The labels of the last lesson promise performance; this lesson is about flying it and proving it. First the specific system functions that let a PBN (performance-based navigation) route bend, transition and offset; then the error arithmetic that makes the performance measurable, and the monitoring that watches each error while the aircraft flies.
Legs, turns and offsets
Two curved-path functions carry the syllabus's definitions:
an RF (radius to fix) leg — a curved leg of constant radius, flown between two fixes as part of a procedure;
an FRT (fixed radius transition) — a turn of fixed radius connecting one en-route segment to the next.
An RF leg is a drawn arc, and the aircraft must stay on it: it is important to respect the flight director guidance and the speed constraints associated with an RF procedure, because the radius only works if the groundspeed, and with it the bank the flight director commands, stays within what the arc was designed for. At ordinary waypoints, the question is how the corner is flown: the difference between a fly-by turn and a fly-over is where the turn happens:
fly-by — the turn is anticipated, cutting the corner inside the waypoint so the aircraft joins the next leg without overshooting;
fly-over — the aircraft crosses the waypoint first and turns after it, rejoining the next leg from the outside.
One lateral function completes the set: an offset flight path is a route flown parallel to the parent route, displaced laterally from it by a selected distance: the track keeps every turn of the original while riding beside it.
Path terminators
Procedures reach the navigation computer as code, and the coding has a standard: the ARINC (Aeronautical Radio, Incorporated) 424 path terminators set the standards for coding the SIDs (standard instrument departures), STARs (standard instrument arrivals) and IAPs (instrument approach procedures) from the official published government source documentation into the ARINC navigation database format. The name says what they do: a path terminator defines a specific type of termination of the previous flight path: each coded leg states how it ends, and the chain of endings is the procedure.
The error arithmetic
For performance to be required, error must be measurable, and the syllabus splits it three ways:
PDE (path definition error) — the error between the desired path and the path actually defined in the system;
FTE (flight technical error) — the error in following the prescribed path, whether it is flown by the auto-flight system or by the pilot;
NSE (navigation system error) — the error in the system's estimate of position; the accuracy of a navigation system may be referred to as NSE.
Stack them and the total appears: the geometric sum of the PDE, the FTE and the NSE equals the TSE (total system error), and navigation accuracy depends on the TSE: the X of the last lesson's labels is a bound on exactly this quantity. Geometric is the operative word: the components combine like the sides of a right triangle, the square root of the sum of their squares, not by simple addition, so error contributions of 0.3 NM and 0.4 NM make a TSE of 0.5 NM, the 3-4-5 triangle again, and not 0.7.