Refer to figure or to chart AT(HI)5 from Jeppessen GSPRM.
A pilot wishes to check their position using a radio navigation aid. The RB NDB (74°45'N 095°W) is tuned in the ADF. Given the following, calculate the direction of the position line from the NDB to the aircraft's position to be plotted on the Polar Stereographic Chart.
DR Position: 75°10'N 089°58'W
RMI Reading: 295°
Refer to figures.
There are a few steps to this question, so it can be a little bit tricky. As always, it is best to start with drawing out a quick diagram of the problem - where the aircraft is relative to the NDB. Navigation to and from NDBs is done on great circles - which are approximately straight lines on aeronautical charts. (This is the same for VOR radials).
The RMI displays the magnetic heading from the aircraft to the NDB. The magnetic variation applies at the aircraft as this is where the signal is measured. The aircraft's position lies almost exactly on the 35°W variation line, so we will use a variation of 35°W
We can find the True Track from the aircraft to the station using the mnemonic:
Variation West, Magnetic Best, therefore the True Great Circle Track is: 295° - 35° = 260°(T)
In order to calculate the line from the NDB to the aircraft (at the NDB), we need to calculate the convergency. We need to draw another diagram to orient ourselves:
- Convergency = Change longitude x sin(parallel of origin)
- Convergency = (95° - 89°58' ) x sin(90°) = 5°
- (The conversion angle is half of this, 2.5°)
The GCT from the NDB to the aircraft at the aircraft will be 260° - 180° = 080° (T)
The convergency tells us by how much this GCT will change from the NDB to the aircraft. Referring to the diagram, we can see that the heading will decrease as we move West towards the NDB.
We subtract the convergency from the GCT at the aircraft to find the heading of the line to be drawn at the NDB; 80 - 5 = 075°(T).
Note: The parallel of origin for a Polar Stereographic chart is 90°N/S. This means the change in longitude = convergency.
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