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You don't need to be that good in math. It would be rare that you'd have to calculate it on the fly. Just one of the numbers you pre-calculate for the airplane, like knowing the power/configuration settings that will give you predicted performance. True, to do it "exactly" you're really talking about groundspeed, but a 30-kt tailwind will have less net effect on your calculations at 300 KTS than at 90.
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Agreed. Once the basic calculations are known, they're simply applied wherever necessary. For example, the 3 mile turn radius (or 0.5 for lighter aircraft), can be applied inflight, or in preflight planning/study of the plate. Same with arc to radial calculations. For example, say you want to fly the 20 DME arc and turn inbound on the 090 degree radial from the south. 60 to 1 rule says arc distance divided into 60, multiplied by the turn radius of the aircraft (for my case, again, 3), equals the lead radial. So 20 divided into 60 equals 3. 3 times 3 equals 9, or 9 radials of lead on a 20 DME arc. So crossing the 099 (or 100 radial rounded up), start the left turn to intercept the 090 radial inbound. Again, this formula can conceivably be applied to a light aircraft, but isn't necessarily very practical, since most of the calculations already come out to the CDI coming alive anyway, whereas for faster aircraft, the idea is a lead radial, since when the CDI comes alive, you're already too late. But again, as Midlife said, once the basic calculations are known, the need for the mental math while airborne isn't really needed.
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I think it's really about describing where the arc is rather than how to enter it. Might as well use ATC-standard for this, which is the same as Mike's suggestion. From the ATC Handbook para 2-5-2
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b. Arcs about VOR-DME/VORTAC/TACAN/MLS NAVAIDs. State the distance in miles from the NAVAID followed by the words "mile arc," the direction from the NAVAID in terms of the eight principal points of the compass, the word "of," and the name of the NAVAID.
EXAMPLE-
"Two Zero mile arc southwest of O'Hare Runway Two Seven Left M-L-S."
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Once the pilot understands and can visualize where the arc is in relation to where she is, it's really no different than a charted arc. Of course, the visualization part can cause the same consternation so many of us have with uncharted holds.
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That's good to read. I was taking a guess on my answer. I'd forgotten about the 8 cardinal points for reference vice 4 cardinal points that I was thinking. Re-learn something every day!