Spheroid & Ellipsoid (BOL, WGS84)

[Pieter Boelen]

Nautical calculations are based on the Nautical Mile (NM).
Not to be confused with:

• 'nM' = nano.Mega = 10^-9 * 10^6 = the numeric value 0,001 = milli = 'm' in prefix
  
• 'Nm' = Newton.metre = [default SI unit of force] * [default SI unit of distance]
  
• 'nm' = nanometre = 10^-9 * [default SI unit of distance]

A Nautical Mile is a unit of distance, just like 'metre [m]'.
Just like the metre, it is based on the circumference of the Planet Earth.
As such, it is allowed to keep using this unit despite the existence of SI units.

The Nautical Mile is defined as exactly 1852 m (no decimal places; this is an exact value).
It is also defined as one arc minute of a degree.
There are 60 minutes in an hour and 360 degrees in a circle.
Therefore there are 60 * 360 = 21.600 nautical miles as the circumference of the Earth.

An NM is 1852 m and therefore the circumference of the Nautical Earth is exactly
21.600 * 1852 = 40.003.200 m.

 

[Pieter Boelen]

The Earth is a 3D object and not a 2D one like a circle.
Therefore it can be approximated as a sphere with a radius.
This radius is 40.003.200 / ( 2 * π ) ≈ 6366707,019 m.

'π' = Greek letter pi = 3,141592654...
'≈' = 'approximately equal to' = '=~'

 

[Pieter Boelen]

The actual Earth is of course not a perfect sphere.
It has mountains and underwater there are deep trenches.
This strange form can be approximated as a 'geoid' or 'basically a potato'.

Even that is too complicated to calculate with and so it can be further simplified as an 'ellipsoid' or 'a flattened sphere'.
A 'flattened sphere' is still a sphere and therefore 'a sphere = an ellipsoid'.
But the reverse is not true. An ellipsoid is not necessarily a sphere.

Depending on the area of the world, a different ellipsoid can be chosen to most closely approximate the real shape.
This is called a 'datum' (not to be confused with the Dutch word for 'date' which is also 'datum').
Over the years, many (groups of) nautical charts have been made; each with its own different datum.
There was, for example, a general 'European Datum' in use, which was created in 1950 and is known as 'ED50'.

As a different reference system per area is massively inconvenient and error-prone, a general 'World Geodetic System' was created.
The first was from 1960, with updates in 1966, 1972 and 1984.
'WGS84' was the final update (for now?) and is currently in widespread use in, for example, all Global Position System (GPS) systems.
It is possible to switch advanced GPS units to a different datum, but WGS84 is the default.

 

[Pieter Boelen]

'Sphere geometry' (= "BOL-goniometrie' in Dutch) is very simple and requires just basic secondary school math.
It also fits exactly with the definition of the Nautical Mile, making it easy to understand the results with virtually zero inaccuracies or chances for error.

Therefore, wherever actual position accuracy does not influence risk to human life or damage to property,
I believe we should agree to use the 'BOL' definition as our primary system.
'WGS84' is allowed as secondary system if (and only IF) the specific use absolutely requires it.
It should not be used 'just because' or 'for the sake of being fancy'.

A misplaced sense of scientific accuracy has an inherent danger of its own.
It massively increases the chances of human error in the implementation.
It also makes results far less simple to interpret and therefore actively prevents human error-checking.

The Earth is objectively round and not flat; no matter what certain people might want to believe and 'prove'.
This is a massive inconvenience as humans, but especially computer systems, really don't like dealing with anything other than flat surfaces.
3D is bad enough on its own; but 3D and wrapped around is an absolute nightmare to compute.
Therefore: DON'T TRY IT!
Unless you unequivocally and without a shadow of a doubt absolutely have to.

Never forget the multi-million dollar US fighter plane that very nearly crashed just because it crossed the International Date Line.
Which, to be clear, is an imaginary man-invented line that completely does not exist in real life.

Let's be safe; not stupid!
And for the record, 'being TOO smart = being stupid'.
A good programming rule is KISS: Keep It Simple, Stupid!!!

 

[The Nameless Pirate]

This was a nice read, thank you!