Development and evaluation of an RNP AR approach procedure under tight airspace constraints

Required navigation performance authorization required (RNP AR) approach (APCH) procedures are a special form of approaches with vertical guidance (APVs) where stricter navigation system requirements in terms of accuracy, integrity and functionalities allow smaller obstacle clearance areas and the use of curved legs in all approach segments. That leads to very flexible approach design possibilities compared to other instrument approach procedures. This paper guides through the development and initial evaluation of an RNP AR approach on runway 15L at Isa Air Base in Bahrain. The establishment of instrument approaches on this runway has been complicated so far because the final approach would have led straight through the controlled traffic region (CTR) of an adjacent air base. We show that entering the CTR, which ends less than 3.3 NM before the runway threshold, can be avoided with an RNP AR approach by employing a curved leg in the final approach segment and the highest possible navigation accuracy of RNP 0.1—two unique features of RNP AR APCH. We then fly and test the developed procedure in an Airbus A320 full-flight simulator under the wind and weather conditions considered by the procedure design rules. The results show that the actual navigation and flight technical performance met the required one under all conditions without the bank angle and effective glide path limits being exceeded. An initial flight test with a Boeing B737-800 showed that the approach can also be flown with sufficient accuracy in practice.


Introduction
Despite their low importance for global air traffic, airports like Cristiano Ronaldo International of Funchal, Madeira or Innsbruck Airport in Austria are known worldwide for their challenging approaches [1]. Rapidly rising terrain but also surrounding airspace can prevent the operation of an instrument landing system (ILS), which still is predominantly used for precision approach (PA) procedures. Nonprecision approaches (NPAs) based on radio navigation aids are often offered alternatively instead. However, because of the higher minima and lower precision associated with those procedures, the ability to approach an airport in unfavorable conditions (e.g., low visibility) becomes severely restricted [2]. Moreover, such conventional procedures often require a conservative and inflexible procedure design, making it hard to establish them where spatial constraints are tight [3].
This gap has been closed by approaches with vertical guidance (APVs), a new approach category consisting solely of approach procedures developed under the ICAO performance-based navigation (PBN) concept. As opposed to NPAs, they also offer vertical guidance but do not achieve the same accuracy as PAs in the final approach [4]. APVs are classified as either Required Navigation Performance approaches (RNP APCHs) or Required Navigation Performance Authorization Required approaches (RNP AR APCHs) [5, p. I-A- [1][2][3][4][5]. The main difference between both lies in higher performance requirements with RNP AR APCH that require the aircraft operator to show evidence of aircraft capability and sufficient crew training before obtaining authorization from the State regulatory authority to conduct such procedures. In return, RNP AR APCH offers greater flexibility in procedure design due to improved navigational accuracy, integrity and additional functionalities. The most relevant advantages over RNP APCH can be seen in smaller obstacle clearance areas (the areas around 1 3 the approach track that must be clear of obstacles) due to higher possible accuracies and that curved legs may also be used in the final approach segment. For instance, RNP AR APCH allows lateral accuracies (95 percent total system error, TSE) of 0.1 NM in all approach segments while RNP APCH only allows 0.3 NM in the final and 1 NM in all other approach segments [6]. That increases the chance of being able to establish three-dimensional instrument approaches also where terrain, obstacle or airspace constraints prohibit more conventional procedures.
Isa Air Base (OBBS) in Bahrain is an aerodrome suffering from such constraints. As depicted in Fig. 1, it lies less than 8 NM south-east of another airfield-Sakhir Air Base (OBKH)-which is located right within the extension of runways (RWYs) 15L/33R, the only ones used for normal operations at OBBS. As a result, the only existing instrument approach into the air base is an ILS approach on RWY 33R so that RWY 15L cannot be approached except for a basic visual approach. Moreover, as OBKH is protected by a control zone (CTR) that ends less than 3.3 NM short of RWY 15L, every approach on this runway must be coordinated closely with air traffic control at Sakhir Air Base to avoid interfering with their arriving or departing traffic [7]. In the worst case, the current situation can lead to Isa Air Base becoming effectively cut off if visibility is low (e.g., due to dust haze) and RWY 33R cannot be used for landings (e.g., due to tailwind). This weather-related dependency could be eliminated by developing an instrument approach for RWY 15L with sufficiently low minimums. However, if the developed approach also ensured that approaching aircraft would always stay out of the CTR, it would besides become possible to facilitate the air traffic management between the air bases and, at best, take steps towards enabling independent simultaneous operations into and out of both airfields in the future. Since flying over the CTR while approaching RWY 15L is not feasible due to the CTR's height, the new approach would have to include a turn towards the runway quite late before touchdown, e.g., as if the existing missed approach procedure for RWY 33R is flown backwards (see Fig. 1). We aim to show that such an approach can (exclusively) be realized as an RNP AR APCH procedure.
Detailed system and training requirements for RNP AR approaches, along with implementation guidance, can be found in the PBN Manual (ICAO document 9613) [5]. The Fig. 1 Current approach situation at OBBS [7]. As visible, a straight final approach would lead right through the CTR. The new approach must include a turn very close to the runway to enable approaching aircraft to avoid entering the CTR. That turn (see turquoise markings) can also be split into two separate RF legs without the minimum CTR distance being impacted. This helps maximizing the minimum dis-tance, which occurs at the critical point, as lower turn entry (FAP) altitudes lead to smaller radii. That is illustrated in the inset, which shows the position of the outer containment area boundaries corresponding to FAP altitudes of 1300 ft (yellow), 1400 ft (green) and 1500 ft (blue) near the CTR. Their endpoints are marked with 'X' (the one for 1500 ft is out of range) construction rules for RNP AR APCH are described in ICAO document 9905: Required Navigation Performance Authorization Required (RNP AR) Procedure Design Manual [6].

The basics of RNP AR APCH
The history of RNP AR APCH dates back to 1996, when Alaska Airlines conducted the first-ever RNP AR approach on RWY 08 at Juneau International Airport, Alaska. There, the airline had been frequently suffering from delays and disruptions due to bad weather until the new approach procedure enabled them to lower the minimums for landing and improve their operational performance [8]. At first, the US Federal Aviation Authority approved it as a Special Airworthiness and Aircrew Authorization Required (SAAAR) procedure before officially recognizing the type later as RNP SAAAR procedures [9]. The official change from RNP SAAAR to RNP AR and the introduction at ICAO level then came with the publication of the PBN manual in 2008 [10,11].
Each approach procedure normally consists of four different segments: The initial, intermediate and final as well as the missed approach [3]. Most procedures have fixed performance requirements that become higher towards the threshold, however RNP AR APCH allows the required lateral accuracy to be, within a certain range, flexibly chosen with the highest possible value being available in all approach segments. That accuracy is expressed as RNP X, where X is the TSE in NM that must be achieved at least 95% of the flight time [6, p. 2-2]. RNP AR APCH allows values as low as RNP 0.1, meaning it is the approach procedure offering the highest lateral accuracy outside of the final approach [3]. Since RNP only applies to lateral performance, specifications like RNP AR APCH also contain requirements for vertical guidance that can be provided by systems using either barometric altitude or augmented GNSS [5, p. I-A- [1][2][3]. Under PBN, the approach segments consist of different waypoints that are connected using specified leg types, called path terminators [3]. One of them are radius to fix (RF) legs, which describe curved paths based on a constant radius between two fixes [12]. They constitute another specialty of RNP AR approaches since they may, unlike in any other procedure, be used in all approach segments. That results in RNP AR APCH being the only procedure allowing curved legs in the final approach [5].
RNP AR APCH is based on the use of an aircraft-based augmentation system or a similar GNSS augmentation, however the navigation sensor requirements also address the use of an inertial navigation system (INS) for integrated GNSS/ INS position solutions and distance measuring equipment (DME) as a reversionary navigation mode [5, pp. II-C-6-8f.].
In general, the design of instrument approaches depends much on their protection against obstacles, which is provided down to the obstacle clearance height (OCH) by two kinds of obstacle clearance areas-primary and secondary areas, the decision altitude and to a lesser extent also in the visual segment after reaching the OCH by further obstacle clearance areas [3]. RNP AR APCH only uses primary areas, which have a semi-width equal to 2 × accuracy value of the respective approach segment, i.e., between 0.2 and 2 NM. The minimum obstacle clearance (MOC), which is provided in the vertical direction, changes with different approach segments between 300 m for the initial and 0 m (in most cases) for the missed approach. The lowest possible decision altitude/height (DA/H), at which the landing must be aborted if the required visual reference to continue the approach has not been established, is 250 ft above the corresponding threshold elevation [6].
At Isa Air Base, RNP AR APCH constitutes the only possibility to avoid entering the CTR during an approach on RWY 15L due to the fact that all other APVs and PAs mandate a straight final segment that must be between 3 (RNP APCH) and 6 NM (ILS) long, combined with larger obstacle clearance areas towards the CTR (e.g., of 0.95 NM semi-width for RNP APCH with LPV minimum) [3]. Hence, the main advantage of RNP AR APCH does not only lie in curved legs within but also high accuracies beyond the final approach.

Procedure construction
Since vertical navigation based on GNSS augmentation systems is not available, we develop the approach based on the use of a barometric vertical navigation (baro-VNAV) system and for aircraft of speed category D or lower, i.e., the indicated air speed (IAS) at threshold must not exceed 165 kt [6].
The required reference frame for RNP AR APCH must be "a conventional x, y, z coordinate system with its origin at the Landing Threshold Point (LTP) and parallel to the world geodetic system 84 ellipsoid. The x-axis is parallel to the final approach track: positive x is the distance before threshold and negative x is the distance after threshold. The y-axis is at right angles to the x-axis. The z-axis is vertical, heights above threshold being positive" [6, p. 4-2]. Assuming that the last part of the final approach is aligned with the runway centerline, this equals an east-north-up frame with origin at the threshold (THR) of RWY 15L, rotated until the x-axis lies on the (extended) centerline and points in the same direction as RWY 33R.

Straight final approach segment
The top priority when designing the approach is to avoid violating OBKH CTR. That requires the new approach to include a tight left turn towards the runway whilst being quite close to it. Even though RNP AR APCH allows radiusto-fix legs in the final approach, the turn must not end directly at the runway. Instead, a straight segment between the exit point of the RF leg, called final approach roll-out point (FROP), and the LTP is mandated whose minimum length is defined by the greater of two requirements: [6, p. 4-22].
First, the FROP must be located at least 150 m above the LTP. That yields a minimum length D 150 (see Eq. 1).
Secondly, the FROP must be located so that it is reached at least 15 s before the aircraft reaches the OCH if the missed approach is based on RNP 1 or 50 s if the missed approach is based on a higher navigation accuracy or RNP APCH. With the 15-s requirement keeping the required length smaller, we use RNP 1 for the missed approach, which yields a minimum length D 15s (see Eq. 2).
where RDH is the reference datum height, VPA denotes the vertical path angle, OCH is the obstacle clearance height and V TAS is the True Airspeed (TAS).
Since the turn cannot end at the runway, it should at least end as close to the runway as possible, i.e., D 150 and D 15s need to be minimized. The greater of both values sets the position of the FROP, from which we can construct the turn.
The RDH is the height of the glide path above threshold and the VPA is the angle of the glide path. Steep VPAs and large RDHs minimize the distances. The recommended RDH for CAT D is 50 ft plus or minus 5 ft, thus we choose 55 ft. The VPA can be chosen between 3 (standard) and 3.1 • . Higher VPAs have the disadvantage that they might lead to exceeding the maximum permitted effective VPA of 3.503 • (final approach) on hotter days, which is caused by the temperature-related pressure altimeter errors of uncompensated baro-VNAV systems. They output a lower than true altitude when it is hotter than modeled by the International Standard Atmosphere (ISA), leading the effectively flown VPA to be higher [6]. As it does become very hot in Bahrain during the summer, we keep the VPA at 3 • which leads to a D 150 of 2541.6 m.
The TAS for D 15s must be based on a flight at aerodrome elevation (139 ft, [7]) and with 15 • C above ISA (ISA+15). As lower speeds minimize D 15s , we choose the corresponding indicated airspeed (IAS) at the minimum possible value of 165 kt for the final approach. The OCH can only be obtained from an obstacle assessment for the final and missed approach segments [6]. However, as we have not yet constructed any of them, we must estimate the OCH and use that value to build a test version of the approach. Once it is possible to construct the obstacle assessment surfaces (OASs) required for a full obstacle assessment, we must conduct such an assessment to verify the OCH before we can release the procedure. The estimate should be as accurate as possible to avoid having to revise the approach later. With RNP AR APCH, the OCH is determined using a total of three OASs as explained in Ref. [6]: The final approach OAS, the missed approach/Z surface and a horizontal surface in between. It equals the sum of the height of the highest real or equivalent approach obstacle, whichever is greater, and a height loss margin (161 ft for CAT D). The height of equivalent approach obstacles refers to calculated imaginary heights (equivalent heights) of obstacles penetrating the Z surface and is used for comparison as those obstacles are located in an area of the missed approach where aircraft are assumed to be climbing again, i.e., the greatest physical (real) obstacle height does not necessarily lead to the largest OAS penetration. Even though we cannot yet determine the exact coordinates of each OAS, it is possible to determine the beginning of the Z surface, i.e., the start of climb (SOC) corresponding to a fictitious OCH' equal to the applicable height loss margin (here: 161 ft). Its threshold distance is calculated according to Eq. (3) as the horizontal distance to the point where the height loss margin is reached on the glide path less the transition distance (TrD). The TrD, in turn, is calculated as in Eq. (4) and can also be determined [6, p. 4-39].
GS refers to the flown ground speed during the go-around (see Ref. [6] for calculation details). With the missed approach RNP of 1, it causes a transition distance of 4466.5 m that puts the SOC at (−)3850 m down the runway behind the threshold of RWY 33R. Knowing that the final approach OAS must end before the threshold of RWY 15L, significant parts of the air base (depending on whether they lie within the missed approach splay, which describes the lateral OAS bounds, or not) must hence be covered by the horizontal surface at threshold level. The AIP does not list any obstacles in approach and take-off areas but three aerodrome obstaclesthe north and south antennas along with a water tower-of which the north antenna is tallest with 157 ft height above THR RWY 15L [7]. By transforming its coordinates into the reference frame, we can prove that the antenna's lateral and longitudinal threshold distance is small enough to be located within the missed approach splay with the splay being based on the highest possible navigation accuracy of RNP 0.1 for the final approach and the OCH that would be caused by the north antenna (318 ft; 157 ft + 161 ft). Since neither the approach chart for RWY 33R nor current satellite images show any indication of higher obstacles in the vicinity of the air base, we set the OCH at 318 ft. For D 15s , that yields a distance of 2954 m, which also determines the FROP position.

Final approach turn construction
To stay clear of the CTR, we need to minimize the turn radius (r) leading to the FROP. r is calculated based on a turn rate (R) (see 5), which depends on the flown TAS, the tailwind component (TWC) and the flown bank angle ( ).
Greater turn rates lead to smaller radii, which can be achieved with higher bank angles and lower speeds. We set the bank angle at the maximum possible value of 20 • [6, p. [3][4][5][6]. The tailwind and the TAS both depend on altitude, the TAS additionally requires the flown IAS (165 kt) and the outside temperature. Even though higher temperatures increase the TAS and cause larger radii, we want to ensure that the procedure is safe to fly even on the hottest days of the year. With temperatures occasionally climbing above 47 • C during summer, we base the turn construction on a temperature deviation of ISA+35 [13]. Higher altitudes equally cause greater radii because they lead to a higher TAS and usually more tailwind (Ref. [6] provides tables with generic TWCs for different altitudes). The construction must be based on the highest altitude in the turn, which is reached at the entry point as the straight segment VPA is extended into the turn [6, pp. 3-3f.]. Consequently, the height difference between the entry and the exit point grows with the turn length and knowing that higher altitudes lead to larger radii, we need to find a compromise between the track change achieved through the length of the turn and the resulting radius. Assuming that entering the CTR can be avoided, the most critical point within the turn is where the distance to the CTR becomes minimal. Figure 1 shows that the turn and the CTR boundary first converge until the south-eastern endpoint of the CTR (hereafter called "SE point") but diverge behind it with the CTR boundary suddenly changing into a right turn while the approach track continues as a left turn. That causes the minimum distance to the CTR to be reached at a yet unknown "critical point" near the SE point (see Fig. 1). To provide the maximum possible distance between the approach track and the CTR, the turn should not begin behind that point. We now minimize the radius by starting the turn at or just before the critical point with a larger total track change being achieved by employing another RF leg beforehand that we use as intermediate approach segment. Due to the converging-diverging track configuration, since RF legs are tangent to their in-and outbound tracks at their entry and exit points, respectively, and since the previous turn would follow the same turn direction, its larger radius would not influence the minimum distance to the CTR (see Fig. 1). As the turn entry point serves as final approach point (FAP)-the beginning of the final approach-it can (like other relevant fixes) only be established at round altitudes in 100-ft increments [6]. Consequently, we need to find the round altitude that is reached within the turn closest to but still before the critical point when used for the turn construction (TAS, R, r). Since the shape of the turn and hence the position of the critical point change with different "construction altitudes", we need an iterative approach to do so: First, we choose an initial altitude (here: 1500 ft), calculate the resulting turn plus the minimum distance to the CTR and determine the critical point and its height. These steps are repeated until lowering the construction altitude leads to the critical point falling out of the turn (see inset of Fig. 1). The results are summarized in Table 1 and show that this is the case if the turn entry altitude falls below 1400 ft. We thus choose 1400 ft as the FAP altitude.
As aircraft almost always fly a bit off track due to errors, it is important that the minimum distance is not calculated from the nominal approach track but from the containment area, within which the aircraft position can be assumed with sufficient certainty. For RF legs, that is the area between the outer and inner turn area boundaries, which are themselves RF legs. They cover the same angular sector as the nominal turn, though with radii being increased or decreased, respectively, by 2 × navigation accuracy (here: RNP 0.1). As we only need to consider the lateral domain in this case, we assume that their height equals the height of the nominal track on the same radius (for obstacle assessment purposes, also the MOC needs to be determined) [6, p. 4-10]. The areas are shown in Fig. 2 as part of a three-dimensional profile of the entire final approach segment. As shown in the inset of Fig. 1, the iterative determination of the critical points proved that the minimum distance to the CTR always occurs towards the SE point (as expected) on the radial line from the turn center to the SE point. The latter is not surprising either with the shortest distance theorem stating that the minimum distance between a point (SE) and a line (outer turn area boundary) is always described by the perpendicular line between both. Before finishing the final approach segment, it must be checked whether the effective VPA (caused by temperature-related pressure altimeter errors) does not deviate too significantly from the design VPA for the expectable temperature deviations from ISA according to the instructions in Ref. [6]. With a VPA of 3 • , the upper effective VPA limit is reached at ISA+33.5 (48.5 • C at sea level). Since that is hotter than the average hottest temperature (45.01 • C, see Ref. [6, p. 4-27]), the chosen VPA is proven safe to fly all year long. If we had selected the steeper VPA of 3.1 • at the beginning, the maximum allowable temperature would have sunk to 38.9 • C, a temperature that is regularly exceeded in Bahrain during the summer months [13].

Intermediate and initial approach segments
The intermediate approach segment "is the segment in which aircraft configuration, speed and positioning adjustments are made for entry into the [final approach segment]" [6, p. 4-16]. It begins at the intermediate fix (IF) and is preceded by the initial approach that begins at the initial approach fix (IAF) [3]. We choose the IAF to be TYLOS, an already existing waypoint in the vicinity of the aerodrome that is also part of the ILS approach on RWY 33R (see Fig. 1).
To reach the FAP out of TYLOS, the approach must first lead straight ahead (initial approach) down to a point where a left turn towards the FAP (intermediate approach) is initiated. With any turn making the procedure more complex, we choose to follow the track from RABAD to TYLOS also out of TYLOS down to the point where it intersects with the RF leg (we prefer them due to smaller obstacle clearance areas) from the FAP. That way, the approach can also be started out of RABAD (e.g. after a go-around) without having to fly another turn at TYLOS. With the in-and outbound tracks plus the FAP being set, there is only one possible geometry for the RF leg, which is determined as follows: The in-and outbound tracks are extended until they intersect. The turn center is then located where the bisector line intersects with the line perpendicular to the outbound track at the FAP. The radius equals the length of the perpendicular  r = 5171 m ). The VPA has a standard value of 1.4 • or lower for the intermediate approach. Since 1.4 • yield an IF altitude of 2256 ft, we select 2200 ft to achieve a round IF altitude, leading to a VPA of roughly 1.3 • . As the intermediate turn has been constructed on a geometric basis as a required ground track, it must also be checked whether the radius is at all flyable within the allowed speed and bank angle limits. For ISA+35 and the optimum bank angle of 18 • , that is only the case if the highest possible speed restriction of 180 kt IAS is applied. [6] The initial approach has a horizontal length of more than 6.7 NM, which would place the IAF at approximately 3900 ft with the standard initial approach VPA of 2.4 • [6]. We place it at 3000 ft instead, especially considering the tight speed restrictions for the intermediate and the final approach that become increasingly hard to manage with greater descent rates. However, we issue altitude constraints for both the IAF and the IF to designate their altitudes as minimum altitudes that may also be passed higher if the aircraft can cope with the steeper descent (coded as e.g. 'A3000+', see Ref. [3] for details). The resulting minimum initial approach VPA equals 1.08 • . The entire approach profile from the IAF down to the runway is depicted in Figs. 3 and 4.

Missed approach segment (MAS)
The MAS starts at the OCA/H point, where the OCA/H is reached on the nominal glide path, and ends at the point where a new approach, holding or return to en-route flight is initiated [6]. Its construction is strongly tied to obstacle assessment, which is thoroughly explained in Ref. [6]. In summary, a go-around at the OCA/H point is modeled in three phases (initial descent, horizontal and climb segment) that also serve as the framework for the construction of the MAS.
Our aim for the missed approach is to bring the aircraft back to RABAD, as the horizontal distance to TYLOS is too small to enable a climb to at least 3000 ft (IAF minimum altitude) with the climb segment gradient being only 2.5%. To keep the procedure as simple as possible, we first implement a climb straight ahead. This is followed by the necessary left turn towards RABAD as an RF leg, ending on the initial approach track from RABAD to TYLOS. We found the RF leg tangent to that track at RABAD and tangent to the x-axis (final approach track) at a yet unknown missed approach turning fix (MATF) to have a radius of r = 4970.1 m. It can only be flown with the minimum possible speed restriction of 185 kt IAS and the maximum possible bank angle (20 • ) for ISA+35 [6].
The straight segment consists of the descent, the horizontal and the climb segment. As depicted in Fig. 3, the entire segment lies on the x-axis of the reference frame so that the position of the SOC' (beginning of the climb segment after the transition distance to the OCA/H point) can be determined by subtracting the threshold distance of the OCA/H point (x-coordinate) from the transition distance (4466.5 m, see Eq. 4). From there, the 2.5 gradient is applied which yields altitudes of 1973.9 ft for the MATF and 3285.5 ft for RABAD, i.e., the missed approach is long enough to enable the climb to at least 3000 ft. Figures 3 and 4 show the entire missed approach segment including the vertical profile, which includes the initial height loss of 161 ft putting the aircraft at 157 ft above threshold-the height of the north antenna as the tallest obstacle.

Obstacle assessment
With the obstacles mentioned in Sect. 3.1, the initially chosen OCH of 318 ft remains, since the northern antenna is indeed the controlling obstacle, causing the most relevant OAS penetration within the FAS and the MAS. The obstacle assessment also revealed that the initial approach is clear of obstacles for the least restrictive RNP value of 1 while the intermediate approach requires RNP 0.1 along with the final approach. That is because a lower RNP (e.g., RNP 0.2) would lead to the intermediate approach containment areas legs (see Ref. [12], ARC = RF leg). '*' refers to the three aerodrome obstacles from the AIP. This figure corresponds to the vertical profile shown in Fig. 4 slightly overlapping the FAP, reaching into the CTR (see Ref. [6, p. 4-4]).

Simulator and flight validation
Guidance on procedure implementation is provided in the PBN manual. Amongst others, it requires a procedure validation that is split up in ground and flight validation. Its purpose is to verify all obstacle and navigation data, the data used for the procedure construction as well as the information on the approach chart and to assess the flyability of the procedure. For RNP AR APCH, ground validation should always involve a simulator assessment [5].

Simulator assessment
The simulator assessment took place on FT76, a Lufthansa Aviation Training Airbus A320-214 level D full-flight simulator (certified according to EASA CS-FSTD (A)) with two pilots (Captain: ATPL, First Officer: CPL, both with valid A320 type rating). We performed a total of six approaches followed by either a go-around shortly before reaching the OCA/H (which equals the DA/H in our case) or a touch-andgo landing. In particular, the assessment dealt with different wind and weather conditions that are summarized in Table 2.
Every approach was started out of a predetermined position south-west of TYLOS with an aircraft gross weight of 60 t, up to 6 t below the maximum landing weight [14]. During the approach, we recorded a variety of (simulated) flight parameters such as the calibrated airspeed (CAS) and the roll angle along with the true aircraft position (latitude, longitude, height). We then used them to determine whether the actual navigation accuracy, as given by cross-track error (CTE) and the vertical error, met the required one, i.e., whether the nominal approach track could be safely maintained. Besides, we examined whether the RF legs of the intermediate and the final approach could be safely flown under heavy tailwind and high temperatures without the maximum permitted bank angle and effective VPA values being exceeded.
Scenarios 1 and 2 serve as control scenarios (CAVOK = Clouds And Visibility OK, more in [15]) that differ in the speed management (Airbus-specific): If flying with managed speed, the speed is controlled by two Flight Management Guidance Computers (FMGCs) that set a target speed according to the entries in the flight management system, the Flight Control Unit (FCU, control panel for the autopilot and autothrust functions), the current aircraft configuration and the current flight condition [16]. During the approach, the target speed mainly depends on the flap setting. In our case, the intermediate approach was entered with flaps 2 (of 4) and the landing gear was selected down after passing the IF. Flaps 3 and then flaps full were selected shortly thereafter. Flaps 2 already commands the so-called F speed (see Ref. [17]), which was around 140 kt IAS based on the A320 being a CAT C aircraft [14], meaning that the intermediate and final approach RF legs were flown slower than for what they had been designed (180 and 165 kt IAS, respectively). As we wanted to assess the flyability of the approach for the more critical aircraft category D, we increased the approach speed by selecting the speed directly at the FCU using the procedure design values, i.e. 180 kt shortly before passing the IF, 165 kt shortly before passing the FAP and the actual approach speed shortly before leaving the final turn. Figure 5 shows the measured speeds (CAS) from all scenarios, the 180-kt and 165-kt limits are marked in black.
In consequence, the CTE (see Fig. 7 for all scenarios) grew from between +15 m (+ equals to the right of the track) near the IF and −24 m (− equals to the left of the track) during the final approach to −36 m near the FAP with selected speed. However, those values are still very small compared to the tolerable RNP 0.1 TSE of 185.2 m. The roll angle (see Fig. 6 for all scenarios) increased from between 6 and 8 • with managed speed to between 10 and 12 • with selected speed. The vertical error (see Fig. 8 for all scenarios) is mainly considered within the final approach, as the initial and intermediate segments just have minimum altitudes published. In Fig. 8, the error is depicted along with a limit of 22  5 Simulator assessment: CAS during the scenarios. All but scenarios 1 and 6 were supposed to be representative of CAT D aircraft, whose approach speeds cannot be-by procedure design-assumed below 180 kt IAS for the intermediate approach and 165 kt IAS for the final approach. We therefore increased the approach speed typical of an A320 (#1) to those values during the more critical RF legs m in red, which is the maximum tolerable deviation within the FAS as monitored by the pilots. If that value is exceeded below the glide path, a go-around must be performed as it is the case if the monitored lateral deviation exceeds 1x RNP (applies to the entire approach). Besides, we added the required 99.7% vertical accuracy from the PBN manual for the final approach in magenta, which is height-dependant and varied around 30 m [5]. In both scenarios, the vertical error was well within the 22-m limit. Scenario 3 is based on scenario 2 with medium tailwind but standard temperatures whereas scenario 4 uses heavy tailwind and maximum temperatures. Since the simulator did not allow to specify wind values below 4200 ft apart from the surface wind but interpolated between the two values, we were not able to simulate the maximum allowed tailwind at the FAP (@1400 ft: 038/44 kt) given that the north-east wind would have caused too much tailwind upon landing. Instead, we chose the surface and upper-level wind so that the interpolated wind blew parallel to the track a bit ahead of the FAP, still within the intermediate approach. Therefore, the effective wind speeds at the FAP from Table 2 do not equal the TWC but are a bit higher as the wind is hitting the aircraft slightly from the left. In scenario 3, the FAP TWC equals more than half of the allowed maximum whereas it is just a few knots below it in scenario 4.
The wind and temperature differences are also reflected in the recorded roll angles which increased from 12 (#3) to between 16 and 17 • (#4) within the intermediate approach and from 15 (#3) to partially 19 • (#4) within the final approach. Thus, the maximum allowed roll angle (20 • ) was not reached even in very challenging conditions. Equally, the lateral deviations grew over scenarios 2-4 with a maximum of −46 m at the FROP within scenario 3 and −63 m before the FROP within scenario 4. Scenario 4 also included flying the entire missed approach where the CTE did not become greater than 70 m. As those values are all well within 1×  Scenario 6 was flown manually based on flight director cues. All deviations are within 1 × RNP as the required navigation accuracy RNP, the lateral accuracy is considered good. There is one distinctive pattern in the CTE that can probably be explained with the FMGC and flight control logics: Before the IF, the aircraft always flies a bit to the right of the track, then crosses the nominal track within the intermediate turn and keeps to the left of the track for the rest of the approach. The second transition back from left to right within scenarios 5 and 6 can be explained with the concluding touch-and-golanding. As the aerodrome was not included in the standard data base of the simulator, it had been added manually beforehand but was placed in the wrong spot a bit too far to the west, requiring the pilots to manually deviate to the right to land on the runway.
The vertical error needs to be treated differently. The error behavior in scenario 3 can be compared well to scenario 2 and features a slightly larger deviation below the glide path at the FAP ( −12 m), followed by an overshoot of up to 14 m before the aircraft returns to a position slightly below the glide path without ever infringing on the 22-m limit. These bumps in the error profile can likely be explained with slight accelerations to keep the selected speed at the same time, causing a nose-up pitching moment. The vertical error in scenario 4 is significantly larger. The FAP is overflown 38 m higher than planned at more than 1520 instead of 1400 ft. After a short time however, the error becomes continuously smaller and the nominal glide path is captured shortly before reaching the OCH. As the recorded altitude is true altitude and not indicated altitude, we conclude that the FMS in the simulator did not include a temperature correction model so that the increased outside temperature caused pressure altimeter errors putting the aircraft at higher (true) altitudes. We used the deviation and the remaining track miles for each measurement to calculate the effective VPA, which is shown in Fig. 9. Obviously, the maximum allowed value of 3.503 • was never exceeded despite the values within the turn being close to it. Moreover, with the nominal glide path being captured in time within the straight segment (see Figs. 9 and 8) and the simulated temperature being the maximum that was used for the construction, we do not consider the flyability of the approach to be impaired. Neither do we assume a degraded vertical accuracy as the plotted 99.7% values are only valid for ISA temperatures [5].
Scenario 5 equals scenario 4 but with restricted visibility (overcast (OVC) with ceiling at 800 ft, 3000 ft visibility) so that the runway did not come in sight until the aircraft left the final turn. The error behavior is similar to scenario 4, the slightly larger vertical error approximately 5 km before the THR (the glide path is again captured in time) can be Fig. 8 Simulator assessment: Vertical error during the scenarios. The 22-m limit, at which a go-around must be performed in most cases, is plotted in red along with the required 99.7% vertical accuracy for ISA conditions in magenta. The minimum altitude restrictions for the IAF and the IF were met in all cases as was the required accuracy for the final approach-except for scenarios 4 and 5. These were dominated by extremely high temperatures (ISA+35), leading to pressure altimeter errors putting the aircraft at higher true altitudes (see Fig. 9) Fig. 9 Effective VPA for scenarios 4 and 5, which were dominated by extremely high temperatures (ISA+35). As visible, they caused pressure altimeter errors leading to flying above the nominal 3-• VPA. The upper limit for the effective VPA (3.503 • , plotted in red) was not exceeded explained with the sudden speed reduction conducted by the pilots to prepare the aircraft for the touch-and-go-landing. Scenario 6 differs from the others in that the captain flew the approach manually with assistance from the coupled flight director (F/D) and autothrust. It involved good weather with a light wind from the left upon landing and standard temperatures. Despite the manual flying, the actual navigation accuracy was barely degraded: It reached from +23 m at the IF to −67 m within the final approach turn in the lateral direction and varied between +10 and −10 m in the vertical direction. The small deviations prove that an RNP AR approach does not necessarily have to be flown by the autopilot to obtain the required accuracy, a skilled pilot can achieve sufficiently small flight-technical errors as well.
We evaluate the outcome of the simulator test positively. We were able to show that the approach is safe to fly not only in ideal but also in very critical conditions (as far as mandated by the procedure design). Especially the intermediate and final approach RF legs, which are more challenging to fly due to their small radius and low altitude, were accurately flown also at higher aircraft and wind speeds without exceeding the maximum allowed roll angle. The lateral deviations in all approach segments were significantly smaller than RNP 0.1, the vertical deviations varied within the limits for ISA temperatures and grew with temperatures above ISA due to the pressure altimeter error, though without the resulting effective VPA exceeding its limit. We assume that the approach can cope well with the conditions in Bahrain and can also be flown safely with larger aircraft, as shown by the tests with higher approach speeds.

Flight test
We carried out a flight test using a B737-800 aircraft in January 2021. It consisted of two complete approaches, each followed by a go-around shortly before reaching the OCH. The flight was conducted in the morning with a light westerly, later north-westerly wind at surface level, 21 • C (ISA+6) and improving visibility after some morning haze. Under the assumption that the wind direction did not significantly change until 4000 ft altitude, the aircraft experienced headand crosswind within the intermediate approach, which then slowly turned into light tailwind within the FAS. We use the GPS position information from the electronic flight bags in the cockpit to calculate the lateral navigation accuracy just as we did for the simulator assessment. We do not consider the vertical error since the electronic flight bag does not record barometric altimeter data and GPS measurements are not precise enough in the vertical direction. Figure 10 shows the results for the CTE.
During the the first approach, the deviations varied from −42 m while intercepting the initial approach to +38 m during the final turn. The second approach was-probably due to less wind-a bit smoother with CTEs between −34 m (initial approach) and +20 m (near the FAP). Thus, the lateral accuracy was more than sufficient during both approaches and lies within the range that we achieved in the simulator assessment with standard temperatures plus zero and medium wind speeds, respectively.
For a complete flight validation report, as e.g. partially published as supplemental material to Ref. [18], additional data would need to be recorded and evaluated before the procedure can be published in the national AIP.

Conclusion
We developed an RNP AR APCH procedure to RWY 15L of Isa Air Base in Bahrain. The approach enables approaching aircraft to avoid violating the control zone of the neighboring air base and features sufficiently low minimums to permit operations also in bad weather. The approach follows the reverse direction of the existing missed approach procedure on the opposite runway: It begins south-east of the field with a downwind leg as initial approach, followed by two RF legs as intermediate (larger radius) and final approach (smaller Fig. 10 Test flight: Lateral deviations during the two approaches based on EFB GPS position measurements. The deviations are well within 1× RNP as the required navigation accuracy radius), achieving a track change of almost 180 • towards the runway, which is connected by a required straight segment of minimum length. Establishing such an approach within the given constraints would have been impossible with any other approach procedure type. Our developed approach is able to fulfill both mentioned requirements due to the combination of two unique design characteristics that are only available with RNP AR APCH: First, the application of curved segments inside the final approach segment, which enables track changes and thus flying by the control zone even shortly before landing. Secondly, the possibility of requiring a high navigation accuracy (RNP 0.1) for all approach segments, which keeps the containment areas small enough to not violate the control zone while the obstacle clearance altitude remains small. Even with these highest performance requirements, however, the minimum distance between the containment areas and the CTR becomes less than 50 m, emphasizing how tight constraints in the application environment of RNP AR APCH can be.
The procedure evaluation, consisting of a full-flight simulator assessment using an Airbus A320 and a first flight test using a Boeing B737-800, yielded positive results. In the simulator, we generated extreme weather conditions as far as permitted by the procedure design. This included especially heavy tailwinds during the turn towards the runway and high temperatures leading to a higher ground speed. Despite those challenging conditions, the required total system error in the lateral and vertical direction could be easily met without other flight parameters (roll angle, effective glide path angle) exceeding their limits. The test flight confirmed the general flyability in practice. It did take place in smooth conditions and was performed with an aircraft of approach category C (maximum approach speed of 140 kt, i.e., less than the CAT D value of 165 kt used for the procedure design). A standard flight validation, however, would not wait for challenging environmental conditions either. The certifying authority now needs to assess the procedure-specific hazards in a safety report and generate a flight validation report using more comprehensive aircraft data.
Funding Open Access funding enabled and organized by Projekt DEAL. Open Access funding enabled and organized by Projekt DEAL.
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