March 2012 

NASA/CR–2012-217343

Airborne Precision Spacing (APS) Dependent 

Parallel Arrivals (DPA)

Colin L. Smith 

Lockheed Martin Engineering and Sciences Company, Hampton, Virginia
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March 2012 

NASA/CR–2012-217343

Airborne Precision Spacing (APS) Dependent 

Parallel Arrivals (DPA) 

Colin L. Smith 

Lockheed Martin Engineering and Sciences Company, Hampton, Virginia
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 
1 

Table of Contents 

Abstract ...................................................................................................................... 3 

1. Introduction ......................................................................................................... 3 

a. Introduction 3 

b. Operations Terminology 4 

2. Objectives ......................................................................................................... 5 

a. Research Questions 6 

3. Methodology ......................................................................................................... 6 

a. Airspace Environment 6 

b. Traffic Scenario 7 

c. Aircraft Distribution 7 

d. Wind 8 

e. Independent Variables 9 

f. Dependent Variables 11 

g. Spacing Commands 11 

h. Aircraft Assignments 11 

i. Simulation Facility 14 

j. Runs 14 

4. Validation ......................................................................................................... 15 

a. Purpose 15 

b. Findings 15 

5. The Impact of Two-Target Operations ..................................................... 16 

a. Purpose 16 

b. Findings 16 

6. Stability of Operations ............................................................................... 17 

a. Purpose 17 

b. Findings 17 

7. Other Findings ............................................................................................ 19 

a. Radar Separation 19 

b. Alteration to the Schedule 19 

c. The Stagger Aircraft as the Primary Aircraft 19 

d. Schedule Sensitivity 20 

8. Conclusions ......................................................................................................... 21 

Appendix A List of Acronyms ............................................................................... 22 

Appendix B Validation Data ............................................................................... 23 

Appendix C Separation Violations ................................................................. 28 

Appendix D Commanded Speed Changes ..................................................... 28 

Appendix E CrossingTimeError ............................................................................... 29 

References ................................................................................................................... 39 
2 

Tables and Figures 

Table 1 Aircraft Distribution ............................................................................... 8 

Table 2 Final Experiment Matrix .................................................................. 10 

Table 3 Separation Violations ............................................................................... 16 

Table 4 Number of Commanded Speed Changes ..................................................... 17 

Table 5 CrossingTimeError ANOVA & F-Test ..................................................... 19 

Figure 1 One-Runway operations vs. Parallel-Runway operations ............. 4 

Figure 2 One-Target vs. Two-Target operations ..................................................... 5 

Figure 3 In-Trail vs. Stagger spacing ................................................................. 5 

Figure 4 Approach Chart for KDFW .................................................................. 7 

Figure 5 APS Wind for 06MAR09 with Altitudes Selected for ASTAR ............. 9 

Figure 6 Aircraft Type and Runway Assignment Example .......................... 13 

Figure 7 Aircraft Scheduling Example ................................................................. 14 

Figure 8 Distributions of Differences in ATA ..................................................... 15 

Figure 9 CrossingTimeError ............................................................................... 18 

Figure 10 Even Spacing Configuration ................................................................. 20 
3 

Abstract 

The Airborne Precision Spacing (APS) team at the NASA Langley Research Center (LaRC) has 

been developing a concept of operations to extend the current APS concept to support dependent 

approaches to parallel or converging runways along with the required pilot and controller 

procedures and pilot interfaces. A staggered operations capability for the Airborne Spacing for 

Terminal Arrival Routes (ASTAR) tool was developed and designated as ASTAR10. ASTAR10 

has reached a sufficient level of maturity to be validated and tested through a fast-time 

simulation. The purpose of the experiment was to identify and resolve any remaining issues in the 

ASTAR10 algorithm, as well as put the concept of operations through a practical test. 

The experiment was designed to progress through three comparisons, building up a validation of 

ASTAR10 and then testing ASTAR10 for performance. First ASTAR9 and ASTAR10 were given 

identical one-runway scenarios, and the results were compared for consistency. Second, 

ASTAR10 was given a two-target scenario and a one-runway scenario designed to produce the 

same spacing. ASTAR10’s performance was then tested under various criteria, including wind 

forecast error, different runway separations, and both one-target-two-runway and two-targettwo-runway scenarios. 

The work resulted in significant insights to be integrated into the NASA Langley Air Traffic 

Operations Lab (ATOL) and Cockpit Motion Facility (CMF) simulators for use in future APS 

studies and will aid in the preparations for subsequent human-in-the-loop (HITL) studies. 

ASTAR10 was validated and the significance of a secondary target was established. Both the 

APS Dependent Arrivals concept of operations and the ASTAR10 algorithm were refined. 

1. Introduction

a. Introduction 

Improved arrival efficiency, in terms of both capacity and environmental impact, is an important part of 

improving National Airspace System (NAS) operations. The Airborne Precision Spacing (APS) team at 

the NASA Langley Research Center (LaRC) has been developing a concept of operations to extend the 

current APS concept to support dependent arrivals to parallel approaches along with new pilot and 

controller procedures and pilot interfaces [1]. This is intended to allow aircraft managing their own 

spacing to land on parallel runways, achieving improved arrival precision and airport capacity while also 

allowing aircraft to utilize Optimized Profile Descents (OPD) to improve fuel efficiency. This would 

result in greater aircraft throughput at the runways, less fuel consumption and noise on approaches, and 

Air Traffic Control (ATC) traffic planning at a more strategic level [2-4]. This system could be utilized at 

existing airports as well as considered in the design of future airports. 

To achieve successful development and field-testing of integrated air/ground arrival operations 

procedures, the technology readiness level, or maturity, of the airborne spacing tool needed to be 

increased. Tools, procedures, and interfaces to allow airborne spacing based on two targets were 

developed to expand current airborne spacing operations to support dependent, parallel approach 

operations (also called staggered operations). A staggered operations capability for the Airborne Spacing 

for Terminal Arrival Routes (ASTAR) tool was developed and designated as ASTAR10. The tool allows 
4 

spacing relative to two target aircraft including one that lands on a different runway. The ASTARequipped aircraft is instructed to achieve the assigned spacing behind two aircraft, one landing on the 

same runway, resulting in in-trail spacing, and the other landing on a parallel runway, resulting in stagger 

spacing. The required stagger distance is dependent on the distance between runway centerlines. A 

runway separation of 2500 ft to 4000 ft requires a 1.5 nmi stagger distance, while a separation 4000 ft to 

9000 requires a 2.0 nmi stagger distance. 

ASTAR10 has reached a sufficient level of maturity to be validated and tested. A simulation experiment 

of the new precision spacing concept was performed to allow for refinements to the concept of operations 

as well as provide a first look at possible benefits and system performance improvements of these new 

operations. The work resulted in significant insights to be integrated into the NASA Langley Air Traffic 

Operations Lab (ATOL) and Cockpit Motion Facility (CMF) simulators for use in future APS/ASDO 

studies and will aid in the preparation for subsequent human-in-the-loop (HITL) studies. This experiment 

consisted of analyses of fundamental performance and operations. It did not include any HITL elements 

or advanced performance elements. 

b. Operations Terminology 

In this paper, four criteria are used to distinguish the particular operations. These criteria are: the number 

of runways in use, whether the spacing aircraft is tracking one target or two, whether the target aircraft is 

approaching the same runway or a parallel runway as the spacing aircraft, and whether the target aircraft’s 

spacing criteria are the dominant criteria. 

The number of runways represents a high-level variable. One-runway operations mean that only one 

runway is in use, thus all aircraft land on that runway, in-trail behind one another, with only one possible 

target. If more than one parallel runway is in use, the operation is a parallel approach operation. This is 

illustrated below in Figure 1. 

Figure 1: One-Runway operations vs. Parallel-Runway operations. 

In parallel operations, aircraft can space off of an aircraft approaching the same runway, an aircraft 

approaching a parallel runway, or both aircraft simultaneously. If the spacing aircraft is only spacing off 

of one aircraft, it is called a one-target operation. If the spacing aircraft is spacing off of aircraft 

approaching both runways, it is called a two-target operation. Note that in one-target operations, the 

spacing aircraft may space off of only the aircraft approaching a parallel runway, while ignoring an 

aircraft approaching the same runway, or vice versa. Also note that the number of targets only refers to 

how many aircraft are being used for spacing operations, not how many aircraft are present. Thus, onetarget operations may be in use when there are multiple aircraft that could be targeted. This is illustrated 

below in Figure 2. 
5 

Figure 2: One-Target vs. Two-Target operations. 

If a target aircraft is approaching the same runway as the spacing aircraft, the spacing is said to be in-trail 

spacing. If the target aircraft is approaching a parallel runway, the spacing is said to be stagger spacing. 

Two-target operations necessarily use both in-trail and stagger spacing, while one-target operations may 

use either one. This is illustrated above in the one-target diagrams of Figure 2. 

Finally, in two-target operations, a distinction is made between a primary target and a secondary target. 

When determining this, the spacing aircraft calculates a resultant spacing position for each spacing 

aircraft. The aircraft whose spacing interval results in a spacing position further back is defined as the 

primary target, while the secondary target’s spacing interval results in a closer spacing position. The 

spacing aircraft precisely meets the spacing interval of the primary aircraft, while exceeding or meeting 

the spacing interval of the secondary aircraft. This is illustrated below in Figure 4. 

Figure 3: Primary vs. Secondary targets. 

2. Objectives 

The purpose of the experiment was primarily to identify and resolve any remaining issues in the 

ASTAR10 algorithm, as well as put the concept of operations through a practical test. This was done 

during the development of the experiment scenarios. The experiment itself was divided into two 

segments. The first segment was used to validate ASTAR10 against ASTAR9, the previous iteration of 

the algorithm, while the second segment was used to address several research questions. 
6 

a. Research Questions 

During the development of the concept of operations several research questions were identified which 

could be answered by one or more system performance studies. This experiment was designed to address 

two of these: 

What is the impact of two-target operations versus one-target operations in a parallel approach 

environment? 

o Hypothesis: Two-target operations will yield fewer separation violations against the 

secondary aircraft, since spacing is being managed against both targets. 

How stable are one- and two-target stagger operations? 

o Hypothesis: Both operations will be equally stable. 

3. Methodology 

a. Airspace Environment 

Portions of the Dallas-Ft. Worth International Airport (KDFW) airspace environment were simulated in 

the experiment. To meet the objectives of this experiment, two pairs of runways were needed: one pair 

separated by 2500 ft to 4300 ft and the other pair separated by 4300 ft to 9000 ft. No two pairs of KDFW 

runways satisfied these criteria so a new “virtual” runway was added. Runway 18V was placed between 

existing runways 18R and 17R. Approaches to runways 18R and 18V are separated by 2500 ft while 

runways 18V and 17R are separated by 5100 ft. OPDs were designed that ended at the appropriate ILS 

for each runway. A chart of the 18R/18V/17R arrival paths is shown in Figure 5. The southwest arrival 

path is split into two separate routes farther out (at approximately 153 nmi out from the runway). Note 

that the final approach leg for approaches from the west was extended to avoid head-on base legs and 

introduce the possibility of an aircraft intercepting its final approach leg prior to that its stagger target 

aircraft doing so. 
7 

Figure 4: Approach chart for KDFW. 

b. Traffic Scenario 

The traffic scenarios for this batch study consisted of 50 aircraft to each of the selected parallel runways 

(e.g., KDFW 18R and 18V or 18V and 17R). Initialization of the aircraft was at cruise altitudes and 

speeds approximately 60 nmi prior to Top-of-Descent. Aircraft spacing within or between streams 

consisted of a mix of in-trail and staggered aircraft depending on the scenario objectives. Several sets of 

initial parameters (aircraft type, weight, altitude, and speed; route distribution) were used across test 

conditions to enable aircraft-to-aircraft performance comparisons between the test conditions, while also 

providing multiple variations. 

c. Aircraft Distribution 

The aircraft type and route distributions were generated from statistics derived from a single day of 

operations at DFW. The aircraft types observed were then pruned to aircraft types available for 

simulation in TMX. The results are shown in Table 1 below. 
8 

Table 1: Aircraft Distribution 

BADA 

Model* 

Aircraft 

Types 

Ref. Mass 

Mkg 

Ref. 

Weight Klb 

VstallLanding Number 

Observed 

Observed 

% Percent Used 

CRJ1 

Canadair 

Regional 

Jet 21.0 46.2 108 76 7.8 10 

A319 A319 60.0 132.0 94 66 6.8 10 

B737 B737-700 60.0 132.0 103 87 8.9 15 

MD83 MD-83 61.2 134.6 112 633 64.9 25 

B753 B757 101.6 223.5 109 71 7.3 15 

B763 B767-300 150.0 330.0 113 16 1.6 10 

B773 B777 237.6 522.7 111 24 2.5 10 

B744 B747-700 285.7 628.5 118 2 0.2 5 

*The BADA Model number represents the identification of the aircraft model in the simulation software 

The observed statistics significantly over-represented MD83 aircraft and the northeast quadrant. As the 

purpose of the experiment was not to model an actual DFW traffic environment, these statistics were 

modified to represent a more general distribution. The aircraft type distribution can be seen above in the 

Percent Used column, while the quadrant distribution was split 50/50 by east/west and 60/40 by 

north/south, resulting in an aircraft distribution of 30/30/20/10/10 for the northeast, northwest, southeast, 

and two southwest routes. 

d. Wind 

One of the wind conditions described in Ref [5] was used in this experiment. The wind scenario chosen 

was the data set for March 6, 2009. It was selected as having reasonable characteristics in strength, 

direction, and variation. 

Charts of the selected data set were inspected to determine ten altitudes that would produce representative 

interpolations of the four tabulated parameters, true wind speed and direction, and forecast wind speed 

and direction. The truth wind was used to determine actual aircraft performance, while the forecast wind 

was used for scheduling and aircraft trajectory predictions. Ten data points were used to describe the 

truth and forecast winds in the TMX software. The results of this process are depicted in Figure 6. 
9 

Figure 5: Truth and Forecast wind from the 06MAR09 dataset with altitudes selected for this experiment. 

The characteristics shown in the chart are wind speeds of 60-70 kt at cruise altitudes, 30-40 kt between 

20,000 and 10,000 ft, 40-50 kt between 10,000 and 5000 ft, and 15 kt at the airport surface. The wind 

direction is WNW at cruise altitudes, S between 20,000 and 13,000 ft, SW between 13,000 and 8000 ft, 

and SSE at the surface. Aircraft on approach encountered slight crosswinds from the right veering to 20 

degrees from the left at the runway threshold. 

The wind models for this study were then generated using the interpolated speed and direction values for 

the ten selected altitudes. The wind fields were laterally homogeneous throughout the region of the 

simulation. 

e. Independent Variables 

The independent variables for this experiment were wind (varying from no wind, to wind with accurate 

forecast, to wind with a forecast error), runway separation (2500 ft or 5100 ft), and number of target 

aircraft (one- or two-target operations). The final experiment matrix is provided below in Table 2: 
10 

Table 2: Final Experimental Matrix 

Scenario Active Runways Wind/Forecast Error Spacing/Operations 

1 18R None/No In-Trail One-Target 

2 18R None/No In-Trail One-Target 

modified spacing goal (see text) 

4 18R/18V None/No Two-Target 

5 18V/17R None/No Two-Target 

6 18R/18V Nominal/No Two-Target 

7 18V/17R Nominal/No Two-Target 

8 18R/18V Nominal/Yes Two-Target 

9 18V/17R Nominal/Yes Two-Target 

10 18R/18V None/No One-Target 

11 18V/17R None/No One-Target 

12 18R/18V Nominal/No One-Target 

13 18V/17R Nominal/No One-Target 

14 18R/18V Nominal/Yes One-Target 

15 18V/17R Nominal/Yes One-Target 

Scenario 1 was run with both ASTAR9 and ASTAR10 software, thereby providing a validation test for 

ASTAR10’s one-runway operations. Scenarios 2 and 4 were designed to produce the same spacing 

between sequential aircraft, but with one-runway operations for scenario 2 and two-runway, two-target 

operations for scenario 4, thereby providing a validation test for ASTAR10’s two-target operations. From 

there on, scenarios 4 through 9 and scenarios 10 through 15 were designed as mirror sets, with scenarios 4 

through 9 using two-target operations while scenarios 10 through 15 used one-target operations. Within 

each operations grouping of scenarios, the scenarios were also divided between wind conditions. Thus, 

scenarios 4, 5, 10, and 11 experienced no wind, scenarios 6, 7, 12, and 13 experienced wind with an 
11 

accurate forecast, and scenarios 8, 9, 14, and 15 experienced wind with a forecast error. Scenarios also 

alternated between runway configurations, so that all even-numbered scenarios landed on runways 18R 

and 18V, while all odd-numbered scenarios landed on runways 18V and 17R. For the purposes of 

comparing operations differences, this allows a direct 1-to-1 comparison of scenarios 4 and 10, 5 and 11, 

6 and 12, 7 and 13, 8 and 14, and 9 and 15, while also isolating wind conditions and runway differences. 

The statistical analyses compared the scenarios accordingly. 

f. Dependent Variables 

The dependent variables tracked for data analysis, taken from the simulation software, were the closest 

direct-line distance between the spacing aircraft and the traffic-to-follow (TTF2ClosestCG), the arrival 

error (CrossingTimeError), the total number of speed changes (SpdChanges(total)), and the actual time of 

arrival (ATA). The closest distance was used to identify separation violations with respect to the second 

target when comparing scenarios 4 through 9 to scenarios 10 through 15. If the closest point was below 

the minimum separation requirements, a violation would have occurred. Arrival error was used as a 

performance metric when comparing scenarios 4 through 9 to scenarios 10 through 15. The ideal arrival 

error was zero, with either a positive or a negative error indicating less than perfect performance. The 

speed changes generated by the ASTAR10 algorithm to meet the spacing goal were not separated from 

the speed changes required by the arrival procedure. Arrival time was used to calculate achieved stagger 

spacing in Scenario 4 and achieved in-trail spacing in Scenario 2. To do this, the arrival time of one 

aircraft was compared to that of the following aircraft. The difference between them was the in-trail 

spacing for scenario 2 and the stagger spacing for scenario 4. The scenarios were designed so that 

Scenario 4’s stagger spacing should have been comparable to Scenario 2’s in-trail spacing. Arrival error 

could not be used because of the nature of the spacings being compared. Arrival time was used solely for 

validation purposes. Closest distance was used to answer the first research question. Arrival error and 

the number of speed changes were used to answer the second research question. 

g. Spacing Commands 

Spacing commands were given to the aircraft depending on their in-trail or stagger requirements. The 

required in-trail wake-vortex separations were 2.5 nmi, 4 nmi, and 5 nmi, depending on the interaction of 

leading and following aircraft weight class. These requirements were given a 0.5 nmi buffer and then 

converted into times using an assumed final approach speed (FAS) of 139 knots and incorporating the 

forecast wind. The stagger spacing requirements were 1.5 nmi for 18R/18V and 2.0 nmi for 18V/17R. 

These requirements were given a 0.2 nmi buffer, and the 18R/18V requirement was expanded to 2.1 nmi 

to ensure 3 mile separation prior to final approach (required to maintain radar separation prior to final 

approach, see section 7.a). The stagger requirements were given as distances. 

h. Aircraft Assignments 

Two sequences of 100 random numbers were generated and assigned to a sequential numbering scheme 

(in its original, random order) using Microsoft Excel Spreadsheet's Rand() command. The results were 

then separately re-ordered according to the sequences of random numbers, resulting in two random 

sequences of a sequential numbering scheme. Aircraft and routes were sequentially assigned to the 

separate sequences of random numbers according to their statistical distribution (20% = 20 AC). The 
12 

tables were then re-sorted according to the sequential numbering scheme, resulting in a single numbering 

scheme ordering from 1 to 100 and a random association of aircraft and routes. 

Aircraft were taken from the random table and assigned to runways in order, according to direction of 

origin (routes from the east were assigned to the eastern runway, etc). This resulted in two sequences of 

random aircraft, one to each runway. The runway assignments were then blended together in a stagger 

pattern, with aircraft being assigned to alternating runways, and in-trail spacing time was derived from the 

resulting table. Each aircraft then had a separate Estimated Time of Arrival (ETA) calculated from its intrail spacing and stagger spacing time separations. The larger of the two values becomes the primary 

spacing command. The aircraft this command related to was called the primary aircraft, while the other 

aircraft being spaced against was called the secondary aircraft. In this simulation, secondary aircraft were 

assigned a ‘no closer than’ spacing command, meaning that positive errors (representing being farther 

away than the spacing command required) were ignored. The ETA for next aircraft was then calculated 

based on those for previous aircraft and specified spacing times. The time-differences between the 

aircraft were then calculated. This sequence of aircraft, routes, and ETA differences was then entered 

into the existing Scenario Generator to generate a TMX input file with ASTAR9 (in-trail only) spacing 

commands. This file was then manually edited to include the appropriate ASTAR10 stagger and 

secondary-target spacing commands. Below, Figure 7 details an example random schedule generation of 

four aircraft, while Figure 8 shows how the scheduled spacing and primary/secondary relationships were 

determined. 
13 

Figure 6: Aircraft type and runway assignment example. 
14 

Figure 7: Aircraft scheduling example. 

i. Simulation Facility 

Traffic Manager (TMX) software, the simulation environment for the experiment, is a multiple aircraft 

simulation environment developed by the National Aerospace Laboratory (NLR) of the Netherlands. It 

was originally designed in 1996 to study airborne separation assurance with multiple aircraft interactions 

in a Free Flight environment. It has been continually developed since that time by both the NLR and 

NASA Langley for use in a wide range or simulation projects [6]. It is capable of generating, simulating, 

and managing multiple aircraft simultaneously in an airspace simulation. The ASTAR development team 

has integrated the ASTAR10 algorithm into TMX, allowing the aircraft to fly using ASTAR10 

procedures. The version of TMX used was v9.3.07. It was implemented on a single desktop computer. 

j. Runs

Each scenario was run under two different randomly generated traffic conditions, as described previously. 

Each of these conditions was then run twice, employing performance randomization factors built into 

TMX, including pilot model reaction times, atmospheric and sensor noise, and randomized sampling 

time. This provided a total of 4 iterations of each scenario. 
15 

4. Validation 

a. Purpose

The ASTAR10 algorithm represents a new modeling software package, with substantial changes from the 

previous iteration. It is thus important to validate its performance against the previous algorithm to 

ensure it maintains sufficiently accurate performance. 

b. Findings

In comparing the performance of ASTAR10 to ASTAR9, the differences between arrival spacing was 

compared, using ATAs. ASTAR9 presented a sample size of 198 values (99 for each of two traffic 

scenarios), while ASTAR10 presented 396 (99 for each of two traffic scenarios; each scenario run twice). 

Because of this discrepancy, the ASTAR10 data was averaged between the runs of each traffic scenario, 

resulting in 198 values. It was expected that there would be no difference in the spacing performance 

between ASTAR9 and ASTAR10. An F-test was performed to test this hypothesis. The F-value was 

0.10 and the p-value was 0.75. From this, the null hypothesis that there is no statistically significant 

difference between the two data sets was supported. 

In comparing the performance of ASTAR10’s one-target operations (scenario 2) to its two-target 

operations (scenario 4), a sample size of 396 values for each scenario was obtained. The F-value was 

0.04 and the p-value was 0.83. From this, the null hypothesis that there is no statistically significant 

difference between the two data sets was supported. The results are shown below in Figure 9. 

Figure 8: Distributions of differences in ATA. 

0 

10 

20 

30 

40 

50 

60 

70 

80 

0 20 40 60 80 100 120 140 160 

Number of Occurrences 

Achieved Spacing 

2-1 

2-2 

4-1 

4-2 
16 

5. The Impact of Two-Target Operations 

a. Purpose

The first research question asked what the impact of two-target operations vs. one-target operations is. 

This question was asked in order to assess the importance of a secondary target. It had been considered 

that the aircraft may be able to maintain separation with both targets simply by monitoring their primary 

target aircraft, and that any secondary aircraft would necessarily stay a greater distance away. This was 

uncertain in ASTAR10, however, because the algorithm does not maintain current spacing, but rather 

predicted spacing at the runway. It is thus possible for current spacing to be either greater than or less 

than the desired spacing at the runway. The amount of difference between current spacing and final 

spacing is monitored, allowable error is reduced as an aircraft gets closer to the runway, and a spacing 

buffer is included to ensure that minimum separation standards are not violated. However, a secondary 

aircraft’s error with its own primary could place it out of position, and thus too close to another trailing 

aircraft. 

b. Findings

In addressing the first research question TTF2ClosestCG values were compared to the required separation 

criteria. Each scenario had a sample size of 100. No statistically significant variation was observed; 

however, a noticeable, if minor, difference was observed. While the two-target operations saw no 

separation violation against the secondary aircraft, the one-target operations saw a total of 4 such 

violations, out of a total of 2328 aircraft. Given the nature of these events, this difference is considered 

significant, if infrequent. Operationally speaking, one separation violation per 582 aircraft is 

unacceptable. These violations are occurring specifically because the spacing between an aircraft and its 

secondary target is not being monitored. Since the purpose of identifying a second target is to avoid 

separation violations with it, the hypothesis that two-target operations will see fewer separation violations 

against the secondary aircraft was supported. The results are below in Table 3. 

Table 3: Separation Violations 

Separation 

Violations 1-1 2-1 1-2 2-2 

Scenario 4 0 0 0 0 

Scenario 5 0 0 0 0 

Scenario 6 0 0 0 0 

Scenario 7 0 0 0 0 

Scenario 8 0 0 0 0 

Scenario 9 0 0 0 0 

Scenario 10 0 0 0 0 

Scenario 11 0 0 0 0 

Scenario 12 0 0 0 0 

Scenario 13 0 1 0 1 

Scenario 14 0 0 0 0 

Scenario 15 0 1 0 1 
17 

6. Stability of Operations 

a. Purpose

The second research question asked how stable one- and two-target operations are. Because two-target 

operations represent a new capability, it was important to establish the stability of the aircraft arrival 

streams. This fact was emphasized early in the experiment development as many arrival streams resulted 

in periodic excessive spacing. The problem was identified as resulting from a transition from time-based 

stagger spacing to distance-based stagger spacing for final approach. The time-based spacing commands 

had been based on an average final landing speed, which was used to convert from the distance 

requirements to the time-based spacing command. The distance-based commands for final approach, 

however, allowed the ASTAR algorithm to use each aircraft’s individual speed in performing 

calculations, thus resulting in a different spacing. Specifically, aircraft typically attempted to gain about 2 

seconds. Each individual aircraft was able to do this for its own spacing, but all aircraft after them would 

then have to advance the same amount. Because of this, each aircraft would not only need to gain its own 

2 seconds, but also 2 more seconds for each aircraft ahead of it in the arrival stream. This sum continued 

to build until one aircraft was incapable of making up the time, resulting in a single, large spacing error 

and then restarting the process. This issue was resolved by changing the stagger spacing commands to 

distance-based spacing throughout the entire route. 

b. Findings

In addressing the second research question, two variables were considered. Each scenario produced a 

total of 100 samplings in the first variable, which was the number of recorded speed changes. The results 

of the chi-square tests showed a statistically significant difference between scenarios 5 and 11, 6 and 12, 

and 7 and 13. The differences, however, were varied, showing preference for different conditions in 

different scenarios. The results are below in Table 4: 

Table 4: Number of commanded speed changes. 

Speed Changes 1-target 2-target 

4 vs. 10 2981 2840 

5 vs. 11 3181 3348 

6 vs. 12 5113 4697 

7 vs. 13 3408 4534 

8 vs. 14 5841 5888 

9 vs. 15 5104 4978 

Each scenario produced a total of 100 samplings in the second variable, which was the arrival error. The 

results of the single-factor ANOVA, as performed for each set of scenarios, showed no statistically 

significant difference. Additionally, an F-Test was performed for each set of scenarios, which indicated a 

minor but statistically significant difference under ideal conditions as well as under wind error conditions. 

The results of both tests are below in Table 5 and Figure 10: 
18 

Table 5: CrossingTimeError ANOVA & F-Test 

Scenarios 

ANOVA 

F-Value 

ANOVA 

P-Value 

F-Test 

F-Value 

F-Test 

P-Value 

4 vs. 10 0.122243 0.726707 0.871045 0.084183 

5 vs. 11 0.039274 0.842957 0.787677 0.008671 

6 vs. 12 0.167455 0.682494 0.926049 0.221617 

7 vs. 13 2.363388 0.124609 1.053499 0.301475 

8 vs. 14 0.179685 0.671758 0.818369 0.022805 

9 vs. 15 0.173960 0.676729 1.368358 0.000893 

Figure 9: CrossingTimeError. 

The lack of difference under wind conditions without error as well as the lack of any such significance in 

the ANOVA indicate that this may be the result of a Type I error, or false positive, in the F-Test. 

Because the differences in the number of speed changes commanded were inconsistent, the addition of a 

second target does not appear to change the stability of the operations at all. 

-10 

-8 

-6 

-4 

-2 

0 

2 

4 

6 

8 

10 

Run 4 Run 10 Run 5 Run 11 Run 6 Run 12 Run 7 Run 13 Run 8 Run 14 Run 9 Run 15 

Crossing Time Error in Seconds 

CrossingTimeError 

1st 1/4 

Min 

Median 

Max 

3rd 1/4 
19 

7. Other Findings 

a. Separation Prior to Stagger Operations

During the development of this experiment, difficulties with maintaining separation during the stagger 

operations were found. The goal of the stagger operations was to achieve as high runway throughput as 

possible while each aircraft performed an OPD. However, it was found that, with the closer spaced 

runways that only required 1.5 nmi stagger distance, radar separation would not be maintained prior to the 

aircraft being established on their final approach course. The reduced separation standard for the 

staggered approach only applies once both aircraft are established on their final approach course. 

Effectively the aircraft had to have a 3 nmi stagger distance as they turned on to their final approach 

course, but 1.7 nmi stagger distance as they landed. This led them to speed up significantly to try and 

achieve the 1.7 nmi spacing that was used for stagger operations. This was operationally unacceptable 

and would lead to instabilities for a string of aircraft. This was not a problem for the further separated 

runways which require 2 nmi stagger spacing as the 2 nmi plus the separation between the runways 

achieved the 3 nmi radar separation requirement. The possible solutions would be to either provide 

vertical separation before the aircraft were established on their final approach course or adjust the stagger 

spacing to support the 3 nmi lateral separation. The former is how operations are generally handled in 

today’s operations but would require one of the aircraft to fly a low, level segment and would lose much 

of the benefits the OPD was providing. The latter option was chosen and a stagger spacing of 2.1 nmi 

was used. 

b. Alterations to the Schedule

At the beginning of the experiment, it was intended to test whether or not the time of assignment of the 

stagger target was important. It was identified as stagger, rather than secondary, because a secondary 

aircraft may be an in-trail aircraft, and it was assumed that the in-trail aircraft would be relevant from the 

moment spacing was assigned. A stagger aircraft may not be within range for spacing operations until 

much later, however. Upon consideration of how this testing would be achieved, it was noted that 

assigning the stagger aircraft at a later time would change the arrival schedule of the affected aircraft if 

the stagger aircraft was also primary. This would then change the schedules of every aircraft behind the 

affected aircraft. This is the scheduling equivalent of pop-up traffic, and was designated an off-nominal 

condition. Testing of how ASTAR10 could manage pop-up traffic and schedule changes is a subject for 

further study. 

c. Stagger Aircraft as the Primary Aircraft

At the beginning of the experiment, it was conceived that the stagger aircraft would typically be the 

secondary aircraft. One question was how easy it would be to identify when the stagger aircraft was the 

primary aircraft, as well as how frequently that occurred. In the production of the initial scenarios, it was 

noted that the stagger aircraft being the primary aircraft, while not the norm, was not unusual. As the 

experiment plan was developed and spacing standards were adjusted, this changed to the point that the 

majority of aircraft were seeing a stagger aircraft as their primary aircraft. Throughout the whole process, 

it was noted that the identification of primary and secondary aircraft could follow simple rules. In a timebased system, the calculations are simple. If the in-trail spacing command is more than twice the stagger 

spacing command, it is primary. If it is less than twice the stagger command, the stagger command is 
20 

primary. In a distance-based system, this becomes more complicated; but because any individual airspace 

will have a finite set of spacing options, simple rules can be produced. For example, in the final 

scenarios, the stagger spacing commands were large enough that only the largest in-trail spacing 

command of 5 nmi was more than twice the stagger command. This meant that the stagger command was 

always primary unless the in-trail command was for 5 nmi, or a non-heavy aircraft following a heavy 

aircraft. Different stagger commands may change the transition point between in-trail and stagger 

spacing dominance, but would not lead to confusion, because any particular runway separation will have 

a set stagger command, and thus a set transition point. 

In the process of analyzing this issue, another oddity was noticed. It is possible for both the in-trail 

aircraft and the stagger aircraft to produce the same ETA for the subject aircraft. This occurs due to a 

peculiar 4-aircraft structure depicted below in Figure 11: 

Figure 10: Even spacing configuration. 

In the depicted configuration, the first heavy acts as a fixed ETA from which everything else can be 

judged. The second heavy and the first large have separate and unique ETAs for their primaries and 

secondaries, but the second large will see the same ETA for both of them. This can be logically deduced 

by noting that the distance from the first heavy to the second large is the same whether taken through the 

second heavy or the first large. A standard should be developed for which command will take 

precedence, and any visualization system may need to take account of this oddity, as any visual tracking 

of the current spacing target may result in rapid and frequent transitions from one target to another, which 

could prove distracting to pilots. 

d. Schedule Sensitivity

In the original experiment plan, it was intended that time-based spacing be used for both in-trail and 

stagger spacing requirements. This proved problematic as the current ASTAR algorithm requires a 

distance-based spacing for stagger aircraft on final approach. Time-based spacing uses a single assumed 

FAS for all aircraft, as the calculation is done at the scheduling stage. By contrast, distance-based spacing 

allows ASTAR to use each aircraft’s own FAS in the scenario. The conversion from one to the other 

inevitably produced sizable errors. Individual aircraft could cope with these errors, but the effect became 

cumulative, with each aircraft facing not just its own error, but also the errors of all aircraft in front of it. 

In implementing this distance-based spacing, it was noted that the initial stagger spacing and the final 

approach stagger spacing required two different spacing commands. The initial command calculated a 

distance-to-go or in-trail-equivalent spacing, while the second command calculated direct-line spacing. 

This difference produced substantial errors in the initial tests, leaving aircraft with as much as 9 seconds 
21 

to make up in final approach, with the cumulative effects exceeding the capability of following aircraft to 

make up. When noticeable errors persisted, more in-depth analysis showed the remaining problem was 

schedule-based. The schedule was such that aircraft were being delivered to the airspace too slowly, so 

that by the time one aircraft appeared, its lead aircraft was already too far ahead to be caught up to. The 

problem was traced to the assumed FAS, which was still used in scheduling calculations for all spacing 

commands. The initially assumed FAS of 130 kt was slower than the average FAS in the simulation, so 

the ‘average’ aircraft saw an error. In attempting to find a better assumed FAS, it was noted that 

variations as small as 1 kt produced substantial changes in the behavior of the traffic stream across the full 

100 aircraft. The final solution was a FAS of 139 kt, with wind influencing the schedule for appropriate 

scenarios. This still was not without error, however, as the A319s in the simulation still occasionally 

violated separation even with a half-mile buffer zone, resulting in a total of 33 violations out of 4752. 

These were caused by A319 final approach speeds in the range of 124 kt, 15 kt slower than the assumed 

FAS, resulting in the same time spacing command being converted into substantially lower distance 

spacing (4.85 nmi vs. 5.5 nmi). In future research, it is suggested that scheduling use final approach 

speeds based on individual aircraft types. 

8. Conclusions 

This experiment was conducted in an effort to refine and test the ASTAR10 algorithm and the underlying 

concept of operations. During the development of this experiment, a number of software and integration 

errors were detected and resolved. The issue of time-based spacing versus distance-based spacing was 

also highlighted for further discussion. Additionally, several questions as to the performance of the 

algorithm, such as how it would meet the radar separation requirement, what impact alterations to the 

spacing schedule would have, and how frequent and obvious the stagger aircraft being the primary aircraft 

would be, were addressed. Finally, ASTAR10 was validated and the use of a secondary target was shown 

to be important for performance, though not as important as had initially been thought. 
22 

Appendix A 

List of Acronyms 

APS - Airborne Precision Spacing 

ASDO - Airspace Super-Density Operations 

ASTAR - Airborne Spacing for Terminal Arrival Routes 

ATA - actual time of arrival 

ATC - Air Traffic Control 

ATOL - Air Traffic Operations Lab 

CMF - Cockpit Motion Facility 

DPA - Dependent Parallel Arrivals 

ETA- Estimated Time of Arrival 

FAS - final approach speed 

HITL- human-in-the-loop 

KDFW - Dallas-Ft. Worth International Airport 

LaRC - NASA Langley Research Center 

NAS - National Airspace System 

NLR - National Aerospace Laboratory (Netherlands) 

OPD - Optimized Profile Descents 
23 

Appendix B 

Validation Data 

Run2-1-1 ATA DTime Run2-2-1 ATA DTime Run2-1-2 ATA DTime Run2-2-2 ATA DTime 

BGD0002 1922.25 41.5 BGD0002 1913 44.5 BGD0002 1922.5 42.5 BGD0002 1910.75 42 

AEX0003 1974 51.75 AEX0003 1961.5 48.5 AEX0003 1974.25 51.75 AEX0003 1963 52.25 

ABI0004 2061.75 87.75 INK0004 2052.25 90.75 ABI0004 2062.75 88.5 INK0004 2049.25 86.25 

FSM0005 2114 52.25 AEX0005 2105 52.75 FSM0005 2114.25 51.5 AEX0005 2102.75 53.5 

INK0006 2168 54 ABI0006 2166.25 61.25 INK0006 2170 55.75 ABI0006 2164.75 62 

AEX0007 2251.75 83.75 FSM0007 2218.75 52.5 AEX0007 2249.5 79.5 FSM0007 2217 52.25 

BGD0008 2307.25 55.5 ABI0008 2270 51.25 BGD0008 2308 58.5 ABI0008 2268.75 51.75 

AEX0009 2369.25 62 FSM0009 2322.75 52.75 AEX0009 2370.25 62.25 FSM0009 2321.75 53 

BGD0010 2426.75 57.5 INK0010 2376.5 53.75 BGD0010 2427.25 57 INK0010 2376.5 54.75 

AEX0011 2478.25 51.5 FSM0011 2428.75 52.25 AEX0011 2478.25 51 FSM0011 2427.75 51.25 

BGD0012 2533.75 55.5 INK0012 2486.25 57.5 BGD0012 2534.25 56 INK0012 2483.75 56 

FSM0013 2618.75 85 AEX0013 2537.25 51 FSM0013 2618 83.75 AEX0013 2536 52.25 

ABI0014 2675 56.25 ABI0014 2592.5 55.25 ABI0014 2674.5 56.5 ABI0014 2590.75 54.75 

AEX0015 2727.5 52.5 FSM0015 2644.25 51.75 AEX0015 2727.75 53.25 FSM0015 2643 52.25 

INK0016 2811.25 83.75 BGD0016 2735.5 91.25 INK0016 2811 83.25 BGD0016 2733.75 90.75 

FSM0017 2866 54.75 FSM0017 2785.5 50 FSM0017 2866 55 FSM0017 2783 49.25 

INK0018 2929 63 ABI0018 2841.5 56 INK0018 2931.75 65.75 ABI0018 2839.5 56.5 

FSM0019 2982.25 53.25 AEX0019 2926.5 85 FSM0019 2982.75 51 AEX0019 2925.75 86.25 

BGD0020 3039.5 57.25 ABI0020 2981 54.5 BGD0020 3039.25 56.5 ABI0020 2981.5 55.75 

AEX0021 3098.25 58.75 FSM0021 3035 54 AEX0021 3094 54.75 FSM0021 3034.5 53 

BGD0022 3155.5 57.25 BGD0022 3122.25 87.25 BGD0022 3155.25 61.25 BGD0022 3121.75 87.25 

AEX0023 3214.5 59 AEX0023 3176 53.75 AEX0023 3214.5 59.25 AEX0023 3174.75 53 

BGD0024 3272.25 57.75 BGD0024 3233.5 57.5 BGD0024 3273.75 59.25 BGD0024 3231.25 56.5 

FSM0025 3323 50.75 FSM0025 3313.75 80.25 FSM0025 3324.25 50.5 FSM0025 3313.5 82.25 

BGD0026 3377.5 54.5 BGD0026 3371.5 57.75 BGD0026 3379.25 55 BGD0026 3372.5 59 

FSM0027 3427 49.5 AEX0027 3435.75 64.25 FSM0027 3428.75 49.5 AEX0027 3437.5 65 

INK0028 3487.5 60.5 BGD0028 3486.5 50.75 INK0028 3488.25 59.5 BGD0028 3490.75 53.25 

AEX0029 3538.25 50.75 AEX0029 3541.5 55 AEX0029 3538.75 50.5 AEX0029 3541.75 51 

BGD0030 3595.25 57 BGD0030 3597.75 56.25 BGD0030 3596 57.25 BGD0030 3597.25 55.5 

FSM0031 3647.5 52.25 AEX0031 3649 51.25 FSM0031 3647.75 51.75 AEX0031 3648.75 51.5 

BGD0032 3703.5 56 BGD0032 3706 57 BGD0032 3704.25 56.5 BGD0032 3706 57.25 

AEX0033 3751.25 47.75 AEX0033 3756.75 50.75 AEX0033 3755.75 51.5 AEX0033 3757.25 51.25 

BGD0034 3838.75 87.5 BGD0034 3845 88.25 BGD0034 3840.75 85 BGD0034 3846.25 89 

AEX0035 3888.75 50 FSM0035 3898.75 53.75 AEX0035 3892.75 52 FSM0035 3900 53.75 

ABI0036 3954.75 66 INK0036 3954.75 56 ABI0036 3959 66.25 INK0036 3955.25 55.25 

FSM0037 4008.5 53.75 AEX0037 4005.25 50.5 FSM0037 4010 51 AEX0037 4005.25 50 

ABI0038 4063.75 55.25 BGD0038 4058.75 53.5 ABI0038 4065.5 55.5 BGD0038 4059.5 54.25 

FSM0039 4114.25 50.5 FSM0039 4111.75 53 FSM0039 4117.5 52 FSM0039 4112.5 53 
24 

BGD0040 4183.25 69 BGD0040 4168.5 56.75 BGD0040 4183.75 66.25 BGD0040 4168.5 56 

FSM0041 4235.75 52.5 FSM0041 4218.5 50 FSM0041 4236 52.25 FSM0041 4215.5 47 

ABI0042 4299.5 63.75 BGD0042 4274 55.5 ABI0042 4301.25 65.25 BGD0042 4275.5 60 

AEX0043 4375.25 75.75 FSM0043 4337 63 AEX0043 4377.25 76 FSM0043 4336 60.5 

BGD0044 4430.75 55.5 INK0044 4393 56 BGD0044 4434.25 57 INK0044 4391.5 55.5 

AEX0045 4483.75 53 AEX0045 4445 52 AEX0045 4483.75 49.5 AEX0045 4444.25 52.75 

BGD0046 4569.5 85.75 BGD0046 4510.25 65.25 BGD0046 4572.25 88.5 BGD0046 4509.5 65.25 

FSM0047 4624.5 55 AEX0047 4556.75 46.5 FSM0047 4623.75 51.5 AEX0047 4555.75 46.25 

INK0048 4679 54.5 BGD0048 4624 67.25 INK0048 4677.25 53.5 BGD0048 4623.25 67.5 

FSM0049 4764.75 85.75 FSM0049 4678.5 54.5 FSM0049 4763.25 86 FSM0049 4677.75 54.5 

INK0050 4820.5 55.75 BGD0050 4765.25 86.75 INK0050 4820.25 57 BGD0050 4765 87.25 

AEX0051 4871.75 51.25 AEX0051 4818.25 53 AEX0051 4872.5 52.25 AEX0051 4817.75 52.75 

BGD0052 4928.25 56.5 ABI0052 4881.25 63 BGD0052 4928.75 56.25 ABI0052 4880.75 63 

FSM0053 4978.5 50.25 AEX0053 4956.25 75 FSM0053 4979.5 50.75 AEX0053 4956.5 75.75 

ABI0054 5033.75 55.25 BGD0054 5013 56.75 ABI0054 5035 55.5 BGD0054 5013 56.5 

AEX0055 5087.25 53.5 AEX0055 5064.25 51.25 AEX0055 5089.75 54.75 AEX0055 5065.75 52.75 

ABI0056 5149.75 62.5 BGD0056 5120.75 56.5 ABI0056 5152.25 62.5 BGD0056 5122.75 57 

FSM0057 5202.5 52.75 FSM0057 5180 59.25 FSM0057 5204.25 52 FSM0057 5181 58.25 

BGD0058 5259 56.5 INK0058 5239.25 59.25 BGD0058 5260.75 56.5 INK0058 5239 58 

FSM0059 5339.75 80.75 FSM0059 5323.25 84 FSM0059 5341.25 80.5 FSM0059 5324.75 85.75 

BGD0060 5398.25 58.5 ABI0060 5382 58.75 BGD0060 5402.5 61.25 ABI0060 5380.5 55.75 

AEX0061 5458.5 60.25 FSM0061 5432.5 50.5 AEX0061 5460.75 58.25 FSM0061 5432 51.5 

BGD0062 5514 55.5 BGD0062 5489 56.5 BGD0062 5518.25 57.5 BGD0062 5488.25 56.25 

FSM0063 5575.75 61.75 AEX0063 5540.5 51.5 FSM0063 5577.25 59 AEX0063 5540.25 52 

BGD0064 5634.5 58.75 BGD0064 5604 63.5 BGD0064 5635 57.75 BGD0064 5604.75 64.5 

FSM0065 5685 50.5 FSM0065 5654 50 FSM0065 5686 51 FSM0065 5656 51.25 

BGD0066 5772.75 87.75 BGD0066 5711.75 57.75 BGD0066 5773 87 BGD0066 5713.25 57.25 

AEX0067 5826 53.25 AEX0067 5770.25 58.5 AEX0067 5826.5 53.5 AEX0067 5767.75 54.5 

BGD0068 5878 52 ABI0068 5847.5 77.25 BGD0068 5879 52.5 ABI0068 5846.5 78.75 

FSM0069 5933.25 55.25 AEX0069 5898.5 51 FSM0069 5933.75 54.75 AEX0069 5900.75 54.25 

ABI0070 5997 63.75 BGD0070 5963.25 64.75 ABI0070 5999.5 65.75 BGD0070 5966.5 65.75 

AEX0071 6047.75 50.75 FSM0071 6016.25 53 AEX0071 6052 52.5 FSM0071 6019.5 53 

INK0072 6136.25 88.5 BGD0072 6104.5 88.25 INK0072 6140.25 88.25 BGD0072 6105.25 85.75 

FSM0073 6189.75 53.5 FSM0073 6157.25 52.75 FSM0073 6195 54.75 FSM0073 6158.5 53.25 

BGD0074 6246.25 56.5 BGD0074 6215.5 58.25 BGD0074 6251 56 BGD0074 6218.25 59.75 

FSM0075 6298.25 52 FSM0075 6278.25 62.75 FSM0075 6300.75 49.75 FSM0075 6279.25 61 

BGD0076 6355 56.75 INK0076 6335.75 57.5 BGD0076 6356 55.25 INK0076 6334.5 55.25 

AEX0077 6405.75 50.75 FSM0077 6423.25 87.5 AEX0077 6407.25 51.25 FSM0077 6422.5 88 

BGD0078 6472 66.25 BGD0078 6476.25 53 BGD0078 6474.75 67.5 BGD0078 6476 53.5 

FSM0079 6522 50 AEX0079 6527 50.75 FSM0079 6524.75 50 AEX0079 6526.75 50.75 

BGD0080 6578.25 56.25 BGD0080 6586.5 59.5 BGD0080 6580.75 56 BGD0080 6585 58.25 

FSM0081 6638.5 60.25 FSM0081 6635.25 48.75 FSM0081 6642 61.25 FSM0081 6634 49 

BGD0082 6697 58.5 INK0082 6690.75 55.5 BGD0082 6697.5 55.5 INK0082 6688.5 54.5 
25 

FSM0083 6784 87 FSM0083 6742 51.25 FSM0083 6784.25 86.75 FSM0083 6740.5 52 

INK0084 6838.5 54.5 BGD0084 6798.5 56.5 INK0084 6838.25 54 BGD0084 6796.5 56 

AEX0085 6890.5 52 AEX0085 6883 84.5 AEX0085 6891.25 53 AEX0085 6881 84.5 

BGD0086 6947.25 56.75 INK0086 6937.75 54.75 BGD0086 6946.75 55.5 INK0086 6936.25 55.25 

FSM0087 6996.75 49.5 FSM0087 6989.75 52 FSM0087 6995.5 48.75 FSM0087 6988.75 52.5 

ABI0088 7051.75 55 ABI0088 7054.5 64.75 ABI0088 7053.75 58.25 ABI0088 7050 61.25 

AEX0089 7112.25 60.5 FSM0089 7106.5 52 AEX0089 7114.75 61 FSM0089 7105.5 55.5 

BGD0090 7167.5 55.25 ABI0090 7161.5 55 BGD0090 7171.5 56.75 ABI0090 7162.25 56.75 

FSM0091 7218.75 51.25 FSM0091 7215.5 54 FSM0091 7222.25 50.75 FSM0091 7216 53.75 

BGD0092 7283.75 65 BGD0092 7300.75 85.25 BGD0092 7289 66.75 BGD0092 7301.5 85.5 

FSM0093 7335 51.25 AEX0093 7351.75 51 FSM0093 7336 47 AEX0093 7352.75 51.25 

INK0094 7401 66 BGD0094 7416.5 64.75 INK0094 7406.5 70.5 BGD0094 7416.5 63.75 

FSM0095 7454.25 53.25 FSM0095 7472.25 55.75 FSM0095 7454.25 47.75 FSM0095 7472.75 56.25 

INK0096 7542.75 88.5 BGD0096 7558.25 86 INK0096 7547.25 93 BGD0096 7559 86.25 

FSM0097 7592.5 49.75 FSM0097 7611.25 53 FSM0097 7599 51.75 FSM0097 7611.75 52.75 

ABI0098 7650.5 58 INK0098 7672 60.75 ABI0098 7651.75 52.75 INK0098 7672.5 60.75 

FSM0099 7704.25 53.75 FSM0099 7720.25 48.25 FSM0099 7706 54.25 FSM0099 7722 49.5 

FSM0100 7783 78.75 FSM0100 7864.75 144.5 FSM0100 7785.5 79.5 FSM0100 7866.75 144.75 

Run4-1-1 ATA DTime Run4-2-1 ATA DTime Run4-1-2 ATA DTime Run4-2-2 ATA DTime 

BGD0002 1932.5 52 BGD0002 1920.75 52 BGD0002 1932 51.5 BGD0002 1921.5 53 

AEX0003 1983.75 51.25 AEX0003 1971.5 50.75 AEX0003 1983 51 AEX0003 1971.25 49.75 

ABI0004 2076 92.25 INK0004 2065.25 93.75 ABI0004 2075.5 92.5 INK0004 2065 93.75 

FSM0005 2128.25 52.25 AEX0005 2124.5 59.25 FSM0005 2128.5 53 AEX0005 2124.5 59.5 

INK0006 2178.5 50.25 ABI0006 2181.25 56.75 INK0006 2178.75 50.25 ABI0006 2181.5 57 

AEX0007 2270.75 92.25 FSM0007 2234.5 53.25 AEX0007 2271.25 92.5 FSM0007 2234.75 53.25 

BGD0008 2322 51.25 ABI0008 2286.75 52.25 BGD0008 2322.5 51.25 ABI0008 2288 53.25 

AEX0009 2387.25 65.25 FSM0009 2338.5 51.75 AEX0009 2387.5 65 FSM0009 2339 51 

BGD0010 2440 52.75 INK0010 2397.75 59.25 BGD0010 2439.25 51.75 INK0010 2398.25 59.25 

AEX0011 2491.75 51.75 FSM0011 2446.25 48.5 AEX0011 2492.5 53.25 FSM0011 2446.75 48.5 

BGD0012 2543.5 51.75 INK0012 2500.5 54.25 BGD0012 2544 51.5 INK0012 2500.75 54 

FSM0013 2634 90.5 AEX0013 2557.5 57 FSM0013 2634.75 90.75 AEX0013 2557.5 56.75 

ABI0014 2683 49 ABI0014 2609 51.5 ABI0014 2687.25 52.5 ABI0014 2609.25 51.75 

AEX0015 2739 56 FSM0015 2659.75 50.75 AEX0015 2742.75 55.5 FSM0015 2660.5 51.25 

INK0016 2825.75 86.75 BGD0016 2754.25 94.5 INK0016 2831.25 88.5 BGD0016 2754.5 94 

FSM0017 2881.5 55.75 FSM0017 2806.75 52.5 FSM0017 2886.5 55.25 FSM0017 2808.25 53.75 

INK0018 2943.75 62.25 ABI0018 2859.75 53 INK0018 2948 61.5 ABI0018 2860 51.75 

FSM0019 2994.25 50.5 AEX0019 2949 89.25 FSM0019 2998.25 50.25 AEX0019 2950 90 

BGD0020 3048 53.75 ABI0020 3003.75 54.75 BGD0020 3052 53.75 ABI0020 3004.75 54.75 

AEX0021 3110.75 62.75 FSM0021 3055.75 52 AEX0021 3114.75 62.75 FSM0021 3056.75 52 

BGD0022 3160 49.25 BGD0022 3147.75 92 BGD0022 3165 50.25 BGD0022 3148.75 92 

AEX0023 3226 66 AEX0023 3196 48.25 AEX0023 3231.5 66.5 AEX0023 3197.5 48.75 

BGD0024 3287 61 BGD0024 3258.25 62.25 BGD0024 3293 61.5 BGD0024 3259.25 61.75 

FSM0025 3339.5 52.5 FSM0025 3338 79.75 FSM0025 3345.75 52.75 FSM0025 3340.25 81 
26 

BGD0026 3394 54.5 BGD0026 3391.75 53.75 BGD0026 3399.5 53.75 BGD0026 3392.5 52.25 

FSM0027 3450 56 AEX0027 3456 64.25 FSM0027 3454.5 55 AEX0027 3458.25 65.75 

INK0028 3510.25 60.25 BGD0028 3505.5 49.5 INK0028 3514.75 60.25 BGD0028 3507.5 49.25 

AEX0029 3564.75 54.5 AEX0029 3559.75 54.25 AEX0029 3568.5 53.75 AEX0029 3561.25 53.75 

BGD0030 3619 54.25 BGD0030 3612.75 53 BGD0030 3622.5 54 BGD0030 3613.25 52 

FSM0031 3675 56 AEX0031 3665.75 53 FSM0031 3679.25 56.75 AEX0031 3665.5 52.25 

BGD0032 3727.75 52.75 BGD0032 3715.75 50 BGD0032 3732.25 53 BGD0032 3718 52.5 

AEX0033 3785.5 57.75 AEX0033 3770.25 54.5 AEX0033 3789 56.75 AEX0033 3771.5 53.5 

BGD0034 3871 85.5 BGD0034 3860 89.75 BGD0034 3875 86 BGD0034 3862 90.5 

AEX0035 3922.75 51.75 FSM0035 3917 57 AEX0035 3926.5 51.5 FSM0035 3918.75 56.75 

ABI0036 3987.5 64.75 INK0036 3974.5 57.5 ABI0036 3991.75 65.25 INK0036 3977 58.25 

FSM0037 4039.5 52 AEX0037 4026.25 51.75 FSM0037 4042.5 50.75 AEX0037 4027.75 50.75 

ABI0038 4089.5 50 BGD0038 4077.75 51.5 ABI0038 4092.75 50.25 BGD0038 4078.75 51 

FSM0039 4139.25 49.75 FSM0039 4129.25 51.5 FSM0039 4143 50.25 FSM0039 4130.5 51.75 

BGD0040 4205.5 66.25 BGD0040 4180.25 51 BGD0040 4207.75 64.75 BGD0040 4181 50.5 

FSM0041 4255.25 49.75 FSM0041 4230.75 50.5 FSM0041 4258 50.25 FSM0041 4231.5 50.5 

ABI0042 4321.5 66.25 BGD0042 4283.25 52.5 ABI0042 4324.25 66.25 BGD0042 4281.75 50.25 

AEX0043 4397.75 76.25 FSM0043 4348 64.75 AEX0043 4400.5 76.25 FSM0043 4348 66.25 

BGD0044 4447.25 49.5 INK0044 4401 53 BGD0044 4450.25 49.75 INK0044 4399.25 51.25 

AEX0045 4497 49.75 AEX0045 4457.5 56.5 AEX0045 4500 49.75 AEX0045 4456.25 57 

BGD0046 4589.5 92.5 BGD0046 4519.25 61.75 BGD0046 4592.25 92.25 BGD0046 4517.25 61 

FSM0047 4643.25 53.75 AEX0047 4573.5 54.25 FSM0047 4643.25 51 AEX0047 4570.75 53.5 

INK0048 4692.75 49.5 BGD0048 4638.75 65.25 INK0048 4693.25 50 BGD0048 4634.75 64 

FSM0049 4785.5 92.75 FSM0049 4690.5 51.75 FSM0049 4785.5 92.25 FSM0049 4687.25 52.5 

INK0050 4840.75 55.25 BGD0050 4783 92.5 INK0050 4841.5 56 BGD0050 4777 89.75 

AEX0051 4893 52.25 AEX0051 4834.75 51.75 AEX0051 4893.25 51.75 AEX0051 4829.25 52.25 

BGD0052 4942.5 49.5 ABI0052 4900.5 65.75 BGD0052 4943 49.75 ABI0052 4894.75 65.5 

FSM0053 4994.5 52 AEX0053 4977 76.5 FSM0053 4995.25 52.25 AEX0053 4972 77.25 

ABI0054 5047 52.5 BGD0054 5033.5 56.5 ABI0054 5047.5 52.25 BGD0054 5027.5 55.5 

AEX0055 5099.5 52.5 AEX0055 5088 54.5 AEX0055 5100.25 52.75 AEX0055 5084 56.5 

ABI0056 5164 64.5 BGD0056 5145.75 57.75 ABI0056 5164.25 64 BGD0056 5143 59 

FSM0057 5218.5 54.5 FSM0057 5205.25 59.5 FSM0057 5218.25 54 FSM0057 5201.5 58.5 

BGD0058 5280.5 62 INK0058 5261.25 56 BGD0058 5280.25 62 INK0058 5259.5 58 

FSM0059 5361.75 81.25 FSM0059 5348.25 87 FSM0059 5361 80.75 FSM0059 5345.25 85.75 

BGD0060 5416.5 54.75 ABI0060 5403.75 55.5 BGD0060 5415.5 54.5 ABI0060 5402 56.75 

AEX0061 5478 61.5 FSM0061 5454.5 50.75 AEX0061 5476.5 61 FSM0061 5453 51 

BGD0062 5530 52 BGD0062 5505 50.5 BGD0062 5528.25 51.75 BGD0062 5503.25 50.25 

FSM0063 5594 64 AEX0063 5560 55 FSM0063 5592.5 64.25 AEX0063 5558.5 55.25 

BGD0064 5647.25 53.25 BGD0064 5621.5 61.5 BGD0064 5646 53.5 BGD0064 5619.25 60.75 

FSM0065 5701 53.75 FSM0065 5676.25 54.75 FSM0065 5700.75 54.75 FSM0065 5674.75 55.5 

BGD0066 5790.5 89.5 BGD0066 5727 50.75 BGD0066 5788.75 88 BGD0066 5726 51.25 

AEX0067 5855 64.5 AEX0067 5792.5 65.5 AEX0067 5853.75 65 AEX0067 5791.5 65.5 

BGD0068 5904.75 49.75 ABI0068 5869.25 76.75 BGD0068 5904 50.25 ABI0068 5869.25 77.75 
27 

FSM0069 5956.75 52 AEX0069 5923 53.75 FSM0069 5956.75 52.75 AEX0069 5923.75 54.5 

ABI0070 6021.75 65 BGD0070 5986.5 63.5 ABI0070 6021 64.25 BGD0070 5988.25 64.5 

AEX0071 6072.75 51 FSM0071 6040.25 53.75 AEX0071 6072.5 51.5 FSM0071 6040.25 52 

INK0072 6165.5 92.75 BGD0072 6130.75 90.5 INK0072 6165 92.5 BGD0072 6131.25 91 

FSM0073 6228.25 62.75 FSM0073 6181.75 51 FSM0073 6227.5 62.5 FSM0073 6182.5 51.25 

BGD0074 6288.5 60.25 BGD0074 6234.5 52.75 BGD0074 6287.75 60.25 BGD0074 6232.75 50.25 

FSM0075 6338.25 49.75 FSM0075 6298.25 63.75 FSM0075 6338.25 50.5 FSM0075 6298.5 65.75 

BGD0076 6386.25 48 INK0076 6351.5 53.25 BGD0076 6387.25 49 INK0076 6350 51.5 

AEX0077 6434 47.75 FSM0077 6442.5 91 AEX0077 6437.25 50 FSM0077 6442 92 

BGD0078 6502 68 BGD0078 6494 51.5 BGD0078 6504.25 67 BGD0078 6492.5 50.5 

FSM0079 6549.75 47.75 AEX0079 6545.5 51.5 FSM0079 6553.75 49.5 AEX0079 6544 51.5 

BGD0080 6599.25 49.5 BGD0080 6605.5 60 BGD0080 6605.25 51.5 BGD0080 6605.5 61.5 

FSM0081 6666 66.75 FSM0081 6656.25 50.75 FSM0081 6670 64.75 FSM0081 6656.5 51 

BGD0082 6717.75 51.75 INK0082 6710 53.75 BGD0082 6722 52 INK0082 6710.25 53.75 

FSM0083 6809.25 91.5 FSM0083 6761.25 51.25 FSM0083 6812.75 90.75 FSM0083 6761.5 51.25 

INK0084 6866.25 57 BGD0084 6813.25 52 INK0084 6870 57.25 BGD0084 6813.75 52.25 

AEX0085 6922.75 56.5 AEX0085 6903.5 90.25 AEX0085 6927.5 57.5 AEX0085 6903.75 90 

BGD0086 6974.25 51.5 INK0086 6957 53.5 BGD0086 6981.75 54.25 INK0086 6957 53.25 

FSM0087 7027 52.75 FSM0087 7010.75 53.75 FSM0087 7035.75 54 FSM0087 7010.75 53.75 

ABI0088 7076 49 ABI0088 7072.75 62 ABI0088 7087.75 52 ABI0088 7073.5 62.75 

AEX0089 7141.75 65.75 FSM0089 7126 53.25 AEX0089 7152.25 64.5 FSM0089 7126.25 52.75 

BGD0090 7188.75 47 ABI0090 7180.25 54.25 BGD0090 7201.75 49.5 ABI0090 7180.25 54 

FSM0091 7240 51.25 FSM0091 7237.5 57.25 FSM0091 7254.5 52.75 FSM0091 7237 56.75 

BGD0092 7304 64 BGD0092 7323.75 86.25 BGD0092 7318.5 64 BGD0092 7323.25 86.25 

FSM0093 7354.5 50.5 AEX0093 7374.25 50.5 FSM0093 7369.75 51.25 AEX0093 7373.75 50.5 

INK0094 7421.5 67 BGD0094 7441 66.75 INK0094 7437.5 67.75 BGD0094 7440.5 66.75 

FSM0095 7473.25 51.75 FSM0095 7497.75 56.75 FSM0095 7490.75 53.25 FSM0095 7497.5 57 

INK0096 7564.75 91.5 BGD0096 7585.25 87.5 INK0096 7581.75 91 BGD0096 7585.5 88 

FSM0097 7621.75 57 FSM0097 7638.5 53.25 FSM0097 7639 57.25 FSM0097 7638.5 53 

ABI0098 7672 50.25 INK0098 7699.5 61 ABI0098 7690.5 51.5 INK0098 7700.25 61.75 

FSM0099 7729 57 FSM0099 7747.75 48.25 FSM0099 7749.25 58.75 FSM0099 7748 47.75 

FSM0100 7806.75 77.75 FSM0100 7891.5 143.75 FSM0100 7827.25 78 FSM0100 7891.75 143.75 
28 

Appendix C 

Separation Violations 

Separation 

Violations 1-1 2-1 1-2 2-2 

Run 1 0 0 0 0 

Run 2 0 0 0 0 

Run 4 0 0 0 0 

Run 5 0 0 0 0 

Run 6 0 0 0 0 

Run 7 0 0 0 0 

Run 8 0 0 0 0 

Run 9 0 0 0 0 

Run 10 0 0 0 0 

Run 11 0 0 0 0 

Run 12 0 0 0 0 

Run 13 0 1 0 1 

Run 14 0 0 0 0 

Run 15 0 1 0 1 

Appendix D 

Commanded Speed Changes 

SpdChanges(total) 1-1 2-1 1-2 2-2 

Run 1 669 690 672 686 

Run 2 678 664 658 664 

Run 4 747 698 843 693 

Run 5 858 732 862 729 

Run 6 1284 1245 1274 1310 

Run 7 869 835 869 835 

Run 8 1488 1429 1479 1445 

Run 9 1288 1264 1288 1264 

Run 10 737 671 736 696 

Run 11 844 830 844 830 

Run 12 1323 1029 1316 1029 

Run 13 1133 1134 1133 1134 

Run 14 1496 1440 1504 1448 

Run 15 1252 1237 1252 1237 
29 

Appendix E 

CrossingTimeError 

4-1-1 4-2-1 4-1-2 4-2-2 5-1-1 5-1-2 5-2-1 5-2-2 6-1-1 6-1-2 6-2-1 6-2-2 

0.5 -0.25 0.25 -0.25 0.5 -0.5 1.25 0 0.5 0 0.5 0.75 

-0.628 -0.534 -1.108 0.328 -0.145 1.645 0.022 2.259 0.144 -0.83 0.097 1.237 

-0.024 -0.934 -0.14 -1.743 -0.605 -0.707 -0.699 -1.312 -0.502 -0.691 -1.314 -0.689 

0.85 1.85 0.85 0.85 0.85 0.85 1.1 0.85 0.36 1.11 0.86 0.86 

0.911 0.572 1.5 0.866 0.609 0.4 1.013 0.204 -0.38 0.024 0.351 -0.071 

-0.226 -0.498 -0.008 0 0.002 -1.083 0.07 -1.364 -2.018 0.12 -1.364 0.62 

-0.15 -0.059 0.1 0.111 0.1 -0.737 -0.15 -0.508 -0.64 0.436 -1.14 0.564 

-0.89 -0.14 -0.778 0.561 -0.467 -0.93 -0.247 -0.929 -1.362 -1.007 -1.107 -0.969 

0 -0.412 0 -0.953 0 -1.385 0 -1.737 0.62 -1.121 0.62 -1.151 

1.248 0.218 0.622 0.242 0 0.042 0.5 0.062 0.32 -0.019 0.155 0.112 

0.042 -2.052 1.564 -2.046 1.368 -1.407 0.95 -1.177 0.59 -1.082 -1.07 -0.911 

1.282 -0.29 0.697 -0.594 2.543 -0.622 1.712 -1.092 -0.901 -0.53 -1.527 -0.522 

-0.15 -0.575 -0.4 -0.654 -0.15 -0.739 -0.15 -0.6 0.36 -0.116 0.36 0.358 

-2.182 0.194 1.233 0.282 1.07 -1.435 0.359 -1.104 -0.953 -1.51 -2.616 -1.024 

0.881 -0.356 0.334 -0.038 0.375 -0.507 0.312 -0.323 0.153 0.159 -0.455 -0.067 

0.1 3.1 1.35 3.1 0.85 1.6 1.1 2.85 0.11 1.36 0.36 1.36 

1.466 0.373 1.426 0.989 1.423 1.15 1.309 0.652 0.532 -0.51 0.387 -0.734 

1.5 -0.017 0 -1.094 0.412 0.424 -0.783 -0.039 0.62 -0.145 0.62 -0.687 

-0.672 -0.4 -0.401 -0.65 -0.219 -0.65 -0.206 -0.4 -0.015 -0.39 0.012 -1.14 

0.113 1.225 -0.111 0.984 1.691 0.961 1.718 0.776 -0.759 -0.052 -0.697 -0.107 

0 0.22 0 0.225 -0.632 0.208 0.251 0.288 0.12 -1.204 -0.88 -0.783 

-1.387 1.6 -0.753 1.6 0.06 1.6 -0.057 1.35 -0.791 0.86 -2.356 0.86 

-1 -1.718 0 -0.955 -0.5 -0.353 0 -0.873 0.62 -2.013 0.12 -0.063 

0.021 1.099 0.383 0.48 1.477 0.845 0.813 0.554 1.076 3.562 1.127 -0.523 

-0.528 -0.65 -0.143 0.1 0.559 0.35 0.645 -0.15 -0.565 0.61 -0.331 0.61 

0.681 0.379 0.07 -0.601 1.53 0.043 1.168 -0.714 -2.561 0.142 -1.378 0.025 

2.854 1.5 1.838 1.5 0.25 -0.183 0.362 0.47 -0.304 2.988 -0.19 2.217 

0.564 -1.994 0.359 -2.504 0.228 -1.824 0.349 -0.926 -1.361 -2.349 -1.173 -1.251 

-0.606 -0.696 -1.352 -0.893 -0.314 -0.279 -1.716 -0.402 -1.096 -2.765 -1.121 -1.257 

-0.683 1.254 -0.962 -0.055 -0.548 -0.572 -1.154 -0.436 -1.453 -1.451 -2.328 -0.364 

0.079 0.338 0.419 0.042 -1.153 -1.292 -0.771 -0.74 -0.824 -2.14 -1.29 -1.065 

-0.97 -0.94 -1.017 1.308 -2.397 -2.074 -1.418 -1.552 -3.346 -1.391 -2.161 -1.072 

0.144 1.041 -0.492 -0.009 -0.829 -0.505 -0.983 -0.399 0.794 -0.727 0.41 0.133 

0.6 1.6 0.35 1.6 0.6 1.85 0.6 0.85 1.11 -0.14 0.86 1.36 

-0.132 1.081 -0.433 0.941 -1.019 0.372 -1.51 0.324 -0.012 0.301 -0.094 0.793 

0 0.505 0 1.373 0 0.335 0 0.185 -0.38 -0.8 0.12 -0.337 
30 

0 0.22 -0.665 -0.703 -1.557 -0.124 -1.962 -0.127 1.379 -0.587 0.887 -0.442 

-1.781 -1.318 -1.485 -1.827 -1.269 -0.491 -2.556 0.287 0.049 -2.915 0.138 0.169 

-2.145 -0.266 -1.724 -0.125 -2.385 -1.786 -2.604 -2.089 1.002 -1.795 0.548 -0.901 

-0.5 -1.238 -1.5 -1.64 -1 -1.687 -1.5 -1.183 1.12 -1.928 0.62 -1.426 

-0.463 -1.296 0.139 -1.407 -1.404 -1.296 -1.185 -1.486 0.957 -1.052 -0.457 -1.358 

-0.5 0.74 0 -1.465 -0.5 -0.28 0 -0.209 0.62 -1.751 1.12 -0.756 

0.1 0.5 0.1 0 0.1 0 0.1 -0.5 -0.39 0.62 0.11 0.12 

-0.799 1.061 -0.437 -0.081 -1.632 0.496 0.277 1.071 -2.083 -1.778 -0.297 -1.134 

-0.751 1.935 -0.806 2.138 -1.111 1.348 -1.035 2.028 -1.686 0.721 -1.782 -0.031 

-0.15 2 -0.4 1.5 -0.4 1.094 -0.15 0.624 -0.39 0.12 -0.64 -0.38 

0.805 0.284 -1.39 -0.375 0.87 0.666 0.169 0.177 -0.567 0.986 -0.49 -0.503 

-1.56 3 -1.185 1 -0.154 2 -0.871 1.5 -1.947 1.62 -1.84 1.12 

-0.15 0.5 -0.4 0 -0.4 0 -0.15 0 0.11 1.62 -0.89 0.12 

-0.179 1.6 0.053 -0.15 0.14 0.35 0.173 0.6 -1.444 -0.14 -1.473 0.11 

-0.732 0.851 -0.776 1.043 -0.392 1.063 -0.901 0.943 -0.051 0.41 -0.341 -0.235 

-0.868 1 -0.975 1 -0.868 1 0.12 0.5 -0.658 0.62 -2.949 0.12 

0.511 -0.4 0.848 0.35 0.645 0.1 0.326 -0.15 -0.27 0.61 -0.741 0.36 

0.676 1.566 0.631 0.311 1.005 1.071 1.513 2.513 -0.659 -0.101 -1.069 0.055 

1.17 0.432 1.388 2.283 1.175 1.734 1.211 -0.411 0.332 0.251 0.056 -1.128 

0.5 0.397 0 1.816 1 1.474 1.967 0.647 0.62 1.027 0.62 -3.076 

0.679 1 0.241 1 1.128 -0.258 1.098 -1.132 -0.714 2.12 -0.596 0.62 

1.236 -0.609 1.255 1.609 1.25 0.304 1.38 0.194 -1.132 1.097 -0.404 -0.853 

0.6 0.35 0.1 1.1 0.35 0.35 0.6 0.1 1.11 0.86 1.11 0.36 

0.018 0.382 -0.688 1.829 0.43 0.001 0.221 0.25 -0.644 0.504 -0.59 -0.246 

0 0.172 -1 -0.25 0 0.161 0 0.008 -0.38 -0.192 0.12 -0.225 

-0.486 -1.353 -0.55 -1.218 -0.046 -0.397 0.279 -0.176 -1.476 -0.707 -1.746 -1.079 

-0.5 -0.204 -0.5 0 -0.5 -0.143 -0.5 -0.087 0.62 0.117 0.62 0.194 

0.5 0 0.794 -0.5 1 0.181 1 -0.82 -0.048 0.62 -0.217 0.12 

0.857 0 2.051 0 1.037 -0.5 0.774 -0.5 -1.684 0.62 -1.112 -0.38 

0.6 -0.921 0.35 -0.419 0.35 -1.329 0.1 -1.189 0.11 0.543 -0.14 -1.933 

3.017 0 3.425 0.5 1.803 0 1.173 0.5 1.439 0.12 0.593 0.62 

-0.751 -0.15 -0.178 0.85 0.628 -0.4 0.171 -0.15 -1.294 0.11 -2.769 -0.14 

0.331 -0.334 1.296 0.603 -0.001 0.428 0.011 0.048 -0.36 0.374 -1.553 1.234 

0.5 0.5 0.5 2.5 1.5 0.027 1 0.465 0.62 0.12 -0.38 0.12 

-0.685 1 -1 0 0.206 -0.5 0.177 0 0.125 -0.38 0.306 0.12 

1.35 1.6 1.6 0.6 0.35 1.6 0.35 2.35 0.86 1.36 0.86 1.36 

1.199 -0.043 1.332 -0.294 0.879 -0.197 0.899 -0.158 1.708 -0.905 1.387 -1.114 

-0.781 1.163 -0.346 -0.997 0.17 -0.121 -0.284 -0.023 -0.838 -0.262 -1.629 -0.271 

-1.589 0 -1.354 -0.5 -1.534 -0.5 -1.474 0 -1.207 1.12 -1.512 1.62 

-2.79 0.5 -1.799 1 -1.541 0.5 -1.504 0.5 -3.849 -0.237 -3.259 -0.273 

-3.846 1.6 -1.334 1.1 -1.395 0.85 -1.401 0.85 -2.302 1.61 -1.691 1.86 
31 

-1 -0.858 0.5 -1.081 -0.111 -0.372 -0.23 -0.121 -0.38 -0.658 -0.38 -1.593 

-2.995 0.299 -0.727 0.254 -0.305 0.203 -1.394 0.212 0.642 -0.411 -0.654 -0.575 

-3.453 -0.771 -1.398 0.186 -0.406 -0.066 -1.023 0.099 -2.288 -0.988 -4.231 0.089 

-0.5 -1.309 0 -0.837 0 -2.034 0 -1.255 -0.38 -1.569 -0.88 -1.515 

-1.258 0.359 -0.879 0.355 0.311 0 0.438 -0.694 -0.265 -0.222 0.027 -0.918 

0.85 -0.29 0.35 -0.372 0.85 -0.756 0.35 -1.415 0.36 -0.093 0.86 -1.297 

-0.12 -1.82 0.22 -1.575 0.537 -0.644 -0.379 -1.308 -0.256 0.301 0.256 0.032 

-0.298 -0.15 0.487 -0.15 2.71 0.1 -0.136 0.1 0.619 -0.14 0.24 -0.14 

-1.47 0.193 1.101 0.127 -0.024 0.363 0.197 -0.233 -0.567 -0.377 -3.289 -0.554 

-1.046 -0.209 0.366 -0.303 0.181 -0.031 1.342 -0.501 0.598 0.344 -1.709 -0.22 

-3.805 -1 -1.009 0 -1.338 -0.5 -0.69 -1 0.481 0.62 -1.914 -0.38 

-1.5 0.222 0 -0.066 0 -0.18 0 0.317 0.62 1.546 -1.38 -0.179 

-3.49 2.252 -0.632 2.25 -1.297 0.038 -1.113 -0.261 -1.522 -0.317 -0.758 -1.564 

-1.286 0.743 -0.09 0.708 -0.405 0.852 0.442 1.839 -0.658 0.858 -1.555 0.779 

-1 0.85 0.5 0.6 0.5 1.35 0.5 1.85 0.12 0.86 -0.88 0.86 

0.146 -0.276 0.926 -0.182 0.202 -0.115 2.792 -1.24 -0.726 -0.714 -1.709 -0.841 

1 0.5 2.5 0.5 0.5 0 1 0 0.62 0.62 -0.38 -0.38 

0.237 0.72 2.171 0.669 1.424 1.179 1.438 1.851 0.09 1.167 -1.004 0.755 

0.6 1.85 2.1 2.35 1.85 0.6 2.85 1.35 0.86 0.61 0.86 0.61 

-0.313 -0.056 -0.051 -0.153 0.761 0.358 0.743 0.208 -0.013 -0.049 0.462 -0.32 

-1.78 0.236 -0.734 1.013 0.165 0.393 0.737 1.507 -1.183 1.012 -3.319 1.405 

0.501 -2.675 2.435 -3.573 0.607 -2.168 0.572 -1.453 0.147 -0.71 -0.134 -2.065 

-0.2 1.1 0.3 1.35 0.3 1.1 -0.2 1.1 -0.26 1.36 -0.76 1.86 

7-1-1 7-2-1 7-1-2 7-2-2 8-1-1 8-1-2 8-2-1 8-2-2 9-1-1 9-1-2 9-2-1 9-2-2 

0.25 -0.25 0.502 -0.25 2.75 1.5 3.25 1 2.5 1 2.5 1.25 

0.304 0.238 0.39 -0.435 -4.73 -0.399 -3.931 -3.165 -0.349 0.057 -1.235 -1.613 

-1.181 -1.305 -1.361 -0.925 -1.953 -1.624 -1.601 -1.901 -0.131 -1.792 -2.067 -1.576 

-0.39 0.61 -0.39 0.61 1.86 2.36 3.36 2.11 1.36 1.61 1.61 2.11 

0.149 -0.215 0.234 -0.179 -2.585 0.359 0.625 0.836 1.384 0.886 1.33 0.602 

-1.704 -1.747 -1.596 -1.701 -2.012 1.12 3.071 1.62 0.25 2.679 0.168 -0.083 

-0.39 -1.23 -0.39 -1.447 1.36 -0.707 1.86 -0.568 1.36 0.451 1.36 2.214 

-0.977 -2.311 -0.631 -1.233 0.655 -0.253 2.333 -0.296 -0.63 -0.572 0.335 -0.422 

0.62 -2.522 0.62 -2.704 2.62 -0.927 3.62 -0.796 1.62 -0.609 2.12 -0.386 

0.96 -0.18 0.715 -0.319 0.71 1.962 1.331 3.078 -0.756 -1.797 0.419 0.606 

1.069 -2.086 1.232 -1.796 -0.352 2.429 -0.097 1.438 -2.007 2.736 -1.832 1.942 

0.259 -1.027 0.491 0.057 -2.808 -1.424 0.016 -1.198 -2.628 -1.524 -2.619 -1.433 

-0.14 -1.048 0.61 0.16 1.61 -2.094 1.86 -1.495 1.86 -3.743 1.61 -2.908 

-1.262 -1.709 -0.613 -0.553 -2.424 -1.815 -1.574 -1.736 -2.077 0.01 -2.217 0.5 

0.274 -1.032 0.176 0.092 1.499 0.794 -2.015 1.037 0.942 1.099 0.429 1.769 

0.36 0.86 0.11 1.36 1.86 4.86 1.11 2.86 1.11 4.86 1.36 3.36 

1.67 -0.677 1.363 0.258 0.408 -0.816 -0.593 -1.333 0.351 -0.66 0.436 -0.874 
32 

-0.331 -1.554 -0.303 -0.522 2.12 2.04 1.12 -0.283 -0.164 0.317 -0.204 -0.542 

-1.004 -1.14 -1.015 -0.39 -1.703 1.61 -2.879 1.36 -1.344 1.36 -1.395 1.11 

-0.59 -0.436 -0.476 0.341 -0.562 -1.959 -0.287 -1.285 0.015 0.73 0.009 0.202 

0.12 -0.639 -0.38 -0.147 0.62 -1.486 1.12 -2.053 1.12 -0.821 1.12 -1.178 

-0.431 0.11 0.035 0.11 -1.779 0.86 -3.187 1.86 0.648 1.11 -0.011 0.61 

0.12 -0.512 0.62 1.262 0.62 -0.741 1.62 1.932 2.12 -0.748 2.12 -0.977 

1.601 -0.961 2.306 0.173 -1.53 -2.292 1.402 -1.33 1.015 0.058 1.031 -0.738 

-0.513 -0.39 -0.223 -0.14 -1.05 1.11 -0.626 1.36 -1.468 0.36 -1.751 0.86 

-0.516 0.14 -0.43 0.437 -3.758 -1.596 -1.394 -0.716 -0.665 -2.64 -1.529 -0.492 

-0.607 0.05 -0.114 0.193 -0.477 3.62 -0.024 3.62 -0.72 -1.937 -0.795 1.994 

-1.159 -1.98 -1.095 -0.828 -2.407 -0.015 0.249 -4.38 -0.701 -4.424 -1.552 -1.641 

-1.653 -2.009 -1.072 -1.634 -3.236 -3.171 -1.891 0.436 -0.756 -2.782 -2.15 -1.898 

-0.092 1.304 0.085 -1.04 1.431 -1.599 0.299 -1.149 0.145 -1.862 -2.306 0.133 

0.183 -0.138 0.354 -0.969 3.394 -3.183 1.545 -0.711 0.514 -2.83 -0.596 -0.21 

-0.269 0.33 -0.286 -0.736 -0.172 -2.038 -0.346 0.632 0.174 -3.121 -2.122 -2.754 

0.074 -0.028 0.739 -0.073 0.646 0.217 -0.981 -3.141 0.215 -0.476 0.071 -2.905 

1.36 0.86 1.36 0.36 2.36 3.36 2.36 2.86 3.11 1.86 1.36 4.11 

0.119 0.743 0.321 1.05 -0.259 0.049 -0.575 -0.48 -0.257 -1.555 -1.607 -0.066 

0.12 0.449 1.419 -0.016 1.12 0.95 1.62 0.178 1.619 -1.7 1.12 -0.642 

0.818 -0.031 1.064 -0.016 0.639 1.023 -0.145 0.486 0.22 -1.241 -1.621 -0.333 

0.123 0.544 0.212 0.422 0.146 -1.844 0.046 2.9 -1.134 -2.599 -1.859 0.922 

0.789 -1.443 0.565 -0.627 -0.298 0.03 0.668 0.246 -0.725 -1.824 -1.436 0.136 

1.12 -1.633 0.62 -0.573 1.62 -1.621 1.62 -2.56 0.62 -1.301 1.12 -3.334 

0.173 -1.989 0.323 -0.503 -0.673 -1.245 -0.347 -0.079 -1.304 0.426 0.561 0.305 

0.62 -0.828 0.62 0.346 1.62 -0.445 2.12 -1.429 1.12 -0.052 1.62 -0.572 

-0.39 0.12 0.11 0.12 1.61 1.12 1.86 1.62 0.86 1.62 1.61 1.12 

0.442 -0.335 -0.254 0.705 -2.778 -0.32 -0.449 -0.839 -0.846 0.275 -1.198 0.586 

0.081 0.228 -0.953 0.772 -2.16 0.192 -0.961 0.938 -1.928 0.296 -0.861 0.579 

-0.14 1.547 0.11 1.369 0.11 1.12 0.61 1.12 1.61 0.728 0.86 1.265 

-0.505 0.451 -0.604 1.308 -1.427 -0.273 -1.705 -0.193 -1.386 -0.27 -1.097 0.21 

-0.52 1.12 -0.348 1.12 -0.089 1.62 0.159 2.12 3.066 1.62 -2.528 2.62 

-0.64 0.62 -0.14 0.62 1.36 1.12 0.86 1.62 0.61 0.62 0.61 1.12 

-1.268 -0.14 -1.125 0.36 1.336 1.36 -1.565 0.86 1.822 0.86 -2.101 1.11 

0.088 -0.129 -0.377 0.983 1.14 0.347 -3.567 -1.406 0.196 0.632 -1.114 -0.271 

-0.033 0.62 -0.199 1.12 -5.92 1.12 -3.674 1.12 -0.291 1.12 0.8 1.12 

-0.512 -0.39 -0.651 0.11 0.024 2.61 -2.349 1.11 -0.62 1.61 1.736 -0.14 

-0.064 0.313 -0.178 0.696 -1.96 2.637 -1.931 -0.936 -2 0.518 -0.016 -1.589 

0.845 -0.303 0.765 -0.122 0.009 0.504 -2.091 -0.284 -0.984 1.709 -1.516 -0.733 

0.62 0.136 0.62 0.359 2.12 -1.26 1.12 0.764 2.12 1.589 2.12 -1.907 

-0.068 -0.427 0.086 -0.834 -0.376 2.62 -3.089 2.12 -0.226 -0.872 -1.154 -0.476 

0.001 -0.434 0.542 -0.915 0.986 -0.114 -1.902 -1.426 2.681 -0.78 -0.3 -0.731 
33 

-0.14 0.11 0.61 -0.14 1.86 0.86 2.11 1.11 1.86 1.11 1.61 1.11 

-0.46 -0.923 -0.189 -0.912 -1.364 -2.154 1.28 -0.088 -0.991 -1.525 -2.415 -1.001 

0.62 -1.164 0.976 -0.783 1.62 -1.415 3.62 -1.215 1.12 -1.825 1.12 -2.527 

-0.098 -1.532 -0.637 -1.712 -3.162 -2.402 2.498 -0.332 -1.23 -2.672 -2.226 2.672 

0.12 -0.575 0.12 -0.188 0.62 -0.972 1.12 1.143 -0.38 -0.599 -0.38 2.82 

1.047 1.299 0.157 0.222 -0.344 0.62 2.12 1.12 -0.826 0.555 -1.385 -1.546 

-0.648 0.12 -1.065 0.62 2.879 1.12 -1.054 2.12 -2.686 0.62 -2.782 1.12 

0.11 0.239 -0.14 0.861 0.86 3.753 1.11 -0.514 0.61 -1.035 0.61 0.382 

0.867 0.62 1.087 1.12 1.458 5.62 1.806 2.12 0.618 3.62 0.78 2.12 

-0.761 -0.39 0.376 0.11 -3.31 1.11 -3.35 0.61 -0.488 1.61 2.639 1.86 

-0.17 0.287 -0.164 0.542 -0.924 1.834 -1.559 0.274 0.397 0.809 0.532 1.363 

0.12 0.154 -0.38 -0.904 0.12 1.12 0.62 1.12 1.12 -0.699 1.62 -0.649 

1.169 0.12 0.889 0.12 -1.075 1.12 -0.943 0.12 0.394 0.62 0.168 1.12 

0.61 1.36 0.86 1.36 1.36 2.36 1.86 2.36 2.11 1.86 2.11 2.86 

1.348 -0.171 1.166 -1.4 -0.482 -1.938 -0.059 -2.473 0.907 -1.863 1.565 -1.098 

-0.042 0.402 -0.173 -0.276 -1.506 -2.548 -2.924 -1.497 -2.47 -1.685 -1.364 0.095 

-1.194 1.12 -1.49 0.12 -2.884 1.62 -3.046 2.12 -2.871 1.62 -2.821 1.62 

-0.704 -0.88 -1.084 -0.38 -3.071 -1.653 -2.807 -0.679 -1.822 -0.634 -0.483 1.12 

-0.504 1.11 -0.599 0.86 -2.568 2.86 -1.394 2.61 -0.63 2.11 -0.608 2.36 

1.31 -1.265 1.154 -0.387 1.62 -3.096 1.12 -2.984 -0.804 -2.708 -1.706 -1.352 

0.153 -0.9 0.356 0.649 -2.109 2.502 -2.115 0.324 -0.843 -0.155 -0.939 -0.131 

-0.267 1.583 -0.183 0.266 0.11 -2.076 -3.325 1.761 -0.755 2.717 -1.979 -0.148 

-0.88 -0.853 0.12 -0.793 0.62 1.26 0.62 1.764 0.12 1.685 -0.38 -2.232 

0.62 -0.15 1.429 -0.21 1.237 2.268 -3.317 -0.925 1.205 0.131 0.096 1.804 

0.36 -0.48 0.61 -0.698 2.36 -6.099 1.86 0.123 0.86 -1.226 1.61 -4.42 

0.017 0.328 0.381 -0.373 0.424 -3.507 -0.333 -2.595 0.101 -1.889 -0.965 0.23 

-0.169 0.11 -0.293 -0.14 -0.474 2.11 -2.221 2.36 0.969 1.86 0.348 1.86 

-0.021 0.845 -0.169 0.87 -1.87 2.735 -3.657 1.947 -3.328 2.372 -0.836 2.78 

-1.152 0.966 -1.98 1.186 -1.252 1.386 -1.029 0.714 -6.614 1.659 0.729 -4.126 

-0.884 0.676 -1.848 0.571 -1.18 2.12 -1.172 2.12 -2.898 0.664 -3.346 1.62 

-0.38 0.228 0.12 -0.018 0.12 0.414 0.62 3.565 1.62 0.201 1.62 -5.018 

0.923 -1.63 0.976 -1.893 -4.017 0.178 -3.471 1.869 -4.543 -1.311 1.883 2.189 

10-1-1 10-2-1 10-1-2 10-2-2 11-1-1 11-1-2 11-2-1 11-2-2 12-1-1 12-1-2 12-2-1 12-2-2 

0.25 -0.5 0.75 -0.5 1.5 0.25 0.75 0.25 0.75 0 0.5 0 

0.025 -0.783 -0.02 1.209 0.415 1.702 0.441 1.478 -0.001 -0.369 0.128 -0.508 

-0.069 -0.785 -0.118 -1.926 -1.229 -0.466 -0.603 -0.581 -1.548 -1.571 -1.847 -2.244 

1.1 0.85 0.85 1.1 1.1 0.6 1.6 0.85 0.86 0.86 0.36 0.86 

1.344 0.82 1.075 0.315 0.283 0.407 0.382 0.227 0.079 0.162 -0.381 -0.18 

-0.523 0 0.837 -1 -0.562 -0.5 -0.485 -1 -2.292 0.12 -1.894 0.12 

-0.4 0.3 -0.15 -0.225 0.1 -0.117 -0.15 0.057 -0.14 0.343 -0.14 0.54 

-2.541 1.279 -1.808 -0.767 -0.963 0.038 -1.712 0.85 -0.702 -0.962 -0.662 -1.1 
34 

0 -1.263 0 -1.938 0 -1.148 0 -0.676 0.62 -1.11 0.62 -1.364 

-1.444 0.063 -1.082 0.613 -0.77 0.138 -1.394 1.122 0.111 0.025 -0.816 0.036 

0.35 -2.105 0.299 -1.941 -0.149 -1.903 0.262 -1.121 -0.32 -0.814 -0.002 -1.329 

0.417 0.2 0.417 -0.395 -0.197 0.274 0.292 -0.548 -0.746 -0.479 -0.829 -1.385 

0.1 -0.459 -0.15 -0.229 -0.15 -0.27 -0.15 -0.356 0.36 0.428 -0.14 -0.296 

0.404 0.353 0.597 0.488 0.178 0.006 0.203 -1.161 -1.221 -0.918 -2.622 -2.24 

0.616 -0.408 0.556 0.327 0.3 -0.1 0.531 -0.075 0.068 0.212 -0.106 -0.965 

0.6 2.6 0.85 2.6 -0.15 2.6 0.6 1.85 0.11 1.36 0.11 1.36 

1.213 0.557 1.868 0.974 1.149 0.658 1.05 0.593 0.399 -0.606 -0.257 -0.945 

1 -0.579 0 -0.451 0.5 -0.098 0.5 -0.851 0.62 -0.066 0.62 -1.473 

-0.757 0.1 -0.712 -0.9 -0.215 -0.4 -0.34 -0.9 -0.028 0.11 -0.181 -0.14 

0.173 0.512 0.538 1.117 0.923 0.582 0.044 0.782 -0.018 0.025 -0.748 0.234 

0 0.318 -0.5 0.271 -0.5 0.203 -0.5 0.219 0.62 -0.471 -1.38 -0.415 

-1.083 2.35 -0.108 1.35 -1.396 1.35 -1.505 1.6 -0.238 1.36 -2.017 0.36 

-0.5 -0.952 -0.5 -1.48 -1 -0.94 -1.5 -0.349 0.62 -0.207 0.12 -1.181 

1.265 0.365 1.084 1.291 -0.309 0.93 0.479 0.563 1.044 -0.16 1.146 -1.705 

0.744 0.1 1.257 0.1 -0.426 -0.15 -0.674 -0.15 -0.166 0.36 -0.158 0.11 

1.767 -0.602 1.067 0.489 0.469 -0.62 0.376 -0.327 -2.343 -0.608 -1.246 0.502 

2.343 1.5 2.837 1 1.092 1.5 2.477 1.5 -0.106 2.12 -0.324 1.62 

0.945 -2.038 0.48 -1.11 3.132 -1.844 0.513 -2.556 -1.423 -1.19 -1.249 -2.344 

-1.545 0.507 -0.612 0.536 -0.584 -0.3 -1.409 -0.619 -1.066 0.399 -1.101 -0.486 

-1.016 1.752 -1.02 0.286 -0.193 -0.014 -0.384 0.831 -1.571 -0.984 -2.067 2.068 

0.42 -1.701 0.667 1.267 -0.489 0.333 0.614 -0.769 -1.836 -0.981 -0.119 -0.271 

-0.171 -0.312 -0.95 0.328 -0.649 -0.745 -0.446 -1.165 -3.565 -1.093 -2.378 -0.765 

-0.589 0.421 -0.994 -0.23 0.009 1.389 -0.23 1.469 0.153 -0.44 0.228 2.103 

0.6 1.85 0.35 2.1 0.35 2.6 0.6 2.6 1.61 1.36 1.11 1.36 

-0.669 0.963 -0.706 0.819 -1.241 1 -1.855 0.62 0.019 0.506 -0.012 0.699 

0 0.993 0 0.308 0 0.574 0 1.383 -0.88 0.141 -0.88 0.439 

-1.743 -0.981 -1.7 -1.094 -1.801 -0.761 -2.228 -0.814 -2.304 -0.257 -2.242 -0.265 

-2.613 -0.627 -2.606 -2.223 -2.087 -0.273 -4.01 -1.166 -1.288 0.826 -1.051 -0.117 

-2.034 -0.26 -2.338 -0.339 -1.914 -0.251 -1.196 -0.836 0.912 -0.73 0.945 -1.483 

-1.5 -0.644 -1.5 -1.549 -1 -1.232 0 -0.271 0.62 -1.377 0.62 -2.936 

-0.809 -1.376 -0.806 -0.839 -0.747 -0.41 -0.476 -0.22 0.316 -0.024 0.147 -2.366 

0 -0.764 0 -0.204 0 -0.189 0 0.076 0.62 -1.167 0.62 3.024 

0.35 0 0.6 0 0.6 -0.5 0.1 0 0.61 -0.38 0.36 0.12 

-0.606 -0.998 -0.995 -0.256 -0.611 -0.669 0.344 0.351 0.787 -1.3 -1.108 -0.339 

-0.217 2.56 -0.85 2.576 -1.076 2.67 -0.491 2.379 -0.799 1.226 -1.206 0.943 

-0.4 1 -0.15 0.5 0.35 1 1.6 1 -0.14 0.12 -0.14 -0.88 

1.178 0.695 1.112 1.098 1.994 0.577 1.773 0.931 -0.497 0.035 0.065 -0.187 

-0.727 1.5 -0.534 2 -0.156 1 0.072 1.5 -2.364 1.62 -0.721 1.12 

-0.15 0.326 0.1 1.663 -0.65 1.759 -0.15 1.787 -1.39 -1.274 0.11 -0.273 
35 

-0.295 -0.15 -0.515 0.35 0.076 0.85 0.203 0.35 -1.443 -0.14 -1.321 0.36 

-0.172 0.976 -1.116 1.081 -0.381 1.014 -0.873 1.051 -0.217 -0.185 0.304 -0.181 

-0.727 0.5 0.121 1 -0.65 1.5 -0.082 1 -2.565 0.62 3.282 0.62 

-0.172 0.35 0.855 0.6 0.524 0.6 0.952 0.35 -1.606 0.11 3.766 -0.14 

1.048 0.585 1.365 0.56 0.551 1.169 2.078 0.779 -2.242 0.367 0.786 -0.612 

1.048 2.439 3.094 0.81 1.085 1.176 0.777 2.192 -0.867 -0.351 3.749 -0.098 

1 2.255 2.5 2.031 2 2.233 0.5 1.374 -0.38 0.748 0.12 -0.283 

-0.132 1 0.708 0.5 1.202 0.5 0.938 1 -0.758 1.12 -0.653 1.12 

0.626 0.841 1.192 0.773 3.025 1.566 2.013 0.207 -0.486 -0.406 -0.65 -0.628 

0.6 2.1 0.35 1.35 0.35 1.85 0.35 0.1 0.86 0.36 -0.14 0.11 

0.57 0.225 0.002 0.657 0.171 0.486 -0.244 0.356 -0.6 -0.819 -2.407 -0.351 

0 -0.515 0.5 0.399 0 0.027 0 -0.318 0.62 -0.639 0.12 -0.164 

-0.143 -1.627 -0.822 -0.799 -0.282 -1.386 -0.15 -1.488 -1.318 -2.128 -1.03 -1.768 

-1 0.007 -1.5 0.332 -1 -0.108 -1 -0.351 -0.88 -0.003 0.62 -0.177 

0.59 1 0.272 2 0.505 0 0.16 0.5 -0.574 -0.38 -0.061 0.12 

0.297 -0.706 1.53 0.417 0.587 0.342 1.292 0.435 -1.104 -0.601 -1.406 0.354 

0.35 0.064 0.35 0.168 0.6 0.964 0.35 0.401 -0.89 -3.061 -0.14 -0.987 

2.007 0.5 1.991 0 1.379 0 1.111 0.5 1.587 0.62 1.528 1.12 

0.896 -0.4 -1.044 0.1 0.191 0.35 -0.564 0.6 -2.446 -0.39 -0.156 0.11 

1.456 0.253 0.558 0.682 0.27 0.413 0.158 0.329 -0.409 0.316 -0.648 0.445 

0.5 1 0 1.5 0 1 0 0.5 -0.38 1.12 -0.38 -0.38 

-0.341 0.43 -0.821 1.261 0.258 0.304 0.236 0.374 -0.338 0.239 0.092 0.244 

1.1 2.85 1.35 1.6 0.85 2.35 0.6 2.35 0.36 1.11 0.86 0.86 

1.262 0.967 1.277 0.406 0.966 0.627 0.935 0.535 1.296 -0.498 1.413 -0.629 

0.105 1.105 -0.307 0.502 0.235 1.242 0.382 1.538 0.109 -0.625 -0.788 1.349 

-1.575 0 -1.511 0 -1.794 0 -1.741 -1 -1.685 1.12 -1.865 1.62 

-3.096 1.127 -2.95 0.069 -2.565 0.291 -2.378 0.842 -3.554 -1.946 -3.242 -0.823 

-4.199 1.85 -4.192 0.85 -0.372 0.85 -3.694 1.35 -1.946 0.61 -2.179 1.36 

-0.5 -1.025 -1 -1.162 0 0.351 0 0.15 -0.38 -1.716 -0.38 -0.177 

-3.436 0.276 -3.258 0.109 -1.323 0.223 -1.735 0.169 -0.583 -0.274 -0.335 -0.037 

-2.998 -0.271 -2.918 -0.758 -1.268 0.345 -3.648 0.28 -4.303 -0.237 -3.748 0.493 

0 -1.176 0 -1.114 -0.5 -1.701 -1.5 -2.022 -1.38 -1.516 -0.38 -1.604 

-0.749 0.418 -0.774 -0.552 0.078 -0.841 -1.196 -0.224 -1.749 -0.863 -1.25 -0.891 

0.35 -0.085 1.35 -0.48 0.35 -1.094 0.35 -0.705 0.61 -1.188 0.36 -0.491 

0.361 -1.391 -0.123 -0.75 0.311 -1.428 0.406 -1.23 -0.746 0.013 -0.308 0.213 

-0.195 -0.9 0.039 0.35 0.122 0.35 -0.635 0.1 0.144 0.11 1.255 0.11 

-1.231 -1.407 -2.294 0.176 -0.517 -0.121 -2 -0.249 -1.525 0.161 2.382 0.358 

-3.653 0.295 -0.969 -0.283 -0.524 -0.293 -1.419 -0.29 -0.199 0.162 0.531 1.075 

-2.549 0.5 -2.588 -1 -3.698 -0.5 -3.243 0 -2.678 -0.38 -0.498 0.62 

-1.5 1.02 -1.5 0.384 -0.5 0.351 -2 0.595 -0.88 0.294 1.12 1.1 

-3.402 1.75 -2.821 2.25 -1.449 0.259 -2.964 2.03 -0.106 -0.906 -1.202 -0.725 
36 

13-1-1 13-2-1 13-1-2 13-2-2 14-1-1 14-1-2 14-2-1 14-2-2 15-1-1 15-1-2 15-2-1 15-2-2 

0.25 -0.25 0.5 -0.25 3.25 0.75 3.25 2 2.5 1 2.5 1.25 

0.524 0.06 -0.603 0.06 -2.438 -3.192 -2.171 -3.079 -0.342 0.048 -0.917 0.06 

-0.997 -1.292 -0.995 -1.232 -3.912 -1.959 -0.002 -1.307 -1.898 -1.983 -1.789 -1.878 

-0.14 0.86 -0.14 0.86 3.86 2.11 2.36 2.36 2.36 1.86 1.86 2.36 

-0.374 0.621 -0.622 -0.139 0.974 0.838 0.712 0.546 0.787 0.511 -0.688 0.243 

-1.098 0.12 -1.549 -0.38 -0.012 1.62 -0.016 1.12 0.051 1.12 -1.341 1.12 

-0.39 0.47 -0.39 -0.357 1.61 -0.56 2.36 -0.637 0.86 -0.548 0.86 -0.49 

-0.562 -0.043 -0.538 -2.207 -1.571 -1.372 3.162 -0.375 2.926 -1.628 -0.72 -1.749 

0.62 -1.447 0.62 -2.664 1.62 -2.553 3.12 -0.984 3.12 -2.013 1.62 -2.927 

0.547 0.475 0.746 -0.198 -1.597 1.183 -0.511 2.037 0.005 0.343 -0.97 -0.384 

1.021 -0.947 -0.568 -2.136 -0.285 -0.74 0.339 -0.679 0.191 -1.536 -0.883 -3.538 

-0.239 -0.013 0.265 -1.198 -0.103 2.714 -2.187 -1.21 -0.191 1.242 -1.365 -2.06 

0.61 0.341 -0.14 -0.786 1.36 -1.041 2.61 -2.544 2.61 1.557 1.11 -1.8 

-0.634 -0.186 -2.312 -1.711 -1.608 -1.37 -0.801 -0.652 -1.757 -0.005 -3.224 -3.212 

0.336 0.709 -0.394 -1.158 -1.926 0.669 0.104 1.006 0.39 1.023 0.374 -1.029 

-0.14 1.86 0.11 0.86 1.61 4.86 1.36 2.86 1.11 2.86 1.61 2.36 

0.288 0.385 0.473 -1.027 0.275 -0.816 -0.4 -1.365 -0.443 -0.981 0.567 -0.929 

1.12 -0.49 0.12 -1.36 1.62 3.905 1.12 -0.278 1.12 -1.205 1.62 -2.246 

0.14 -0.89 -0.741 -1.14 -1.476 1.61 -2.089 1.86 -1.002 0.86 0.087 1.36 

-0.318 0.251 -0.039 0.002 0.74 -0.868 -1.985 0.194 -2.394 -0.638 -0.48 0.412 

0.12 -0.017 0.12 -0.147 1.12 -1.44 1.12 -2.221 0.62 -1.711 1.12 -0.376 

0.473 0.36 -0.673 0.36 -1.567 0.86 -2.466 0.86 0.848 1.11 -0.312 0.86 

0.12 0.526 0.118 -0.292 1.12 -0.389 1.62 -1.608 2.12 -1.383 1.12 -1.33 

1.379 0.08 1.726 0.356 0.326 -2.208 1.125 -2.314 1.359 -1.24 0.715 -1.902 

0.029 -0.39 -0.224 -0.64 -2.274 1.11 -0.805 1.11 -0.576 0.86 -2.189 0.86 

-0.287 1.007 -0.676 -0.009 -2.552 -1.792 -1.729 -1.394 0.059 -1.246 -1.798 -1.233 

-0.551 1.12 0.21 1.12 -1.231 4.12 0.071 3.12 0.108 2.62 -0.382 2.62 

-1.035 -1.12 -0.054 -1.214 -1.705 2.142 1.24 0.272 -0.166 -0.643 -2.685 -2.543 

-1.658 0.271 -0.835 -2.256 -3.01 -3.987 -1.434 -0.265 -2.225 0.851 -2.813 0.446 

-1.22 1.651 -1.137 -0.892 -2.421 -1.563 0.086 -1.489 -0.354 0.363 2 0.259 

-0.458 -0.331 -1.008 -1.162 -2.001 -2.963 0.655 -1.589 -1.241 -3.314 2.252 -1.729 

0.211 -0.903 -1.634 -1.261 -3.909 -2.164 0.339 -2.125 -2.209 -0.713 0.167 -0.689 

0.11 0.296 -0.083 0.409 -1.699 -1.145 1.572 0.435 -0.287 -2.382 -1.171 -1.813 

1.36 0.86 0.86 0.36 4.11 2.36 2.86 2.36 1.86 2.36 2.36 2.61 

0.132 0.659 -0.566 0.293 -0.218 -0.571 -0.621 -0.53 -0.344 -0.476 1.377 -0.46 

0.62 0.273 0.62 0.229 1.62 0.074 1.12 0.015 1.12 -1.345 1.12 -2.288 

-0.662 -0.175 -0.45 -0.851 -2.471 3.414 -2.629 3.198 -2.007 -1.342 -2.132 -0.544 

-0.036 0.462 -0.755 -0.267 0.143 -2.444 -0.121 -1.997 -1.139 -1.428 -1.453 -0.862 

0.217 -0.485 -0.399 -0.827 0.642 0.43 0.345 0.029 -0.035 -2.204 -0.63 -1.349 

1.12 -0.984 0.62 -0.53 1.62 -2.542 1.62 -2.635 1.12 -2.124 1.62 -2.347 
37 

0.531 -0.871 -0.184 -0.663 -0.694 -2.329 -0.597 -2.643 -0.798 -1.324 -0.476 -0.752 

1.12 0.112 0.62 0.209 1.12 -2.21 2.12 -1.156 1.62 -0.922 1.12 -0.255 

-0.39 -0.38 -0.14 0.62 0.61 1.12 2.86 1.62 1.86 1.12 0.86 1.12 

-0.473 -1.715 0.257 -0.339 -4.15 -0.875 -2.449 -0.921 -2.782 -2.159 -2.814 -1.218 

-0.548 -0.6 -1.768 0.136 -1.464 4.091 -1.046 1 -1.767 -1.534 -1.83 0.238 

-0.39 -0.88 -0.64 0.62 0.86 1.12 0.61 1.12 0.61 1.12 0.61 1.12 

-0.684 0.276 -1.631 0.374 -0.795 -0.073 -0.743 -0.451 -1.476 2.239 -1.497 0.39 

-1.244 0.12 -1.677 1.12 0.368 1.62 -1.647 1.62 -2.056 2.62 -1.054 1.62 

-0.64 -0.028 -1.14 0.829 0.86 -1.75 1.11 -2.172 0.11 -0.384 1.11 -1.637 

-1.184 -0.39 -1.316 -0.14 -0.785 1.11 -1.321 1.36 -0.407 1.11 -1.203 2.36 

-0.492 -0.253 -0.334 -0.6 1.015 -2.461 -2.654 2.571 -0.061 -0.21 -0.274 0.108 

-0.074 0.12 -1.858 0.12 -2.18 2.12 1.357 1.62 1.7 1.12 -1.304 1.62 

-0.505 0.11 -1.75 0.11 2.319 1.36 2.938 4.11 1.089 1.86 -0.878 1.36 

-0.194 -0.408 -1.49 0.359 -1.404 0.802 0.23 -2.234 -2.214 0.17 0.044 -0.34 

0.83 -0.13 0.022 -0.261 1.046 -0.099 3.662 -2.94 -0.866 0.039 2.744 0.053 

0.62 0.316 0.12 0.35 3.12 3.906 2.12 -1.138 2.12 -0.181 2.12 -0.448 

-1.241 0.62 -1.219 1.62 -0.059 2.12 1.471 2.12 -0.964 1.62 -1.066 1.62 

-1.22 -1.081 -0.239 0.835 1.106 -0.493 -5.738 0.698 1.418 -1.967 -0.932 -0.059 

-0.39 0.36 1.11 0.61 1.86 1.61 2.11 1.11 2.11 1.11 1.61 0.86 

-0.134 0.321 -0.331 0.736 -2.108 -0.598 -0.862 -1.936 -1.217 -0.526 -1.059 -0.999 

0.62 -0.16 0.12 0.147 1.12 0.305 2.12 -1.871 1.62 -1.084 1.62 -1.461 

-0.433 -1.418 -1.279 -0.29 -3.898 1.705 -1.981 -3.493 -1.588 2.025 -1.16 -2.959 

0.12 0.092 0.12 0.133 0.62 0.692 -0.38 3.651 0.12 0.962 0.12 -0.419 

0.115 -0.88 0.508 0.62 0.793 1.12 -1.923 1.12 -1.039 1.12 -2.943 1.12 

-1.415 -0.497 -0.25 -0.326 0.445 -0.622 -2.42 2.049 -1.575 -0.603 -0.037 -1.308 

0.11 -0.391 0.11 0.111 1.11 -0.639 0.61 0.855 0.86 -0.572 1.61 3.311 

1.759 0.62 0.389 0.62 1.895 2.12 -0.103 4.62 0.147 2.62 1.555 3.12 

0.458 0.11 -0.355 -0.14 -2.605 0.61 -4.672 1.36 -3.2 0.61 0.861 1.36 

0.038 1.124 -1.206 0.493 -0.365 -0.189 -1.827 1.087 -1.94 -0.017 0.882 0.944 

0.12 0.12 -0.88 0.62 1.12 1.12 0.62 1.62 0.62 1.12 1.12 1.62 

0.769 -0.123 -0.577 0.761 -0.088 -2.882 -1.076 -1.04 -0.929 -1.697 0.303 -1.737 

1.11 1.61 0.36 1.36 1.86 2.36 2.36 2.11 1.61 2.11 1.36 2.11 

1.196 -0.612 0.843 0.61 0.166 -1.509 1.098 -1.085 0.754 -1.688 0.668 -1.739 

-0.123 -0.363 -1.033 1.692 -2.03 2.332 0.117 -1.23 -2.898 -2.373 -3.286 -0.123 

-1.459 0.62 -1.896 1.12 -3.462 2.12 -1.567 2.12 -2.665 1.62 -2.966 1.62 

-1.821 -1.594 -2.416 -0.6 -2.825 -0.828 -1.953 -2.164 -2.656 -2.949 -1.774 -2.582 

-0.648 1.36 -1.381 1.11 -2.07 2.36 1.724 2.86 -1.063 2.11 -1.264 2.36 

0.12 -0.675 -0.88 -0.43 0.62 -2.87 4.62 -2.286 1.62 -1.642 1.12 -1.731 

0.724 -0.167 -0.81 0.023 -1.135 -1.398 1.247 1.014 -1.181 2.52 -1.795 -0.932 

-0.125 -0.87 -1.712 1.6 -3.665 -2.807 -0.225 0.05 -2.66 0.042 -3.089 2.28 

0.12 -2.094 -0.38 -0.36 0.12 -1.542 1.12 1.53 -0.38 -1.412 0.12 1.253 
38 

1.16 -0.508 0.073 0.107 -2.192 -2.051 2.087 -0.99 -1.134 2.93 -1.911 -0.046 

0.36 -0.751 0.61 -0.52 2.11 -2.389 2.11 0.01 1.61 0.527 1.61 0.484 

0.116 -0.523 0.303 -0.216 -0.648 -3.252 1.4 -2.988 -0.558 -1.67 -0.617 -0.144 

0.211 -0.39 0.272 -0.89 -2.518 1.61 -6.794 1.86 0.22 2.11 -0.674 1.86 

-0.713 0.033 -0.138 0.51 3.012 -0.241 -3.379 0.782 -0.986 3.24 -2.347 0.707 

-1.834 0.011 -2.072 0.968 2.108 0.537 -8.663 1.497 0.254 2.318 -0.562 0.496 

-0.732 0.12 -2.255 0.62 0.155 2.12 -4.264 2.12 -0.44 2.12 -2.531 2.12 

0.12 -0.066 -1.38 0.796 2.12 -0.233 3.62 0.82 2.12 0.435 0.12 0.978 

0.382 -0.826 -0.087 -0.586 1.463 0.5 1.659 0.425 -3.769 0.83 -2.893 -0.543 
39 

Reference

[1] Barmore, Bryan E., Baxley, Brian T., Abbot, Terence S., Capron, William R., Smith, Colin 

L., Shay, Richard F., Hubbs, Clay: A Concept for Airborne Precision Spacing for Dependent 

Parallel Approaches. NASA TM-2012-217346, 2012. 

[2] Abbott, Terence S., Barmore, Bryan E., Baxley, Brian T., Capron, William R., Murdoch, 

Jennifer L.: Evaluation of an Airborne Spacing Concept to Support Continuous Descent 

Arrival Operations. ATM Seminar, 2009. 

[3] Abbott, T., Barmore, B., Krishnamurthy K.: Airborne-Managed Spacing in Multiple Arrival 

Streams. ICAS Congress, Yokohama, Japan, August 29 - September 3, 2004. 

[4] Barmore, B., Abbott, T., Capron, W., Baxley, B.: Simulation Results for Airborne Precision 

Spacing along Continuous Descent Arrivals. AIAA-2008-8931, 2008 

[5] Wieland, Frederick, Santos, Michel, Krueger, William, Houston, Vincent E.: Performance of 

Airborne Precision Spacing under Realistic Weather Conditions. Digital Avionics Systems 

Conference, 2004, IEEE, pp 2.A.2-1 – 2.A.2-13. 

[6] Bussink, Frank J.L., Doble, Nathan A., Barmore, Bryan E., Singer, Sharon, A Fast-Time 

Simulation Environment for Airborne Merging and Spacing Research, Digital Avionics 

Systems Conference, 2004, Vol. 1, IEEE, pp. 3.A.4-3.1-9. 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

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Contractor Report

 4. TITLE AND SUBTITLE

Airborne Precision Spacing (APS) Dependent Parallel Arrivals (DPA) 

5a. CONTRACT NUMBER

NNL07AA00B

 6. AUTHOR(S)

Smith, Colin L.

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 NASA Langley Research Center

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The Airborne Precision Spacing (APS) team at the NASA Langley Research Center (LaRC) has been developing a concept of 

operations to extend the current APS concept to support dependent approaches to parallel or converging runways along with 

the required pilot and controller procedures and pilot interfaces. A staggered operations capability for the Airborne Spacing for

Terminal Arrival Routes (ASTAR) tool was developed and designated as ASTAR10. ASTAR10 has reached a sufficient level 

of maturity to be validated and tested through a fast-time simulation. The purpose of the experiment was to identify and 

resolve any remaining issues in the ASTAR10 algorithm, as well as put the concept of operations through a practical test.

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Airborne spacing; Dependent runways; Interval management; Parallel runways

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