Q1. Which of the following differences in latitude will produce the greatest difference between the initial great circle track and the mean great circle track, between two points which are separated by 10 changes of longitude?
60 N and 55 N. – The “difference between Initial GC Track and Mean GC Track” is the Conversion Angle (CA). Formula: CA = 0.5 * dLong * sin(Mean Lat). To maximize CA for a fixed dLong (10°), you must maximize the Sine of the Mean Latitude. The pair 60N-55N has the highest mean latitude (57.5°), thus the highest conversion angle.
Q2. What is the great circle track (measured from the starting position) from 70S 030 W to 70 S 060 E.
132 T – Route is Eastbound along 70S. Rhumb Line (RL) track = 090°T. In Southern Hemisphere, GC track is “concave” to the pole (bends South). This means Initial GC track > RL track. Calculation: Conversion Angle = 0.5 * dLong * sin(Lat) = 0.5 * 90 * sin(70) ≈ 42.3°. Initial GC = 090 + 42.3 = 132.3°T.
Q3. An aircraft is in the position (86°N, 020°E). When following a rhumb line track of 085°(T) it will:
fly via a spiral to the North Pole – A constant True Track (Rhumb Line) of 085° means the aircraft is flying generally East but with a 5° component towards North (090° is pure East). Since it constantly maintains a northerly component in the polar region, it will spiral inwards until it reaches the North Pole.
Q4. An aircraft takes off from A (68 S 010E) and follows a great circle track to B (62 S 017E). On track A to B great circle track:
decreases by 6 degree – Movement is generally Eastward (10E to 17E). In the Southern Hemisphere, Great Circle tracks decrease as you fly East (Convergency rule). The change in track is equal to Earth Convergency. Conv = dLong * sin(Mean Lat) = 7° * sin(65°) ≈ 6.3°.
Q5. An aircraft passes position A (60°00’N 120°00’W) on route to position B (60°00’N140°30’W). What is the great circle track on departure from A?
279° – Flying West along 60°N. Rhumb Line = 270°T. In Northern Hemisphere, GC lies North of RL. For a Westbound flight, this means the Initial Track is greater than 270°. Conversion Angle = 0.5 * dLong * sin(Lat) = 0.5 * 20.5 * sin(60) ≈ 8.9°. Initial Track = 270 + 8.9 = 278.9° (round to 279°).
Q6. An aeroplane flies from A (59°S 142°W) to B (61°S 148°W) with a TAS of 480 kt. The autopilot is engaged and coupled with an Inertial Navigation System in which AB track is active. On route AB, the true track:
increases by 5° – Movement is Westward (142W to 148W) in the Southern Hemisphere. Rule: In SH, Westbound Great Circle tracks increase. Change = Convergency = dLong * sin(Mean Lat) = 6° * sin(60°) ≈ 5.2°.
Q7. A great circle track joins positions A (59 S 141 W) and B (61 S 148 W). What is the difference between the great circle track at A and B?
It increases by 6 – Similar to previous question. dLong = 7°. Mean Lat = 60°. Conv = 7 * sin(60) ≈ 6.06°. Westbound in SH = Track Increases.
Q8. The angle between the true great-circle track and the true rhumb-line track joining the following points: A (60°S 165°W) B (60°S 177°E), at the place of departure A, is:
7.8° – This angle is the Conversion Angle (CA). dLong = 15° (to 180) + 3° (from 180) = 18°. CA = 0.5 * dLong * sin(Lat) = 0.5 * 18 * sin(60) ≈ 7.79°.
Q9. An aircraft takes off from A (20N 30E) and follows a great circle track to B (30 N 60E). The great circle track at A is:
13 degree less than B. – Movement is Eastbound in Northern Hemisphere. Rule: NH Eastbound -> Track Increases. Therefore, Track A must be less than Track B. Difference = Convergency = dLong * sin(Mean Lat) = 30 * sin(25) ≈ 12.7° (round to 13°).
Q10. 1. The constant of the cone, on a Lambert chart where the convergence angle between longitudes 010°E and 030°W is 30° is:
0.75 – Constant of the Cone (n) = Chart Convergence / Change in Longitude. dLong = 10°E to 30°W = 40°. Convergence = 30°. n = 30 / 40 = 0.75.