ATP question

[Officer Kite]

Fair enough well OK here it goes.

Q 1 ->

For this we need to use the conversion angle formula.

CA = 1/2 (Change in Longitude x SIN Latitude)

From the question we can establish our longitude will change by 10 degrees and our latitude is 56N

So back to the formula ... CA = 1/2 (10 x SIN 56) ... = 1/2 (8.29) = 4.1 deg ... so 4 degrees.

Now we have to refer back to the question to decide what we're gonna do with this 4 degrees. Once you establish we are heading west along the same line of latitude we can say we are heading 270 degrees. We are also in the northern hemisphere and heading west, this means when departing we are gonna head further north than simply following the rhumb line of the 56N latitude line, this shortens our journey time, we know exactly how much we need to turn north of the 56N line of latitude by using the CA formula as above. So adding 270 + 4 = 274. Again, this will be our heading on departure and will be constantly decreasing ever so slightly en route to ensure we are following the great circle line between the 2 points.

Paco also made a good point about the 'INS' equipped thing in the question. It's simply the authority's way of telling you you're going to follow a great circle path.

Q 2 ->

For this we need to know how many degrees North we have gone from our initial starting position. 1 degree of longitude is 60nm, so 2950nm is 49.167 degrees. This is 49 degrees and 10 minutes (.167 x 60minutes per degree = 10 minutes), so we have gone north 49 Degrees and 10 minutes.

Our initial starting position was 04 deg 10' S. We are clearly going to end up in the northern hemisphere, so I find it easier to start off at 49 10 N and subtract the southerly starting position to get our overall final position. So 49 10 N - 04 10 S = 45 00 N.

Now I'm going to presume you meant we turned left by 90 degrees because the other answers don't make sense if we were to turn left 99 degrees (we'd be heading back south when all the answer options are either at our current latitude of 45 00 N or higher).

It should be said though that the answer is clear at this point as +TSRA said, as we are clearly going to cross the anti-meridian and transfer from a W to an E longitude our position will be 45 00N XXX XX E, only one answer option suits this.

Anyway, if we're going north and it says we turn left 90 degrees we are going west now. It says 314 km, we need this in NM, dividing any number in km by 1.852 gives you the NM equivalent. So 314 / 1.852 = 170nm. So we move left (changing our longitude) by 170nm. To find our change in longitude in degrees at this particular latitude we're gonna need another formula.

Departure = distance along a rhumb line. Our rhumb line in this instance is the 45 00 N line of latitude.

Dep = Change in longitude (in minutes) x COS Latitude.

We're going to use this formula to find our change in longitude to complete the second part of our coordinates.

We have our departure as 170NM, we have our latitude also as 45N. So ...

170 = Ch Long x COS 45 ... = Ch Long = 170 / .707 = 240 minutes of Longitude. 240 minutes of longitude divided by 60 gives us 4 degrees as being the change of our longitude. So from 17822W we're heading west 4 degrees.

So 178 22 W + 4 degrees = 182 22 W, so we have an excess of 2 degrees and 22 minutes above 180. Simply subtract 2 degrees 22 minutes from 180 degrees to get 177 degrees and 38 minutes ... 177 38 E is the final position.

So 45N 177 38 E is the answer.

Apologies if the very final bit is difficult to imagine, it would be far easier to explain in person and with a globe in hand, it might be difficult to imagine but hopefully you can understand it and it clicks.

This explanation also assumes an understanding of when to add and subtract the conversion angle, having a quick look at flight radar and seeing what paths aircraft take when heading west/north and in south/north hemisphere should help to gain a vision, it's easier to see for long haul flights. This is how I always remembered it and it's drilled it in, others in my class drew out some small diagrams that helped them remember it until it stuck, I'm sure your course materials have something on it.