Navigation and Aircraft Performance
Navigation fundamentals
The great circle is the shortest path over the earth; the rhumb line is a constant track and longer. Track is the path over the ground, heading is where the nose points, and the difference is drift. Magnetic heading = true heading minus easterly variation (variation east, magnetic least). VOR gives magnetic radials, DME slant range, NDB relative bearings, and ILS a localiser and typically a 3-degree glidepath (about 300 ft per NM).
PBN covers RNAV and RNP; RNP adds on-board performance monitoring and alerting. Controllers need the aircraft's navigation capability to know which routes and separation minima apply.
Performance
TAS plus wind gives groundspeed. Climb gradient percent = height gained divided by distance; 3.3 percent is roughly 200 ft per NM. V1, VR and V2 define the take-off regime. Wake categories (Light, Medium, Heavy, Super) drive wake separation.
Traps
Mixing heading with track, magnetic with true, or NM with km. Assuming a faster aircraft always closes a gap - if it is behind and faster, yes; ahead and slower, yes.
Worked example - rate-one turn
At 3 degrees per second, turn diameter in NM is approximately TAS/100. At 300 kt TAS, diameter is about 3 NM, radius 1.5 NM. This explains why a 300 kt aircraft needs roughly 1.5 NM to turn 90 degrees and why holding patterns have such generous dimensions at high level.
Rule of thumb
For approach spacing, 3-degree glidepath = 300 ft per NM; a 700 ft-per-minute descent at 140 kt ground gives roughly that path.