Easting / Northing to LatLon Accuracy

[eldiddio]

Hi,

I have been using this class to convert a bunch of Easting / Northing, I found when checking the converted values against a map that the LatLng was slightly off.

When the results where compared against a online tool for I noticed that the only difference was the length of the results.

To test this I adjusted LatLng.php

$this->lat = round($lat, 5);
$this->lng = round($lng, 5);
to
$this->lat = round($lat, 13);
$this->lng = round($lng, 13);

This changes moved the point on the map by about 100 meters and was more accurate.

Does the class support getting LatLng out in a longer format?

Thanks for the great work!

[eldiddio]

A follow up to this, when I run

new OSRef(533498, 181201))->toLatLng()

Results: 51.51346, -0.07592,

This is close but not accurate when checking with Google Maps. When I use this form http://www.bgs.ac.uk/data/webservices/convertForm.cfm

Results: 51.5139688159, -0.0775306313912

The results from the form are different and accurate, do I need to change the way i load the class to get accurate results?

Thanks Again!

[dvdoug]

Hi

So there are a few issues at play here - in the below I'm going to assume you're not familiar with any of the intricacies of geographic co-ordinates and I'll dumb it down a bit in the interests of brevity. A fuller explanation of everything can be found in https://www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf

Basically:

• 5dp latitude/longitude represents an accuracy of about 1m. 6 dp would be an accuracy of about 10cm, and 13dp would claim to represent sub-millimetre accuracy
• the Earth is not perfect sphere or ellipsoid - it's bumpy and lumpy
• as such, when doing the maths an approximation is used to try and use an ellipsoid shape that "best fits" the planet
• there is no single correct best fit - in the UK, Ordnance survey modelling uses an ellipsoid that best fits the way the UK is placed on the planet
• when the GPS people did their modelling they used a different ellipsoid that better fits most of the planet, but doesn't fit the UK quite as well
• as such, depending on which model you use the same set of lat/long numbers actually represent a different spot on the ground
• there are ways to convert between the various models (UK to GPS), but without huge databases of surveying data to back them up they're not perfect - purely algorithmic conversion results in small errors of up to 5m (which is good enough for most purposes)

Conclusions:

• since the output of any modelling conversion is going to have an error of up to 5m, the choice to round to 5dp (1m) is on purpose - otherwise the results will be off when compared to e.g. a direct GPS reading.
• when you convert from northing/easting to lat/long you're still in the UK model of the world as used by OS. However Google maps is almost certainly using the GPS model. If you do ->toLatLng()->toWGS84() you'll get the set of co-ordinates that I think you're expecting.

Hope that helps?
Doug

[dvdoug]

Assuming this helped you out - if not, please do reopen :)