THE SAFE ZONE FOR PAIRED CLOSELY SPACED PARALLEL APPROACHES: IMPLICATIONS FOR PROCEDURES AND AUTOMATION

THE SAFE ZONE FOR PAIRED CLOSELY SPACED PARALLEL APPROACHES: IMPLICATIONS FOR PROCEDURES AND AUTOMATION Steven Landry and Amy R. Pritchett Georgia Institute of Technology Abstract Changes to air traffic control procedures and requirements for on-board automated systems can be investigated by examining the dynamics of collision potential between two proximate aircraft along closely spaced parallel approaches (CSPA). For these aircraft, there exist relative aircraft positions and trajectories that can and cannot provide separation assurance and wake avoidance. These relative positions comprise a safe zone (an area in which separation assurance and wake avoidance is provided), which depends on assumptions about aircraft dynamics, pilot performance, alerting system performance, wake transport mechanics, and a determination about the blunders for which protection should be afforded. A systematic evaluation of the dynamics of the safe zone was performed, with implications for the design of paired CSPA procedures. Introduction Current Air Traffic Control (ATC) procedures effectively limit the number of aircraft that can land at an airport with closely-spaced runways in Instrument Meteorological Conditions (IMC) to be below that allowable in Visual Meteorological Conditions (VMC). This reduction in landing capacity as a function of weather has been identified as a significant source of delay for several major airports, and is caused by the increased longitudinal spacing required during IMC. This increased spacing is dictated by the additional time needed for controller intervention to prevent loss of separation, as compared to see-andavoid during VMC. Closely spaced parallel approaches (CSPA) will reduce or eliminate this additional spacing, thereby restoring capacity during IMC. The reduction in spacing means that the problem of separation assurance must be revisited, since the controller may not have sufficient time to intervene. Two methods have been proposed to address this problem. One method is a reactive approach, using a collision alerting system in addition to, or instead of, the controller to detect blunders and warn the two aircraft. The alerting system may also incorporate escape maneuver logic and displays. A second method is preventive. Prior research has determined that for each pair of aircraft on approach, there is a danger zone along the trailing aircraft s approach path (Pritchett, 999). This danger zone is an along-track area in which the trailing aircraft is in danger of losing separation assurance in case of a blunder by the lead aircraft. The back of this danger zone is also the front of a safe zone. The safe zone, shown in Figure, is the area behind this separation hazard and in front of the crossing of the wake vortex (Hammer, 999). Wake vortex traversing distance between aircraft Safe zone Lead aircraft blunder trajectory Figure. Safe Zone Having the trail aircraft in the safe zone makes it is unlikely that a separation violation will occur, and likely that the wake vortex from the lead aircraft will pass behind the trail aircraft. Paired CSPA is a concept being investigated where the trail aircraft is positioned in the lead aircraft s safe zone and the lead aircraft is placed in front of the

trail aircraft s danger zone (Stone, 998). These safe positions are then maintained throughout the approach. Aircraft and performance, separation between the two aircraft, the types of blunders for which protection is provided, and wake transport dynamics impact the position of the safe zone. Since these factors will not necessarily be constant throughout the approach, the safe zone position and size may change. To implement paired CSPA, the dynamics of the safe zone, and what these dynamics mean for potential procedures and automation, must be well understood. This paper outlines the results of a systematic evaluation for paired CSPA approaches that examined how the safe zone changes with respect to the factors mentioned above. This work is intended to compliment the current body of research into technologies for CSPA. First, the parameters that drive the dynamics of the safe zone during CSPA are identified. Then, how the safe zone changes as each parameter is varied is determined. Next, the parameter space in which a viable safe zone exists is identified. Finally, the consequences of these findings for potential procedures and automation for CSPA are discussed. Safe Zone Parameters and Dynamics The location of the front of the safe zone can be found analytically from examination of potential future trajectories and current positions of the two aircraft. The location of the back of the safe zone is dependent upon wake transport dynamics, the lateral separation between the aircraft, and the trailing aircraft. Since a wide range of relative vertical positions is possible for both the aircraft and the wake, separation can not be guaranteed in the vertical plane. Instead, the safe zone provides assurance of separation in the horizontal plane. The front of the safe zone is dependent upon the separation between the two aircraft on approach. The separation between any two moving objects in two-dimensional space is given by: D = [ x ( t) x ( t)] + [ y ( t) y ( t)] [] The values of x(t) and y (t) represent the position of the aircraft throughout time. The coordinate frame for the aircraft is given in Figure, where the origin is placed at the position of the lead aircraft (aircraft ), which begins a blunder toward the trail aircraft (aircraft ) at t =. The blunder finishes at Ψ T =, and the lead aircraft then flies along a Ψ & straight path offset from its original course by Ψ degrees. { x (), y ()} = {,} x Ψ { x ( T), y( T)} { x (), y ()} Figure. Geometry of Equations The aircraft positions are then given by the following equations: x ( t) = y ( t) = T T x ( t) = x () + v t y ( t) = y () where: v v v cos( τ ) dτ + v ( t T v sin( τ ) dτ + v ( t T = of lead aircraft = of trail aircraft Ψ = blunder heading change Ψ & = blunder heading change rate )cosψ )sin Ψ y [] These equations are valid for t > T (after the blunder is completed). The equations

also assume that the blunder heading change rate is achieved instantly, an assumption that was tested and found to have negligible consequences to the solutions. Evaluating the integrals yields the positions of the two aircraft at any time after the is completed: v x( t) = sin Ψ + v( t T )cos Ψ v y( t) = ( cos Ψ) + v( t T )sin Ψ and x ( t) = x () + v t y ( t) = y () [ 3] [ 4 ] These expressions can be put back into equation. Both sides of that equation can then be squared to remove the square root. The result is a quadratic function with respect to time, shown in equation 5. D + = ( x () + + t) + ( 3 4t) [5] To simplify the equation, constants were introduced as follows: 3 4 v = sin Ψ vt = v cos Ψ v cosψ v = ( cos Ψ) y () = v sin Ψ Equation 5, the separation equation, is therefore a function of the following variables: x () Initial longitudinal separation y () Initial lateral separation between aircraft v, v Lead and trail aircraft s Ψ Ψ & Blunder heading change Blunder heading change rate Table. Front of Safe Zone Variables An expression for the time at which the minimum separation occurs can be obtained by taking the first derivative of the separation equation and setting it to zero. This minimum time equation and the separation equation comprise two equations that can be solved simultaneously, yielding a quadratic function with respect to the initial longitudinal separation. The two solutions of this quadratic are the minimum and maximum initial intrail distances that result in a separation violation, where the maximum initial in-trail solution is also the front of the safe zone. For the purposes of this study, 5 feet was used as the criteria for a separation violation, since this value has been used in all previous paired CSPA research. The back of the safe zone (which provides wake protection) is calculated by having the wake cross the lateral distance between the aircraft at the maximum anticipated crosswind. The time it takes for the wake to cross is calculated, and the distance the trailing aircraft can fly in that time is the maximum allowable in-trail distance. The back of the safe zone is therefore determined by the lateral separation between the aircraft, the crosswind, and the of the trail aircraft. The calculations used here for the safe zone are deterministic. The solution does not consider noise, inaccuracy, or uncertainty about parameters, as would a probabilistic model. Rather, specific analytical solutions can choose worst-case values for the variables shown in Table (and crosswind ) given knowledge of the uncertainty surrounding that variable. Results To understand how the front of the safe zone changed as each parameter was varied, solutions to the equations were obtained and graphed for lateral separations of 75 feet to 3 feet, lead and trail s of to 3 knots, heading changes of up to 45 degrees, and up to infinite heading change rates. Several findings of interest are presented here. Note that in most cases the y-axis is labeled min in-trail distance. This value is the minimum allowed distance behind the lead aircraft the trailing aircraft must be, i.e. the front of the safe zone. Effect of Lead and Trail Speeds The effect of lead and trail s is shown in Figure 3. The equations were solved for a 3- degree blunder at 6 degrees per second at a lateral 3

spacing of feet. It shows that as trail increases and lead decreases, the front of the safe zone moves further in trail. 35 3 5 5 5-5 - 3 4 5 6 7 8 9 Trailing aircraft (kts) Lead Figure 3. Effect of Trail Speed on Front of Safe Zone for Various Lead Speeds Effect of Blunder Heading and Blunder Heading Rate Figures 4 and 5 show the changes in the front of the safe zone as the blunder parameters (blunder heading change Ψ and heading change rate Ψ & ) were varied. The curves represent solutions for a lateral separation of feet and a trail of 5 knots. The lead is varied by plus or minus knots. For Figure 4, the heading change rate was 6 degrees per second. For Figure 5, the heading change was degrees. The curves are generally flat above 5 degrees of heading change and degree per second of heading change rate, with very little change in safe zone position as the heading change (Figure 4) and heading change rate (Figure 5) get larger. These figures demonstrate that low values of the blunder parameters yield the most conservative (furthest in-trail) safe zone. The explanation for this finding is that as heading change and heading change rate values increase, the time it takes for the violation to occur approaches the minimum time for the intervening distance to be crossed. It approaches this minimum quickly, and the corresponding safe zone distance in trail changes very little since it is related to the time-to-violation. (kts) 4 6 8 3 5 5 5-5 - 5 5 5 3 35 4 45 5 55 6 Blunder heading change (deg) Trail faster 4 Lead faster Lead minus trail Figure 4. Effect of Blunder Heading Change on Front of Safe Zone 5 5-5 3 4 5 6 7 8 9 Blunder heading change rate (deg/sec) Trail faster Lead faster (kts) - - Lead minus trail (kts) Figure 5. Effect of Blunder Heading Change Rate on Front of Safe Zone There is, however, no corresponding maximum time for the violation to occur. Very low heading change and heading change rate values result in very long times for the conflict to occur. Instead of choosing arbitrary blunder parameters, then, designers can choose a time-to-violation above which a controller has sufficient time to intervene in the case of a blunder, or which provides sufficient time for an automated alert and subsequent human reaction. The corresponding safe zone provides an assurance that, regardless of the type of blunder, a separation violation cannot occur within the prescribed time. Different combinations of Ψ and Ψ &, however, may result in different in-trail requirement solutions, even for the same time-to-violation. In order to determine the pairing of Ψ and Ψ & that produces the most restrictive in-trail requirement, various combinations resulting in the same time-toviolation were run, as shown in Figure 6. This figure represents a time-to-violation of 3 seconds, with a lead of 5 knots and a trail of - -

7 knots, with results plotted for a range of lateral separations. The combination using the lowest heading change rate results in the largest in-trail requirement for the front of the safe zone. The minimum heading change rate occurs where the time to is equal to the time-to-violation desired, in other words, where the separation violation occurs just as the blundering aircraft rolls out of its. This relationship allows the designer to choose the minimum blunder heading rate that results in the desired time-to-violation, with the blunder heading being given by equals time-to-violation. 9 8 7 6 5 4 Ψ = T 75 9 5 35 5 65 8 95 5 4 55 Lateral separation (ft), which Blunder heading change rate (deg/sec) Figure 6. Change in Front of Safe Zone as Blunder Heading Rate Decreases for a Range of Lateral Separations Effect of Time-to-Violation Figure 7 shows the effect of increasing time-to-violation on the front of the safe zone. As expected, in general the front of the safe zone moves back as time-to-violation increases and as lateral separation increases. The results concerning time-to-violation and blunder parameters have significant implications for the design of procedures and uses for alerting systems for CSPA. They suggest that a tradeoff exists between minimum separation for the paired aircraft and the amount of time for which the safe zone provides separation assurance. Longer time-to-violation choices require further distances in trail. Shorter in-trail distances might require the use of an alerting system..5 3 6 6 infinite 5.. 5.. 5.. 75 9 5 35 5 65 8 95 5 4 55 7 85 3 Lateral separation (ft) Time-toviolation Figure 7. Change in Front of Safe Zone as Time-to-Violation Increases Considerations for Missed Approach The safe zone, as described above, only considers the case where the lead aircraft blunders towards the trailing aircraft. The possibility of both aircraft blundering must also be considered. Such a case is particularly likely should both aircraft perform a missed approach. During missed approach, the aircraft will accelerate and climb. Since there is often no positive course guidance on missed approach, and it is often flown manually, dispersion from the desired course becomes a significant likelihood for both aircraft. The equations, therefore, were modified to include blunder heading changes by both aircraft. Larger differences between the aircraft were used, reflecting the variety of missed approach climb and acceleration profiles used across different carriers, equipment, and pilots. Figure 8 is a comparison between the dual blunders used for missed approach calculations and the single blunder used in the earlier calculations. The solutions for this figure used a time-toviolation of seconds, with a lead of 5 knots and a trail of 3 knots, and were solved for a variety of lateral separations. This figure shows that the solutions for dual blunders result in lower minimum in-trail distances than for single blunders. Therefore, it is more conservative to assume a single blunder and use the more distant front of safe zone obtained from the previous equations. However, larger differences between lead and trail aircraft must be accommodated, since the larger differences result in a more conservative front of safe zone (see Figure 3). (sec) 3 4 5

45 4 35 3 5 5 dual blunder single blunder zero. The safe zone begins to collapse at close lateral spacing, high protection time, low lead, and high trail. Figure demonstrates this for knots of crosswind. At a lead of knots, a trail of about 9 knots, a 45- second time-to-violation, and a lateral spacing of 75 feet, the safe zone has zero length. 5 5 75 9 5 35 5 65 8 95 5 4 55 Lateral separation (ft) 4 3 Figure 8. Comparison of Dual vs. Single Blunders Back of the Safe Zone Crosswind, lateral separation, and trail affect the back of the safe zone. The effect of lateral separation on the back of the safe zone is shown in Figure 9 for a range of crosswind s. Max in-trail distance (ft) 45 4 35 3 5 5 5 75 9 5 35 5 65 8 95 Lateral separation (ft) 5 4 55 knot wake 5 knot wake knot wake Figure 9. Effect of Lateral Separation on Back of Safe Zone The back of the safe zone has a greater dependence on lateral separation than the front. As lateral separation decreases, the back of the safe zone moves forward relatively quickly, whereas the front of the safe zone changes more slowly. As the lateral separation goes to zero (as might be the case during a blunder), the back of the safe zone also goes to zero. This means that wake protection is not provided during a blunder, whereas separation assurance is still provided by the front of the safe zone. - - - - -3-4 -5-6 -7-8 -9 - - - Trail minus lead (kts) Figure. Effect of Speed Difference between Lead and Trail Aircraft on Length of Safe Zone The length of the safe zone is one concern, since it impacts the ability of the pilot (or automation) to maintain the aircraft s position within the safe zone. Another concern is how far in trail the safe zone begins. If the safe zone is too far in trail, there will be no capacity increase and hence no benefit obtained from paired CSPA operations. Fortunately, the time-to-violation requirement limits how far in trail the safe zone can begin, thereby retaining the benefit of reduced in-trail separation from normal IMC operations. For the same parameters as in Figure, for example, but at a runway separation of 3, feet, the safe zone begins at about 7,5 feet in trail. This figure represents nearly the maximum value in this study. Regression Results In order to summarize the results, a regression was performed on the results of the equations. The multiple linear regression performed achieved an R-squared of.97, which exceeded all nonlinear regressions tested. The regression equation is: 75 Determination of Procedural Limits In the range of solutions obtained, some combinations of parameters can cause the distance between the front and back of the safe zone to go to 6

X = 483 37.5V where V V Y + 3.7V X = front of safe zone (feet) l t = lead (ft/sec) = trail (ft/sec) = lateral separation (feet) T = minimum l t +.64Y 9.T time until separation lost (sec) The regression confirms the previous findings that:. The front of the safe zone moves back (higher) as the trail increases and lead decreases.. The front of the safe zone moves back as lateral separation increases. Note that the back of the safe zone will also move back in this case since the wake will have a greater distance to traverse. 3. The front of the safe zone moves back as timeto-violation decreases. Although high residuals were found, indicating that the regression equation does not accurately predict the exact value of the front of the safe zone, the high R-squared value suggests that the equation accurately portrays the contributions of the safe zone variables. The front of the safe zone is most affected by the lead and trail s, followed closely by the time-to-violation. Although the actual values for Y are an order of magnitude greater than for V or V (hundreds of feet vs. tens of ft/sec) or for T (tens of seconds), lateral separation still has much less effect on the front of the safe zone as compared to the other parameters. Conclusion Several conclusions are suggested by the results. First, a safe zone exists. The safe zone is dependent upon the airs of the paired aircraft, the lateral separation between them, the blunder parameters, and the crosswind. An example of a safe zone is shown in Figure. In order to compensate for lateral navigation errors, which become problematic since localizer signals for closely spaced runways overlap at some distance from the runway, the trailing aircraft flew a three-degree offset localizer to the final approach fix. This resulted in a time-varying lateral separation. The lead aircraft was allowed to fly a minimum of knots, and the trail aircraft could fly up to knots. The safe zone was calculated to provide 3 seconds of separation protection. Longitudinal distance from lead (ft) - -4-6 -8 - - -4-6 -8 - Lead distance from threshold (NM)..8.5.5 3. 3.75 4.5 5.5 6. 6.75 7.5 8.5 9. 9.75 Figure. Safe Zone Example Front of safe zone 5 knot back of safe zone The length of the safe zone goes to zero in some cases, particularly those with low lateral spacing, high protection times, and large differences between trail and lead. These areas have been roughly mapped out, and are confined to near 75-foot lateral separation, very low lead approach (below knots), and very high trail (above 9 knots). The safe zone lengthens rapidly away from these values, making it potentially compatible with a large variety of aircraft types and runways. Secondly, an analytical solution demonstrated that instead of arbitrarily choosing blunder parameters, a protection time can be chosen, where losses of separation can only occur after this time has elapsed after the beginning of the blunder. The blunder parameters are then chosen based on this time. Larger protection times mean larger in-trail distances and shorter safe zones. Thirdly, the lead and trail s, and the protection time desired, significantly affect the safe zone. It is less significantly affected by the lateral separation between the aircraft. Increases in the trail and protection time cause the front of the safe zone to move back, decreasing its size for a given crosswind. Increases in the lateral separation also cause the front of the safe zone to move back, but have a greater effect on the back of the safe zone, and overall the safe zone lengthens with greater lateral separation. 7

The implications of these findings are that a procedure that uses the safe zone as a means of conflict prevention would need to consider a tradeoff between safe zone distance in trail, and the time-to-violation for which protection is provided. If a time-to-violation value is chosen that provides sufficient time for controller-pilot interaction in the case of a blunder, the procedure may be able to be implemented without the use of an alerting system. If it is determined, however, that in order to obtain sufficient benefit from the procedure, the time-toviolation must be kept low, it is likely that a collision alerting system would have to be used. In addition to the use of an alerting system, the analysis points to other uses of automation. In order to maintain position within the safe zone (or even know the position of the safe zone), the trail aircraft pilot must know the lead aircraft s and its own position relative to lead aircraft. This information may need to be integrated into a flight deck display. In addition, the difficulties posed by dual missed approach may require that the aircraft be provided with positive guidance during missed approach. More detailed analysis may also indicate the potential benefit (or detriment) of autopilot coupled approaches. The safe zone also suggests that in-trail separations may be useful for improving safety in the closely spaced visual approaches currently in use today. The time it takes for a loss of separation to occur for two aircraft on simultaneous visual approaches at 75 feet lateral separation and small longitudinal separation can be less than seconds. The longitudinal separations given by the safe zone calculations can provide guidance on visual in-trail separations that could enhance safety for these approaches. One significant problem remains unresolved. During a blunder, the lateral separation goes to zero as the lead crosses the path of the trail aircraft. Since the wake model is based on the lateral distance between the aircraft, wake protection disappears. Loss of wake protection may also occur during missed approaches in which the lead aircraft is at a much higher than the trail. The analysis for the back of the safe zone, however, did not consider the vertical position of the wake (or the aircraft), and used a very conservative model of wake transport. It may be possible to overcome this limitation with a vertical maneuver, with a better model of wake transport, and/or with wake position sensing or prediction tools. Despite this, the safe zone concept is encouraging, exhibiting sufficient flexibility to support a variety of equipment and potential procedures. The amount of separation assurance would need to be chosen by designers (both the minimum desired separation and the time-toviolation). The s allowed on approach, and how best to handle missed approaches, also needs to be determined. This analysis of the safe zone provides the information necessary to make educated decisions about the types of procedures required to enact paired CSPA, and the potential benefits of automation. Acknowledgements This study is supported by NASA and the FAA, Grant NAG -34, with Vernol Battiste and Gene Wong as Technical Monitors. The input of Anand Mundra and Jonathan Hammer of MITRE/CAASD is also appreciated. References Hammer, J. Study of the Geometry of a Dependent Approach Procedure to Closely Spaced Parallel Runways, 8 th Digital Avionics Systems Conference, St. Louis, MO, 999. Pritchett, A. R. Pilot Performance at Collision Avoidance During Closely Spaced Parallel Approaches, Air Traffic Control Quarterly, Vol. 7, No., p. 47-75, 999. Stone, R. Paired Approach Concept: Increasing IFR Capacity to Closely Spaced Parallel Runways, http://www.asc.nasa.gov/tap/cspa/prdapp.ht ml, 998. 8