india DGCA ATPL exam

[keith williams]

The following is based on the assumption that the aircraft flies a great circle track.

Great circle direction = Rhumb line direction + Conversion Angle

Conversion angle = ½ change in longitude x sin of mean latitude

We do not know the mean latitude, but we know that the chart factor is 0.6. The trick here is to remember that the chart factor is the sine of the mean latitude. So we know that the sine of the mean latitude is 0.6

The change of longitude between A and B is 170E – 130E = 40 degrees.

So we have

So Conversion angle = ½ x 40 degrees x 0.6 = 12 degrees.

The Rhumb Line Track is 095 degrees

Great circle track = Rhumb Line track + conversion angle

So we have

Great circle track at A = 95 + 12 = 107 degrees

And

Great Circle track at B = 95 – 12 = 83 degrees.

So over the change of longitude of 40 degrees we have a change of track of 107 – 83 = 24 degrees. (Which is of course just the convergence)

This means that the track is changing at rate of 24 / 40 = 0.6 degree per degree of longitude. (Which is of course just the chart factor)


All Great circles other than the Equator and the Meridians are convex to the nearest pole. In this case the aircraft is in the southern hemispheres and the track is in a generally easterly direction. As the aircraft progresses along this track it will gradually turn away from the South Pole. It will reach its closest point to the South Pole when its track is 090. From this point onwards it will turn north and its southerly latitude will decrease.

The initial great circle track is 107 so to get to a track of 090 the track must decrease by 107 – 90 = 17 degrees.

The track changes at a rate of 0.6 degrees per degree of longitude change, so a decrease of 17 degrees requires a longitude change of 17 / 0.6 = 28.33 degrees.

Adding this to the initial longitude of 130E give a longitude of 158.33E.

So the aircraft reaches its most southerly position when it is at longitude 158.33E.