proved a violation of the horizontal surface of the center RWY 25C/07C and of the south RWY 25L/07R. None of the OAS, however, was violated, as shown in following Figure 12.
5.2. NOM Application
Flight track data for a six month period at FRA was used for the ANP analysis preceding the CR calculations  .
5.2.1. Outbound Traffic Analysis
All departure routes passing nearby the considered obstacle operating from runway 07C were analyzed (07R routes are farer away, 07L/25R allows landings only). As shown in Figure 13, flight tracks of the northbound departure route (SID) BIBTI 3E were identified as the most relevant ones.
The relevant cross section (the normal plane to the route through the obstacle) was found almost in the straight out segment of BIBTI 3E, at 600 m beyond DER. The route specific flight track’s distribution are shown in Figure 14 at this cross section (BIBTI 3E in red, all other departures in blue).
Figure 11. Location of the critical obstacle-the safety case EDDF.
Figure 12. Excerpt of the obstacle clearance analysis for the runway 07/25C, OLS―left figure, OAS CAT I―right figure.
Figure 14 clearly shows a tendency for aircrafts on BIBTI 3E to climb faster than other traffic following a required PDG of 6.3%. They also initiate the tendency of aircrafts to veer north (more located to the left in the figure) compared to the other traffic.
The SID specific ANP analyses were then performed along the statistical methods as explained in Section 3. Figure 15 shows the determined ANP values and resulting CR iso-risk lines for departing aircraft on BIBTI 3E and all other routes.
The poorest ANP values (XTT and VTT) per class of aircraft and per route are identified in Table 2. It also shows the probability density function’s (PDF) parameter shape before/after the critical 600 m cross section.
The double integration of the PDF both vertically and laterally to the obstacle equals the specific CR per take- off, as shown in following Table 3.
Due to the position of the obstacle at 600 m from DER, the CR VTT value is relatively high with 1.97 × 10−2
Figure 13. FRA Flight tracks for runways in use 07, outbound flights, FANOMOS Data, with obstacle critical cross section (red line).
Figure 14. Relevant cross section passing through the critical obstacle at 600 m DER distance, departures from runway 07C.
Figure 15. Iso-risk lines and ANP values, outbound flights on runway 07C.
Table 2. Statistical parameter along the flight track (critical cross section highlighted in gray).
Table 3. Calculated collision risk for departures.
per departure; whereas the XTT related CR is―at a lateral offset of 1100 m for the obstacle from the route ―negligible with values below 1 × 10−100 per departure, result in an overall collision risk of 4.13 × 10−117 per departure.
5.2.2. Inbound Traffic Analysis
For approaches, both north and center runway are relevant. Applying the same investigation steps as for the departures, we computed, compared to the outbound case, clearly higher ANP values as expected with 99% of all aircraft performing ILS approaches. This leads to respectively smaller CR figures below 1 × 10−117. The calculated CR via ICAO’s CRM  showed as well a negligible CR outside the calculation limits of the CRM program (<1 × 10−15 per approach).
We can thereby conclude that for the normal operations at Frankfurt Airport a collision risk for take-off and landing is below ICAO’s TLS at 1 × 10−7 per operation. The calculated CR below 1 × 10−100 shows both the necessity for scenario based risk analyses, as provided with the DOM, and a further validation of ICAO’s CRM.
5.3. DOM Safety Case Application
5.3.1. Scenario Set-Up
Based on the obstacle’s location as shown in Section 5.1 the following DOM hazard scenarios were identified:
1) Approach RWY 25R
2) Missed Approach RWY 07L
3) Missed Approach RWY 07C
4) Take-off RWY 07C
The following Figure 16 depicts all four scenarios.
All operations on runway 25L/07R and runway 18 were excluded from the investigation as explained in Section 5.2.
5.3.2. DOM Step 1: Vertical Performance Analysis
Applying the minimum climb requirements according to CS-25, we can prove compliance for scenarios 1, 2, and 3. Scenario 4 “Take-off RWY 07C” does not pass the evaluation. Table 4 shows the obstacle conflicting profiles for multi-engine aircraft (negative values indicate a flight path below the highest point of the obstacle):
Consequently, we declare all scenarios but this one as non-critical. Scenario 4 is subject to further investigation along with step 2 to 5.
5.3.3. DOM Step 2: Procedure Design Analysis
In this step three separate phases will be passed:
Phase 1: Analyze the most critical departure route3 along EU-OPS 1.495 standards.
Results: The examination revealed that the obstacle does not penetrate the “take-off funnel”, and so at least does not violate the departure clearance requirements. As explained in Section 4, this is not yet proof of compliance but a pass indicator. Further investigation leads us to:
Phase 2: Examination of the Obstacle Identification Surface (OIS) and PDG according to ICAO PANS-OPS Vol. II.
Results: This sub-step shows that the obstacle violates the OIS both laterally and vertically. As such, a PDG update is necessary to prove a further pass indicator (see Table 5).
Figure 16. Identified DOM hazard scenarios―safety case FRA.
Table 4. Violation altitudes scenario 4.
Table 5. Comparison of minimum procedure design gradients.
Consequently, despite the identified OIS violation, the obstacle will not vertically impact the published take- off procedure, the pass indicator is positive, leaving us with:
Phase 3: Examination of the protection area for turns according to ICAO PANS-OPS.
Results: We derive that the obstacle is located inside the protection area of BIBTI 3E. However, a calculation of the maximum allowable object height at the given location shows remaining clearance so that this pass indicator is also true.
In total, we find all three pass indicators are true without granting combined lateral and vertical compliance, so we will have to continue to step 3:
5.3.4. DOM Step 3: Lateral Performance Analysis
By additionally considering the uncertainties resulting from adverse conditions and engine failure for all relevant aircraft types (e.g. A321, A340, B777F) in the TLPM, Figure 17 depicts the exemplary results of the missed approach performance analysis (OEI right prior passing the obstacle):
Results: The calculations prove that yaw motion induced by engine failure and crosswind (up to 20 kt) can be fully compensated by aircraft flight control. Consequently, no relevant lateral nor vertical deviations from the intended trajectory were identified for scenario 1 to 3 (partly shown in Figure 17). Scenario 4, however, showed vertical violations requiring the execution of step 4.
5.3.5. DOM Step 4: Lateral Flyability of the Critical Trajectory
All aircraft types able to complete the turning departure as set out with the critical trajectory are being identified. So we calculate the required climb out speed to reach the pre-set turn radius linked as follows:
This delivers the following figures in Table 6.
Comparison of design speed with for all relevant aircraft models revealed that the required speed can only be achieved by small multi-engine jet or turboprop aircraft (e.g. Cessna C525A CJ2 or Beechcraft King Air B200GT). Even though this aircraft category is rather rare at FRA (close to pass indicator), we will have to identify the remaining risk, which is assessed in the final step 5.
5.3.6. DOM Step 5: Vertical Performance Analysis of the Critical Trajectory
We finally determine CG and lift-off points under the prescribed unfavorable OEI conditions to calculate the pass altitudes above the obstacle for this aircraft category, again using TLPM.
Table 7 depicts the results for the exemplary members of this aircraft category.
As a result, we prove in step 5 that the critical aircraft category can also safely overfly the critical obstacle with significant clearance according to PANS OPS (e.g. 35 ft./10m). So the SA for this safety case closes with a positive result.
If, however, even step 5 fails (or any preceding step beforehand), the SA methodology allows the investigation to set out mitigation measures, such as cancelling a published route, setting stricter prerequisites to allow
Figure 17. Missed app degraded performance analysis (scenario 2 & 3).
Table 6. Required operational parameter configuration for the critical trajectory.
Table 7. Values for example calculation of crossing altitude.
flying that route (increased PDG or turn radius requirements to aircraft) or just generating appropriate awareness through hot spot advisories in the Aeronautical Information Publications (AIP).
6. Conclusions―Integration Concept into ICAO Doc 9774
Aeronautical studies are supportive means to assess the safety and regularity of operations around airports with ICAO non-compliant obstacles in place (e.g. one that violates the OLS). Doc 9774  , however, does not provide any guidance on how to perform such a study.
This paper presents a methodology which may contribute to standardizing the process. Dealing with both statistically representative hazard scenarios and infrequent events systematically investigated through scenario techniques, the presented model considers all potential flight situations by handling both normal and degraded performance triggered operations. In that sense, it generates a complete risk picture which has already proven useful in several certification processes with the German Ministry of Transport and the German ANS Supervisory Authority BAF. The statistical part relies on dedicated ANP value calculations, stochastic functional approximation leading to validated, procedure-specific probability density functions along any flight track allowing calculation of obstacle CR through double integration. In rare cases (often called as “PDF tails”) we developed a scenario configuration technique assuming worst case environment and aircraft performance related conditions. The resulting 3D trajectories generated through the author’s take-off and landing performance model (TLPM) allows a deterministic (yes/no) collision potential determination by calculating minimum horizontal and vertical performance under unfavorable conditions for all aircraft categories operating at the investigated airport. Beyond this application case, we recall that the model reviews systematically all safety related design criteria for departure and arrival procedures. As such, its application is universe. On-going investigations run in compliance e.g. for Zurich Airport.
As such, we see strong potential for the presented methodology to become a potential candidate for an ICAO DOC 9774, Appendix 3 supplement in order to give specialists a guideline for how to adequately judge formally non-compliant obstacles for safe and regular operations at the airport. It also reveals the need for updating and extending the current ICAO’s collision risk model with correct procedure and flight phase specific ANP values.
The authors thank Deutsche Flugsicherung DFS and Condor Flugdienst GmbH CFG for the provision of data for verification (NOM) and validation purposes (DOM). We also thank Fraport for the kind provision of detailed geometric data and our colleagues Christian Seiß and Martin Schlosser for their tremendous help with the extensive data analysis.
*An application to a Large Close-in Obstacle at Frankfurt Airport’s New Runway System.
1Obstacle clearance altitude is referenced to mean sea level and obstacle clearance height is referenced to the threshold elevation or in the case of non-precision approaches to the aerodrome elevation or the threshold elevation. ICAO Doc 8168, Vol. II, Section I-1-1-6  . Beyond the OCA/H, the approach surface is extended by a Visual Approach Surface (VSS) assuming the reduced aircraft ANP as guidance is formally limited to visual cues.
2“New objects or extensions of existing objects should not be permitted above the conical surface and the inner horizontal surface… except when, in the opinion of the appropriate authority, an object would be shielded by an existing immovable object, or after aeronautical study it is determined that the object would not adversely affect the safety or significantly affect the regularity of operations of aeroplanes”  .
3This is the turning departure route BIBTIE 3E.
4Restricted by other obstacles resp. environmental constraints.
5Pursuant to ICAO PANS-OPS (Pt. 1-Section 2, Chapter 3, Table I-2-3-1) the maximum bank angle until 305 m (1000 ft.) altitude for departures is given by Φ = 15˚.