Some other rules of thumb, with all turns at Rate 1.
1. Lead distance to turn onto the arc from an inbound or outbound radial/bearing (nil wind. Use groundspeed if head or tailwind is significant)
TAS / 200 = nm lead to commence the turn
eg inbound at 180 kts TAS = 0.9 nm lead DME dist to commence the 90 degree turn onto the ARC
2. Lead BRG to commence the turn inbound on final:
Using a lead distance determined using method 1.
60 / DME ARC dist x lead dist = degrees lead needed to commence the turn
eg. 120 kt TAS, therefore Lead dist = 0.6 nm, DME ARC = 12 nm
so, 60/12=5; 5 x .6 = 3.6 deg ie approx 5 deg (rounded). Start the inbound turn 5 deg of arc prior to the inbound radial or track.
This is particularly easy if you have an RMI or RBI. When the head of the needle is at or just after 5 deg above the abeam/wingtip position, commence the turn.
3. On the initial turn to establish on the ARC you will need to turn approx 10 deg more than 90 deg if joining from an outbound track, or approx 10 deg less than 90 deg if joining from an inbound track.
4. Once on the ARC, it can be flown entirely using the DME ie without reference to an azimuth aid. I refer ONLY to maintaining oneself on the arc, NOT determining position around the arc (although that is also possible).
As mentioned by Checkboard, the ARC should be flown as a series of straight segments. You should then find the following:
a. Mininum rate of closure will be when the aircraft's track made good is at 90 deg to the direct track to the DME. This corresponds to the minimum distance to the DME in that particular straight segment.
b. Commence your turn onto the next straight segment prior to reaching the DME ARC distance ie try to keep yourself inside the ARC. That way the arc is always curving to intercept your straight flight path. This means it is self correcting regarding containment within the tolerance. If you get onto the outside of the ARC then it is constantly deviating away from you. This will eventually cause you to exceed the tolerance - unless you adjust your HDG to correct it, of course.
c. You can determine if each of your HDG adjustments is sufficient because if it is, then you should see a rate of closure develop that then reduces as you close with item 'a.' above.
With practice you can contain yourself within the half nm or so inside the arc.
I rather like DME ARCs. Very easy & can be efficient if not too lengthy. With good design they can also have step down altitudes that get eliminate having to lose height in the holding pattern.
Hope this helps.