How to explain unexpected success following a bearing taken from an iPad

Question

I live in northern British Columbia where the relevant declination values are currently

• Magnetic declination: 17° 45.30' East
• Grid declination (for Natural Resource Canada's NTS maps): 16° 17.04' East

I am fairly comfortable using my compass to both 1) acquire a bearing on the ground to plot on a paper map and 2) read a bearing from a paper map to follow on the ground. I understand the importance of having the (roughly) correct declination when transferring a bearing between a map and the real world in either direction.

I believe that grid declination is specific to the mapping product, and a non-NTS map for the same location could use a different Grid North. As a result using my compass with a different map, without changing its declination, could result in navigational error.

My question is for help explaining the following scenario: a colleague had an iPad showing a polygon overlaid on an app using the Web Mercator CRS (900913 / 3857 / 3785). We were starting at one corner of the polygon and our goal was to track along the edge of it. My colleague placed the compass on the iPad screen (held parallel to the ground), aligned the compass's grid lines with the orientation of the map (grid north on the map was parallel to the screen's side bezels) and read the bearing. We followed the bearing and - to my surprise - closely tracked to the desired edge of the polygon. I would expect some risk of magnetic interference from the iPad, with the compass directly on the screen, but this did not appear to be an issue.

Given my belief that grid declination is specific to the mapping product's Grid North I do not understand how this approach was successful.

1. was it purely a coincidence?
2. does the Web Mercator CRS happen to use the same Grid North in my area (NTS maps use NAD83 UTM)?
3. is it possible that error introduced by reading the bearing from the iPad and navigational errors in following the bearing were simply too small to matter, or potentially cancelled each other out?

Answer 1

Let's address what you refer to as "Grid declination". Unfortunately, there are two competing definitions:

First, the definition you are conforming to, is that it is the angle from grid north to magnetic north (see NR Can) -- another name for which is grid-magnetic angle.

A different definition is that it is the (generally very small) angle between true north and grid north (see free dictionary) -- more commonly called grid convergence or meridian convergence.

You are correct that a true bearing equals a magnetic bearing plus the magnetic declination -- assuming the declination is reckoned positive when magnetic north is east of true (and negative when west).

You are also correct that different mapping systems, and different locations within those systems, will vary in where grid north is with respect to true (and hence magnetic) north.

does the Web Mercator CRS happen to use the same Grid North ... NTS maps ...?

No. NTS (Canada's topographic system) maps use the UTM -- a Transverse Mercator -- projection. This means that, depending on your latitude and how far from the central meridian you're at, you will have a grid convergence. In your location it is 17° 45.30' - 16° 17.04' = 1° 28.26' (using your numbers). On the other hand, the Web Mercator is a rectangular projection and all meridians are parallel and aligned with the grid, so there is zero grid convergence everywhere. You still need to correct for magnetic declination, however.

I'm not yet clear whether you attempted to correct your survey bearings for the 18° magnetic declination. If you did correct your bearings for declination then you should expect the good results you got. If you did not correct for declination then there is something I cannot yet explain.

To determine if there was magnetic interference from the iPad -- the result of which is known as magnetic deviation (see sailing issues) -- why not try this: Using compass alone, and free from any possible magnetic interference, find the point on the horizon representing its magnetic north. Carefully rotate the compass around and notice does the needle point consistently to that horizon point? Repeat the process with the compass lying on the powered-on iPad. You should notice whether there is any iPod-induced deviation or not.

Answer 2

In the Canadian NTS series of maps at latitudes below about 60 the maximum difference between grid north and true north is just over 2 degrees.

The grid is a 100,000 meter grid: blocks 100 km x 100 km. The grids are square, but the earth isn't. Square grids simplify the calculations for artillery fire. The calc between grid coordinates and lat/long coordinates is awful.

2 degrees is about as closely as you can read a pocket compass. Ones with sighting mirrors are easier to use to take an actual bearing.

As to why the ipad didn't disrupt your compass: Currents in an ipad are mostly constant DC, and have short paths. While there will be a magnetic field around each segment of circuit board carrying current, most of those have another close by segment carrying current the other way. It takes a loop of current around the device to create a net magnetic field.

The iPad has a built in mag compass chip. To use that I'm sure they went to reasonable lengths to see that the currents in the device didn't affect the chip.

Or maybe you were lucky.

Go out and test it on your local road grid.