For my own benefit a few days ago I was looking at the information for all the North Wales summits and plotting them on the Radio Mobile Mapping Program. I found 8 summits where the Locator information given on the summit information pages does not agree with that calculated (by the program) from the given Lat/Long information. Whilst all of those summits are close to the edge of one or more squares I would have expected the two bits of information to match.

The summits that this applies to are NW-011, NW-014, NW-016, NW-019, NW-024, NW-027, NW-046 and NW-073.

I have tried putting the NGR’s from the SOTA pages into the page at Javascript Calculators .
This also gives the same difference in Locator information (except for NW-011 where the difference is as little as 10m in the NGR value).

…but seriously: How accurate is the program? How accurate is the “Officially recognised summit information”? From time to time summits are rechecked by official bodies, not SOTA, and their heights and locators modified accordingly. Recently a number of mountains have been reclassified as a result of new information. See the thread in this reflector entitled “Scotland QRM Updated”. Trying to find the true summit on a mountain involves a fair bit of guess work on top of surveying skills. Some summits have plateaus stretching over large areas and there are even some that border four locator squares, so not surprising there are anomalies.

In the UK the base information is the six figure OS grid reference. This has a 100m resolution. All the other co-ordinate systems are derived from this base information.

In reply to G3CWI:
Hi Richard
I thought the OS surveys to a resolution of 1 metre or better on the ground; at least they did when I introduced them do digital mapping systems back in the 1970’s, hi.
Most OS Grid coordinates are of course truncated to a 6-figure number giving a resolution of 100 metres in each axis. If anyone is converting from one co-ordinate system to another, they should always go back to the best resolution available. Doing otherwise will increase the risk of inaccuracies in the figures obtained.
73 de Ken

If anyone is
converting from one co-ordinate system to another, they should always
go back to the best resolution available. Doing otherwise will
increase the risk of inaccuracies in the figures obtained.

Ken

True but the Marilyns list was derived by looking at maps not by surveying and thus six figure references were used (as is common practice for most hillwalking applications). Therefore the six figure refs are the best available info and are fit for the original purpose of unambiguously identifying hilltops. Producing an 8-figure list would be hard work!

…I should also of course add that the radio software use by Stewart will have its own terrain database with its own inaccuracies. No free ones use the current OS terrain database as far as know (it is far too expensive). Many therefore rely on Space Shuttle data from NASA or on terrain data extracted from very old OS maps (out of copyright). This extraction process was often done manually in third world countries and the results vary in quality somewhat.

There are plenty of places for errors to accumulate!

The calculations between Lat/Long and Locator in the Radio Mapping Program do not use the Terrain Data (I have it configured to the Shuttle Terrain Data - I can see that where this differs too, but that is NOT what I’m referring to here).

The following are the differences (first are from SOTA DB, second using the conversion from the SOTA DB lat/long in both Radio Mapping an the conversion site in my original post):

“Fields” represent an area 20 degrees of longitude and 10 degrees of latitude. “Squares” break down the field into areas of 2 degrees of longitude and 1 degree of latitude. The “Sub-Square” breaks down “Squares” even further and represent an area of 5 minutes of longitude and 2.5 minutes of latitude. There are 324 “fields” in the world, 100 “squares”(10x10) in each “field”, and 576 “sub-squares”(24x24) in a “square”.

If I’m reading this correctly then:

NW-011 is shown in the DB as Longitude: 3 44 46 W, Latitude: 52 55 0 N - which means that it is right on the border of both IO82DV and IO82DW (Latitude is a exact multiple of 2.5 Minutes).

NW-014 is Longitude: 4 8 24 W, Latitude: 53 0 0 N - right on the border of IO72WX and IO73WA.

NW-024 is Longitude: 4 10 18 W, Latitude: 53 2 30 N - right on the border of IO73VA and IO73VB.

So these 3 could be in either sub-square (if you are on the border I have no idea which one should apply).

However:

NW-016 is at Longitude: 4 0 2 W, Latitude: 52 59 5 N - which is a small fraction West of the 5 minutes longitude border between IO82AX and IO72XX.

NW-019 is at Longitude: 4 5 2 W, Latitude: 53 2 33 N - again a small fraction west of the border between IO73XB and IO73WB.

NW-027 is at Longitude: 3 45 24 W, Latitude: 52 57 32 N - a fraction north of the border between IO82CW and IO82CX (at 52 57 30 N).

NW-046 is at Longitude: 3 24 14 W, Latitude: 52 46 48 N - quite a bit East of the border between IO82GS and IO82HS (at 3 25 0 W).

NW-073 is at Longitude: 3 24 42 W, Latitude: 53 1 6 N - a little East of border between IO82GA and IO82HA (at 3 25 0 W).

Remember that the six figure NGR is the base data. I am not sure that there is any perfect algorithm for converting these into lat/long form. I seem to recall that the various algorithms have varying levels of approximation. I suspect that the transform from lat/long to Maidenhead is an exact one however. Perhaps someone who knows more about this than me could comment?

This is a proper “hard” problem. The problem comes from trying to represent the geographical data of a curved plane on a flat map. At best it’s an approximation made worse by the fact the Earth is not a sphere but an irregular oblate spheroid.

The map projections selected by the OS for the UK are based on the long thin shape of the UK. Such mapping would work for countries like Chile and Portugal but would be less accurate for countries like Spain and France which are much more square.

The next is that the relationship between OS maps and latitude and longitude is not exact for the reasons given above. The OS publish alogorithms that can be used to approximate between lat/long and grid references. But in some parts of the UK the difference between calculating lat/long from the grid ref. compared to measuring it will be less accurate that other places. If you look at these algorithms, then you will see significant floating point maths using trigonometric functions and the use of second and third order terms. At all places there is room for numerical accuracy errors to creep in and accumulate. As soon as you use floating point maths in any algorithm, you have only got an approximate answer no matter how many bits you use!

So what this means is that converting grid refs. to lat/long needs to be done carefully. If the resultant latitude is say 53.999999999 (decimal) degrees then you have reached the point when you can’t be sure which Maidenhead square you’ll be in because the error in the algorithms could mean the correct answer is 54.000000001.

The positions of the summits are given from the 6 figure reference and this is the only known accurate reference. This is only accurate to 100m. In places where the calculated result is not with 100m of the boundary of another reference system then you can believe the result. If you have the condition that you cant be sure which square you are really in, then all you can do is activate from enough positions around the summit reference to ensure you ground position is sufficiently within each boundary as to be beyond doubt. Of course, you have to remain with the vertical activation limit whilst doing this.

Some of the summits that Stewart questions, when converting from OSGB to Maidenhead are definitely questionable, others look like they may well be errors in the database. I don’t believe that the questionable ones can have their Maidenhead locations calculated to any degree of certainty from the 6 figure reference for the reasons given above. Perhaps the best way would be for someone with a GPS set to WGS84 to record the lat/long at the trig point/summit marker and also how far and in which direction you need to move to move between Maindenhead squares. You certainly cannot set a GPS to OSGB and move to the 6 figure position and read the lat/long because all GPS units use the same algorithms to convert between OSGB and WGS84. All you do in that case is run the algorithms, whose absolute accuracy we are questioning, backwards and your result is still questionable.

What I think all this long waffle really says is that only the 6 figure reference should be considered gospel and if a summit appears to be on/near the boundary of another reference system, you should ask the activator to consider moving about a bit to activate both squares!

I am not sure as I do not have one but I believe that GPS’s go to 10 figures and streetmap also give 10 figures. I am not suggesting that 10 figures shoild be used but just a pointer that it could be more accurate.

You are correct in saying that there is no perfect conversion between NGR and lat/long. I have spent some time studying the models used for many of the coordinate systems in order to write logging software for my own use. One of the most interesrting documents that I have found is " A guide to coordinate systems in Great Britain" available to download from - http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystemsinfo/guidecontents/index.html

I am not sure that
there is any perfect algorithm for converting these into lat/long
form.

There is, in a sense. The UK national grid is now DEFINED in terms of a transformation from the GPS-based coordinates. It is not a simple formula, but involves a large lookup table. This is essentially to compensate for errors in the original surveys that are shown up by more accurate surveying.

I seem to recall that the various algorithms have varying levels
of approximation.

Indeed, most pocket GPS units and conversion software will use a transformation formula which is accurate to somewhere in the region of 10m. Since they typically work with coordinates with precision of the order of 1m, the transformed coordinates will be less accurate than the quoted precision might mislead you into believing.

I suspect that the transform from lat/long to
Maidenhead is an exact one however. Perhaps someone who knows more
about this than me could comment?

Yes, lat/long to Maidenhead is exact, and explicitly decreed to use the WGS84 datum (which is NOT the same lat/long as you find on an OS map).

It should be noted in passing that in WGS84 coordinates, all UK summits really are moving, at a velocity of about 2.5cm per year north east. In time, the Maidenhead locators of some summits really will change.

However right now, as others have said, the major source of inaccuracy is the 100m resolution of the 6-figure grid reference that we started from.

It is not a simple formula, but involves a large lookup table

I downloaded this the other day and the table for the UK is about 38Mbytes.

Those old grey-haired giffers like me who grew up with PDP-11s will remember when a 38Mb lookup table would have been considered ludicrous. Now I think my wristwatch has more memory!

Pressure of work has stopped me playing with this but I’ll try and get it running tonight and see what the difference is between 6 figure to lat/long using the traditional algorithm and using the new defined method.

Thanks for that Martin - but let’s be careful not to confuse accuracy
and resolution:

Indeed; that is the distinction I was trying to make. Coordinates read from a typical GPS, or converted using simple transformations, are likely to be quoted to a precision one or two orders of magnitude better than their accuracy.