One Fix, Three Numbers: Correcting Track and ETA
You cross the start-of-leg point at 10:20 UTC. Planned track 180°T, 120 NM to destination, planned ground speed 100 kt, planned ETA 11:32. Forecast wind 250°/20 kt; your wind triangle gave a heading of 170°T at TAS 105 kt. You have held 170°T since departure. At 10:50 a positive fix - two identifiable features plus GPS agreement - places you 45 NM along track and 3 NM left of it. Fuel at departure was 32 US gal usable, consumption 8 gph, and there has been no significant weather. The heading indicator was checked against the compass ten minutes ago and agrees. Your destination has one runway, no instrument approach, and you have no alternate planned.
1. Using the 1-in-60 rule, calculate the track error, the closing angle, and the heading you should now fly. State each assumption.
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Track error (the angle you have already drifted). You are 3 NM off after 45 NM along track.
- Track error = (offset ÷ distance flown) × 60 = (3 ÷ 45) × 60 = 4° left
Closing angle (the angle needed to converge on destination). Remaining distance along track = 120 − 45 = 75 NM; you must close 3 NM in that distance.
- Closing angle = (offset ÷ distance remaining) × 60 = (3 ÷ 75) × 60 = 2.4°, call it 2–2.5°
Heading change. Turn right by the sum: 4 + 2.4 ≈ 6.5°.
- New heading = 170 + 6.5 = about 176.5°T, i.e. fly 176°T or 177°T.
Assumptions to state. That your 45 NM and 3 NM figures are accurate (one fix can be wrong); that the wind stays as it is now rather than as forecast; and that the 1-in-60 approximation is adequate at these angles, which it is below about 10–15°.
The classic error to avoid: setting the heading to the track (180°T) or to track plus closing angle. The correction is applied to the heading you were holding, because that heading contains the wind correction you still need.
2. Derive your actual ground speed and revised ETA from the fix, and say what you would check before accepting the revised figure.
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Ground speed. You covered 45 NM in the 30 minutes from 10:20 to 10:50.
- GS = 45 NM ÷ 0.5 h = 90 kt
That is 10 kt below the planned 100 kt, so the along-track wind component is stronger than forecast.
Revised time to run. 75 NM remaining at 90 kt = 0.83 h = 50 minutes.
- Revised ETA = 10:50 + 50 min = 11:40, eight minutes later than planned.
Checks before you believe it.
- Is 90 kt right, or is the fix wrong? A single fix can be a misidentified feature. The GPS agreement helps; a second fix in 10–15 minutes would settle it.
- Is the trend continuing? If the ground speed keeps falling, the ETA keeps sliding; if it recovers, you have over-corrected. Re-fix rather than extrapolating a forecast.
- Fuel. 30 minutes at 8 gph = 4 gal used, leaving 28 gal = 3.5 h. The remaining 50 minutes burns about 6.7 gal. Fuel is not the constraint here - but note that every minute of lost ground speed is also a minute of reduced margin, and you have no alternate.
3. You are now 6.5° off and have 50 minutes to run. Would you apply the whole correction at once? Give your reasoning.
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The case for applying it now. The correction is small, you have a good fix, the DI agrees with the compass, and the destination has no approach and no alternate - being precisely on track matters at the far end, not at the near end. Applying it now gives maximum time for the correction to work.
The case against. Everything rests on one fix taken 30 minutes in. If the 3 NM offset is a misidentification, a full 6.5° correction could double the error. There is also a subtle trap: after you turn 6.5° right, the drift you had been experiencing does not disappear, so the track you achieve will not be exactly 182.5°T, and the correction will need refining at the next fix anyway.
A balanced plan. Apply the track-error part (about 4° right, now 174°T) and hold that briefly; at the next fix, measure the remaining offset and apply the convergence angle needed over the distance still to run. This converges smoothly and never overshoots.
What to watch. This is exactly the situation where a small error is allowed to grow because nobody re-fixes. Fix at least every 15–20 minutes, and treat any disagreement between the new heading and the DR plot as a reason to fix sooner. With no alternate available, arriving on the centreline is the whole point.