georapper Posted January 26, 2003 Share Posted January 26, 2003 what does anyone think about a multicache that involves giving 3 distances from known caches and let the finders solve a system of linear equations to find the location of the 4th cache, this would involve elevation too? Quote Link to comment
+georgeandmary Posted January 26, 2003 Share Posted January 26, 2003 It's been done, it's fun, but why do you NEED elevation? george Pedal until your legs cramp up and then pedal some more. Quote Link to comment
georapper Posted January 26, 2003 Author Share Posted January 26, 2003 LL are 2 dimensional, by adding the third dimension, height, just adds 1 more equation to the mix. elevation will only be useful if it is at least 20-30% of the total distance given from the known cache to the unknown cache. yeah, this type of multicache has to be thought out carefully, otherwise if the LL distances are more than roughly 5X the elevation deviation, the error introduced by the elevation will be very small and it could be solved using 2D system, 2 equations in two unknowns. i have been doing some field tests in my local area to determine the elevation error. if the error is more than 20-30%, then adding elevation will be unreliable and i won't be able to proceed with the 3rd variable, i'll have to settle for 2D. Quote Link to comment
+georgeandmary Posted January 26, 2003 Share Posted January 26, 2003 Don't forget the surface is curved, and depending on how far away the distances are it can make a difference. george Pedal until your legs cramp up and then pedal some more. Quote Link to comment
+fizzymagic Posted January 26, 2003 Share Posted January 26, 2003 Three points don't give a unique elevation; that's why your GPS doesn't show elevation until you get 4 satellites. Two points also don't give a unique latitude/longitude. Just because there are n equations doesn't mean that you can uniquely solve for n variables. The definitive cache of this type is Disquoi's You Are The GPS, which I emulated in my own Magic Trig cache. Quote Link to comment
+writer Posted January 27, 2003 Share Posted January 27, 2003 Remember that a GPSr, even with a lock on four satellites, can only guarantee you an elevation within 75 feet or so of what it "should" be. Furthermore, the receiver assumes an ellipsoid shape, and not the more complex geoid that represents the average global sea level. The two can differ by hundreds of feet one way or the other. If you are going to provide equations, you should direct cachers to have a barometric-pressure altimeter and remind them to calibrate it before going on the hunt. But even those are only going to be accurate to within 10 feet. So it might be safer to have people read an altitude off a map, where they will all get the same number. Otherwise, how could anyone know that they would get the same solution as you? Quote Link to comment
+Prime Suspect Posted January 27, 2003 Share Posted January 27, 2003 quote:Originally posted by fizzymagic:Three points don't give a unique elevation; that's why your GPS doesn't show elevation until you get 4 satellites. Not true. Consumer GPSs assume that you're probably not in the space shuttle, and so can eliminate one of the two possible positions when only 3 satellites are available. Quote Link to comment
+parkrrrr Posted January 27, 2003 Share Posted January 27, 2003 quote:Originally posted by Prime Suspect: quote:Originally posted by fizzymagic:Three points don't give a unique elevation; that's why your GPS doesn't show elevation until you get 4 satellites. Not true. Consumer GPSs assume that you're probably not in the space shuttle, and so can eliminate one of the two possible positions when only 3 satellites are available. Not not true. All GPS receivers (including consumer receivers) need an accurate time reference, too, so they can't get a 3D fix (4D, including time) without 4 satellites locked. You can get a so-called "2D" fix without the fourth satellite, but it's very approximate (it makes assumptions about elevation that are unlikely to be true unless you just lose the 3D fix for a short time.) Quote Link to comment
georapper Posted January 27, 2003 Author Share Posted January 27, 2003 i've solved a 2D with 3 positions, i can solve a 3D with 3 positions. yeah, there are certain assumptions but it works so i'll go with it. if elevation accuracy is a problem, then it won't work. i'm talking about very short distances, on the order of less than 0.2 miles. the curvature of the earth is a very small error at these small distances. Quote Link to comment
+bigredmed Posted January 27, 2003 Share Posted January 27, 2003 I will give the simple reply that math caches are not much fun for me and I would just skip it. By appointment to the Court of HRM Queen Mikki I. Quote Link to comment
+parkrrrr Posted January 27, 2003 Share Posted January 27, 2003 By the way, it wouldn't be a system of linear equations in any case. The distance calculation involves squares and square roots, which aren't linear. Quote Link to comment
+Prime Suspect Posted January 27, 2003 Share Posted January 27, 2003 quote:Originally posted by Warm Fuzzies - Fuzzy:Not not true. All GPS receivers (including consumer receivers) need an accurate time reference, too, so they can't get a 3D fix (4D, including time) without 4 satellites locked. Absolutly right. I was reading "elevation" but my brain was telling me "position". Hey, it was very late... Quote Link to comment
+CoronaKid Posted January 27, 2003 Share Posted January 27, 2003 ...I avoid the math ones. I vowed I would never do another useless math equation once I finished advanced calculus in college. Besides, I already feel nerdy enough just wearing a GPS device. Why add another element of nerdiness? --CoronaKid Quote Link to comment
dsandbro Posted January 27, 2003 Share Posted January 27, 2003 The rough rule of thumb is the vertical positional error is 3x the horizontal. Like most 'rules of thumb' individuals will experience situations where that is not true, but is sufficiently accurate for generalizations. ======================================== Friends don't let Friends geocache drunk. Quote Link to comment
dsandbro Posted January 27, 2003 Share Posted January 27, 2003 More important is WHY? I geocache because it's an excuse to get outside and hike around. If I want to do more math I'll just stay at work. ======================================== Friends don't let Friends geocache drunk. Quote Link to comment
+georgeandmary Posted January 27, 2003 Share Posted January 27, 2003 quote:Originally posted by Dave54:More important is WHY? I geocache because it's an excuse to get outside and hike around. If I want to do more math I'll just stay at work. Do you hunt caches harder than 1/1? Why? george Pedal until your legs cramp up and then pedal some more. Quote Link to comment
georapper Posted January 27, 2003 Author Share Posted January 27, 2003 just had an idea. if i give the location in 2D for 3 points, then at each point i will provide a distance to the 4th unknown point and provide an elevation error correction factor. that's all elevation is, a correction factor for a 2D surface, that's redundant, i know. by providing a "correction foctor", i don't have make the distance between the 4th unknown point and the 3 known points short and small relative to elevation. this way, i can provide any distance i want to the 4th unknown point and make up any number i want as the correction factor. i don't have to make a short multicache and i don't have to worry about elevation errors between gpsr's. this is great, i'm excited. by the way, this is a very simple linear system of 3 equations. the quadratic terms cancel out early in the equating process and you are left with 3 very simple linear equations. i will describe how to do this on the webpage for the multicache. by the time i'm done describing how to do this, if someone can't do it in a few minutes, what's the purpose of going to school? just to have something to forget? this is what i do for leisure. Quote Link to comment
+sbukosky Posted January 27, 2003 Share Posted January 27, 2003 I'm not certain where you are going with this. Cheesehead Dave made one called ''Gee, I'm a Tree'' which involved triangulation math. I loved it and plan to do one like it in a different area. My point though, is that only a small number of people took the time to do it. But, its a big world so go for it. Steve Bukosky N9BGH Waukesha Wisconsin Quote Link to comment
+nincehelser Posted January 27, 2003 Share Posted January 27, 2003 Those with math anxiety can always ask someone for a little help. George Quote Link to comment
+Doc Ott Posted January 28, 2003 Share Posted January 28, 2003 quote:Originally posted by Dave54:More important is WHY? I geocache because it's an excuse to get outside and hike around. If I want to do more math I'll just stay at work. You just stick to your 1/1 caches there bub. But understand that some of us like the outdoors AND math. We are not freaks either, we are geeks. Nothing burns me more than people who put down people who excel at different things than themselves. In regards to the original post, do the calculation with and without the elevation correction. Do you get the same Lat/lon either way? Probably, so who cares what the elevation is? When you are actually at the cache there is one possible elevation, right? If you plan on putting it in a tree (and getting the exact elevation above the ground) then you have to have a hyper accurate lock, or put it in a 200' tree I did a cache (http://www.geocaching.com/seek/cache_details.aspx?ID=40996) that requires very long distance/bearing calculations (>800 miles for one of them) that you must use ugly great circle math. I enjoy doing these tyoes of caches almost as must as I enjoy making them. -Doc Ott A day without thermonuclear fusion is like a day without sunshine. Quote Link to comment
+Smitherington Posted January 28, 2003 Share Posted January 28, 2003 Doc Ott's cache with long distance/bearing calculations was the one I had most fun with yet. I was able to be the first finder. But I didn't do any calculations. I just used my map program and the distance/bearing feature. Thanks Doc for the great cache!! Quote Link to comment
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