Robust Emergency Aircraft Avoidance Solutions for Commercial Aircraft Formations
Item Type Conference Paper; Presentation Authors Saber, Safa I.; Feron, Eric
Citation Saber, S. I., & Feron, E. M. (2023). Robust Emergency Aircraft Avoidance Solutions for Commercial Aircraft Formations. AIAA AVIATION 2023 Forum. https://doi.org/10.2514/6.2023-3260 Eprint version Post-print
DOI 10.2514/6.2023-3260
Publisher American Institute of Aeronautics and Astronautics
Rights This is an accepted manuscript version of a paper before final publisher editing and formatting. Archived with thanks to American Institute of Aeronautics and Astronautics.
Download date 21/06/2023 07:23:06
Link to Item http://hdl.handle.net/10754/692575
Robust Emergency Aircraft Avoidance Solutions for Commercial Aircraft Formations
Safa Saber∗and Eric Feron†
King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
There is increasing interest in wake surfing formation flight as a way to decrease CO2 emissions in commercial air transportation. While the fuel efficiency benefits of formation flight have been proven over 20 years of research and flight experimentation, implementation of formation flight in air transportation operations has been limited by safety concerns. This work continues our series which explores aircraft escape contingency planning for commercial aircraft formations. Previous works in the series laid out requirements for commercial formation operations, presented baseline escape and exit plans drawn from pilot experience, and evaluated optimized modeling as a method of generating insight into formation escape and exit plans.
Model-generated paths were found to be compatible with pilot-generated plans, however, a significant difference was noted between the two. While the pilot-generated plans were more general, accounting for differences in initial conditions and emergency aircraft maneuvering with a single plan, the model-generated plans were specific solutions. Small changes to initial conditions or emergency aircraft maneuvering generated significantly different solutions.
Solutions which change due to small perturbations are undesirable from a pilot perspective.
This work presents model-generated formation emergency aircraft avoidance solutions which are more robust to emergency aircraft maneuvers and initial formation positions and evaluates them using pilot expertise.
I. Introduction
T
he benefits of wake-surfing formation flight for fuel efficiency have been explored and proven over 20 years through works both analytical [1–9] and experimental [10–15]. Recent interest in reduction of CO2 emissions in air transportation has focused investigation efforts on the safety, operational feasibility, and cost of implementing commercial aircraft formation flight in air transport operations [16, 17].The outstanding safety record of the air transportation industry in recent decades is due in part to the way it plans for contingencies. In order to operate, an air transport aircraft must have a verified contingency plan, or ‘Plan B’, for each historically credible contingency. If one of these contingencies were to occur, its Plan B must allow the aircraft to attain a safe landing. Standard operations as well as operations over high terrain or overwater should not be initiated unless a safe landing can be made during contingencies such as poor weather, engine failure, loss of cabin pressure or electrical failure. The construction of these Plan Bs for individual aircraft configurations, routes and scenarios is referred to as
“Plan B engineering," [18] and any new procedure must be Plan B engineered prior to implementation.
While there is pressure on the air transport operational community in the direction of commercial aircraft formations [19], Plan B engineering for commercial formation operations has not been investigated. Boeing has been involved in significant research over the last two decades involving fuel saving benefits, ride quality and aircraft durability during formation flight. Possibilities for airline operations are mentioned in the research, but planning for internal formation contingencies has not been addressed [16]. Airbus promoted a demonstration of its wake surfing formation flight test in 2021, and the public documentation included a preliminary commercial formation flight Concept of Operations (ConOps) [20]. The presentation includes a few comments about internal formation contingencies, but the discussion is limited to formations of two aircraft in mono-directional airspace. The documentation makes it clear that Plan B engineering has not yet been done for more difficult bi-directional airspace or larger formations. Despite its importance to the realization of commercial formation operations, Plan B engineering for formation internal separation and escape is almost absent from public literature.
Our first publication in this series detailed requirements for commercial aircraft formation flight and presented pilot-generated escape and exit plans for formations of up to 7 aircraft [21]. The next two papers were dedicated
∗Graduate Research Assistant, Mechanical Engineering, safa.saber[at]kaust.edu.sa, Experimental Test Pilot (USAF), Commercial Airline Pilot.
†Professor, Electrical, Computer, and Mechanical Engineering, eric.feron[at]kaust.edu.sa, AIAA fellow.
to building and evaluating an optimization modeling approach to internal formation escape and exit solutions. The model-generated solutions compared well and were compatible with the pilot-generated plans [22, 23].
However, a significant difference was found between the pilot-generated plans and the model-generated solutions.
The pilot-generated plans were robust to changes in initial aircraft positions and changes in emergency aircraft maneuvers during the exit, but the model-generated paths were not. The optimal solution was, of course, optimized for the specific scenario, but a slightly different scenario frequently generated a significantly different solution. This was considered undesirable from a formation pilot’s perspective. A continually changing exit plan could significantly degrade situational awareness during aircraft exit maneuvers.
This work presents an optimized model formulation modified to find emergency aircraft avoidance solutions which are robust over a range of emergency aircraft maneuvers and initial formation positions. The model-generated paths are compared to previously-generated pilot plans and are evaluated using pilot expertise.
II. Model Formulation
A. Model description
The model is intended to provide insight into generation of safe trajectories for commercial formation aircraft during an emergency exit contingency such as the exit sketched in Fig. 1. The emergency aircraft in this scenario is the trail aircraft shown in red. An exit by the trail aircraft is the simplest exit scenario because no maneuvering is required of the blue and green aircraft in the formation. A different scenario in which an emergency lead aircraft must exit the formation would require a trail aircraft to maneuver to avoid it and then rejoin the formation. These types of more difficult scenarios will be presented below.
Aircraft within the model must abide by high-altitude commercial aircraft performance limitations and are constrained to avoid other formation aircraft and their wake turbulence. The optimized model minimizes aircraft maneuvering (𝐽maneuver) to avoid formation aircraft and wake turbulence while minimizing distance from formation position on the assigned course and altitude (𝐽position) in order to generate safe trajectory solutions for formation aircraft.
Fig. 1 Illustration of a trail aircraft emergency exit from a 3-aircraft formation.
The discrete-time model is based in a 3D high-altitude Earth-based near-inertial reference frame in which non-inertial effects are negligible over the formation maneuver time period (<1 min). The coordinate system of the model and figures is attached to the reference frame and is centered on an ATC-assigned formation course (𝑥1 =0) and altitude (𝑥3 =0) in the high-altitude airborne environment. The directions of the 3D coordinate system are referred to as along-course (𝑑=1), cross-course (𝑑 =2) and altitude or vertical (𝑑 =3). Mixed-integer linear programming (MILP) was chosen due to the simplicity of implementation and past successes in aircraft trajectory generation [24].
The trajectory optimization problem may be to
minimize𝑥 , 𝑣 ,𝑢𝐽 =𝐽maneuver(𝑥 , 𝑣 , 𝑢) +𝐽position(𝑥) (1)
subject to
∀𝑖∈ {1· · ·𝑇},∀(𝑝, 𝑞) ∈ {1· · ·𝐴}2, 𝑞 > 𝑝,∀𝑑 ∈ {1· · ·3}, 𝑥(𝑖+1)𝑝 𝑑=𝑥𝑖 𝑝 𝑑+ (𝑣𝑖 𝑝 𝑑+𝑊𝑑)Δ𝑡 ,
𝑣(𝑖+1)𝑝 𝑑 =𝑣𝑖 𝑝 𝑑+𝑢𝑖 𝑝 𝑑Δ𝑡 , 𝑣𝑖 𝑝 𝑑 ∈ V, 𝑢𝑖 𝑝 𝑑 ∈ U, 𝑥𝑖 𝑝 𝑑 ∉S𝑞, 𝑥𝑖 𝑝 𝑑∉W𝑞,
(2)
where𝑖is the time index over𝑇 total time steps each havingΔ𝑡duration, and𝑝and𝑞are aircraft in a set of 𝐴total formation aircraft. The design variables𝑥 , 𝑣 ,and𝑢are aircraft position, velocity, and acceleration respectively. Aircraft are constrained to maneuver within velocity limitationsVand acceleration limitationsU, avoid other formation aircraft S𝑞, and avoid wake turbulenceW𝑞. While wind is included in the model as𝑊𝑑, it is set to zero in these results.
B. Requirements and Assumptions
Formations are a part of standard operations in the armed forces context, however, internally regulated formations of commercial aircraft are very rare. Because commercial formation operations are not yet established, we began by presenting requirements for the commercial formation system, formation aircraft, and formation operations in an earlier work [23], and these are used as a foundation for the optimized model. An abbreviated version of those requirements is included below along with model assumptions specific to this implementation.
1. Formation System
Commercial formation operations requires a formation system which allows formation wake tracking and formation aircraft system communication. This formation system must run within the formation itself without aid from any ATC system due to the necessity for distant Oceanic Track airspace operations. Degradation of aircraft systems which impact formation operations must be monitored on each aircraft and also communicated to other formation aircraft. System degradation which impacts safety must trigger an exit from the formation.
Due to the difficulty of maintaining formation position in close proximity to the wake vortex, formation operations are to be flown by the autopilot from initiation of formation join through exit from the formation. A formation exit or escape will be flown by the autopilot and monitored by the pilots. In the case of an autopilot failure, the pilots must execute the escape manually. Due to this contingency, a verified exit/escape should be displayed to the pilots at all times.
2. Emergency Aircraft
Emergency aircraft must be given maneuvering priority. All other aircraft must avoid them. It is assumed in this implementation that emergency aircraft will avoid each other and does not constrain them to maintain separation from one another. Nominal (non-emergency) formation aircraft must avoid all emergency aircraft and other nominal aircraft.
These constraints are included in the model and detailed in Section II.D.
A significant assumption made in this implementation is that emergency aircraft will maneuver in the horizontal and descending directions but will not climb. While most emergencies at high altitude result in maintaining altitude and then descending, this assumption does not cover all scenarios. A climbing emergency such as a powered stall or an aircraft wake turbulence incursion resulting in a nose-high aircraft upset is not covered by this implementation.
3. Formation Aircraft Performance
Commercial aircraft frequently cruise near maximum aircraft operational altitude to maximize fuel efficiency, however, a formation aircraft must be able to maneuver to avoid other formation aircraft if necessary. Therefore, each aircraft must maintain a minimum performance and maneuvering capability to enter or remain in formation. The minimum performance capability required of aircraft in the model is detailed in Table 1.
4. Limitations on Flight Path Requirements
Flight paths of formation aircraft must always preserve a minimum separation distance between aircraft. Minimum separation required by the model is 1,000 ft as detailed in Table 1. Minimum separation distance must allow for pilot recognition of formation system separation failure and allow intervention and maneuvering by the pilots in order to
avoid a collision. Formation flight paths must also maintain sufficient separation from the wake turbulence of other formation aircraft. Minimum model wake turbulence separation is detailed in Section II.E.
Escape paths planned by the formation system must not be outside the performance limitations of each aircraft and must be simple enough to be flown manually by the pilots in case of autopilot failure.
C. Performance Constraints (VandU)
Commercial aircraft spend the majority of their flight time near the coldest portion of the atmosphere in order to maximize fuel efficiency. However, due to the thin atmosphere at these altitudes, aircraft performance and maneuvering is limited.
The model results presented here are based on narrow-body aircraft performance at cruise altitude, and these performance constraints are shown in Table 1. Narrow-body aircraft were chosen because of the sheer number in service and because formation flight is more difficult with smaller and lighter aircraft. Wake vortices are stronger and last longer when generated by heavier aircraft, therefore, lighter aircraft must fly closer formations than heavier aircraft to gain the same fuel efficiency benefits. Lighter and heavier aircraft will likely fly in separate flocks due to significant differences in efficient cruise Mach.
Table 1 Narrow-body aircraft model constraints
Direction Separation (S𝑞) Velocity (V) Acceleration (U) Horizontal 1,000 ft 725 – 785 ft/sa 0 – 15 ft/s2/ 25°bankb
Vertical 1,000 ft -40 – 10 ft/sb 0 – 15 ft/s2
a0.75 – 0.81 Mach at 36,000 ft standard day (FL360).
bClimb rate subtracts from available horizontal acceleration.
Due to the linear nature of the model, maximum horizontal velocity and acceleration which would normally be vectors constrained to lie inside a circle had to be approximated instead by vectors inside a polygon with sixteen equal sides (hexadecagon) using binary variables. A hexadecagon was chosen in order to balance computational complexity while staying close to the intended maximums. The approximation causes a possible 2% error in these values which is considered acceptable due to variability in individual aircraft performance capability. Minimum speed is approximated in a similar manner by constraining the vector to lie outside the hexadecagon. A more detailed explanation of this implementation is available in [24].
Finally, climb capability and acceleration capability are closely linked in aircraft maneuverability. An aircraft near maximum climb does not have much capability to maneuver horizontally at the same time. Therefore, the model subtracts aircraft climb rate from available horizontal acceleration as noted in Table 1.
D. Aircraft Separation Constraints (S𝑞)
The model scenario begins with a formation of𝐴aircraft initialized in a specified formation. At scenario start, the formation includes two different kinds of aircraft. There are𝑁nominal (non-emergency) aircraft and𝐴−𝑁emergency aircraft in each formation scenario. The model is required to separate every nominal aircraft position at every time index 𝑖by 1,000 ft from every other nominal aircraft point position at the same time index. The optimized nominal aircraft trajectories are the model output.
The emergency aircraft initiate emergency procedures at the maneuver start time and proceed to exit the formation.
The most extreme trajectories possible for the emergency aircraft (within performance constraints) are inputs to the model. Sample emergency trajectories are shown in Fig. 2(a) for a lead emergency aircraft. A lead aircraft is not surfing a wake and may turn either left or right while slowing or continue straight at maximum speed. A trail emergency aircraft is constrained by the wake vortex next to it and it is assumed that it will not turn directly into this wake turbulence.
Therefore, a trail emergency aircraft can only continue straight at maximum speed or turn away and slow as depicted in Fig. 2(c). All emergency aircraft eventually descend in order to proceed toward landing.
The model takes the emergency trajectory of each emergency aircraft with the most extreme positions in each direction (near and far along-course, cross-course extremes, and high and low altitude) and forms an emergency aircraft
(a) (b)
(c) (d)
Fig. 2 Possible trajectories of an emergency (a) lead or (c) trail aircraft and avoidance airspace due to an emergency (b) lead or (d) trail aircraft.
separation cuboid [25]. In the sample trajectory shown in Fig. 2(b), three lead aircraft trajectories are shown, one continuing straight east (labeled ‘E’), one turning left to the north (N) and one turning right to the south (S). The model uses Aircraft E as the farthest along-course aircraft, while Aircraft S is used as the closest along-course aircraft. Aircraft S and N are used as the extremes in the cross-course direction, etc. These extreme positions are used to build the aircraft separation cuboid shown in red shading in Figs. 2(b) for a lead aircraft or 2(d) for a trail aircraft, and all nominal aircraft are required to avoid it by 1,000 ft in every direction.
The aircraft separation constraint is implemented by constructing cuboids of airspace through which no other aircraft is permitted to fly and is enforced using binary variables𝑎𝑖 𝑝 𝑞 𝑑 𝑠[26]. The constraint is written
∀𝑖 ∈ {1· · ·𝑇},∀𝑝 ∈ {1· · ·𝑁},∀𝑞 ∈ {1· · ·𝐴}, 𝑞 > 𝑝,
𝑥𝑖 𝑝 𝑑−𝑥𝑖 𝑞 𝑑 𝑠 ≥𝑅𝑑−𝑀 𝑎𝑖 𝑝 𝑞 𝑑 𝑠 with 𝑠=1, ∀𝑑 ∈ {1· · ·3},
−𝑥𝑖 𝑝 𝑑+𝑥𝑖 𝑞 𝑑 𝑠 ≥𝑅𝑑−𝑀 𝑎𝑖 𝑝 𝑞 𝑑 𝑠 with 𝑠=2, ∀𝑑 ∈ {1· · ·3},
3
∑︁
𝑑=1 2
∑︁
𝑠=1
𝑎𝑖 𝑝 𝑞 𝑑 𝑠≤5,
(3)
where𝑝is any nominal aircraft,𝑞is any formation aircraft (nominal or emergency),𝑅𝑑is minimum separation set to 1,000 ft,𝑀is an arbitrary large number,𝑑is the dimension, and𝑠is the side of the dimension. At any time step𝑖 over the total set of time steps𝑇, the position of the nominal aircraft,𝑥𝑖 𝑝 𝑑, must be 1,000 ft away from𝑥𝑖 𝑞 𝑑 𝑠where
𝑥𝑖 𝑞 𝑑 𝑠is either another nominal aircraft position or the boundary of an emergency aircraft separation cuboid.
E. Wake Turbulence Avoidance Constraints (W𝑞)
Nominal formation aircraft are required to avoid wake turbulence from all other formation aircraft, both nominal and emergency. Wake turbulence from a nominal aircraft is modeled as cuboids centered on past aircraft positions descended in altitude by the wake turbulence descent rate of 5 ft/s multiplied by the time difference between the current time index and the time index of the past position. The wake turbulence avoidance cuboid is set at 140 ft in total cross-course distance, 140 ft in altitude, and aircraft along-course distance traveled during the time index in along-course length. The model is required to find a trajectory for each nominal aircraft which avoids these wake turbulence cuboids from all other nominal aircraft for each time step.
The nominal aircraft are also required to avoid wake turbulence from any of the possible emergency aircraft trajectories. Wake turbulence cuboids are built from the possible emergency aircraft trajectories the same way it builds the emergency aircraft separation cuboids described above in Section II.D. However, the emergency trajectory wake turbulence cuboids persist and descend at 5 ft/s. Figures 2(b) and 2(d) depict emergency trajectory wake turbulence cuboids in gray as viewed from above. The model is required to find nominal aircraft trajectories which avoid both nominal and emergency aircraft wake turbulence airspace.
While avoidance of persistent and drifting wake turbulence was published in our earlier work [23], the avoidance of wake turbulence from any possible emergency aircraft trajectory is a new addition and is expressed
∀(𝑖, 𝑗) ∈ {1· · ·𝑇}2, 𝑗 < 𝑖,∀𝑝∈ {1· · ·𝑁},∀𝑞∈ {1· · ·𝐴}, 𝑞 > 𝑝,
𝑥𝑖 𝑝 𝑑− (𝑥𝑗 𝑞 𝑑 𝑠+ (𝑖−𝑗)𝐷𝑑) ≥𝐿𝑑−𝑀 𝑏𝑖 𝑗 𝑝 𝑞 𝑑 𝑠 with 𝑠=1, ∀𝑑 ∈ {1· · ·3},
−𝑥𝑖 𝑝 𝑑+ (𝑥𝑗 𝑞 𝑑 𝑠+ (𝑖−𝑗)𝐷𝑑) ≥𝐿𝑑−𝑀 𝑏𝑖 𝑗 𝑝 𝑞 𝑑 𝑠 with 𝑠=2, ∀𝑑 ∈ {1· · ·3},
∑︁3
𝑑=1
∑︁2
𝑠=1
𝑏𝑖 𝑗 𝑝 𝑞 𝑑 𝑠 ≤5,
(4)
where𝑝is any nominal aircraft,𝑞is any formation aircraft (nominal or emergency),𝐿2and𝐿3are set to 70 ft (70%
of aircraft wingspan) in the cross-course and altitude directions, and𝐿1is set to distance traveled in the along-course direction (𝐿1 =𝑣𝑗 𝑞 𝑑 𝑠Δ𝑡) to avoid sampling error. 𝑀is an arbitrary large number,𝑑is the dimension and𝑠is the side of the dimension. 𝑥𝑗 𝑞 𝑑 𝑠is the position at any past time step 𝑗of either a nominal aircraft or the boundary of an emergency aircraft wake turbulence cuboid. At any time step𝑖over the total set of time steps𝑇, the position any nominal aircraft,
𝑥𝑖 𝑝 𝑑, must be𝐿𝑑away from the past wake turbulence position𝑥𝑗 𝑞 𝑑 𝑠descended by𝐷𝑑 multiplied by the difference of
the two time steps (𝑖−𝑗). The wake turbulence descent rate is active only in the vertical direction (𝐷3=−5𝑓 𝑡/𝑠) and is zero in the along-course and cross-course directions in this implementation (𝐷1=𝐷2 =0).
F. Cost Function (𝐽)
The optimized model cost function consists of two parts,𝐽maneuverand𝐽position. Fuel is expensive and maneuvering is difficult at high altitude. Therefore,𝐽maneuverpenalizes each nominal aircraft at every time step for any acceleration or climb. Climb is weighted 50 times more than acceleration in the emergency exit scenario presented here.𝐽position is a penalty assessed when the nominal aircraft are outside the assigned course and altitude. Every nominal aircraft is penalized at every time step for its cross-course distance away from final course and vertical distance away from assigned altitude. These two costs are equally weighted and added together to form the model cost function𝐽.
G. Optimization
MILP has been successfully used in the past for aircraft trajectory generation and was chosen for its simplicity in implementation and broad user and tool base [24]. The optimized model in this implementation takes the following inputs; aircraft performance, wingspan, initial formation positions and velocities, final formation position constraints, cost function weights and emergency aircraft trajectories. These are simple to change but must be chosen prior to the optimization. The scenario is executed as a single optimization problem. The model is not intended to be used in real-time due to increased complexity due to wake turbulence avoidance.
The model is implemented in Python using commercially-available Gurobi optimization software on a MacBook Pro M1 Max machine. Solution times for larger formations of 7-aircraft range from one to five hours.
III. Model Results
A. Wake Surfing Formation and Model Initial Formation Position
The aircraft are initialized in a V formation as depicted in Fig.3. The V formation was chosen because aircraft in the formation can use wingtip vortices on both sides of the course line. By alternating sides as shown in Fig.3 aircraft can minimize along-course distance for wake surfing while maintaining escape options to opposite sides.
Fig. 3 Diagram of a 3-aircraft V formation with standard spacing (not to scale).
Fuel efficiency benefits while wake surfing have been found between 2 and 50 times the vortex-generating aircraft’s wingspan in trail in the along-course direction [14, 15]. Best fuel efficiency in the cross-course direction has been measured between 80-100% of the vortex-generating aircraft’s wingspan from its centerline and within 20% of its altitude in the vertical direction.
Formation final width for the cost function in these results is set to 80 ft (80% of the aircraft’s wingspan) and the altitude is set to 0 ft (on altitude) in order to capture the closest formation constraint possible. Along-course distances between aircraft have been explored between the closest distance possible, 1,010 ft (due to the aircraft minimum separation constraint of 1,000 ft), and 3,000 ft, a distance beyond which the aircraft on the second wingtip (Aircraft 3 in Fig. 3 at a distance of 60 wingspans) may not be able to benefit from wake surfing. Results are most interesting and applicable to finding robust solutions between 1,010 ft and 2,020 ft and these are presented below.
B. V Formation - Standard Spacing
Model results begin with a formation in standard V formation at closest possible spacing as depicted in Fig. 3. The lead aircraft is the farthest along-course aircraft, the next aircraft is 1,010 ft behind the lead and on its left, the next aircraft is 1,010 ft behind the second aircraft but on the lead’s right side, etc. The aircraft in this standard spacing are
equally spaced along-course and on alternating sides of the formation. With the exception of the lead aircraft, each aircraft is initialized in position to surf the wake vortex of the aircraft preceding it.
1. Middle aircraft exit from a 5-aircraft V formation
Figure 4 shows a 5-aircraft formation at minimum along-course spacing of 1,010 ft from which Aircraft E1 and Aircraft E2 initiate emergency operations and exit the formation. Aircraft E1’s possible trajectories include any path between continuing straight at maximum speed to a maximum-banked turn away from wake turbulence at minimum speed as shown in red in Fig. 4. Aircraft E2’s possible trajectories are indicated by the two edge trajectories shown in yellow. In this scenario, the two trail nominal aircraft are both 2,020 ft in trail of their respective emergency aircraft at the maneuver start.
Fig. 4 Top and side views of two middle emergency aircraft exits from a 5-aircraft V formation.
The lead aircraft, Aircraft 1 shown in blue, does not need to maneuver for the emergency aircraft behind it, and it continues on course and on assigned altitude. The trail nominal aircraft, Aircraft 2 and Aircraft 3, maneuver to avoid
the emergency aircraft paths and wake turbulence by turning with them away from the course line. They then climb over the emergency aircraft wake turbulence and turn back toward their new formation positions shown in the figure as gray shading. Once the emergency aircraft have descended and gain sufficient separation from the assigned formation altitude, Aircraft 2 and 3 descend and resume formation position at assigned altitude behind the lead aircraft.
This is a successful result from a pilot’s perspective. Each nominal trail aircraft is able to avoid the emergency trajectories and wake turbulence with reasonable maneuvering and reform with the lead aircraft.
2. Lead aircraft exit from a 5-aircraft V formation
A lead aircraft exit from a 5-aircraft formation with along-course spacing of 1,010 ft between aircraft is presented in Fig. 5. Three edge trajectories for the emergency aircraft, Aircraft E1, are shown in red, one to the left, one to the right, and one continuing straight.
Fig. 5 Top and side views of a lead emergency aircraft exit from a 5-aircraft V formation.
In this scenario, Aircraft 1 is the closest aircraft to the emergency trajectories due to the alternating along-course spacing of the formation. While all other aircraft are 2,020 ft away from the aircraft preceding them on their side,
Aircraft 1 is 1,010 ft from the emergency aircraft in along-course distance.
Aircraft 2 and 4 are able to avoid the emergency trajectory with a slight right turn, climb, and slight turn back toward course line. Once the emergency aircraft gains sufficient spacing from the assigned altitude, they descend into formation position on the right side of the formation.
Aircraft 1 is the farthest along-course nominal aircraft and is, therefore, designated the new formation lead aircraft.
However, due to its close position behind the emergency aircraft, Aircraft 1 has to make a significant turn away to the left at maximum bank angle to preserve separation and then climb to clear the emergency trajectory’s wake turbulence.
The turn and climb force it to separate 750 ft in cross-course distance from the rest of the formation before it is able to turn back. Aircraft 3 turns away slightly, climbs over the wake turbulence from both Aircraft E1 and Aircraft 1. Aircraft 3 then waits above formation position for Aircraft 1 to rejoin the formation before descending into position.
While this result is the optimized solution to the lead emergency exit scenario, it is not a desirable solution from a pilot’s perspective. Though Aircraft 1 is the new lead aircraft of the nominal formation, it must travel a significant distance away from the formation to maintain separation from the emergency trajectory before being able to climb and return to lead the formation. Aircraft 1’s maneuvering is due to its position very close behind the emergency aircraft, and its separation maneuvering causes its flight path to cross underneath Aircraft 3’s flight path twice. Crossing maneuvers are undesirable from a pilot’s perspective because crossing makes it difficult for pilots to monitor the maneuvering, ensure spacing, and intervene in the case of an autopilot failure. The minimum spacing of 1,010 ft behind an emergency trajectory is separated enough for a single-scenario solution, however, the resultant maneuvering indicates that 1,010 ft spacing is too close to obtain a robust solution to the scenario.
C. V Formation - Modified Spacing
As demonstrated in the previous section, nominal aircraft positions behind an emergency trajectory less than approximately 2,000 ft generates solutions with undesirable maneuvering. Therefore, the next set of results use a modified formation with more than 2,000 ft of along-course spacing between aircraft in order to move toward a robust exit avoidance solution.
Fig. 6 Diagram of a 4-aircraft V formation with modified spacing (not to scale).
A 4-aircraft V formation with modified spacing is shown in Fig. 6. The formation is still a V formation with aircraft on both sides of the lead, however, the second aircraft’s spacing is increased to 2,020 ft behind the lead on the left side, the third is kept at 1,010 ft behind the second aircraft (3,030 ft behind the lead on its right side), and each subsequent aircraft is spaced along-course by 1,010 ft. This initial positioning allows for at least 2,020 ft in along-course spacing between each aircraft on its side of the formation.
1. Lead and trail aircraft exit from a 7-aircraft V formation
Figure 7 shows the model-generated solution to a scenario in which the lead aircraft and both trail aircraft of a 7-aircraft formation initiate emergency operations and exit the formation. The pilot-generated plan for the same scenario is shown in Fig. 8 [21]. All aircraft on the left side of the formation are spaced at 2,020 ft in along-course distance.
While Aircraft 2 on the right side of the formation is spaced 3,030 ft along-course from Aircraft E1, the rest of the aircraft on the right side of the formation are also spaced at 2,020 ft in along-course distance.
Fig. 7 Top and side views of model-generated paths for lead and trail aircraft emergency exits from a 7-aircraft formation.
Aircraft E1 has possible trajectories shown in red turning left, going straight, or turning right. These trajectories have the most effect on the closest nominal formation member, Aircraft 1. Aircraft 1 turns left slightly, climbs over the wake turbulence from Aircraft E1 and then turns back toward the course line. Once Aircraft E1 descends and gains sufficient spacing from the formation assigned altitude, Aircraft 1 descends into position on the course line as the new formation lead aircraft. Aircraft 3 executes a similar turn, climb and descent into formation position on the left side of Aircraft 1. Aircraft 2 and 4 on the right side turn slightly right, climb and clear the emergency trajectory and then descend into position on the right side of the formation. Aircraft 3 is more distant from Aircraft E1 at 3,030 ft in along-course distance, and the extended spacing allows the right side formation members to climb without as much turn as the left side formation members. The trail aircraft, Aircraft E2 and E3, are included in the scenario for completeness but they do not affect the maneuvering of the aircraft preceding them.
This is a successful solution from a pilot’s perspective. Both sides of the formation are able to avoid the possible emergency trajectories and wake turbulence by executing small lateral maneuvers while staying in formation position with respect to one another. These types of maneuvers are easy for pilots to anticipate and monitor.
2. Comparison with pilot-generated lead and trail aircraft exit from a 7-aircraft V formation
The pilot plan shown in Fig. 8 [21] was constructed prior to the creation of the optimized model and is used as a baseline for comparison with the model-generated results for the same scenario shown in Fig 7. The pilot plan shows the lead emergency aircraft continuing straight ahead and the 2ndand 3rdelements of the formation climbing to give the emergency room to maneuver. This plan does not show lateral maneuvering by the nominal formation members due to the assumption that the lead emergency aircraft will not maneuver in the lateral direction within the first 10 seconds of the emergency. The trail emergency aircraft do not affect the other formation members.
The model-generated and pilot-generated plans are very similar. Both show the nominal aircraft climbing to avoid possible maneuvering by the emergency aircraft and then descending once the emergency is clear. The main difference between the two plans is the slight lateral maneuvering by the nominal formation members in case the lead emergency aircraft turns immediately. Immediate maneuvering is unlikely but possible, and in this case, the model-generated solution is more robust than the pilot-generated plan.
3. Three middle aircraft exit from a 7-aircraft V formation
Figure 9 shows the model-generated solution to a scenario in which a middle aircraft on the left side and two middle aircraft on the right side of a 7-aircraft formation initiate emergency operations and exit the formation. The pilot-generated plan for the same scenario is shown in Fig. 10 [21].
The lead formation aircraft, Aircraft 1, is unaffected by the emergency maneuvering behind it, and it continues on its assigned course and altitude. Aircraft E1’s possible trajectories, shown in red, turn left and away from the formation at maximum bank angle or continue straight at maximum speed. Aircraft 2 and 3 on the left of the formation and behind Aircraft E1 turn left to avoid the emergency trajectory, climb above the wake turbulence, and then turn back toward the course line. While Aircraft 2 climbs immediately, Aircraft 3 initiates its climb later than Aircraft 2 and does not climb as high due to its position farther away from the emergency trajectory. Once Aircraft E1 descends and gains sufficient spacing from the formation assigned altitude, Aircraft 2 and 3 descend into position on the left side of the formation.
On the right side of the formation, possible trajectories for Aircraft E2 and E3 include continuing straight or turning right. Aircraft 4 turns right, climbs to clear the wake turbulence of both emergency aircraft and then turns back toward the formation. Once both emergency aircraft on the right side clear formation altitude, Aircraft 4 descends into formation position.
This is a successful solution from a pilot’s perspective. The nominal aircraft are able to avoid the emergency aircraft trajectories and wake turbulence with simple maneuvers while maintaining formation position with respect to one another. Avoidance of the emergency aircraft with minimal disruption of the nominal formation positioning allows for easy monitoring by pilots and intervention if necessary in case of autopilot failure.
4. Comparison with pilot-generated three middle aircraft emergency exits from a 7-aircraft formation
The pilot plan shown in Fig. 10 [21] was constructed prior to the creation of the optimized model and is used as a baseline for comparison with the model-generated results for the same scenario shown in Fig 9.
The pilot-generated plan shows the lead aircraft continuing on course and on altitude and the three nominal aircraft turning away and climbing to avoid the emergency aircraft. Once they have sufficient spacing above the emergency, they
Fig. 8 Pilot-generated plan for lead and trail aircraft emergency exits from a 7-aircraft formation [21].
Fig. 9 Top and side views of model-generated paths for three middle aircraft emergency exits from a 7-aircraft formation.
Fig. 10 Pilot-generated plan for three middle aircraft emergency exits from a 7-aircraft formation [21].
turn back toward the course line and wait for the emergency aircraft to descend. Once the emergency aircraft clears the assigned altitude, they descend into formation position behind the lead aircraft.
The model-generated and pilot-generated plans are almost the same. The only difference is that the pilot-generated plan shows all nominal aircraft climbing at the same time and to the same avoidance altitude where the model-generated plan shows staggered climb timing and lower avoidance altitudes where possible. The model-generated plan is slightly more efficient due to the lower avoidance altitude, but it adds more complexity for pilot monitoring when the nominal formation aircraft are executing slightly different climb profiles. If avoidance maneuvers like these were to be adopted, further research would be required to investigate whether the added complexity of scenario-specific differences is worth the minor fuel efficiency benefit in a contingency scenario.
D. Robust Solution to Lead and/or Middle Aircraft Exit
Fig. 11 Top and side views of robust model-generated paths for lead and middle aircraft emergency exit from a 7-aircraft formation.
Figure 11 shows a 7-aircraft V formation with modified spacing from which the lead and second aircraft on the right exit the formation. This configuration of emergency aircraft is chosen specifically to find robust avoidance maneuvers for aircraft on both sides of the formation when spaced at 2,020 ft or greater in along-course spacing on each side.
Aircraft 1, 2 and 4 on the left side of the formation turn away to the left to maintain distance from Aircraft E1’s emergency trajectory. They then turn back toward the course line as Aircraft 1 climbs over the wake turbulence. Aircraft 2 and 4 climb in order as each one approaches the wake turbulence while maintaining approximate formation position with Aircraft 1. Once Aircraft E1 descends and gains sufficient spacing from formation altitude, Aircraft 1, 2 and 4 descend into formation position on the left side. Aircraft 3 and 5 on the right side of the formation execute similar maneuvers to the right to avoid both emergency aircraft.
The modified initial spacing and exit scenario shown in Fig. 11 presents the most robust emergency exit solution generated by the optimized model. Aircraft 1 and 3 are both 2,020 ft in along-course distance from the emergency aircraft and, therefore, execute the same avoidance maneuvers on their respective sides of the formation. The nominal formation members behind them follow their lateral maneuvers, staying in formation position, and climb and descend as necessary to avoid the emergency trajectories and wake turbulence. As long as aircraft are no less than 2,020 ft in along-course distance from the aircraft preceding them on their side of the formation, based on the model performance constraints, these maneuvers ensure avoidance of any level or descending emergency aircraft maneuver.
IV. Conclusion
The model is shown to be able to generate avoidance trajectories for nominal aircraft which are robust to changes in initial formation separation and any lateral or descending emergency aircraft trajectory. The model-generated solutions compare well with pilot-generated solutions and can be generated for either specific emergency aircraft configurations or a more general emergency exit scenario which covers all individual spacing configurations outside a minimum distance.
Acknowledgments
This research was funded by King Abdullah University of Science and Technology’s baseline support.
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