DME Holding

DME slant range is ignored in the design of instrument approach procedures. As to DME Arcs, the minimum radius is 7 miles.
And DME arcs are parts of instrument approaches, so they are always at low altitude.

And the tolerance is the broad side of a barn -- a whole mile.
 
So, I just want to confirm because there seems to be some confusion. The instructions from ATC would be:
- hold northwest
- GFK 120 radial
- 10 DME

I understand he's holding southeast of the GFK VOR, but he is in fact holding northwest of the holding point. So therefore the cardinal direction from ATC's instructions would be to hold northwest?
Yes. There has been some question about the exact phraseology - 10 mile DME or 10 mile fix- but otherwise everyone in the thread ultimately agrees that is correct. A hold northwest of a fix that is 10 miles from GFK on the GFK 120 degree radial.
 
And DME arcs are parts of instrument approaches, so they are always at low altitude.

And the tolerance is the broad side of a barn -- a whole mile.

It's more like the whole farm. One mile may be what you are striving for when you fly it and what ATC is kinda hoping for if they are using Radar to separate you from other aircraft, and it may be the "tolerance" to certify that the DME reciever is within "limits," but the separation minima is a whole lot more. Using DME arcs to separate aluminum from aluminum it's 5 miles when less than 35 miles from the NAVAID, and 10 miles when 35 or more miles from the NAVAID. I don't know exactly what it is for separating aluminum from rocks, but it's more than one mile.
 
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