DME Arc Turn Anticipation with Wind
You are flying a DME arc at 15 NM from a VOR, tracking clockwise toward the 090° radial, which is the inbound course for the approach. TAS is 120 kt, and the wind is 360°/30 kt. Your current radial is 070°, and the aircraft is established on the arc. The autopilot flies a standard-rate turn (3°/s) at 120 kt, which gives a turn radius of about 0.65 NM; at 150 kt the same rate gives about 0.80 NM. The VOR is serviceable, but the DME has a published accuracy of ±0.5 NM or 3% of distance, whichever is greater. You are at 4,000 ft.
1. Calculate the lead radial for starting the turn to intercept the 090° radial.
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Lead angle = arcsin(r/R) = arcsin(0.65/15) = 2.48°. Because the arc is clockwise toward 090°, start the turn at radial 090 − 2.48 = 087.5°, i.e. about 087°30′. At standard rate the 90° turn takes 30 s, so the aircraft covers the turn while the DME remains near 15 NM if the turn is started at the correct lead. If the turn is delayed until the 090° radial, the aircraft will overshoot the inbound course and need a large correction.
2. Compute the DME accuracy tolerance at 15 NM and explain how it affects the lead point.
Read the worked answer
DME tolerance = greater of 0.5 NM and 3% of 15 = 0.45 NM, so ±0.5 NM. At 15 NM, 0.5 NM subtends 0.5/15 rad = 1.91°. The indicated 15 NM arc could actually be 14.5 to 15.5 NM. The lead angle then varies from arcsin(0.65/15.5) = 2.40° to arcsin(0.65/14.5) = 2.57°, so the lead radial range is about 087.4° to 087.6°. The DME error is small for the lead; the larger issue is ground speed and bank angle. Use the DME distance as a cross-check, not as a precise turn cue.
3. With the wind at 360°/30 kt, estimate the groundspeed on the arc at the 090° radial and decide whether the 0.65 NM lead is conservative.
Read the worked answer
At radial 090 the aircraft is east of the VOR; the clockwise arc tangent is south (180°). Wind 360/30 is a direct tailwind, so GS = 120 + 30 = 150 kt. Standard-rate turn radius at 150 kt = V/ω = (150 × 0.5144)/(3 × π/180) = 77.2/0.05236 = 1,474 m = 0.80 NM. New lead angle = arcsin(0.80/15) = 3.06°, so lead radial = 086.9°, about 1° earlier than the no-wind 087.5°. The 0.65 NM lead is too late at 150 kt; start at 087° or slightly earlier, and monitor the CDI because the wind may change around the arc.