Track error and closing angle from a single fix
You are on a leg from A to B, 120 NM apart, planned magnetic track 270°, TAS 115 kt, forecast wind 200/15. After 40 minutes you obtain a fix from a VOR/DME that places you 8 NM right of the planned track and 62 NM from A along track. You have been steering a constant heading. B lies over a range of hills with a published minimum safe altitude of 5,500 ft; you are at 4,500 ft. Visibility is 20 km, and the terrain between you and B rises steadily.
1. Compute your track error, the closing angle to B, and the heading change needed.
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Along-track distance from A is 62 NM; the leg is 120 NM, so 58 NM remain to B.
Track error (angle between planned track and the line from A to your position) = arctan(8/62) ≈ 7.4°, to the right. So you have been drifting right, meaning the wind or your heading is pushing you right.
Closing angle (angle at your position between the line to B and the planned track) = arctan(8/58) ≈ 7.9°, to the left.
Total heading change = track error + closing angle ≈ 7.4° + 7.9° ≈ 15.3° to the left. New heading ≈ 270° − 15° = 255°M.
Note the assumption: this is the one-in-sixty rule applied to a single fix and assumes the wind stays constant. It gets you to B, not precisely onto the original track. If you wanted to regain track before B, you would apply the track error alone (about 7°) until back on track, then the closing angle.
2. Your altitude is 4,500 ft and the MSA ahead is 5,500 ft. What is the immediate priority and what do you do?
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The immediate priority is terrain clearance, not track-keeping. You are 1,000 ft below the published minimum safe altitude with rising terrain ahead and only 58 NM to run. Climb now, before working out the heading.
Actions in order:
- Apply climb power, establish a positive rate, and set 5,500 ft or higher as the target. If the aircraft cannot out-climb the terrain gradient, turn away from the high ground immediately.
- Advise ATC (if in controlled airspace) of your position and intention to climb.
- Only once established in the climb, apply the 15° left heading change.
- Re-check the MSA for the whole area, not just the track: the published figure may apply only within a defined radius of a navaid, and your position 8 NM right of track may be outside it.
The navigation error is secondary. A 15° heading change is worth nothing if you fly it into a hill.
3. How would you use the fix to update your wind estimate for the remainder of the leg?
Read the worked answer
You have covered 62 NM along track in 40 minutes, so your along-track groundspeed is 62/0.667 ≈ 93 kt. Your planned GS can be computed from TAS 115 and wind 200/15 on track 270°: the wind is 70° off track, crosswind = 15 × sin70° ≈ 14.1 kt, headwind = 15 × cos70° ≈ 5.1 kt, so planned GS ≈ √(115² − 14.1²) − 5.1 ≈ 114.1 − 5.1 ≈ 109 kt.
Actual GS is 93 kt, 16 kt slower than planned, and you have drifted 7.4° right. That is consistent with a stronger wind from a more southerly direction than forecast. A wind of roughly 210/30 would produce about that drift and that speed loss. Use that as the working estimate for the remaining 58 NM: expect about 58/93 ≈ 37 minutes, and expect continued right drift, so hold the 15° left correction and re-fix at the next opportunity.
Also revise your fuel and ETA for the destination using 93 kt, not 109 kt: the leg will take about 77 minutes, not 66.