this will not work in a lot of cases. I also made a case in the last thread about it and noticed no one attempted to refute the logic.

It's a function of probability. My GPS is accurate to 20' normally. Or less. Theirs is about the same. On average using Monte Carlo simulations (meaning I look at my GPS when I'm standing at the cache) it's within 20' 90% of the time.

 

Most of the time it doesn't matter that their 20' and my 20' can add up to 40'. Sometimes it will but that's limited to 10% of the time. What matters is that unless something is completely FUBAR (and that happens) it won't be over 40' total.

 

So 90% of the time you can tell which rock, which light pole, which fence post, which tree, or which sprinkerl head the cache is at. Assuming that within the 20' there isn't a tree, rock, sprinkler head, light pole and fence post. To tell which side of the rock would take a large rock.

 

Since I don't know how to use a compass to enhance a GPS I'll focus on using a map. Reading the map to take bearing has error, the bearing you shoot with the compass has error and your own eyeballs have error reading the bearing. I don't know what it adds up to but odds are it's about the same as shooting that bearing to the cache off the GPS pointer.

 

All I can gather is that this is all personal preference because we all seem to be finding caches well enough.

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The technique works, period. The mathematical reasons behind it may not be obvious (probability problems usually aren't), but they are quite sound.

The technique does not work, period. The math is unequivocal. And what is especially funny, given your invoation of statistics, is that the math has nothing to do with statistics! It's quite simple geometry; anybody with a year of high-school geometry could prove your assertion wrong.

 

Please stop repeating misinformation in the forums. Thank you.

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The technique works, period.  The mathematical reasons behind it may not be obvious (probability problems usually aren't), but they are quite sound.

The technique does not work, period. The math is unequivocal. And what is especially funny, given your invoation of statistics, is that the math has nothing to do with statistics! It's quite simple geometry; anybody with a year of high-school geometry could prove your assertion wrong.

 

:grin: Ahh, there's the rub: This is not a geometry problem. It has very little if anything to do with geometry. It is a probability problem.

 

Let's dump the language of geometry. Let's not call it "bearings." Let's call it "frozbits." Your meter tells you which frozbit to take to get to where you want to go. You punch in a frozbit number and a distance, push the magic yellow button, Scotty activates the Transporter on the starship Enterprise, and you wind up "there." If you are very close to the cache then in the worst case there are 360 possible frozbit-numbers that you could see on your machine; any one of which could be equally right. (Scotty will start complaining about strained dilithium-crystals soon...) If you are thirty feet away there are about 90 possible frozbits. (That Starbucks is starting to sound really good.) From five hundred feet away, there are only four or five possible frozbit numbers that you could see on your machine. (And as a free bonus, now one of those four is considerably more probable than the others, if you let your frozbit-machine settle down.)

 

Why, then, is it better to be far away? Because your odds of getting it right are now one in four, instead of one in three-sixty. Whether you now use that information by pressing a yellow button, or by taking a compass bearing and going for a walk, it all works out the same! :(

 

Why is this not actually a geometry problem? Because: geometry has to do with points. It is not the mathematics of regions. Geometry must have at least one known point. Your GPS pretends that you are precisely at the point where it thinks it is, and that the cache is precisely where the owner said it was .. thus two points .. and it gives you a bearing between those two points as if they were correct, but knowing that it isn't. What the GPS gives you is therefore, "a bearing plus or minus x degrees," and the $99.99 question is: how large is x? More to the point: what can we do, in the field, to minimize the possible range of "x?" By moving far away, I reduced x from 360 to 4. To make that work, I used a $60 compass.

 

Surely you cannot argue with me that:

  • if your GPS is not precisely knowledgeable of your position, (as we have agreed)...
  • it necessarily follows that: ...
  • it cannot be precisely knowledgeable about your bearing to any other point either, whether that point is known or is estimated.
  • And it certainly cannot be precisely knowledgeable about the proper bearing if both points are estimates!

If we cannot agree on this, truly we cannot agree on any thing. :rolleyes:

 

Being no more able than anyone else to alter these bullet-points, I arranged myself in space to reduce the influence of these inevitable sources of error. I like having four ways to go instead of more than three hundred.

Edited by HIPS-meister
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