[Qgis-user] Help with scales in print layouts for geographic CRS

[Greg Troxel]

Nyall Dawson <nyall.dawson at gmail.com> writes:

> In all cases (projected OR geographic) the scalebar logic is:
>
> 1. Create a horizontal line across the width of the layout map
> 2. Calculate the length of that line using great circle/ellipsoidal
> calculations, based on the project's ellipsoid settings.
> 3. Compare the length of the ellipsoidal line vs the map width to
> calculate the corresponding scale

That is a very straightforward approach with easy-to-understand
semantics.

> So qgis scalebar calculations are ALWAYS based on great
> circle/ellipsoidal lengths*.

And more precisely, a true geodesic between two points varying in x and
with constant y in the layout CRS.  For north-up (at least ish)
projections, that means a line of constant latitude.

For a lat/lon CRS in the layout, at mid latitudes, it's going to mean
that the scale in the y axis is smaller by about 110km/70km; a square in
lat/lon is taller than it is wide (and plus it's not a square, but
that's less obvious).  Equivalently, a square on the ground has a larger
difference in longitude than it does in latitude.  Or maybe I have that
backward, but using lat/lon in a layout does not preserve shapes.

This is what I was trying to get at: a single concept of scale is really
only valid for a projection that has the same scale in x and y.  Which I
think is true iff the projection is conformal.  And it's only truly
valid if the scale doesn't change over the layout, which is probably
~never exactly true, but many projections aim to have it remain close
enough to be treated as constant (e.g. UTM).

Which is a long way of getting around to "if you are using lat/lon as
the axes in your layout, either you are doing something odd on purpose
or you probably should rethink your approach."  If you really do mean
it, I would find the explanation of why interesting.

> * Unless the project itself is set to not use ellipsoidal calculations
> and only use planar calculations, in the project properties dialog

Presumably those calculations are in the project CRS's xy space, and
would typically (when used sensibly) be grid distance in UTM, some State
Plane Coordinate System, or similar.
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