ATPL theory questions

[Alex Whittingham]

OK here we go, for gyro experts to comment on. Paco, I get TW of 9 degrees not 1 degree, I don't understand the 0.32 in your formula. I think if you are going to express TW as a rate the formula is (east west groundspeed*tan lat/60)*hours flown which gives the same answer as working it out as convergency.

Solution:

Calculate convergency, conv = ch long sin mean lat = 10 sin 60 = 8.6 deg,
Conversion angle = 1/2 convergency = 4.3 deg
Rhumb line = 090 deg T, therefore initial great circle track = 090 - 4.3 = 085.7 deg T
This will also be initial gyro heading as they are aligned
Final GC track will be 090 + 4.3 = 094.3 deg T

Assuming first of all for the sake of argument that the great circle track is followed by reference to other instruments (INS?) and the gyro is compensated for latitude the total gyro drift will be:
ER + LN + TW
= ([-15 sin 60]*1.5) + ([+15 sin 60]*1.5) + (-10 sin 60)
= (-13) + (+13) + (-9)
= -9
So the final gyro heading will be 094.3 – 9 = 085.3

Now modifying the above so that we continue to fly the GC track by other means but the gyro is now not compensated for latitude, the total gyro drift will be
ER + LN + TW
= ([-15 sin 60]*1.5) + (0) + (-10 sin 60)
= (-13) + (0) + (-9)
= -22
So the final gyro heading in this case will be 094.3 – 22 = 072.3

By which calculations we can see that flying a constant gyro heading/track is not going to follow the shortest (great circle) route. Is it true that flying the ‘average gyro heading/track’ will still get us from A to B by a curved track lying to the north of the great circle? I think so.

If so the ‘average’ to approximate to the GC track without latitude nut correction is (085.7+072.3)/2 = 079 deg

I can't immediately see logically why any calculations should be based on gyro corrections applied to the rhumb line track as we are after the shortest path but, interestingly, if you follow the same argument through and try and fly a rhumb line track by other means the initial true and gyro headings would be 090, the final true heading would be 090, gyro errors would be the same -22 so final gyro heading would be 068, and the average gyro track also 079. This is because the average great circle track is 090, and by averaging out initial and final gyro headings on a great circle track we average out the 'great circle elements' and arrive at the same answer. At one level not surprising because we would not expect to find two constant gyro headings/tracks between two points.