You depart point A at 12:15 and begin a planned route of 80 NM. Your initial heading is 235º. At 12:27 you pass a rail track crossing your path at 90º after travelling 40 NM. At 12:33 the pilot realizes he/she is 4 NM to the left of the intended track. What heading should you fly to reach your intended destination and what will be your ETA?
Refer to figure.
With the information provided by the question text, we can calculate the aircraft’s ground speed. The aircraft departs at 12:15 and we know that at 12:27 (after 12 minutes), the aircraft has covered 40 NM.
- Ground speed = (40 ÷ 12) x 60 = 200 kt
At 12:33, the aircraft would have covered a further 20 NM:
- 12:33 – 12:27 = 6 min
- (200 kt x 6 min) / 60 = 20 NM
At 40 NM + 20 NM = 60 NM along the route (12:33), the aircraft is 4 NM to the left of the intended track.
Calculate the TKE (Track Angle Error) to give us the heading correction in order to parallel our intended track:
- TKE = (distance off track × 60) ÷ distance along track
- TKE = (4 × 60) ÷ 60
- TKE = 4°
If we alter our heading by 4° (towards the original track) we will parallel our original track. In order to re-join the original track, we must calculate the track correction for the distance to go:
- TKE = (distance off track × 60) ÷ distance to go
- TKE = (4 × 60) ÷ 20
- TKE = 12º
So turning 4° will parallel our track, and turning an extra 12° on top of that will direct us to the final destination. Therefore, 4° + 12° = 16º would be the total alteration required (to re-join the original track).
- The deviation was to the left, therefore we must fly 16º to the right. Track = 235º + 16º = 251º
The aircraft 80 NM – 60 NM = 20 NM away from the destination. At 200 kt, it will cover 20 NM in 6 minutes.
- The destination will be reached at 12:33 + 6 min = 12:39
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