1

The Tissot's indicatrix of an Azimuthal Equidistant projection shows ellipses being stretched along latitudes.

How can I calculate the degree (amount) of this distortion? That is, what is the ratio of major axis to minor axis of a Tissot ellipse as a function of latitude (assuming the center of projection is the north pole)?

Edit: Found numerical values on the GIS help page.

Degrees from center     Percentage of scale distortion along parallels
15                      1.2
30                      4.7
45                      11.1
60                      20.9
90                      57

I can interpolate this well and get what I need. But would still be good to know what the analytical formula is. Feels like a function of cos(latitude) since an Azimuthal Equidistant projects latitudes with linearly increasing distance from center instead of cosine.

Azimuthal Equidistant Tissot's indicatrix

2

You can find the scale distortion from the latitude with this simple formula (latitude in radians) given an origin at the North Pole:

(pi/2) - lat
------------
  cos(lat)

This will give you the ellipse's ratio you're looking for.

Example with 60°N:

(pi/2) - (pi*60/180)
--------------------   = 1.04719...
   cos(pi*60/180)

Which is a 4.7% distortion as stated in ArcGIS Help.

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