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Geocachers' Gpsrs


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Partly as a result of Garmin's misnomer of the Figure of Merit which they wrongly label as "Accuracy", there is a lot of confusion amongst many geocachers who don't quite know what the accuracy of a typical geocacher's GPSr actually is.

 

In the science of position-fixing the word "accuracy" has a very particular meaning. It is defined as the degreee of closeness to the true value. If your GPSr knew the true value of the Lat/Long of its antenna, it would surely tell you, and the "accuracy" figure would always be zero.

 

So, how do we measure the accuracy of a typical geocacher's GPSr? What we need is a few dozen volunteers to log their measured position at a known point such as a trig pillar. Thanks to the existence of the Snowdon virt, we already have just such a dataset.

 

I wrote a little macro to scrape the Lat/Long data from the cachelogs on the cachepage and paste them into a spreadsheet to do some analysis. The results are most instructive and very interesting.

 

First I converted the grid co-ords shown on the TrigpointingUK.com website for this trig pillar into WGS Lat/Long using the rigorous polynomial method to derive the True value, against which all observations are compared to measure the actual accuracy of the GPS readings.

 

The True value of the trigpoint is: 53° 04.1093'N 4° 04.5738'W

 

Taking a straightforward average of all 74 valid logs made by the geocaching community, without any filtering or weighting or applying any of the least squares or other other processing techniques to refine the fix, the crude average comes to 53° 04.1093'N 4° 04.5741'W, which is just 0.37m (14½ inches, in old money) from the stated True value. That is a remarkable accuracy and is actually smaller than the single metre precision of the listed co-ordinates of the adopted "true" position. Well done, geocachers! It is a magnificent demonstration of the power of GPS averaging when measuring a position.

 

Much more important than the accuracy of the overall average is the accuracy of individual fixes. After all, we never have the luxury of taking 74 separate fixes with dozens of different GPSrs on dozens of different days when geocaching. What matters most is the average error.

 

In this sample the average of all 74 fix errors is 3.18 metres. 56.8% of fixes were that good or better.

 

There are many ways of mathematically defining the spread of a cluster of datapoints such as position-fixing data. The one most favoured by the military when assessing the accuracy of weapons systems such as bombs, missiles and gunfire is the Circular Error Probable. CEP is defined as the radius of a circle within which 50% of the shots land. The CEP of our 74 geocachers' data is 2.83m. CEP does nothing to describe the other 50%, so statisticians, surveyors and other scientists prefer another measure. One favoured measure is called Standard Deviation or sigma. The sigma value of our Snowdon sample is 3.41m.

 

All of these various measures of accuracy seem to be telling us the same thing: the accuracy of the fixes is typically around three or four metres.

 

40% of fixes were better than 2m

74% of fixes were better than 4m

91% of fixes were better than 6m

96% of fixes were better than 8m

 

Let's put that actual accuracy into context. The Ordnance Survey themselves only claim an absolute accuracy of <± 2.8 metres for the co-ordinates on their rural and urban 1:2,500 sheets and an absolute accuracy of <± 4.1 metres in mountain and moorland environments on their 1:10,000 sheets.

 

The precision of the GC.com format at this location is just 2.16m, so our average accuracy of 3.18 metres is quite remarkable.

 

Well done, geocachers!

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That is impressive.

I'd like to see an equivalent test done under tree cover, say, in different seasons. After all, poor GPS fix is my favourite excuse in DNF logs, and I don't want to give that one up without a fight.

Yes, that is impressive indeed.

 

Things should get better under tree cover with the next generation of GPSR's using the SIRFSTAR III chipsets, which can track much weaker signals and therefore maintain a fix long after traditional receivers have lost it. Having said that, if it's too weak, its accuracy is of course compromised to varying degrees.

 

We use a PDA and therefore can upgrade the GPS part, and our SIRFSTAR III Bluetooth mouse has proved amazing under the deepest of cover so far (even in a closed glovebox in the car!!)

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I'd like to see an equivalent test done under tree cover

One of several reasons why I think this sample is very representative of typical geocachers using typical GPSrs in typical conditions is that the Snowdon summit actually emulates tree cover, despite a total absence of trees.

 

The satellites which contribute most to a position fix (Lat/Long) are the ones lowest down in the sky. The ones above about 60° from the horizon are good for altitude measurements, but in geocaching we don't care about the indicated altitude.

 

Because there are usually so many people clustered around the trigpoint at the summit of Snowdon, and because the radio waves of the frequency used by GPS cannot pass through human bodies, the receiving conditions for the GPSrs used in this sample actually emulate very dense tree cover.

 

Cheers, The Forester

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I'd like to see an equivalent test done under tree cover

One of several reasons why I think this sample is very representative of typical geocachers using typical GPSrs in typical conditions is that the Snowdon summit actually emulates tree cover, despite a total absence of trees.

 

The satellites which contribute most to a position fix (Lat/Long) are the ones lowest down in the sky. The ones above about 60° from the horizon are good for altitude measurements, but in geocaching we don't care about the indicated altitude.

 

Because there are usually so many people clustered around the trigpoint at the summit of Snowdon, and because the radio waves of the frequency used by GPS cannot pass through human bodies, the receiving conditions for the GPSrs used in this sample actually emulate very dense tree cover.

 

Cheers, The Forester

I'm no expert myself, but wouldn't signal reflection play a part here - even if it can't travel through the human body, it could potentially bounce off various objects stationed around about? This must be how our new SIRF III GPS can achieve a signal in 'spooky' conditions where it seems there is no way it could possibly get one?

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Taking a straightforward average of all 74 valid logs made by the geocaching community

I've seen this mentioned a few times and heard people talk about it loads of times but nobody has been able to give me a straight answer. So, here goes again :(

 

How do you obtain an average when using coords? A worked example would be great

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You say that 96 per cent of fixes were better than 8 metres. Just out of curiosity, how bad were the other 4 per cent? :( (Well, someone had to ask... :( )

Data lying under the tails of the distribution curve should never be ignored, even though they are not representative of the whole.

 

The unrepresentative fixes were 8.63m, 9.26, and 10.38m out.

 

That's as bad as it gets.

 

It's not bad.

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is there an explanation in lamens terms for what you are talking about?

Other than the fact I got the jist that you are talking about accuracy of a GPS, I really haven't got a scoob on what all those big words and explanations are!

Sometimes it's not really possible to make things much more simple, and mathematics is often one of those times (or things).

 

What Forester is telling us, is that there are many ways to define words like "average" and "accuracy" (in the latter case, formally, there's one right way and several wrong ways!), and that although they all produce different results, they basically show that GPS technology is - on average (!) - pretty accurate (!).

 

PS: I just worked out what "lamens" means (having seen it used by two posters in as many days now). I guess you mean "in layman's terms".

:(

Edited by sTeamTraen
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just devilishly wondering which turns out to be most accurate in practice :(

i guess weather conditions will play a big part in this....

 

i dont know if this is relevant or not but i get a better accuracy using metric readings rather than good old feet and inches.

 

B.

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Nice work! and surprisingly accurate.

 

The cynic in me is forced to ask the following questions...

 

How is the OS coordinate for the trig point derived?

Presumably it is determined using some form of GPSr?

If so are we not just testing that a GPSr reads the same as another GPSr?

 

Please note, the above questions are asked out of a genuine sense of curiosity, I'm not trying to be difficult, honest.... :(

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If so are we not just testing that a GPSr reads the same as another GPSr?

 

Surely that is what we are trying to do in Geocaching. Comparing the reading of our GPSr with that of the cache owner's GPSr at the time he set the cache

 

The other thing arising from this is that the error could be up to twice the accuracy. If the owners GPSr had an error of say 8M to the north when he set the cache and your's has an error of 8M south when you are searching for it, then your "zero" will be 16M from the "True" position. :(

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How is the OS coordinate for the trig point derived?

By triangulation, hence the name "triangulation point".

 

First a baseline is measured very accurately. This was originally done with metal bars and chains. The first baseline in the Ordnance Survey's triangulation was measured on Hounslow Heath, where Heathrow Airport's main runways now lie.

 

Once you have measured the length of the baseline you can then measure the angles from each of its ends to other points. Call the ends Points A & B. By measuring the angles at each of those points to a third point, C, you can compute the side lengths of the triangle. Then you repeat to points D, E, F, G etc. You cover the entire country with this primary triangulation network.

 

Latitude and Longitude is measured at at least one point (usually more than one) by astronomical observations. This absolute position is then carried throughout the triangulation network.

 

 

Presumably it is determined using some form of GPSr?

No. The triangulation network of the UK was measured entirely by theodolite.

 

It's only very recently that the Ordnance Survey has abandoned triangulation and embraced GPS. They are continuing to maintain a few of the trig pillars. You can see their details under "passive station" list at gps.gov.uk. The network was adjusted in December 2002 to iron out the wrinkles in the old triangulation with GPS data.

 

The Snowdon trig pillar is not part of that GPS network.

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Cool. I had assumed that all trig points had been re-measured using GPSr in 2002 but am happy to be corrected :(

 

What is really impressive is that the guys at the OS managed to get the position of the trig down to around 1 foot (as meaasured by multi billion pound GPS system using atomic clocks and lots of numerical computing) using measurements expanded out accross the trig network from Hounslow.

 

Is the position of the trig used the one recalculated in 2002 using the updated network?

 

It would be very interesting know how close the OS originally got the position using the just the triangulation network in the days before the advent of numerical computing...

 

Thanks for this informative thread :(

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I am glad to say my reading was close to the actual position, The weather was a bit damp though.

It was a very busy day and there was a catchers meet in the café. I allowed my GPS'r to settle for about 5 Min's on the "average position" setting.

 

The reading on my GPSIII with 25ft EPE was :-

N53.04.111

W04.04.570

Alt 3580ft

 

 

d4932d9d-67de-409a-93ac-63380d0b0c12.jpg

 

Snowdon Summit is also the most logged trigpoint on T:UK with 57 recored visits.

 

This trigpoint:

Is ranked 54th

Has a mean score of 8.07/10 (from 57 logged visits)

Was First logged: 15th Aug 1967

Was Last logged: 17th Sep 2005

 

Of the 57 logged visits,

8 recorded a location and of these....

All were within 114m

The average error was 21m

1 was exact

Edited by Deego
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What is really impressive is that the guys at the OS managed to get the position of the trig down to around 1 foot (as meaasured by multi billion pound GPS system using atomic clocks and lots of numerical computing) using measurements expanded out accross the trig network from Hounslow.

The absolute accuracy of the old optical triangulation network wasn't actually all that good. Once we had satellites to play with, such as the old Transit system, we found that there were some quite significant errors. This became a major pain in the proverbial when we were trying to measure the positions of oil production platforms to very high degrees of accuracy because the shore reference stations were often incompatible with eachother. This was made even worse for us hydrographers because the OS had a policy of "throwing their errors into the sea" when adjusting their triangulation network(s).

 

It was even worse when you had to try to tie in the national geodetic systems of two countries. I was the Project Surveyor for the laying of the electricty cable for France to Jersey and it was extremely difficult to tie in the co-ordinates of survey stations between the two countries because of the incompatibilites between the triangulation networks involved. It was even more difficult when we set up the first DGPS network to cover the North Sea. One solution was to devise a special variant of WGS84 for the North Sea which was called WGS84*SEA. It was a nightmare! Some major oil reservoirs straddle the median line between the UK and Norway and just a metre difference in co-ordinates involves a heck of a lot of money, so the whole thing rapidly became very political.

 

It's all been resolved now with the adoption of a Europe-wide version of WGS84.

 

Is the position of the trig used the one recalculated in 2002 using the updated network?

 

I don't think so, but I don't know the full provenance of the co-ords. I pinched them from the excellent Trigpointing website.

 

The accuracy of co-ords in triangulation networks are not usually expressed in ± terms of metres, but as a proportion of the side lengths of the triangles. In a First Order network the accuracy is anywhere between 1:60,000 and 1:250,000. Accuracy of observed angles is usually better than 1 arc-second. Side lengths are typically 50 to 80km, though some long lines of up to 150km were necessary to include places such as Shetland in the network.

 

I suspect that the accuracy of our averaged fix is probably better than the accuracy of the co-ords I adopted in this exercise. Such is the power of averaging when measuring a position with GPS.

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is there an explanation in lamens terms for what you are talking about?

Other than the fact I got the jist that you are talking about accuracy of a GPS, I really haven't got a scoob on what all those big words and explanations are!

Sometimes it's not really possible to make things much more simple, and mathematics is often one of those times (or things).

 

What Forester is telling us, is that there are many ways to define words like "average" and "accuracy" (in the latter case, formally, there's one right way and several wrong ways!), and that although they all produce different results, they basically show that GPS technology is - on average (!) - pretty accurate (!).

 

PS: I just worked out what "lamens" means (having seen it used by two posters in as many days now). I guess you mean "in layman's terms".

:D

Thank you I had managed to suss out that he was talking about the general accuracy of the GPS, but thanks for reminding me that I had already stated that much.

 

Also thank you for pointing out my spooling mistake, I'll watch out for some that you may make in the future :o

 

Sometimes it's not really possible to make things much more simple

One of my heroes once said that:

The truth should be expressed as simply as possible, but never more so.

 

Sadly I believe in this case you have failed. I am obvioulsy in the minority of the people posting in this thread, but I would bet that there are people out there that don't know what the following words or phrases mean, without looking it up -

 

rigorous polynomial method.

 

without any filtering or weighting or applying any of the least squares or other other processing techniques to refine the fix, the crude average comes to 53° 04.1093'N 4° 04.5741'W, which is just 0.37m (14½ inches, in old money) from the stated True value.

 

Circular Error Probable. CEP is defined as the radius of a circle within which 50% of the shots land. The CEP of our 74 geocachers' data is 2.83m. CEP does nothing to describe the other 50%, so statisticians, surveyors and other scientists prefer another measure. One favoured measure is called Standard Deviation or sigma. The sigma value of our Snowdon sample is 3.41m.

 

of <±

 

There are more within your post that takes several readings to understand what it says.

 

Now I am not arguing that there is undoubtfully usefull and interesting information contained within the Foresters finding, but being a qualified communications and first aid instructor I couldn't agree more that the truth should be expressed as simply as possible, but never more so.

 

I have always found that when someone doesn't understand what I have expressed, then I should endeavour to explain in a different way, such as in layman's terms (spelt correctly this time I hope).

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I have a virtual and US benchmark that people have been recording their coordinates there for years. It's a US benchmark so you can compare against your reading. If you do the analysis I think you'll find that the results regarding accuracy match the one's you've been getting.

 

Of course most of the reported distance are in feet not meters. We're still fairly backwards over here across the pond.

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You cover the entire country with this primary triangulation network.

 

See this map of the lines observed during the Primary Triangulation (including later corrections), this quite nicely demonstrates the triangles mentioned.

 

As for where the coords on TrigpointingUK come from, they are from the OS themselves. The positions for all the primary trigpoints (about 200) are known to the nearest milimeter* (0.001 of a meter). The coords for the Secondary Trigpoints are known (of which Snowdon is one of the 1900 or so) to .01 of a meter*. There is then a further 3700 Third/Forth order trigs, generally expressed to 0.01 of a meter. T:UK uses all these values rounded to the nearest meter.

 

* however I can't really comment on how accurate these measurements were found to be when compared to modern equipment.

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Once or twice ( as Haggis knows ) I have compared my GPS (settled and averaged) reading with posted coordinates. At Arthur's seat in Edinburgh my recorded HEIGHT on the GPS was 4 FEET different, and that was probably accounted for by the fact that I laid my GPS on top of the trig point. So even height triangulation from satellites can be brilliant.

 

What has always impressed me in geocaching is the issue of repeatability of reading. I know this is not the same as accuracy against some other bench marked system but some cache setters are continually able to post cache locations which are repeated on my GPS consistently to within one last digit - or less than 6 feet in some cases. Other setters of caches cant post a GPS location to ithin 150 metres. WHY oh WHY oh WHY the differences in competence.

 

Haggis may your breast swell with pride - yours are always spot on.

 

It is also interesting ( I've only done it once in a while ) is to mark on something like MS Autoroute for all caches the posted location and the 'found' location. This is similar to the exercise above as it gives a good spread of results, but the vast majority are very close indeed to the posted results. [MS Autoroute can resolve to quite a high degree of accuracy, and you can use the measure tool to see the difference.]

 

I think the problem for some cache setters is severalfold: failure to realise that the GPS lags behind your horizontal movement across the planet: standing still helps and some GPSs need several minutes ( my GARMIN 12 does ) to settle down; failure to average; failure to revisit the set cache at different times to check the original coords ( diff satellites visible ); reliance on 'tree cover' or other excuses to avoid diligence in setting - and of course some GPSs simply dont seem to calculate as accurately as others. I rely on my old GARMIN 12 because ( very very slow as it is ) its stunningly accurate when it has settled down.

 

OK apologies for this diatribe :DB):o

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Thanks for that, Barry.

 

Have you, by any chance, got a copy of the original OS data sheet for the Snowdon 2nd order trig? Have you got their full precision co-ords?

 

I wish I had downloaded the whole lot when the OS still had them all on their website.

 

It seems like it was only yesterday that the boogers charged a hundred quid a pop to sell a copy of each datasheet!

 

Cheers, The Forester

PS are you by any chance the same Barry Hunter who worked aboard Arctic Surveyor and other Manta/Oceaneering jobs?

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Other setters of caches can't post a GPS location to within 150 metres. WHY oh WHY oh WHY the differences in competence.

The 100+m discrepancies in the UK are usually due to having been measured with Airy's spheroid and the OSGB36 datum instead of WGS84.

 

It's an easy mistake to make and is not necesssarily a matter of competence.

 

I can immediately recall three or four caches which I've found to have suffered from this mistake, one of which was set by someone who is actually very competent in rural navigation.

 

Cheers, The Forester

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I think the problem for some cache setters is severalfold:.......... failure to average;

I repeat my query from above. How do you do an average with coords?

 

Or is it just a simple add them up and divide by the number of coords?

You have farted and I heard it.

 

Yes. It is it just a simple add them up and divide by the number of coords, at least at the simplest level, which is what I did with my simple average of geocachers' co-ordination of the Snowdon trig point.

 

The average of all geocachers' co-ords is within a foot or so of the 'official' co-ords. when you simply add them up and divide by the number of coords.

 

Cheers, The Forester

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The 100+m discrepancies in the UK are usually due to having been measured with Airy's spheroid and the OSGB36 datum instead of WGS84.

 

I think you're probably right on that and Richmond Park ( and its sisters ) are probably an example of that.

 

As to whether this error is one of competence or not? Mmmm errr jury's out on that one especially as the setter in this case is the Cotswold Outdoor shop. In my lowly view, if a cache is consistently reported as not in the given location, then the setter's original posting needs checking ( at the very least ).

 

How do you do an average with coords?
Apologies - I was referring to the averaging of the GPS readings - not quite the same.

 

:o

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I was referring to the averaging of the GPS readings - not quite the same.

There are some fancy tricks with data to smooth out the wrinkles, but a simple averaging of GPS data by adding up all the Lats and all of of the Longs and dividing by the number of readings gives you a very good reading of the actual position of the fixed point.

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Have you, by any chance, got a copy of the original OS data sheet for the Snowdon 2nd order trig?  Have you got their full precision co-ords?

 

I have 260985.94,354374.64 for Snowdon Summit Third order trig built 06-Oct-61, extracted from a partial extract from the OS's digital db. It appears I may of been wrong saying it was a 2nd (or it might of been a 2nd order before replaced in '61)

 

[if wondering Snowdon was never a Primary, instead nearby Garnedd Ugain was the primary]

 

I have never seen any of the original datasheets, but would be very interested in seeing them. In fact it appears they may be going to the National Archives at some point.

 

I wish I had downloaded the whole lot when the OS still had them all on their website.

 

The datasheets? Are you sure they where on the site as I didnt know they ever became digitised.

 

PS are you by any chance the same Barry Hunter who worked aboard Arctic Surveyor and other Manta/Oceaneering jobs?

 

Not me I'm afriad!

Edited by barryhunter
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Other setters of caches can't post a GPS location to within 150 metres. WHY oh WHY oh WHY the differences in competence.

The 100+m discrepancies in the UK are usually due to having been measured with Airy's spheroid and the OSGB36 datum instead of WGS84.

 

It's an easy mistake to make and is not necesssarily a matter of competence.

 

I can immediately recall three or four caches which I've found to have suffered from this mistake, one of which was set by someone who is actually very competent in rural navigation.

 

Cheers, The Forester

What does Airy's spheroid mean? hmmmm.gif

 

I also get the distinct feeling that the last paragraph is aimed at myself, (I really do wish you would just be open with your comments) I will openly admit that a few of my caches have discrepencies with the co-ords, but in all the cases I have gave explanation and warning on the cache page about it.

 

I get the feeling that you may be refering to PhD. Which you said your co-ords were better, perhaps they were but 2 metres in my opinion doesn't make much difference, espescially when the clue said 'you'll be stumped if you don't find this' and there is a huge tree stump that you could fit 2 adults lying side by side into it, extremely close to the co-ords, and is were the cache was hidden.

 

Now I have had it pointed out to me that I may be very defensive and forthcoming regarding posts by yourself. Well these people would be correct.

This is mainly because you CAN work out the averaging of co-ords and you THINK that people who can't are below you. This is shown by the way that you say your co-ords are better than the given one's, such as in this log. I personally find logs like these extremely arrogant and obnoxious, which in your case I am afraid is not just a one off type of log.

 

Perhaps saying something along the lines of, 'I found the co-ords to be out I make them to be ???'. That to me is a lot more polite.

I do believe that you are the only person to struggle with the co-ords for PhD.dontknow.gif

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PS: I just worked out what "lamens" means (having seen it used by two posters in as many days now).  I guess you mean "in layman's terms".

:blink:

Also thank you for pointing out my spooling mistake, I'll watch out for some that you may make in the future ;)

As I said, you were the second person to use it in a couple of days, so I was wondering if it was a trend. I noticed it mainly because when I lived in Holland I knew a (very nice... too nice for me, in fact) girl whose last name was "Lamens" :blink:

 

By all means point out my typos; I'm not normally a "spelling corrector" type of person (except with my kids!) because I make my fair share, but if I can dish it out, I can take it :lol:

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PS: I just worked out what "lamens" means (having seen it used by two posters in as many days now).  I guess you mean "in layman's terms".

:blink:

Also thank you for pointing out my spooling mistake, I'll watch out for some that you may make in the future ;)

As I said, you were the second person to use it in a couple of days, so I was wondering if it was a trend. I noticed it mainly because when I lived in Holland I knew a (very nice... too nice for me, in fact) girl whose last name was "Lamens" :blink:

 

By all means point out my typos; I'm not normally a "spelling corrector" type of person (except with my kids!) because I make my fair share, but if I can dish it out, I can take it :lol:

I too had seen the other typo on Layman's, without thinking I just went ahead and spelt it that way. I actually had a feeling that it was wrong, but in this case was too lazy to check first.

 

Sorry for having a go at you adore.gif

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shhh Haggis - you are a little sensitive -

 

;):blink::blink:

Phd was fine - spot-on in my book - a little wander on the final digit.

 

Down south we do have some well intentioned 'plonkers' who simply are unable to post correct coordinates. I've now stopped looking outside a 30 metre radius of a posted position.

 

One day someone will create a UK website of regular caches and their posted coords allowing us to add the found coords - could make interesting reading.

 

today's colour is GREEN

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the GPS lags behind your horizontal movement across the planet: standing still helps and some GPSs need several minutes

Can anyone explain why this is? The GPS satellites are all in low orbits, so the relative velocities between each satellite and the GPSr will be quite large. How is it that the software on the GPSr can cope with satellites flying around the sky, but can't cope with the receiver crawling around the earth?

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