Distance measuring using GPS & Google Earth

[+Mr Mercator]

I've been setting a series of caches called "Mercator Projections" which involves projecting and measuring from distant reference points to locate the cache. My latest one uses Everest, Ben Nevis and Snowden to locate a micro in Essex (some say I may have gone a bit too far on this one!).

 

The distances using my Garmin etrex Summit HC vary from those measured using Google Earth on all 3 references point by 0.11% (Google Earth gives a shorter distance). This translates to distances of 400m to 8,000m and could make locating a cache almost impossible. I would have half expected the distances to be virtually identicial as I assume both the Garmin and Google Earth use the WGS84 datum, but would not expect Google Earth to be spot on due to the angle of the view from the satellite perhaps.

 

It was the consistent variance I didn't understand and that suggests there is an underlying reason for it that some techie might be able to explain. I enjoy maps and working with the GPS but am no expert.

 

Thanks in advance for any ideas. And yes before anyone says it, it may be a bit of nerdy topic and I probably need to get out more.

[+Master Mariner]

I have used two points, one in the Himalayas and one in eastern England, to calculate two distances. The points are rounded to the nearest degree to avoid any input errors.

 

1. 28 00.000N; 087 00.000E

2. 52 00.000N; 001 00.000E

 

Using a geodesic calculation the distance found is 7345.163km

Using a rhumb line calculation the distance is 7688.558km

 

A difference of over 300km.

 

Having a quick look at Google Earth Pro, I guess that they use geodesic calculations for their ruler tool as the line appears straight on the geodesic. If it was a rhumb line then the ruler line would appear curved over that sort of distance.

 

Key the above co-ords into your GPSr and see to which distance they come closest.

Edited January 15, 2010 by Master Mariner

[+Moote]

I would have thought that because Google uses mapping data which is originally from the OS, and other mapping agencies in other Countries, that they actually use the local datum for that country. Therefore distance between different countries would not be accurate

[+Mr Mercator]

Thanks for your comments, much appreciated. Entering the co-ordinates as Master Mariner suggested gave me the 7,345km figure - I assume the geodesic measurement is the same as the "great circle" (the shortest distance on the earth's surface between two points)?

 

I now know exactly what a rhumb line is thanks to Master Mariner and Wikipedia - "a line crossing all meridians of longitude at the same angle, i.e. a path derived from a defined initial bearing. On a plane surface this would be the shortest distance between two points. Over longer distances and/or at higher latitudes great circle routes provide the shortest distances. However the inconvenience of having to continuously change bearings while travelling a great circle route makes rhumb line navigation appealing in certain instances".

 

Also I hadn't thought about Moote's point about local datums - it would be interesting to know exactly how Google created their maps.

[+Master Mariner]

Thanks for your comments, much appreciated. Entering the co-ordinates as Master Mariner suggested gave me the 7,345km figure - I assume the geodesic measurement is the same as the "great circle" (the shortest distance on the earth's surface between two points)?

 

I now know exactly what a rhumb line is thanks to Master Mariner and Wikipedia - "a line crossing all meridians of longitude at the same angle, i.e. a path derived from a defined initial bearing. On a plane surface this would be the shortest distance between two points. Over longer distances and/or at higher latitudes great circle routes provide the shortest distances. However the inconvenience of having to continuously change bearings while travelling a great circle route makes rhumb line navigation appealing in certain instances".

 

Also I hadn't thought about Moote's point about local datums - it would be interesting to know exactly how Google created their maps.

 

 

I try to avoid the term "great circle" as that brings back memories of when I used my sextant and did spherical trignometry to get a position. We worked on a sphere in those days! With WGS84 the shape of the earth is now defined as an oblate spheroid, ie it is fatter around the equator than over the poles and that is why I refer to it as a geodesic.

 

I think that Google reduce all the satellite imagery to WGS84 for x,y coordinates. I am not sure if they correct the imagery in the z (altitude) direction. If confused about that comment, look at the imagery of Canary Wharf in London docklands. On the south side of the tower, I think it's the south side, you can see the full face of the building. If you take the co-ords of the upper corner, and then the lower corner, beneath it, you get two different positions even though both points are in the physical x,y position - unless the building is leaning of course! If you measure between the two points you will see that there is a considerable error.

 

Jsut some more food for thought!

[+Moote]

Also I hadn't thought about Moote's point about local datums - it would be interesting to know exactly how Google created their maps.

 

Google purchase their maps from Tele Atlas, who in turn purchase the mapping data from the various mapping agencies (Ordinance Survey in the UK). As the OS still collate their data in OSGB36, some form of conversion is required to correct this on a global scale. The OS consider the earth as a cylinder (flat North to South and curved East to West). That is why the Country is split up into the Grid squares SJ, TX etc, as this give them the chance to correct errors within their system.

[+Moote]

Thanks for your comments, much appreciated. Entering the co-ordinates as Master Mariner suggested gave me the 7,345km figure - I assume the geodesic measurement is the same as the "great circle" (the shortest distance on the earth's surface between two points)?

 

I now know exactly what a rhumb line is thanks to Master Mariner and Wikipedia - "a line crossing all meridians of longitude at the same angle, i.e. a path derived from a defined initial bearing. On a plane surface this would be the shortest distance between two points. Over longer distances and/or at higher latitudes great circle routes provide the shortest distances. However the inconvenience of having to continuously change bearings while travelling a great circle route makes rhumb line navigation appealing in certain instances".

 

Also I hadn't thought about Moote's point about local datums - it would be interesting to know exactly how Google created their maps.

 

 

I try to avoid the term "great circle" as that brings back memories of when I used my sextant and did spherical trignometry to get a position. We worked on a sphere in those days! With WGS84 the shape of the earth is now defined as an oblate spheroid, ie it is fatter around the equator than over the poles and that is why I refer to it as a geodesic.

 

I think that Google reduce all the satellite imagery to WGS84 for x,y coordinates. I am not sure if they correct the imagery in the z (altitude) direction. If confused about that comment, look at the imagery of Canary Wharf in London docklands. On the south side of the tower, I think it's the south side, you can see the full face of the building. If you take the co-ords of the upper corner, and then the lower corner, beneath it, you get two different positions even though both points are in the physical x,y position - unless the building is leaning of course! If you measure between the two points you will see that there is a considerable error.

 

Jsut some more food for thought!

 

That image is not strictly satellite images (as is the same for most of the City and Town images), they are taken mainly by planes and I believe at 10,000 ft as the plane flies it took a snap and that is geo-referenced. The perspective you see is because the snap was not taken from above. And as the map is 2D you are bound to get such observations as you have pointed out.

 

Some of the deserts and mountain ranges might be satalite though, as are the long pan shots of entire countries

[+The Forester]

Neither of the two methods proposed will produce a correct distance, though for different reasons.

 

Google Earth uses a peculiar inverse gnomonic projection which is good for producing eye-realistic imagery, but is geodetically unsound for accurate measurement of distances over wide areas. The Garmin method seems to me to be differently unsound, though I haven't explored it fully as the resolution is too coarse.

 

Let's take a quantified example: the distance between Snowdon and Ben Nevis's trig pillars.

 

A spheroidal calculation, assuming both points are on the WGS84 spheroid, shows a distance 419,274.66 metres between these two points, but is misleading as both of the points are actually located on tall mountains. Actually, the distance between the two trigs is 419,358.47 metres.

 

Why the disparity? Consider this: The tops of the two towers of the Forth Road Bridge are a few centimetres further apart than their bases, despite the fact the two towers are perfectly vertical. That this is so is similar to measuring the distance between two spokes of a wheel: it depends how far from the centre of the wheel you make your measurement.

 

The Nevis trig has an orthometric height of 1,346.911m, but is 1,407.736m above the WGS84 spheroid.

The Snowdon trig has an orthometric height of 1,086.022m, but is 1,140.855m above the WGS84 spheroid.

 

Forget about Mount Everest. The geodesy over such a huge distance is far too complicated for most people to calculate the co-ords of a geocache from. The geoid has vast undulations along a transect of that line and for most geocachers the geodetic task of back-calculating the true distance to a place in Essex would make their brains hurt.

 

I'd suggest making the thing much simpler by omitting the height of the given points and just doing a simple spheroidal trig calc of the distances on the WGS spheroid. Spheroidal trigonometry is easypeasy for most people who can remember A-level maths. There are also several online calculators to assist that simple calc.

[+GAZ]

Excellent thread Mr Mercator , the replies have been very informative.

[+the pooks]

I'm also finding this very interesting - although I can't understand much. I once wanted to convert from lat lon to xy coords so that I could plot our farm on CAD (Computer Aided Design) program and I got hold of these conversion formulas latlon2xy (it is a Word document because of all the mathematical symbols). I did manage to set up a spreadsheet that did the conversions. Now those formulas are enough to put hair on your chest. Surely if one sticks to WGS84 one should get one answer?

Edited January 19, 2010 by the pooks

[+The Forester]

Surely if one sticks to WGS84 one should get one answer?

 

For geocaching it is very important to stick to WGS84, but when you start getting down to metre-resolution calculation of distances things can start to get quite squirrelly quite quickly, regardless of which geodetic datum and spheroid you choose to use.

 

It's a bit like asking "how far is it to the nearest good pub?". The answer needs an awful lot of detail to be added to the question. F'rinstance: do you intend to go via a motorway; do you intend to go by rail; do you intend to take the canal towpath; have you got a steeple chase class horse; a helicopter? etc etc.

 

A geodesist will give you one answer, if you define the question well enough, but TomTom will give you a quite different answer.

[+The Patrician]

I'm also finding this very interesting

 

There's some good stuff on the OS site - "Guide to coordinate systems in Great Britain" is recommended reading, with further information on the following problems, among others:

 

Myth 1: ‘A point on the ground has a unique latitude and longitude’

Myth 2: ‘A horizontal plane is a level surface’

Myth 3: ‘The true coordinates of a ground point do not change’

Myth 4: ‘There are exact mathematical formulae to change between coordinate systems’

 

http://www.ordnancesurvey.co.uk/oswebsite/...tion/index.html

 

Regards,

 

Neil

[+mcwomble]

This is an excellent thread indeed and explains why my solution to Mr Mercator's puzzle was 234m out from where I found the cache.

I had converted the locations to OS reference and then generated a solution via normal 2D plane geometry.

 

Still I found it in the end.

[+FollowMeChaps]

U lot spent to long at skool - easy answer!

[+Mr Mercator]

Many thanks for all the enlightening contributions from people clearly more knowledgeable than the one who started the thread. It was interesting to read all the explanations and thank you for giving us the benefit of all your experience. The flat earth approach appealed to me - it makes things much simpler. And thanks to Neil for the link to the OS website - I'm certainly a bit wiser for reading it - excellent stuff for us amateur cartographers and navigators. The Forester's post was really good, full of fascinating info.

 

I am grateful to Mcwomble for proving my cache isn't impossible to find. The reference to Everest is of course next to useless and tongue in cheek. I thought the Essex Everest cache might not be so difficult and that people would simply do the reverse of what I did when I set it: enter the co-ordinates of each reference point and then locate the position where the GPS shows all the given distances. As a lot of people have Garmins that would measure the same way as mine I thought it might make it fairly straightforward and get round the problem and different methods of measuring accurately over long distances. But then it's simple when you know where the cache is hidden!

Edited January 27, 2010 by Mr Mercator