Successfully navigating RF legs
One might argue that a "Radius-to-Fix" (RF) leg is simply a constant-radius turn around a specific point . While this is technically correct, there are several particularities that should be clearly understood by the flight crew in order to avoid unpleasant surprises.
The main drivers to define turns with a fixed radius over ground are airspace usage optimization and challenging terrain or obstacle situations. RF legs have first been appearing in "Required Navigation Performance Authorization Required" (RNP AR) procedures , but are now quite often part of “regular” RNP departures, arrivals and approaches. The application of RF legs to the Final Approach Segment (FAS) and the initial and intermediate part of the missed approach is currently limited to RNP AR procedures . As procedure design around the world shift towards Performance Based Navigation (PBN), the number of airmen confronted with RF legs is rapidly growing. The main difference, when compared to a "conventional procedure" using a speed and bank instruction is that it is much more precise in the outcome, but the actual bank value required is not immediately obvious, as it depends on many parameters, such as airspeed, temperature and wind.
Figure 1: Typical RNP departures containing RF legs 
Guidance on how to design a procedure involving RF legs can be found in . It would be beyond the scope of this article to cover the entire procedure design, but some aspects are important also for flight crews:
Turn protection area:
While the ICAO design guidance does require a small extension of the protection area towards the “outside of the turn” using a small "buffer value" , Figure 2 shows that from a practical standpoint, the protection area during an RF leg is very similar to the straight segments before and after. This is obviously one of the main advantages of an RF leg compared to a conventional “fly-over” turning point.
Figure 2: Protection area of RF leg compared to straight segments 
It is thus essential to understand what the RNP value of the procedure at hand actually is.
The procedure may require up to 25 degrees bank angle above 400 ft agl . This ensures some “margin” between the procedure design and the capabilities of the aircraft systems, as the airworthiness requirements demand 30 degrees of bank, as we shall see later.
TAS and wind considerations
The influence of the aircraft speed and local wind are critical. ICAO makes the following recommendation for procedure designers: Extract from :
'The maximum TAS should be based upon the IAS for the maximum height during the turn, corrected for the maximum deviation from the ISA value for the aerodrome'.
'Maximum wind speed is defined as the ICAO standard wind or, where statistical wind data are available, the maximum wind speed within 95 per cent probability on an omni-directional basis.'
RF leg approval process
There are two distinct areas regarding the approval process for RF legs.
1. Airworthiness certification
2. Operational approval
The following summary aims to give a reasonable idea of the requirements. For an exhaustive list, the reader is redirected to the applicable reference material.
The paragraph below lists the most important airworthiness requirements, bear in mind that this analysis is the task of the aircraft manufacturer or the design organization in case of a retro-fit.
The avionics shall not allow selection of a procedure that the aircraft is not capable of executing (e.g.: selection of a procedure containing RF legs, if the aircraft is not approved for such an operation). If this is not feasible, pilot training to identify and avoid RF legs is also accepted .
The guidance systems are required to be capable of commanding up to 30 degrees of bank above 400 ft agl for RNP procedures and also up to 8 degrees below 400 ft agl for RNP AR procedures .
The guidance/flight control system combination shall achieve the required accuracy using at least “roll-steering” capability  .
Any failure affecting the ability to execute RF legs shall be annunciated in the pilot’s primary field of view  .
The ability of the aircraft to maintain an RF leg after such a failure (e.g.: autopilot failure) shall be documented  .
In case of go-around (TOGA application), the guidance mode should remain in NAV and not revert to HDG or TRK. If this is not ensured, additional crew training to select NAV mode has to be specified  .
An electronic map displaying the selected procedure including RF legs shall be available to the flight crew  .
The aircraft documentation shall contain limitations regarding the use of “direct-to” functionality in the context of RF legs (see below)  .
Some airworthiness authorities also require a flight technical error (FTE) analysis for consecutive reversing RF legs as well as for configuration changes during an RF leg .
At ICAO level, operational approval guidance can be found in  and .
In essence, the operator has to document the following three core items:
- The aircraft airworthiness approval for RF legs
- The documented operating procedures including contingencies (OM)
- Evidence of pilot training
Airworthiness approval is typically obtained from the aircraft manufacturer. The operating procedures and contingencies are to be developed by the operator and documented in the Operating Manuals (OM). Pilot training for RF legs may be combined with general PBN training . Based on this documentation, the state of regulatory authority will then issue an operational approval .
Operational procedures and caveats
This section provides some hints for flight crews as to where possible troubles might be encountered:
Adherence to published approach speeds is especially important for procedures containing RF legs, as the bank angle required obviously increases with airspeed. There is no general speed limit for RNP procedures, however in case of an RNP AR procedures containing RF legs, the following speed limits apply:
Figure : EU-OPS speed limits for RNP AR with RF legs 
It is worth noting, that a higher speed may be used, as long as the minima are also increased correspondingly. (I.e. an A320 (cat C) may use the cat D speed and comply with cat D minima) .
It is obviously impossible for the flight crew to know what the “design wind” for a given procedure was. Knowing at what point the maximum bank will be required for the actual wind can also be helpful in detecting a potential problem. Remember that there is a 5 degree “bank margin” between what ICAO allows for procedure design (25 degrees)  and what the guidance system has to be able to command (30 degrees)  .
The flight crew should treat any “direct-to” clearance to a waypoint immediately preceding an RF-leg with greatest caution, as this may place the aircraft outside the protected area, as depicted below.
Figure : A “direct-to” clearance to a waypoint preceding an RF-leg can place the aircraft outside of the containment area  (modified)
RF-legs shall not be intercepted by radar vectors as track alignment is not ensured, similarly to the “direct-to” scenario .
Early missed approach
Beware of the acceleration altitude. If the missed approach contains an RF leg, observe the applicable speed limits and delay acceleration as necessary.
Additional TAS effect (this is for nerds only)
This effect is quite subtle and usually small, however it is worth being aware of, especially for operators of very-high performance aircraft. If the missed approach contains an RF leg, the design requirements assume TAS at the highest published altitude  . If an aircraft initiated the missed approach early and climbs significantly above the published profile (e.g. upon ATC instruction), the actual TAS will be higher.
The development of contingency procedures for “loss of GNSS” or “engine failure” rests with the operator. The airworthiness standards simply “encourage” the designers to provide “redundancy” . Depending on the aircraft type, this places the operator in a rather uncomfortable position. ICAO recommendation for “loss of RF capability during an RF leg” is simply to maintain the bank angle and to roll out on the charted track . This is however not acceptable for RNP AR operations, as there is a requirement for remote (>10^-5/h) failures to be contained within one RNP value .
FMS manufacturer comparison
In a unique experiment, the MITRE corp. was able to compare several typical guidance system (FMS) and aircraft combinations with regard to their tracking performance during RF-legs . Bench test data was provided by the manufacturers, after they had been tasked with the same procedures. It is interesting to see, that not all manufacturers use the same commands (i.e. roll-rate, roll-acceleration), this is obviously influenced by the type of airframe and the capabilities of the respective flight control system. The airframes involved very large (B747) and also rather small (Phenom 100) platforms and corresponding FMS manufacturers included a representative sample of the market . The systems under investigation all met the required navigation performance and thus serve as a very nice example of how a performance-based requirement can be met by different techniques . From an airspace planning perspective, the experiment shows how strictly the trajectories over ground are maintained, despite some significant wind presence .
Figure : Results of the FMS/airframe bench-test RNAV (RNP) RWY 25R, KLGB (best available quality) 
The simulated scenario was intended to create a very demanding situation for the guidance/control system and does NOT represent a useful “real-world” approach scenario with regard to the wind/runway direction. The roll-angle analysis shows how various airframes using different flight control systems can achieve a fairly consistent curved path over ground, irrespective of wind conditions and airspeeds.
 ICAO, doc 8168, PANS OPS, vol. II construction of visual and instrument flight procedures, 6thedition, 2014
 ICAO, doc 9905, Required Navigation Performance Authorization Required (RNP AR) Procedure Design Manual, 1st edition, 2008
 Herndon, Cramer and Sprong, ANALYSIS OF ADVANCED FLIGHT MANAGEMENT SYSTEMS (FMS), FLIGHT MANAGEMENT COMPUTER (FMC) FIELD OBSERVATIONS TRIALS, RADIUS-TO-FIX PATH TERMINATORS, MITRE Corporation’s Center for Advanced Aviation System Development, 2008
 European Commission, EU-OPS, regulation 965/2012, consolidated version, 2019
 FAA, AC 20-138D, Airworthiness Approval of Positioning and Navigation Systems, change 2, 2016
 FAA, AC 90-105A, Approval Guidance for RNP Operations and Barometric Vertical Navigation in the U.S. National Airspace System and in Oceanic and Remote Continental Airspace, 2016
 RTCA, DO-236B, MASPS Required Navigation Performance for Area Navigation, 2003
 Deutsche Flugsicherung, AIP Germany, amdt 10/2018
 ICAO, PBN Operational Approval Manual, doc 9997, 2nd edition, 2015
 ICAO, PBN Manual, doc 9613, 4th edition, 2013
 EASA, CS-ACNS, issue 2, 2019
 AIRBUS, Getting to grips with PBN, issue 1, 10/2016