An aircraft is flying from A to B a distance of 45 NM. The True Course in the flight log is 270°, the forecast wind is 045°T/15 kt and the TAS is 120 kt. After 15 minutes of flying with the planned TAS and TH the aircraft is 3 NM south of the intended track and 2.5 NM ahead of the dead reckoning position.
To reach destination B from this position, the correction angle on the heading should be..
Refer to figure.
Determine the distance along track:
Distance = (130 kt x 15) / 60 = 32.5 NM
The aircraft is 2.5 NM ahead of planned position. Therefore;
- Distance along track = 32.5 NM + 2.5 NM = 35 NM
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 = (3 × 60) ÷ 35
- TKE = 5°
If we alter our heading by 5° (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 = (3 × 60) ÷ 10
- TKE = 18º
The result is greater than 15º and therefore inaccurate. Trigonometry:
tan α = 3 NM / 10 NM
α = tan-1 (3/10) ≈ 17º
So turning 5° will parallel our track, and turning an extra 17° on top of that will direct us to the final destination. Therefore, 5° + 17° = 22º would be the total alteration required (to re-join the original track).
The deviation was to the left; therefore we must fly 22º to the right.
Your Notes (not visible to others)