Applying proper conversion from True to Grid bearing

Question

Assume that Grid North is 1.49 deg W of True North.

Also, the magnetic declination is 13.11 deg.

If I wanted to take gyroscopic surveys (measured from True North) and then convert them to Grid North, what values would be needed to do so correctly?

I've been told to add 1.49 deg to the True North measures to convert them to Grid North measures.

But, I've also been told the opposite, to subtract the 1.49 deg from the True North.

I've also been led to believe that since you are going from True to Grid (in a counterclockwise direction) you would therefore add the -1.49 deg.

Perhaps someone can better explain?

Answer 1

Note: North is just a reference direction. By itself, it doesn't have an angular value. (You and @iant have already hit on that concept.) The difference between two Norths does have an angular value – it is the correction you refer to. A bearing (or azimuth) is a clockwise angle from (some) North to some direction of interest. The confusion for us may be that you're mixing corrections and bearings. It also doesn't help that you refer to magnetic declination which, in the case of the surveys you refer to, is irrelevant.

If you are, as you say, "going from True to Grid (in a counterclockwise direction)" and if you are converting True bearings to Grid bearings then you must add the value 1.49°. Put another way, you subtract the negative value 1.49°. Clear? Of course not! So let's have a look at a declination diagram:

            TN
    GN      |     MN
      \     |     /
       \    |    /
        \ MC|MD /
         \  |  /
          \ | /
           \|/  MB
            o ----------- OH
                
GN: grid north -- direction of map's south-to-north grid lines
TN: true north -- direction of local meridian (aka geographic or geodetic north)
MN: magnetic north -- direction of local magnetic force field

OH: our heading -- direction we're going or looking (aka bearing, azimuth or course)
    Note: this could be anywhere, of course (excuse the pun),  it just happens to
    point east in the diagram

MD: magnetic declination -- angle between true north & magnetic north (aka
    magnetic variation)
    Note: MN may be West or East of TN (ie, MD may be -ve or +ve)

MC: meridian convergence (aka grid convergence) -- angle between true north & grid north
    Note: GN may be East or West of TN (ie, MC may be +ve or -ve)

MB: magnetic bearing -- angle between magnetic north & our heading

Not shown

TB: true bearing -- angle between true north & our heading
GB: grid bearing -- angle between grid north & our heading

Some simple relationships

TB = MB + MD
GB = TB - MC

Returning to your situation, where the meridian convergence is negative

GB = TB - - 1.49° = TB + 1.49°

thus there was some truth in each of your possible answers.

The moral of the story is: draw or examine the declination diagram (for the situation at hand) and things will be clear. But remember, the relative directions of True, Grid and Magnetic Norths will depend entirely on where on Earth you are and where on the map projection you are.

According to IOGP Geomatics guidance note on Grid convergence

The definition of grid convergence is ambiguous, because text books on geodesy, cartography, navigation and surveying are not consistent on how this angle is calculated. In a world where navigation and surveying have become global activities, this has led to considerable confusion.

One convention has grid convergence

positive when True North lies west of Grid North

(that's the one I'm using above) and another has it

positive when True North lies east of Grid North

So that easily explains why you can get apparently conflicting advice!