Multiple Ring Buffer and Geographic Coordinate systems

[RobertStevens]

I have a point dataset: a single point whose coordinates are geographic (WGS_1984). The coordinates of the frame containing this layer are Web Mercator (Auxiliary Sphere). Using ArcGIS basic 10.8.1

I used the multiple ring buffer tool to create a single buffer of radius 1 mile. The tool runs and draws a circle.
When I use the distance measuring widget to measure that radius it reports that the radius is 1.3 miles!

I use the project tool to convert the coordinate of my single point layer to those of the frame (Web Mercator Auxiliary sphere). Use again the multiple ring buffer tool. This time the circle drawn is indeed much smaller, and the distance widget confirms that the radius is  indeed 1 mile.

OK. So you are going to tell me that I should not use that tool  (and very possible other proximity tools) on a layer whose coordinate are geographic. Fine. But why does the tool not report this as an error? It know the coordinate systems of the frame and of the point layer. And how can the discrepancy be 30%? A one mile radius drawn on the tangent plane at a point on a sphere cannot possible differ from a one mile radius drawn on the sphere by as much as 30% - not when the radius of the earth is 4000 miles.

It is only by shear luck that I realised I had a problem. Why is the software unable to alert me to this problem?

[DanPatterson]

The description about planar and geodesic buffers is pertinent here

How Buffer (Analysis) works—ArcGIS Pro | Documentation

The tool's help does warn about what type of buffer to use

Multiple Ring Buffer (Analysis)—ArcGIS Pro | Documentation

and indeed it is best to buffer planar geometry if you can get away with.

also note, web mercator, which is indeed a projected coordinate system.... should never be used for any type of analysis that involves distance and area measures... it is just not up to the task.  Sadly it is web friendly, but unless you are going beyond showing stuff, stick to projections that are suited for analysis and measures.

Addendum

historical readings Tissot's indicatrix - Wikipedia

[RobertStevens]

Dan

Thanks for reply and especially warning about Web Mercator.

I am surprised, when I ran the tool, that there was no popup warning about coordinate systems.
Of course, one should always read the description before using a tool. Fair enough.

But I do not understand how, over a distance of one mile on the earth's surface, which is a small enough area as to be considered flat, that the tool I used based on a point with geographic coordinates can be off by 30%!

There must be some bug in there somewhere.

[DanPatterson]

that is web mercator for you

[RobertStevens]

I have to confess that I still do not understand this.

I understand that if I ask for a buffer of radius one mile to be drawn that it may appear as an ellipse (although hardly detectable as such). I understand that if I have a map whose extents are large compared to the circumference of the earth that a circle of a given  drawn at different latitudes/longitudes may appear to have a different size.

I do not understand, when I ask to create a buffer which is a circle of radius one mile, that I get  two circle of radii seeming different in radius by 30% or so. (still circles as far as the eye can judge) when the point around which I am drawing the circle has coordinates which are geographic instead of projected. The size of the circle should not depend on the coordinates of the point in question whether they be expressed as geographic ones, or projected ones. A point is still a point, and the displayed circles, whether distorted due to the projection or not, should appear identical. And they are anything but.

[DanPatterson]

projection-on-the-fly affects the visual, it is the math that determines the size and shape of something as 'simple' as a circle.  If you want to work with geographic coordinates rather than a suitable projected coordinate system, use tools that support geodesic calculations