RCS Grid Bearings

[Ian Gillespie]

I’m having a little trouble understanding the output in the latest Leica field book stylesheet which led me down this rabbit hole.


LINZ RCS2021 guidelines say we should use Grid Bearings.


And that’s what the latest Leica field book stylesheet shows I believe.


Here is an example:

The coordinates:

RTCM-Ref 0 359377.852 928309.886 56.222

GS0001 358150.588 931748.316 142.073



The field book bearing and distance:



the bearing is 340 21 25.6
The 12d bearing and distance:


The bearing reads 340 21 25.96
The arc-chord correction is 0.36"

OK, It’s not very exciting difference but still a difference equating to 6mm just in a calculation.

And it shouldn’t affect the joins between marks.


The definition I have for Grid Bearings is :

    Angle between grid north and the tangent to the arc at the point. It is measured from grid north clockwise through 360°.

The definition for plane bearing is :

    The angle between grid north and the straight line on the grid between the ends of the arc formed by the projection of the ellipsoidal distance; measured clockwise through 360°.

And the Arc-to-chord correction is:

    the Angular quantity to be added algebraically to a grid bearing to obtain a plane bearing:


But the thing is that the calculations we do in the 12d traverse spreadsheet use plane bearings.
What I mean is if you take out a join between two circuit coordinates the bearing will be a plane bearing. And if you have two GNSS coordinates, for example, and want to start at one and finish on the other you have to use plane bearings.


So, Should the specification be that we show Plane Bearings?
Or should we using Grid bearings for our calculations?


Is there anyone out there that can shed some light?

Attachments:

[Ian Gillespie]

Further to the above I've checked with LINZ and they confirmed that we are to use Grid Bearings.
And the Grid bearings we want to use are those are derived by plane geometry as usual:
i.e.:
𝛥𝐸 =𝐿sin𝜃
𝛥𝑁 =𝐿cos𝜃
𝐸2 = 𝐸1 + 𝛥𝐸
𝑁2 = 𝑁1+ 𝛥𝑁
So that seems ok.

But I have also found that what we refer to as grid bearings the Australians call Plane (or Projection) bearings and that the relationship between their grid bearings and plane bearings is the arc to chord correction.
So in Australia: Grid Bearings = Plane Bearings (Grid Bearings in NZ) +– Arc-to-chord correction.

And the Grid bearings we want to use are those are derived by plane geometry as usual as above (which are called plane or projection bearings in Australia).

So I'm thinking now is if the Leica Field book stylesheet is using the Australian definition for Grid Bearings and that is why the difference equates to the arc-to-chord correction.

[Brent George]

Nice investigation Ian.
I would suggest that all Leica field book style sheet users contact Global Survey to alert them to this finding - and ask them to either flag the difference or produce a NZ Field book style sheet....

(It may as well be 'correct' for NZ use)

[Ian Gillespie]

Global Survey are going to have a look at it so hopefully I will have an answer soon.

[Ian Gillespie]

Just a final note:
Global Survey have kindly updated the stylesheet they have sent us so that the bearings displayed are now NZ Grid Bearings.

It isn't a large difference and depends on the length of the line observed and the distance east or west of the central meridian.

If you round bearings to 0.1" for lines over 1km then it may be apparent.

For example a 3.5km line in Whangarei has a 0.36" difference and a 1km line has a 0.1" difference

A 1.4km line at Cape Reinga has a 0.48" difference which is about as far from the false origin you can get without a boat.

A 1.4km line at Mount Eden has a 0" difference.