An aircraft departs from Waypoint 1 at 10:00 UTC for Waypoint 2 which is 49 NM away. At a fixpoint 27 NM along the route the pilot realizes that the aircraft is 1.5 minutes late. If the planned groundspeed is 80 kt, what is the new groundspeed that should be followed from the fixpoint until Waypoint 2, in order to arrive at Waypoint 2 at the planned arrival time?
Refer to figure.
(1) Calculate the planned arrival time at the Waypoint 2
The pilot was planning to follow a groundspeed of 80 kt to reach Waypoint 2 which is 49 NM away. The planned arrival time at Waypoint 2 is after:
Time (min) = Distance (NM) / Groundspeed (kt) x 60 = 49 / 80 x 60 = 36 min 45 sec
Since the aircraft departed from Waypoint 1 at 10:00 UTC, the planned arrival time at Waypoint 2 is 10:36:45 UTC (10:00:00 + 00:36:45 = 10:36:45).
(2) Calculate the actual arrival time at the fixpoint
The aircraft was planning to follow a groundspeed of 80 kt towards the fixpoint which is 27 NM away. The planned arrival time at the fixpoint is after:
Time (min) = Distance (NM) / Groundspeed (kt) x 60 = 27 / 80 x 60 = 20 min 15 sec
This means that the planned arrival time at the fixpoint is 10:00:00 UTC + 00:20:15 = 10:20:15 UTC. The aircraft arrived 1.5 minutes later than planned, so the actual arrival time at
the fixpoint is 10:21:45 UTC.
(3) Calculate the new groundspeed required
We need to find the groundspeed that will bring the aircraft from the fixpoint to Waypoint 2 at the planned arrival time (10:36:45 UTC). The aircraft arrives at
the fixpoint at 10:21:30 UTC so the time remaining is 10:36:45 - 10:21:45 = 00:15:00 = 15 min. The remaining distance is 49 NM - 27 NM = 22 NM. The new groundspeed required is:
Groundspeed (kt) = Distance (NM) / Time (hr) = 22 NM / (15 min) x 60 = 88 kt
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