January 2014

NASA/TM–2014-218151

Analysis and Simulation of the Simplified 

Aircraft-Based Paired Approach Concept With 

the ALAS Alerting Algorithm in Conjunction 

With Echelon and Offset Strategies

Wilfredo Torres-Pomales, Michael M. Madden, Ricky W. Butler, and Raleigh B. Perry

Langley Research Center, Hampton, Virginia
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January 2014

NASA/TM–2014-218151

Analysis and Simulation of the Simplified 

Aircraft-Based Paired Approach Concept With 

the ALAS Alerting Algorithm in Conjunction 

With Echelon and Offset Strategies

Wilfredo Torres-Pomales, Michael M. Madden, Ricky W. Butler, and Raleigh B. Perry

Langley Research Center, Hampton, Virginia
Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076-1320

443-757-5802
iii 

Abstract 

This report presents analytical and simulation results of an 

investigation into proposed operational concepts for closely 

spaced parallel runways, including the Simplified Aircraft-based 

Paired Approach (SAPA) with alerting and an escape maneuver, 

MITRE’s echelon spacing and no escape maneuver, and a hybrid 

concept aimed at lowering the visibility minima. We found that 

the SAPA procedure can be used at 950 ft separations or higher 

with next-generation avionics and that 1150 ft separations or 

higher is feasible with current-rule compliant ADS-B OUT. An 

additional 50 ft reduction in runway separation for the SAPA 

procedure is possible if different glideslopes are used. For the 

echelon concept we determined that current generation aircraft 

cannot conduct paired approaches on parallel paths using 

echelon spacing on runways less than 1400 ft apart and nextgeneration aircraft will not be able to conduct paired approach 

on runways less than 1050 ft apart. The hybrid concept added 

alerting and an escape maneuver starting 1 NM from the 

threshold when flying the echelon concept. This combination 

was found to be effective, but the probability of a collision can 

be seriously impacted if the turn component of the escape 

maneuver has to be disengaged near the ground (e.g. 300 ft or 

below) due to airport buildings and surrounding terrain. We 

also found that stabilizing the approach path in the straight-in 

segment was only possible if the merge point was at least 1.5 to 2 

NM from the threshold unless the total system error can be 

sufficiently constrained on the offset path and final turn. 

 
iv 

Table of Contents 

ACRONYMS ................................................................................................................................................................. VI

1. INTRODUCTION ................................................................................................................................................ 1

2. SAPA PROCEDURE FOR VARIOUS RUNWAY SPACINGS ....................................................................... 2

2.1. FAST TIME SIMULATION .............................................................................................................................................. 2

2.1.1. ALAS Algorithm Parameters ....................................................................................................................... 3

2.1.2. The tALAS Simulator ...................................................................................................................................... 4

2.1.2.1. tAlas Trajectories ........................................................................................................................................................... 5

2.1.2.2. tAlas ADS-B Error Model ............................................................................................................................................ 6

2.1.2.3. tAlas Configuration and Parameters..................................................................................................................... 6

2.1.2.4. Blunder Trajectory Parameters .............................................................................................................................. 7

2.1.2.5. Escape Maneuver Parameters ................................................................................................................................. 8

2.1.2.6. Monte Carlo Simulation: Random Generation of Parameter Values ..................................................... 9

2.1.3. Results from tAlas Simulations For Various Runway Spacings ................................................. 10

2.1.3.1. Results for a 400-ft Spherical Protection Zone .............................................................................................. 10

2.1.3.2. Results for the FAA Cylinder Protection Zone (SAPA Procedure) ....................................................... 11

2.1.3.3. Results for the FAA Cylinder Protection Zone and Different Glideslopes ........................................ 12

2.1.4. Note Concerning Disabling Alert for Trailing Aircraft .................................................................. 13

2.2. HIGH-FIDELITY SIMULATION RESULTS .................................................................................................................... 14

2.3. OBSERVATIONS ............................................................................................................................................................ 23

3. EVALUATION OF ECHELON SPACING FOR STRAIGHT-IN PROCEDURES .................................... 24

3.1. THE COLLISION-SAFE DISTANCE .............................................................................................................................. 26

3.2. LONGITUDINAL COMPRESSION DISTANCE .............................................................................................................. 26

3.3. FRONT GATE FOR THE CONSTANT SPEED SEGMENT ............................................................................................. 34

3.4. THE WAKE-SAFE DISTANCE ..................................................................................................................................... 36

3.4.1. Modeling Wake Transport ........................................................................................................................ 36

3.4.2. Closest Lateral Separation under Normal Operations .................................................................. 37

3.4.3. Minimum Longitudinal Window under Normal Operations ....................................................... 41

3.4.4. Calculating the Wake-Safe Distance .................................................................................................... 43

3.5. DETERMINING FEASIBLE RUNWAY SEPARATION AND CONCLUSIONS ................................................................ 43

4. TOWARDS LOWER VISIBILITY MINIMA ................................................................................................ 46

4.1. EXPERIMENTAL RESULTS USING MONTE CARLO SIMULATION STARTING 1 NM FROM RUNWAY ............... 46

4.2. A CLOSER LOOK AT THE SAPA ESCAPE MANEUVER WHEN NEAR TO THE GROUND ..................................... 48

4.3. A FIRST LOOK AT AN INTELLIGENT ESCAPE MANEUVER ..................................................................................... 50

4.4. MODIFYING THE OFFSET PAIRED-APPROACH TO ENABLE LOWER DECISION MINIMA .................................. 50

4.5. OBSERVATIONS ............................................................................................................................................................ 53

5. CONCLUSIONS ................................................................................................................................................. 55

6. FUTURE WORK ............................................................................................................................................... 56

REFERENCES ............................................................................................................................................................. 57

APPENDIX A. NEW OFFSET RUNWAY CONFORMANCE ALGORITHM .................................................... 60

APPENDIX B. TALAS SIMULATION VALIDATION ......................................................................................... 62

B.1. RESULTS FOR CYLINDER PROTECTION ZONE AND NO ESCAPE MANEUVER ............................................................. 62

B.2. IMPACT OF MAXT2 ON BLUNDER ANGLE OF INCIDENCE ............................................................................................. 62

B.3. TRACK RATE THRESHOLD SENSITIVITY .......................................................................................................................... 63
v 

APPENDIX C. MEASURING ALAS FALSE ALARM RATE USING MITRE/BOEING TSE MODEL ......... 65

C.1. LATERAL ERROR MODEL ................................................................................................................................................... 65

C.2. RESULTS AND ANALYSIS .................................................................................................................................................... 67

 
vi 

Acronyms 

3D Three-Dimensional 

ADS-B Automatic Dependent Surveillance - Broadcast 

AGL Above Ground Level 

AILS Airborne Information for Lateral Spacing 

ALAS Adjacent Landing Alerting System 

ALE ADS-B OUT Latency Error 

ALT HLD Altitude Hold mode 

API Application Programming Interface 

APP Approach mode 

ATC Air Traffic Control 

CAS Calibrated Air Speed 

CAT Instrument Landing System Category 

CFH Collision-Free Height 

CMF Cockpit Motion Facility 

CONOPS Concept of Operations 

CSPR Closely Spaced Parallel Runways 

DOT Department of Transportation 

EAS Equivalent Airspeed 

EPU Estimated Position Uncertainty 

FAA Federal Aviation Administration 

FAF Final Approach Fix 

FMC Flight Management Computer 

GPS Global Positioning System 

GS Groundspeed 

HDG Heading mode 

HDG SEL Heading Select mode 

HITL Human-in-the-Loop 

IGE In-Ground Effect 

ILS Instrument Landing System 

IMC Instrument Meteorological Conditions 

IS Intruder Ship 

KEAS Knots Equivalent Airspeed 

LDA Localizer Type Directional Aid 

LOC Localizer mode 

MASPS Minimum Aviation System Performance Standard 

MCP Mode Control Panel 

MSL Mean Sea-Level 

MOPS Minimum Operational Performance Standard 

NACp Navigation Accuracy Category for Position 

NACv Navigation Accuracy Category for Velocity 

NE Navigation Error 

NGE Near Ground Effect 

OGE Out-of-Ground Effect 

OS Ownship 

PRM Precision Runway Monitor 

RNAV Area Navigation 

RNP Required Navigation Performance 

RTCA Radio Technical Commision for Aeronautics 
vii 

RWY Runway 

SAP Stabilized Approach Point 

SAPA Simplified Aircraft-based Paired Approach 

SFO San Francisco International Airport 

SPD Speed mode 

tALAS Test simulation for ALAS 

TAS True Air Speed 

TBR To Be Resolved 

TCA Time of Closest Approach 

TCAS Traffic Alert and Collision Avoidance System 

TCH Threshold Crossing Height 

TSE Total System Error 

UTC Coordinated Universal Time 

VERT SPD Vertical Speed mode 

VMC Visual Meteorological Conditions 

WAAS Wide Area Augmentation System 
1 

1. Introduction 

In our previous work, we developed an alerting algorithm and Java/C++ software 

implementations called ALAS [Perry2013]. ALAS (Adjacent Landing Alerting System) is an 

alerting algorithm designed to detect intrusions on closely spaced parallel runways. It employs a 

mechanism for detecting imminent collisions with the adjacent traffic aircraft and a mechanism 

for detecting lateral deviations from the runway centerline in a manner similar to the Precision 

Runway Monitor system [Shank1994]. The algorithm is highly configurable through a set of 

user-specifiable parameters. We also developed a fast-time simulation called tAlas, which was 

able to simulate about 20,000 parallel approaches per minute. The tAlas simulation was used to 

evaluate the ALAS algorithm in the context of a parallel runway separated by 750 ft. The ALAS 

algorithm was also validated using the high-fidelity Cockpit Motion Facility (CMF) simulation 

running on a desktop [Smith2000]. 

This report documents follow-on work conducted in fiscal year 2013. In this work we (1) 

analyzed the use of the ALAS algorithm in the context of various runway spacings, (2) explored 

the potential benefits of using echelon spacing on parallel approaches, (3) investigated the 

potential benefits (e.g. lower minima) of a hybrid procedure where both echelon spacing is used 

until reaching a distance of 1 NM from the threshold and then the ALAS algorithm is applied, and 

(4) developed a new runway conformance algorithm for an offset runway. 
2 

2. SAPA Procedure For Various Runway Spacings 

In this section we use both fast-time and high-fidelity simulation to investigate the capability 

of the ALAS alerting algorithm to maintain safety for various runway spacings. The fast-time 

simulation provides statistically-significant evidence while the high-fidelity simulation is used to 

confirm the results of the fast-time simulation. 

2.1. Fast Time Simulation 

In our previous work [Perry2013] we developed a fast time simulation to test the performance of 

the ALAS algorithm for a runway spacing of 750 ft. A worst-case analysis was performed using 

this simulation and the CMF high-fidelity simulation. The trajectories generated by the fast-time 

simulation did not match the CMF trajectories because the kinematic models used in the tAlas 

simulation were too simple. In this work, we have improved the tAlas simulation [Perry2013] in 

7 ways: 

1. It can now run as a Monte Carlo simulation in addition to a worst-case simulation. 

2. The kinematic turn was improved to include roll-in and roll-out. (This change resulted 

in an escape maneuver that more closely matches the trajectory generated in the CMF 

high-fidelity simulation). 

3. The vertical acceleration ramps up for escapeVsRampTime seconds. 

4. ADS-B latency times were added. 

5. ADS-B position errors are modeled. 

6. The ground speed profile was improved. 

7. The total system error (TSE) decreases linearly as the aircraft approaches the runway 

(see Figure 2-1). TSE has a value of 25 ft at the runway and 131 ft at 5 NM away. 

The threshold TSE is a little below the acceptable TSE of 27 ft for touchdown 

[Kayton1997] and the 5 NM TSE matches the observed 40 m TSE for RNP legs in the 

terminal area [MITRE2013]. 

Figure 2-1: Total System Error decreases as the aircraft approaches its runway 

We have applied the tAlas simulation to two situations: (1) various parallel runways spacings 
3 

using a 3 s ADS-B latency time consistent with the FAA ADS-B Rule [FAA2010 & RTCA2011] 

and (2) various parallel runways spacings using a 1.5 s ADS-B latency time achievable with stateof-the-art technology that complies with standard DO-260B [RTCA2002, RTCA2009, and 

RTCA2011]. 

The revised tAlas can execute about 10,000 parallel approaches per minute, which is roughly 

half the number of the previous version of the simulation. 

2.1.1. ALAS Algorithm Parameters 

The ALAS algorithm has remained unchanged since our previous report [Perry2013] except 

that we have added a capability to perform conformance monitoring for an offset approach (See 

Appendix A). For the reader’s convenience we restate the meaning of the ALAS algorithm 

parameters in this section. 

The ALAS parameters fall into three broad categories: (1) parameters that define the linebased conflict detection region, (2) parameters that control the algorithm, and (3) parameters used 

by the runway conformance tests. 

Line-based Detection 

Parameter 

Meaning Default Value 

ln_front_buffer_red Length of the red-alert buffer in front of aircraft 10,000 ft 

ln_back_buffer_red Length of red-alert buffer in back of aircraft 800 ft 

ln_T_red Lookahead time for red alert 15 s 

ln_front_buffer_yellow Length of yellow-alert buffer in front of aircraft 10000 ft 

ln_back_buffer_yellow Length of yellow-alert buffer in back of aircraft 1400 ft 

ln_T_yellow Lookahead time for yellow alert 35 s 

Internal Parameters Meaning Default Value 

useAbsDistAwayAlg True if additional distance test is used true 

initHeight Altitude difference where algorithm turns on MAX_VALUE 

numPtsTrkRateCalc Number of data points used in track rate 

calculation 

3 

maxPhi Highest bank angle used in search 40

phiIncr Bank angle increment in search 5

trackRateThreshold Track rate threshold that triggers the bank-angle 

sweeep search 

1.0/s 

absDistRed Mininimum horizontal distance that triggers a red 

alert 

486.5 ft 

absDistYellow Mininimum horizontal distance that triggers a 

yellow alert 

545.4 ft 

Runway Conformance 

Parameter 

Meaning Default Value 

redRunwayDist Distance from centerline that triggers a red alert 170 ft 

yellowRunwayDist Distance from centerline that triggers a yellow alert 140 ft 

 
4 

We have changed one ALAS parameter, yellowRunwayDist, from 132 ft to 140 ft. This change 

was necessary to reduce nuisance yellow alerts in the presence of the newly added ADS-B 

position errors. 

2.1.2. The tALAS Simulator 

The test simulation for ALAS (tALAS) is based on kinematic models of the ownship and 

intruder aircraft trajectories. Figure 2-2 to Figure 2-4 illustrate these models and identify some of 

the key parameters. 

 Peak 

Period 

Phase 

Offset 

Reference 

lateral 

oscillation 

(No offset) Forward 

trajectory Lateral 

S(x, y, z) movement 

S(x, y, z)

Runway ɵ Altitude 

Distance from Touchdown Point 

Figure 2-3: Top view of lateral deviation 

Figure 2-4: Side view of landing trajectory 

Figure 2-2: Top view of landing trajectory with blunder and escape maneuver 

Ownship 

Intruder 

T3 

SOSInitial(x, y, z)

T2 

T1 

IS 

SISInitial(x, y, z)

VOSInitial(x, y, z)

VISInitial(x, y, z)

SOSRunway(x, y, z)

SISRunway(x, y, z)

OSRunway 

ISRunway 

Ownship 

Runway

Intruder 

Runway 

escape 

escape 

Tcrossing 
5 

The flight trajectory for the ownship is a straight-line descent following the glide path with an 

optional escape maneuver. The trajectory for the intruder can be either a normal or a blundered 

landing approach. The trajectories are specified separately and are independently executed until 

there is a red alert from ALAS, which triggers an escape maneuver by the ownship. The 

following paragraphs describe the trajectory parameters for the ownship and intruder aircraft. 

2.1.2.1. tAlas Trajectories 

A trajectory has independent forward and lateral components. The forward trajectory 

component specifies the desired path of travel. The lateral component simulates the tracking 

error or wandering that happens due to, for example, wind gusts or control system limit cycles. A 

simple sinusoidal oscillation model is used for the lateral deviation. As shown in Figure 2-3, this 

lateral oscillation is superposed on the forward trajectory and is specified by three parameters: 

peak amplitude, time period, and phase offset. The amplitude of the lateral oscillation decays 

linearly as the aircraft approach the runways to simulate an increase in accuracy and the aircraft 

actually touching down on their respective runways. The trajectories for the ownship and 

intruder have independently specified lateral oscillations. Vector addition is used to combine the 

forward and lateral components for a trajectory’s position and velocity.

 The ownship landing trajectory is specified relative to the position and heading for landing on 

the runway. The position of the runway is specified by the touchdown point, denoted SOSRunway in 

Figure 2-2. The runway heading is denoted OSRunway. The initial position SOSInitial and velocity 

VOSInitial are specified to match the desired descent profile with a specified glideslope angle. An 

escape is triggered by a red alert from ALAS with a specified pilot delay from the time of the 

alert to the beginning of the maneuver. An escape maneuver consists of a vertical climb at a 

constant vertical acceleration and an optional turn away from the intruder. The vertical 

acceleration model has a ramp-up delay after which the acceleration is sustained until the vertical 

speed reaches a specified value. If the escape is initiated above the optional designated minimum 

altitude for an escape turn, the ownship turns to heading escape with bank angle escape. 

Otherwise, the escape maneuver does not include a change in heading. A turn has an optional roll 

time to simulate the time for the bank angle to reach escape. After completing the escape 

maneuver, the ownship continues in a straight line with the specified heading and climbing. 

The intruder trajectory is a straight-line descent with an optional blunder. In Figure 2-2, the 

runway touchdown point and heading are denoted SISRunway and ISRunway. The initial position 

SOSInitial and velocity VOSInitial are specified to match the desired descent profile with a specified 

glideslope angle. A blunder consists of a turn inward toward the ownship with a bank angle IS

SAP 

FAF 

Approach 

Ground Speed 

Ground Speed 

Deceleration 

Lead Speed 

Profile

Trail Speed 

Profile 

Distance from Touchdown Point 

Ground Speed 

Figure 2-5: Ground speed profiles for landing 
6 

turn and a roll time. The turn is executed from time T1 to T2 after which the intruder continues 

in a straight line. The blunder may also include a leveling out component beginning at time T1 + 

TLevel with an optional ramp up delay in the vertical acceleration and continuing until a constant 

altitude is reached. 

At the beginning of a landing case, the aircraft are positioned on the glidepath at or beyond the 

FAF point with the aircraft with lower approach speed ahead of the aircraft with higher approach 

speed. Both aircraft begin the scenario at approximately the same ground speed (between 175 KT 

and 185 KT) and decelerate to reach their respective approach speeds at or before the SAP point. 

The vertical speed is coordinated with the ground speed to ensure that the aircraft remain on the 

glidepath. Alternatively, the aircraft may be initially positioned just before the SAP point with 

their respective final approach speeds. 

2.1.2.2. tAlas ADS-B Error Model 

The tAlas simulation incorporates an ADS-B model with position update delay and error 

components [Eftekari2008]. The position update delay is a single parameter that covers the endto-end processing and communication delay. The position error model has only a horizontal bias 

component and no altitude error component. The horizontal position error has two components, a 

bias that remains constant for an entire trajectory and a jitter component that is recomputed every 

simulation step. The horizontal bias is modeled in polar coordinates with radial and angular 

coordinates (r, ɵ) given by r = N(0, σHFOM) and ɵ = U(0, 2π), where r follows a Normal 

distribution with 0 mean and σHFOM standard deviation, and ɵ has a uniform distribution around a 

full circle. The parameter σHFOM denotes the standard deviation of the GPS horizontal figure of 

merit (HFOM). The jitter component of the position error is an additional radial error term given 

by  = {-0.05σHFOM for p ≤ 0.5, 0.05σHFOM for p > 0.5}, where p = U(0, 1). There is no jitter for 

the angular position error. The reported ADS-B position in Cartesian coordinates is given by 

(xADS-B, yADS-B) with xADS-B = x + ex and yADS-B = y + ey, where (x, y) is the actual horizontal 

position and (ex, ey) is the position error given by ex = (r + )cos(ɵ) and ey = (r + )sin(ɵ). 

2.1.2.3. tAlas Configuration and Parameters 

The tAlas simulation has a wide range of scenario configuration options. The basic 

parameters that change from one case (or trial) to the next during a run specify the initial 

positions and speeds of the aircraft and the timing of the blunder. The parameter values for a 

particular trial can be selected either randomly with specified distributions or deterministically 

within a discretized value range. Runs with random parameter values are intended to determine 

the probability distribution of the minimum distance and the probability of violating the collision 

zone. Runs with deterministic parameter selection are intended to explore a range of possible 

landing cases and discovering worst-case conditions for safety. Additional simulation parameters 

which remain constant during a set of trials specify the runway spacing, landing trajectories 

(including headings and glideslope angles), escape and blunder maneuvers, maximum ground 

speed difference for final approach, lateral tracking error, ADS-B performance (including 

position error and latency), and ALAS configuration. 

The simulation is instrumented to collect data on false alarms, missed alerts, and the distance 

of closest approach. tAlas also incorporates a collision zone around the aircraft according to the 

descriptions given in [FAA2011]. Two collision zone models are available in tAlas: a sphere or a 

cylinder. For each test trial case, tALAS determines: the time of closest approach and the 

corresponding distance in 3D space, as well as the horizontal and vertical distances; whether there 
7 

was an intrusion into the collision zone; whether the intruder crossed the ownship’s centerline and 

the corresponding time of crossing; the time of the first yellow (i.e., level 1) alert; the time of first 

red (i.e., level 2) alert; whether a given red alert was not preceded by a yellow alert; the elapsed 

time from the yellow alert to the red alert; the elapsed time from the red alert to the time the 

intruder crossed the ownship’s centerline; whether there was a red alert without a blunder (i.e., a 

false alarm); and whether there was a violation without a red alert (i.e., a missed alert). tAlas is 

also instrumented to compute the probability of violation of the collision zone. For a set of test 

cases, tALAS can identify the case with the overall minimum approach distance and present a 

complete analysis for it. tALAS generates the test trajectories as time-indexed state sequences. 

These sequences are processed by the instrumentation, and they can also be written to output files 

for post-run visualization and analysis. 

2.1.2.4. Blunder Trajectory Parameters 

The tAlas simulation generates blunders using three time parameters: 

 T1 = Start Time of Intrusion (s) 

 T2 = Duration of Intrusion Turn (s) 

 T3 = Duration after turn (s) 

The horizontal profile of a blunder trajectory is illustrated in Figure 2-6. 

Figure 2-6: Horizontal View for a Blunder Trajectory 

tALAS can also create blunders where the intruder’s altitude levels out at some point or where 

it continues to follow its normal vertical profile. If a vertical level-out is specified then the 

vertical profile is as shown in Figure 2-7. 

Figure 2-7: Vertical View for a Blunder Trajectory with a Level-out Component 

Runway 

Centerlines 

Ownship 

Intruder 

T3 

T2 

T1 



Runway 

Spacing 

Intruder 

Runway ɵ

T1 T2 

TLEVEL 

T3 

Altitude 

Distance from Touchdown Point Glidepath 
8 

The TLevel parameter, which specifies the time the level-out begins, can appear anytime after 

T1, the beginning of the intrusion. If a vertical level-out is not specified, then the vertical profile 

is as shown in Figure 2-8. 

Figure 2-8: Vertical Profile for a Blunder Trajectory without a Level-out Component 

The following is stated at the FAA Flight Systems Laboratory, Closely Spaced Parallel 

Operations (CSPO) website [FAA-CSPO]: 

A blunder occurs when one aircraft on a parallel approach turns toward another aircraft on 

the adjacent approach. Blunder angle severity and frequency are key parameters in the 

determination of parallel runway spacing. Blunder data has been collected in its current 

format since 2008. As of July 31, 2011, there have been over 1.4 million Simultaneous 

Independent Parallel Instrument Approach (SIPIA) Instrument Landing System (ILS) 

operations recorded in less than visual conditions. Of those approaches, there have been 60 

confirmed blunders which varied in frequency and severity. The verified blunders 

predominantly occurred at angles between 5° and 35°, with a majority occurring in the 5° to 

15° range. Until 2010, the blunder assumption used for fast time simulations was fixed at 30°, 

a worst case assumption made in the late 1990’s necessary to meet the agreed upon level of 

safety. The assumption was needed since there was no blunder data available at that time. 

The updated blunder distributions determined from the data collected, along with other 

updates to model parameters, has contributed to more realistic fast-time simulations and 

analysis. 

In our simulations we have set maxT2 = 14 seconds and uniformly sampled the turn time T2

from [1, maxT2]. We uniformly sample the intruder bank angle between 5 and 30 degrees. This 

approach results in incidence angles up to 47° with an average incidence angle of 11° which is 

consistent with the fact that the majority of the historic blunders are within 5° to 15°. We believe 

that our blunder model is conservative because larger incidence angles are more difficult to 

defend against. Kinematically, incidence angles larger than 35° can be achieved, especially at 

larger runway separations. 

2.1.2.5. Escape Maneuver Parameters 

The parameters in Table 2-1 characterize the escape maneuver that was used. 

Intruder 

Runway ɵ

T1 

T2 

T3 TLEVEL 

Altitude 

Distance to Touchdown Point Glidepath 
9 

Table 2-1: Escape Maneuver Parameters 

Parameter Meaning Nominal Value 

escapePilotDelay Time for pilot to react (s) 0

escapeTrack Target track delta () 45

escapeBankAngle Bank Angle of Escape Turn () 30

escapeRollTime Time for Rollout to Complete(s) 6

escapeVsGoal Target vertical speed (fpm) 2000

escapeVsAccel The vertical acceleration (m/s2

) 2.0

escapeVsRampTime Time to ramp up to vsAccel (s) 4.0

2.1.2.6. Monte Carlo Simulation: Random Generation of Parameter Values 

A probabilistic analysis can be obtained by using random sampling of the parameters over the 

parameter ranges. In our Monte Carlo experiments, we used the ranges in Table 2-2. 

Table 2-2: tALAS Trajectory Parameters (Monte Carlo) 

Parameter Meaning Min Value Max Value 

T1 Start Time of Intrusion (s) 0 Computed

(Description given below) 

T2 Duration of Intrusion Turn (s) 1 14

T3 Duration after turn (s) 20 20

bankAngle Bank Angle of Intrusion () 5 30

Peak Max Trajectory error (ft) 131 131

Period Period of Trajectory error (s) 60 70

Phase Phase of Trajectory error () -180 +180

ownshipInitialSx Distance from runway (NM) 5.0 5.5

intruderInitialSx Distance from runway (NM) 5.0 5.5

InitialGs Ground Speed at FAF (KT) 175 185

gsMean Mean GS at SAP (KT) 130 130 

gsSigma Standard Deviation GS at SAP (KT) 10 10 

maxGsDiff Max GS Differential at SAP (KT) 20 20 

The ground speeds of the aircraft decrease from the FAF to the SAP. The simulation starts 

each aircraft on the glideslope near the FAF. The initial ground speed is uniformly sampled from 

an interval of 175 KT to 185 KT. The speeds at the SAP are sampled from a normal distribution 

with a mean of gsMean and a standard deviation of gsSigma. Samples that exceed the minimum 

or maximum are discarded. Also the ground speeds are sampled such that their difference is less 

than or equal to maxGsDiff. Once the ground speeds are selected, the time (T1_max) until the 

intruder reaches an altitude of minAltitudeBlunder is computed. By default minAltitudeBlunder

is 0. The blunder time (T1) is then uniformly sampled from the interval [0, T1_max]. After T1, 

the trial continues an additional extraTimePerTrial seconds, which is typically 90 seconds. We 

allow blunders to occur when the intruder is close to the ground. However, if the ownship is 

already on the ground and the intruder’s trajectory has not crossed the ownship’s centerline and 

there has been no loss of separation and no alert, this test case is not counted. Removing these 

trials increases the loss of separation (LoS) probabilities slightly. When the intruder hits the 
10 

ground, its trajectory is continued at altitude 0. This allows for a collision after the intruder hits 

the ground and skids into the ownship. 

2.1.3. Results from tAlas Simulations For Various Runway Spacings 

In this section we present the tAlas estimates of the probability of a collision given a blunder 

for various runway spacings. We have chosen a target probability of 1E-5/blunder because 

historical data suggests that the blunder rate is less than 1E-4/landing. This gives us an overall 

probability of failure of less than 1E-9/landing. In [Eftekari2011] a table is presented that 

summarizes the rates of aircraft blunders from recent historical data: 

Table 2-3: Summary of No Transgression Zone Violations 

Deviation 

(degrees ) 

FY2008 FY2009 Total Rate Per 

Approach 

< 10 12 8 20 2.55E-05 

10 – 19 2 6 8 1.02E-05 

20 - 29 0 4 4 5.09E-06 

Total 14 18 32 4.08E-05 

The blunder arrival rate averaged over both years for all deviations was 4.08E-05. In 

[Eftekari2011], the authors argue that the first digit is uncertain, so they use a blunder rate of 1E5 and set a target blunder to collision rate of 1E-4. In this paper, we decided to be more 

conservative and set the blunder rate at 1E-4/landing. With this blunder rate, a collision rate of 

no greater than 1E-5/blunder is necessary in order to achieve an overall failure rate of 1E9/landing. 

2.1.3.1. Results for a 400-ft Spherical Protection Zone 

In this section the probability of the center of gravity of the intruder aircraft entering a 

spherical protection zone of radius 400 ft around the ownship is calculated using the tAlas 

simulation. The probabilities and confidence limits were computed using Wilson’s Score Method 

[Wallis2013] at the 99% confidence level. Each row of Table 2-4 was computed using 

10,000,000 simulated landings. Acceptable collision probabilities are indicated in blue font and 

unacceptable probabilities are indicated in red. 

Table 2-4: Monte Carlo Simulation Results for Various Runway Spacing 

Runway 

Spacing (ft) 

ADS-B 

Latency (s) 

Num 

Failures 

Probability Minimum Distance (ft) 

750 1.5 65,475 6.53E-03  2.55E-05 93.46

850 1.5 11,169 1.12E-03  1.06E-05 178.74

900 1.5 4,158 4.16E-04  6.44E-06 219.25

950 1.5 1,395 1.40E-04  3.74E-06 258.65

1000 1.5 395 3.99E-05  1.99E-06 301.21

1050 1.5 141 9.84E-06  9.81E-07 316.55

1100 1.5 28 3.24E-06  5.49E-07 331.37

1150 1.5 7 1.14E-06  3.03E-07 350.87
11 

Runway 

Spacing (ft) 

ADS-B 

Latency (s) 

Num 

Failures 

Probability Minimum Distance (ft) 

1050 3.0 4,528 4.53E-04  6.73E-06 158.55 

1100 3.0 1,812 1.82E-04  4.26E-06 199.20 

1150 3.0 618 6.22E-05  2.49E-06 242.78 

1200 3.0 188 1.92E-05  1.38E-06 288.44 

1250 3.0 43 4.74E-06  6.72E-07 335.35 

1300 3.0 0 4.38E-07  1.48E-07 383.04 

Using this protection zone, a runway separation of 1100 ft or more is needed to reach the 

target probability of collision (i.e. less than 1E-05) for an ADS-B latency of 1.5 s. If the ADS-B 

latency is 3 s, then a runway separation of 1200 ft is required. 

2.1.3.2. Results for the FAA Cylinder Protection Zone (SAPA Procedure) 

In the FAA document [FAA2011], a cylinder of radius 265 ft and height 160 ft is recommended 

for collision studies in the terminal area. It is referred to as the Large Cylinder (or Large Hockey 

Puck). In this model a collision is assumed to occur when the center of gravity of the blundering 

aircraft penetrates the cylinder containing the target aircraft. Using this cylindrical protection 

zone, we obtain more optimistic results. Each row of table was generated using 10,000,000 

simulated landings. 

Using this protection zone, a runway separation of 950 ft or more is needed to reach the target 

probability of collision (i.e. less than 1E-05) for an ADS-B latency of 1.5 s. If the ADS-B latency 

is 3 s, then a runway separation of 1150 ft is required. 

Table 2-5: Simulation Results for Various Runway Spacing: Cylinder 

Runway 

Spacing (ft) 

ADS-B 

Latency (s) 

Num Los Probability Minimum Distance (ft) 

750 1.5 5943 5.95E-04  7.71E-06 93.46

850 1.5 679 6.83E-05  2.61E-06 178.74

900 1.5 171 1.75E-05  1.32E-06 219.25

950 1.5 29 3.34E-06  5.58E-07 258.65

1000 1.5 2 6.38E-07  2.05E-07 301.21

1050 1.5 0 4.38E-07  1.48E-07 316.55

1050 3.0 375 3.79E-05  1.94E-06 158.55 

1100 3.0 115 1.19E-05  1.08E-06 199.20 

1150 3.0 24 2.84E-06  5.12E-07 242.78 

1200 3.0 0 4.38E-07  1.48E-07 288.44 

1250 3.0 0 4.38E-07  1.48E-07 335.35 

These results were obtained using a maximum ground speed difference of 20 KT at the SAP. 

We included this constraint because the SAPA procedure requires this limitation. Removing this 

constraint gives us the following collision probabilities. 
12 

Table 2-6: Simulation Results for Various Runway Spacing: Cylinder (With No Ground 

Speed Difference Constraint) 

Runway 

Spacing (ft) 

ADS-B 

Latency (s) 

Num Los Probability Minimum Distance (ft) 

900 1.5 222 2.26E-05  1.50E-06 168.92

950 1.5 52 5.64E-06  7.36E-07 209.21

1000 1.5 10 1.44E-06  3.49E-07 252.98

1050 1.5 0 4.38E-07  1.48E-07 263.79

1050 3.0 397 4.01E-05  2.00E-06 125.60 

1100 3.0 145 1.49E-05  1.21E-06 163.67 

1150 3.0 30 3.44E-06  5.67E-07 206.35 

1200 3.0 6 1.04E-06  2.86E-07 251.74 

1250 3.0 0 4.38E-07  1.48E-07 298.61 

From Table 2-5 and Table 2-6 we can see that the SAPA ground speed difference constraint 

reduces the probability of collision slightly. This maximum ground speed difference was 

primarily imposed to meet the wake vortex requirements, but it provides a minor benefit here as 

well. Note that either way, a runway separation of 950 ft or more is needed to reach the target 

probability of collision (i.e. less than 1E-05) for an ADS-B latency of 1.5 s and a runway 

separation of 1150 ft is required if the ADS-B latency is 3 s. 

2.1.3.3. Results for the FAA Cylinder Protection Zone and Different Glideslopes 

In this section we present the results of simulations where the intruder’s glideslope is at 2.85° and 

the ownship’s glideslope at 3°. The glideslopes at San Francisco International Airport (KSFO), 

one of the candidate airports for paired approach, were changed in August 2013 to these 

differentiated angles. Differentiated glideslopes bring potential advantages to the procedure. 

When the trail is placed on the higher glideslope, its vertical separation from the lead increases 

with distance from the runway threshold. Therefore, the trail aircraft has a larger vertical 

separation in those segments of the approach where the total system error (TSE) for each aircraft 

is also large. Large TSE increases the probable loss of lateral separation between the two aircraft 

that can occur during normal operation. This decreases the distance that a blundering aircraft or 

its wake must travel to cross the path of the trail aircraft. However, since neither the wake nor 

blundering aircraft are assumed to ascend, additional vertical separation between the aircraft 

increases the possibility that ownship can maintain a safe vertical distance from the wake or 

blundering aircraft even if it the lateral separation drops below the protection zone radius. A 

cylindrical protection zone of radius 265 ft and height 160 ft was used. Each row of table was 

generated using 10,000,000 landings. 
13 

Table 2-7: Monte Carlo Simulation Results for Various Runway Spacing with Differing 

Glideslopes 

Runway 

Spacing (ft) 

ADS-B 

Latency (s) 

Num Los Probability Minimum Distance (ft) 

750 1.5 4316 4.32E-04  6.57E-06 133.91 

850 1.5 299 3.03E-05  1.74E-06 206.88 

900 1.5 38 4.24E-06  6.34E-07 242.28 

950 1.5 3 7.38E-07  2.28E-07 281.18 

1000 1.5 0 4.38E-07  1.48E-07 323.15 

1000 3.0 526 5.30E-05  2.30E-06 149.79 

1050 3.0 129 1.33E-05  1.15E-06 183.14 

1100 3.0 22 2.64E-06  4.92E-07 222.62 

1150 3.0 2 6.38E-07  2.05E-07 263.71 

1200 3.0 0 4.38E-07  1.48E-07 288.44 

Comparing this table with Table 2-5 shows that the differing glideslopes provide about 50 ft 

less runway separation. 

2.1.4. Note Concerning Disabling Alert for Trailing Aircraft 

The runway performance monitor triggers an ALAS alert for the nearest traffic aircraft even if 

that aircraft is trailing the ownship by a large distance. The question naturally arises whether 

there is a longitudinal distance at which the trailing aircraft can be safely ignored. We explored 

this idea in the tAlas simulation. Our first run was to disable the alert if the longitudinal distance 

between the aircraft was greater than 750 ft. This led to a surprising result illustrated in Figure 

2-9. 

In this scenario, the intruder has the faster ground speed and is initially more than 750 ft 

behind the ownship. After the intruder has crossed the path of the ownship, the intruder closes 

the gap between the two aircraft to a longitudinal distance less than 750 ft. At this point, the 

Figure 2-9: Pathological scenario as a result of disabling alerting for trailing aircraft 

Motion 
14 

ALAS alert is no longer suppressed (see orange dot). The escape maneuver follows shortly 

thereafter and a violation of the protection zone occurs. Clearly, if the ownship had not executed 

the escape maneuver, no LoS would have occurred. Now, there are several tests that could be 

performed to prevent this from occurring, but first we search for a minimal distance where this is 

not a problem. 

Table 2-8 shows the simulation results for a runway separation of 950 ft, 1.5 s latency and for 

various longitudinal cutoff distances. Each row was calculated from 10,000,000 simulated 

landings. Again, acceptable collision probabilities are indicated in blue font and unacceptable 

probabilities are indicated in red. 

Table 2-8: Simulation Results for 950 ft Runway with Various Rear Longitudinal Cutoff 

Distances 

Longitudinal Cutoff 

Distance (ft) 

Probability (large cylinder) Minimum 

Distance (ft) 

750 1.92E-02  4.34E-05 2.36

1500 1.96E-03  1.40E-05 2.77

2000 3.23E-04  5.68E-06 7.02

2500 2.44E-05  4.71E-06 37.60

3000 3.34E-06  5.58E-07 258.65

3500 3.34E-06  5.58E-07 258.65

From these results we see that an aircraft must be at least trailing 3000 ft or more 

longitudinally before it can be safely ignored. If it is desirable to disable the ALAS alert for 

aircraft that are trailing behind, then some additional checks should be added to the ALAS 

conformance algorithm to insure that it does not engage after the intruder has passed the 

centerline of the ownship. 

2.2. High-fidelity Simulation Results 

The 2012 SAPA study [Perry2013] concluded that the SAPA procedure, which allows the trail 

aircraft to pass the lead aircraft, could not execute safely at a runway separation of 750 feet 

[Perry2013]. This follow-on study uses the high-fidelity, transport-class aircraft simulation in 

Langley's Cockpit Motion Facility (CMF) to determine whether safe passing is feasible at a larger 

runway spacing of 1050 ft for next generation aircraft and whether aircraft adhering to the FAA 

rule on ADS-B [FAA2010] can safely pass at 1400 ft. 

The simulation setup is as described in the 2012 SAPA study [Perry2013] with some small 

adjustments. In the 2012 SAPA study, the CMF simulation was configured to perform a 

simultaneous parallel approach to runways 28L and 28R at San Francisco International Airport 

(KSFO). The lead aircraft was placed assigned to 28L and the trail aircraft was assigned to 28R. 

The high-fidelity transport model used in the CMF simulation only has the capability to automate 

instrument landing system (ILS) approaches. Therefore, each aircraft maintains its lateral and 

vertical path using the localizer and glideslope signals respectively. To provide 1050 ft and 1400 

ft runway spacing, the location of KSFO RWY28R and its ILS were shifted the necessary 

distance in the navigation database. To model current generation aircraft complying with the 

FAA ADS-B Rule, the latency parameters for ADS-B and ALAS were modified as follows: 
15 

 Ownship State 

o Total Latency (Measurement to ALAS input): 1000 ms 

o Compensated Latency: 600 ms 

 Traffic State 

o ADS-B OUT 

Total Latency (Measurement to Transmission): 2000 ms 

Compensated Latency: 1400 ms 

o ADS-B IN 

Total Latency (Reception to ALAS): 1000 ms 

Compensated Latency: 600 ms 

The FAA rule-compliant ADS-B has an end-to-end latency of 3 seconds. ADS-B latency 

parameters for the next generation aircraft is unchanged from the 2012 study and the end-to-end 

latency is 1.5 seconds. 

The method for selecting the initial condition for each run was also modified. In the prior 

high-fidelity simulation study, the initial position of the trail aircraft was placed at the center of 

the front and rear gates. In this simulation study, the trail aircraft was positioned to ensure a 

collision indication in the absence of an escape maneuver. In other words, the initial position of 

the trail aircraft ensures that separation between lead and trail aircraft is less than 100 feet when 

the lead aircraft blunders onto the trail's path. Thus, this simulation study can determine whether 

the collision can be avoided using ALAS and the escape maneuver. However, this simulation 

study does not examine scenarios where the blunder does not lead to a collision in the absence of 

an escape maneuver. Therefore, this study cannot assess whether there are circumstances under 

which the escape maneuver contributes to a collision that would not otherwise occur. As with the 

2012 simulation study, this simulation study examined both ideal state inputs to ALAS and inputs 

with modeled avionics errors and latencies. Furthermore, trials included execution of the blunder 

and escape maneuver using the stock flight control computer (normal turn) and using an outerloop control algorithm to superpose a wheel command (augmented turn). All blunders were 

conducted as a 30heading change, either while continuing to descend or while leveling off. A 

blunder in the constant speed segment at 10 NM from the threshold and a blunder after the SAP at 

2.5 NM from the threshold were both analyzed. 

Table 2-9 through Table 2-12 show the results for 1050 ft runway separation using nextgeneration avionics with an end-to-end ADS-B latency of 1.5 seconds. Table 2-13 through Table 

2-16 show the results for 1400 ft runway separation using current-rule compliant ADS-B with an 

end-to-end latency of 3 seconds. To identify collisions, a 400-foot collision sphere around the 

aircraft was used. Within the 96 runs conducted for 1050 ft separation, there are 10 collision 

indications (in red font). All ten indications occur using normal autopilot turns against blunders 

where the lead stops its descent. Only one occurs with ideal inputs; the others occur with 

modeled avionics errors and latencies. These collisions, however, are avoided under more 

aggressive maneuvering (augmented turn). There are also five false alerts. False alerts are 

indicated where the alert time is negative. (The latest version of ALAS used to generate the fasttime results in this paper does not produce false alarms when rerun against these CMF 

trajectories. The ALAS algorithm was adjusted as a consequence of these runs.) Within the 96 

runs conducted for 1400 ft separation, there are eight collision indications. Again, these 

indications occur during normal autopilot turns when the blundering aircraft stops its descent. 

Furthermore, all occur with modeled avionics errors and latencies. No collision indications occur 

under more aggressive maneuvering (augmented turn). In addition, no false positive alerts 

occurred. 
16 

These results suggest that it may be possible to perform the SAPA procedure safely at 1050 ft 

separation with next-generation avionics and at 1400 ft separation with current-rule compliance 

ADS-B OUT if the automated escape maneuver is programmed to turn more aggressively than 

under normal autopilot operation. 

Table 2-9: 1050 ft Runway Separation - 30Blunder While Descending During Constant 

Speed Segment, 1.5 s total latency 

Ideal Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 2.12 1038 617 1.62 1034 753 

130 / 122 1.70 1046 734 1.08 1038 880 

138 / 130 1.92 1061 741 1.32 1047 866 

145 / 138 2.00 1063 740 1.36 1051 838 

153 / 145 1.86 1087 759 1.60 1069 791 

160 / 153 2.74 1116 693 1.94 1093 824 

Modeled Avionics Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 3.12 1027 524 3.12 1009 525 

130 / 122 3.20 1036 585 2.58 1025 690 

138 / 130 3.42 1051 591 2.82 1031 668 

145 / 138 3.50 1052 584 2.86 1034 585 

153 / 145 2.86 1084 630 3.10 1050 563 

160 / 153 3.74 1109 604 2.94 1083 641 

 
17 

Table 2-10: 1050 ft Runway Separation - 30Blunder While Level During Constant Speed 

Segment, 1.5 s total latency 

Ideal Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 2.24 1044 377 1.24 1040 770 

130 / 122 1.96 1061 509 1.02 1047 819 

138 / 130 1.58 1062 543 1.24 1045 803 

145 / 138 1.56 1064 523 1.28 1057 717 

153 / 145 1.66 1083 555 0.94 1082 776 

160 / 153 2.60 1103 473 1.54 1089 752 

Modeled Avionics Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 3.24 1035 246 2.74 1019 539 

130 / 122 2.96 1053 329 3.02 1019 512 

138 / 130 3.58 1048 252 2.74 1027 573 

145 / 138 3.56 1048 235 2.78 1036 453 

153 / 145 3.16 1075 324 2.44 1069 495 

160 / 153 4.10 1096 232 2.54 1081 560 

 
18 

Table 2-11: 1050 ft Runway Separation - 30Blunder While Descending During Final 

Approach Segment, 1.5 s total latency 

Ideal Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 1.44 1567 1201 1.56 1181 904 

130 / 122 1.70 1760 1390 1.48 1230 899 

138 / 130 1.54 1765 1390 1.10 1138 895 

145 / 138 1.86 1111 728 1.52 1201 860 

153 / 145 1.90 1154 642 1.12 1192 833 

160 / 153 1.64 1592 1157 1.44 1147 785 

Modeled Avionics Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 2.94 1550 1041 2.56 1167 763 

130 / 122 3.20 1735 1212 1.98 1223 802 

138 / 130 3.04 1743 1214 2.60 1109 744 

145 / 138 -9.64 1143 1143 3.02 1166 639 

153 / 145 -16.10 1261 1253 -13.88 1266 1262 

160 / 153 3.14 1561 1014 2.94 1104 577 

 
19 

Table 2-12: 1050 ft Runway Separation - 30Blunder While Level During Final Approach 

Segment, 1.5 s total latency 

Ideal Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 1.74 1199 720 1.24 1197 941 

130 / 122 1.80 1205 703 1.40 1229 810 

138 / 130 1.42 1134 602 1.32 1149 837 

145 / 138 1.88 1187 586 1.02 1209 894 

153 / 145 1.98 1165 501 1.16 1198 804 

160 / 153 1.74 1116 463 1.00 1165 773 

Modeled Avionics Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 2.74 1187 600 2.74 1177 739 

130 / 122 2.30 1197 631 2.90 1196 576 

138 / 130 3.42 1090 387 2.82 1111 672 

145 / 138 3.88 1148 342 2.52 1182 674 

153 / 145 -15.02 1264 1256 -12.84 1263 1260 

160 / 153 3.24 1080 255 2.50 1127 552 

 
20 

Table 2-13: 1400 ft Runway Separation - 30Blunder While Descending During Constant 

Speed Segment, 3 s total latency 

Ideal Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 2.02 1377 869 1.46 1399 1123 

130 / 122 1.82 1398 992 1.28 1390 1195 

138 / 130 2.08 1410 1001 1.50 1397 1183 

145 / 138 1.70 1414 1043 1.18 1406 1198 

153 / 145 1.96 1435 1033 1.36 1425 1169 

160 / 153 2.36 1467 1014 1.76 1453 1196 

Modeled Avionics Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 6.02 1290 445 5.46 1271 585 

130 / 122 5.82 1333 556 5.28 1283 649 

138 / 130 6.58 1324 493 5.00 1307 701 

145 / 138 6.20 1341 556 5.18 1298 588 

153 / 145 5.96 1376 632 5.36 1315 564 

160 / 153 6.36 1401 576 5.76 1334 554 

 
21 

Table 2-14: 1400 ft Runway Separation - 30Blunder While Level During Constant Speed 

Segment, 3 s total latency 

Ideal Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 2.14 1410 724 1.08 1404 1143 

130 / 122 1.88 1424 831 1.36 1405 1134 

138 / 130 2.00 1426 833 1.02 1403 1184 

145 / 138 1.58 1435 877 1.12 1421 1098 

153 / 145 1.70 1457 921 1.24 1440 1082 

160 / 153 2.64 1470 850 1.34 1449 1143 

Modeled Avionics Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 6.14 1324 130 5.58 1264 502 

130 / 122 4.88 1380 349 5.36 1280 561 

138 / 130 6.00 1357 254 5.02 1299 648 

145 / 138 6.08 1357 203 5.12 1296 463 

153 / 145 5.20 1410 364 5.24 1310 449 

160 / 153 6.64 1404 242 5.34 1337 489 

 
22 

Table 2-15: 1400 ft Runway Separation - 30Blunder While Descending During Final 

Approach Segment, 3 s total latency 

Ideal Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 1.82 1573 1124 1.12 1558 1337 

130 / 122 1.44 1606 1190 1.36 1602 1296 

138 / 130 1.62 1530 1090 1.16 1509 1250 

145 / 138 1.82 1566 1046 1.36 1578 1258 

153 / 145 1.88 1535 960 1.48 1552 1151 

160 / 153 1.64 1489 959 1.34 1519 1155 

Modeled Avionics Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 5.82 1479 764 5.12 1443 865 

130 / 122 5.94 1493 786 5.36 1456 803 

138 / 130 6.12 1398 669 5.16 1356 865 

145 / 138 5.82 1457 649 5.36 1419 731 

153 / 145 0.88 1549 1024 5.48 1381 591 

160 / 153 5.64 1365 524 4.84 1374 680 

 
23 

Table 2-16: 1400 ft Runway Separation - 30Blunder While Level During Final Approach 

Segment, 3 s total latency 

Ideal Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 1.48 1580 1112 1.20 1562 1313 

130 / 122 1.78 1590 1082 1.40 1611 1213 

138 / 130 1.50 1512 960 0.92 1532 1251 

145 / 138 1.78 1566 959 1.40 1584 1222 

153 / 145 2.00 1549 863 1.22 1587 1180 

160 / 153 1.66 1490 826 1.00 1546 1149 

Modeled Avionics Input to ALAS 

Normal Turn Augmented Turn 

Approach 

Speeds of 

Fast/Slow (KT) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

Time to 

Alert (s) 

3D Distance 

at Alert (ft) 

Closest 3D 

Distance (ft) 

122 / 114 4.98 1513 743 4.70 1469 892 

130 / 122 3.78 1552 861 5.40 1454 661 

138 / 130 5.50 1400 522 5.42 1340 795 

145 / 138 3.78 1527 692 5.40 1415 689 

153 / 145 6.00 1431 380 5.22 1426 626 

160 / 153 5.16 1388 348 5.00 1370 630 

2.3. Observations 

The fast-time and high-fidelity simulations provide evidence that it will be safe to use the 

SAPA procedure at 1050 ft separations with next-generation avionics and at 1400 ft separations 

with current-rule compliance ADS-B OUT with an aggressive escape maneuver. The fast time 

simulations suggest that the SAPA procedure may be used down to 1150 ft separations with 

current-rule avionics and down to 950 ft separations with future avionics, though this has not yet 

been validated in the CMF high-fidelity simulation. It seems likely that the use of different 

glideslopes will reduce the allowed separations by another 50 ft. These results depend upon an 

automatic, immediate initiation of the escape maneuver. We have modeled the roll time of the 

turn maneuver and the ramp up of the vertical acceleration in the escape maneuver, but we have 

not included any delay due to a pilot. We have also assumed that this maneuver can be 

performed for all possible blunders. 
24 

3. Evaluation of Echelon Spacing for Straight-In Procedures 

After initial results of the tAlas simulation indicated that the safe runway separation for the 

SAPA procedure was 1100 ft (see Section 2.1.3.1), NASA was encouraged to investigate the 

benefits of using echelon spacing. Echelon spacing requires the trail aircraft to maintain a 

collision-safe distance from the lead aircraft. This section uses statistical analysis to determine 

the runway separations under which echelon spacing is feasible. Statistical analysis was used in 

lieu of a Monte-Carlo simulation for two reasons. First, neither the tAlas nor CMF simulations 

contain a wake transport model useful in determining the wake-safe boundary. Both simulations 

place the aircraft within pre-established wake-safe boundaries. In the 2012 SAPA Study [Perry 

2012], these fast-time simulations used wake-safe boundaries determined from a previous MonteCarlo study performed by Johnson, et. al. [Johnson 2010]. However, Johnson's results could not 

be reused for analyzing the Echelon approach due to a difference in wake transport model (see 

section 3.4.1) and in operating assumptions including total system error, tolerable crosswind, and 

acceptable probability of a wake encounter. Second, though a new Monte-Carlo simulation could 

have been developed to determine new wake-safe boundaries, such a simulation would be subject 

to the same limitations as previous simulations. Namely, the number of runs that are required to 

characterize, with confidence, wake-safe boundaries with a rarity of 1 encounter in 1 billion 

flights necessitate long run times. The long run-times hamper iterative redesign of the procedure 

to converge on a feasible solution. An analytical model can estimate, very rapidly, the wake-safe 

boundary for a given probability of a wake encounter. 

Figure 3-1 depicts the relative geometry of the aircraft in the paired-approach with echelon 

spacing. The trail aircraft must maintain longitudinal distance from the lead aircraft in a range 

defined to avoid two hazards, collision and wake. To avoid collision, the trail aircraft must 

Figure 3-1: Paired Approach with Echelon Spacing 
25 

maintain a sufficient distance from the lead such that the lead will not collide with the trail if the 

lead blunders towards the trail's path. To avoid wake, the trail aircraft must be close enough to 

the lead that the wake of the lead aircraft passes behind the trail in the presence of adverse 

crosswind. The trail must maintain its separation in this range from the loss of altitude separation 

until the lead aircraft crosses the threshold (TBR1

). In the constant speed segments, the two 

aircraft are flying the same speed and the trail can maintain a constant spacing behind the lead. 

However, after the final approach fix (FAF), both aircraft will slow to their final approach speed. 

By design, the final approach speed of the trail aircraft is greater than that of the lead aircraft. 

Therefore, longitudinal separation between the lead and trail will decrease throughout final 

approach. The trail aircraft must accommodate this compression of longitudinal separation 

before reaching the FAF to ensure that it will not drop below the collision-safe distance before 

reaching the threshold. This compression distance grows larger as the approach speed of the lead 

decreases and as the difference in approach speed between the two vehicles increases. 

To determine the feasibility of the procedure for a given pair of aircraft, we must define the 

collision-safe distance, the longitudinal compression distance, and the wake-safe distance. Figure 

3-2 depicts how the collision-safe distance, the longitudinal compression distance, and the wakesafe distance define the required separation between the lead and trail aircraft at the FAF. The 

collision-safe distance and longitudinal compression distance define the front-gate. The wakesafe distance defines the rear-gate. However, the procedure becomes infeasible for a given pair 

of aircraft if the distance between the front and rear gate is not long enough to accommodate the 

deviation in longitudinal separation that can normally occur. Otherwise, the procedure may 

suffer an ineffectual rate of breakouts. In fact, Section 3.4.3 uses the desired breakout rate to 

define the normal deviation in longitudinal separation. Some of the variables that determine these 

distances are subject to variation. These variables include the total system error (TSE) of each 

aircraft (including its components of flight technical error [FTE] and navigation error [NE]), the 

error in the ADS-B reported position of the lead aircraft, and the variation in the actual airspeeds 

of the lead and trail aircraft. Therefore, given a distribution function for these variables (usually 

assumed to be normal), one can statistically analyze the feasibility of the procedure for a desired 

 

1

 The angle at which the lead aircraft can safely intercept the path of the trail diminishes near the ground. 

More aggressive maneuvers will lead to ground contact. For this reason, it may be possible to lift 

longitudinal spacing requirements earlier in the procedure. 

Figure 3-2: Components of Required Longitudinal Separation at the FAF 
26 

probability of successful completion. 

3.1. The Collision-Safe Distance 

Eftekari, et al. [Eftekari2011] performed an assessment of collision-free separation for parallel 

approaches at closely spaced parallel runways. Eftekari defined collision-free as a collision 

probability of 10-9 or less divided between a blunder probability of 10-5 and a probability of 

collision after blunder of 10-4. If a blunder can occur at any point in the procedure, this study 

concluded that the trail aircraft must maintain a longitudinal separation of 750 feet or more within 

the FAF when the runway spacing is 700 feet. If blunders occur only outside the FAF, Eftekari 

determined that the longitudinal separation must be 1500 ft or more up to the FAF. 

Though Section 4.1 presents NASA's analysis of the collision-safe separation to support the 

parallel segment of the offset approach to low minima (which also apply to parallel approaches), 

that work was not completed in time to incorporate into the analysis in this section. Therefore, 

the analysis in this section establishes a 750 ft minimum separation within the FAF and a 1500 ft 

minimum separation outside the FAF. 

3.2. Longitudinal Compression Distance 

Prior to the FAF, the trail aircraft uses speed management to actively control its longitudinal 

separation with the lead. The trail aircraft stops active management of longitudinal separation 

when it reaches its final approach speed (by maintaining separation as the lead aircraft's 

decelerates) or when it reaches the FAF (if it has not detected deceleration by the lead). The trail 

aircraft will then decelerate to its final approach speed and, since the procedure places the aircraft 

with the faster approach speed in the trail position, the longitudinal separation will decrease for 

the remainder of the procedure. However, the trail aircraft continues to monitor the longitudinal 

separation and will breakout if it drops below the collision-free separation. Therefore, to limit 

nuisance breakouts, the trail aircraft must position itself to accommodate the longitudinal 

compression before the aircraft begins to decelerate. 

If the aircraft accurately fly their planned approach speed to the threshold, then the 

longitudinal compression is characterized by the approach speeds of the two vehicles, the rate of 

deceleration, the minimum separation that must be maintained, the height to which minimum 

separation must be maintained, winds, and atmospheric density. Winds and atmospheric density 

come into play because the approach speed is an equivalent airspeed, not a true ground speed. 

This analysis does not include winds. Nevertheless, headwinds tend to increase the compression 

distance as it will lead to a decrease in the true ground speed of the lead aircraft and, therefore, 

increases the time that the trail spends encroaching on the lead. Likewise, tailwinds would tend 

to decrease the compression distance. 

On the other hand, accounting for density with altitude is desirable. At KSFO, assuming a 

1976 standard atmosphere, the equivalent airspeed at the FAF is about 3% lower than the true 

ground speed. From the FAF to touchdown, the elapsed time to threshold is about 3 seconds 

shorter when one converts EAS to TAS than if one assumes that EAS = TAS. The challenge, 

however, in computing compression distance by converting EAS to TAS is that the conversion 

value changes with altitude as density changes with altitude. 

Before incorporating the EAS to TAS conversion, let us first determine the kinematic 
27 

equations for the approach procedures assuming TAS = EAS. As we will see later, we can 

formulate the EAS to TAS conversion in a way that allows us to use these same relations. The 

flight of the lead aircraft is examined first and is shown in Figure 3-3. The lead aircraft's speed 

schedule can be broken into three segments: a constant speed segment, a deceleration segment, 

and a final approach segment. The constant speed segment captures the region from where the 

lead aircraft captures the glideslope until the final approach fix. In this region, the aircraft flies a 

constant EAS assigned by air traffic control. When the lead aircraft reaches the FAF, it begins 

the deceleration segment. In this segment, the aircraft decelerates to its planned final approach 

speed. The deceleration is modeled as a constant that completes the deceleration by the stabilized 

approach point (SAP) at 1000 ft AGL. After the SAP, the aircraft is in the final approach 

segment and flies its planned final approach speed to the threshold. The aircraft is expected to 

initiate a flare maneuver within the neighborhood of the threshold; however, the trail aircraft is no 

longer required to maintain separation at that point. 

To compute the compression distance at the FAF, first calculate the time it takes the lead 

aircraft to travel from the FAF to the threshold crossing height (TCH). The time from FAF to 

TCH is divided into two computations: time from FAF to SAP and time from SAP to TCH. The 

time from FAF to SAP assumes a constant deceleration from the constant segment speed (Vc) to 

the final approach speed (Vf). Thus, the average speed from FAF to SAP is 1⁄2 [Vc + Vf]. Given 

that the FAF and SAP are defined by height above the runway, the distance between these points 

is a function of their heights and the glideslope angle. The time is given by: 

ݐி஺ி՜ௌ஺௉ ൌ ܦሺݖǡ ߛሻ

ܸത ൌ ሺݖி஺ி െ ݖௌ஺௉ሻ

ߛ 

ʹ

൫ܸ௖ ൅ ܸ௙൯

ܶܭ

݂ݏ݌ ൌ ͳ ͅͳͳ͵

൫ܸ௖ ൅ ܸ௙൯ (3-1) 

where, 

 zFAF is the height of the final approach fix in feet, normally 1800 ft 

 zSAP is the height of the stabilized approach point in feet, normally 1000 ft 

Figure 3-3: Speed Profiles of Lead and Trail Aircraft 
28 

	 is the glideslope angle, normal 3

 Vc is the constant segment speed in knots, nominally 180 KT 

 Vf is the final approach speed in knots 

t is the flight time in seconds 

Similarly, the time from SAP to TCH is given by: 

ݐௌ஺௉՜்஼ு ൌ ܦሺݖǡ ߛሻ

ܸ ൌ ሺݖௌ஺௉ െ ݖ்஼ுሻ

ߛ  ௙ܸ

ܶܭ

݂ݏ݌ ൌ ͳͲ͹ͷͶ

ܸ௙

(3-2) 

where, zTCH is the TCH in feet, nominally 50 feet but at KSFO it is 57 ft for the lead aircraft's 

runway RWY28L and 55 ft for the trail aircraft's runway RWY28R. The total flight time from 

FAF to TCH for the lead aircraft is therefore, 

ݐ௔௘௟ௗ ൌ ͳ ͅͳͳ͵

൫ܸ௖ ൅ ܸ௙൯

൅

ͳͲ͸͹ͷ

ܸ௙

(3-3) 

For example, if Vc is 180 KT and Vf is 120 KT, then the tlead is 149.3 seconds. 

Next, given a starting height at the collision-free distance from the threshold (zCFH), calculate 

where the trail aircraft would have been tlead seconds in the past. The conditions on the time and 

rate of deceleration for the trail aircraft complicate this computation. The trail aircraft decelerates 

at the same rate as the lead aircraft when and if it detects the deceleration of the lead aircraft prior 

to the trail aircraft reaching the FAF; otherwise, the trail aircraft decelerates independently. One 

key parameter governing this condition is tdelay, the time delay in the response of the trail aircraft 

to changes in the true state of the lead aircraft. For this study, tdelay is assumed to be 5.0 seconds 

for current generation aircraft and 3.5 seconds for next generation aircraft. Table 3-1 provides a 

breakdown of the estimated tdelay. 

Table 3-1: Estimate of Response Delay in Dependent Operations 

Current Generation Next Generation 

ADS-B OUT Latency (from 

navigation measurement) 

2.0 s 0.7 s 

ADS-B IN Latency 0.5 s 0.5 s 

ALAS Latency 0.5 s 0.3 s 

Pilot Reaction Time 2.0 s 2.0 s 

Total 5.0 s 3.5 s 

Let tI-Trail be the independent flight time of the trail aircraft from the FAF to zCFH. The trail 

aircraft will decelerate independently if (tlead - tI-Trail) < tdelay. Thus, we first compute tI-Trail. The 

equations are identical to those for tlead but zCFH is substituted for zTCH. 

ݖ஼ிு ൌ ݖ்஼ு ൅݀௖௢௟௟௜௦௜௢௡ሺݐܽ݊ ߛሻ ൌ ͷͷ݂ݐ͹ ൅ ͷͲ݂ݐሺݐܽ݊͵ ιሻ ൌ ͻͶǤ͵݂ݐ) 3-4 (

ݐௌ஺௉՜஼ிு ൌ ܦሺݖǡ ߛሻ

ܸ ൌ ሺݖௌ஺௉ െ ݖ஼ிுሻ

ߛ  ௙ܸ

ܶܭ

݂ݏ݌ ൌ ͳͲʹͷ͵

ܸ௙

(3-5) 
29 

ݐூି௧௥௔௜௟ ൌ ݐி஺ி՜ௌ஺௉ ൅ ݐௌ஺௉՜஼ிு ൌ ͳ ͅͳͳ͵

൫ܸ௖ ൅ ܸ௙൯

൅

ͳͲʹͷ͵

ܸ௙

(3-6) 

If the value of tI-trail reveals that the trail aircraft will perform an independent deceleration, then 

the position of the x-axis runway coordinate of the trail aircraft when the lead is at the FAF is: 

ܺூି௧௥௔௜௟ ൌ ܺி஺ி െ  ɀ ൬ܸ௖ ሺݐ௔௘௟ௗ െ ݐூି௧௥௔௜௟ሻ

ݏ݌݂

 (3-7) ൰ ܶܭ

where XFAF is the x-axis runway coordinate of the FAF, nominally -33,392 ft or -5.5 NM; at 

RWY28R, it is -33297 ft. The above equation is valid as long as tI-trail ≤ tlead which should be true 

as long as the final approach speed for the trail aircraft is greater than that of the lead aircraft. 

However, the actual speeds of each aircraft can deviate from their planned speeds. If the trail and 

lead aircraft have the same planned final approach speed, then the actual speed of the trail aircraft 

can be lower than planned and, therefore, lower than the actual speed of the lead aircraft. 

Nevertheless, this situation does not need to be accounted for because as stated in section 3.1, the 

trail must also maintain a collision-free separation at the FAF of 1500 ft. In fact, given that (tlead - 

tI-trail) ≤ tdelay, the maximum longitudinal separation at the FAF for independent deceleration of the 

trail aircraft is Vc tdelay. For next-generation aircraft, a Vc > 254 KT would be required to exceed 

the minimum separation of 1500 ft. That speed is well outside expected variation about the 

CONOPS designed value of 180 KT [MITRE2013]; therefore, an aircraft pair that could get close 

enough to allow independent deceleration of the trail, must instead be separated by 1500 ft at the 

FAF and will perform a dependent deceleration. For current generation aircraft, a Vc > 178 KT is 

required to exceed the minimum separation of 1500 ft. This is within the expected variation 

about design value of 180 KT; therefore, it remains possible for current generation aircraft to be 

positioned for an independent deceleration. 

If the trail aircraft will perform a dependent deceleration with the lead, the trail aircraft's total 

flight time, tD-trail, can be broken into three components: tdelay - the delay in dependent operation 

defined in the previous paragraph, tdecel - the time to decelerate to the final approach speed, and 

tfinal - the time flying at the final approach speed. tdecel is computed using the deceleration of the 

lead aircraft and the final approach speed of the trail aircraft: 

ܽ௟௘௔ௗ ൌ ൬ οܸ

ݐி஺ி՜ௌ஺௉

൰

௟௘௔ௗ

ൌ ൫ܸ௙ െ ܸ௖൯

൫ܸ௖ ൅ ܸ௙൯

ʹ

ߛ 

ሺݖி஺ி െ ݖௌ஺௉ሻ

ݏ݌݂

ܭܶ ൌ ൫ܸ௙

ଶ െ ܸ௖

ଶ൯

ͳ ͅͳͳ͵ (3-8) 

ݐௗ௘௖௘௟ ൌ οܸ௧௥௔௜௟

ܽ௟௘௔ௗ

ൌ ͳ ͅͳͳ͵ ൫ܸ௙ െ ܸ௖൯

௧௥௔௜௟

൫ܸ௙

ଶ െ ܸ௖

ଶ൯

௟௘௔ௗ

(3-9) 

Note that the equation for alead produces an acceleration in units of kt/s so that the equation for 

tdecel produces a time in units of seconds. Now, tfinal becomes the remaining time, tlead - tdelay - tdecel. 

With these times, the x-axis runway coordinate of the trail aircraft performing a dependent 

deceleration can be computed: 

ܺ஽ି௧௥௔௜௟ ൌ െ ൬݀௖௢௟௟௜௦௜௢௡ ൅  ߛ ቀܸ௙ݐ ൅ ௟௔௡௜௙ଵ

ଶ

൫ܸ௖ ൅ ܸ௙൯ݐௗ௘௖௘௟ ൅ ܸ௖ݐௗ௘௟௔௬ቁ

ݏ݌݂

 (3-10) ൰ ܶܭ

The compression distance can now be computed for an aircraft pair: 
30 

݀௖௢௠௣௥௘௦௦௜௢௡ ൌ 

଻ହ଴ ቆܺி஺ி െ ݀௖௢௟௟௜௦௜௢௡ െ ቊ

ܺூି௧௥௔௜௟݂݅ሺݐ௔௘௟ௗ െ ୍ି୲୰ୟ୧୪ሻ ൑ ୢୣ୪ୟ୷

ܺ஽ି௧௥௔௜௟݂݅ሺݐ௔௘௟ௗ െ ୍ି୲୰ୟ୧୪ሻ ൐ ୢୣ୪ୟ୷ቇ (3-11) 

The minimum value of dcompression is 750 ft since the minimum collision-free separation at the FAF 

is 1500 ft which is 750 ft greater than dcollision, the collision-free separation at the threshold. Using 

the above equations, if the lead aircraft final approach speed is 120 KT and the trail aircraft final 

approach speed is 130 KT, then the following values would result for the current generation fleet: 

 tlead = 149.3 seconds 

tI-trail = 137.3 seconds, (tlead - tI-trail) = 12.0 seconds > tdelay so compute XD-trail

tdecel = 50.3 seconds 

XD-trail = -36014 ft 

dcompression = 1967 ft 

Next, incorporate the EAS to TAS conversion: 

்ܸ஺ௌ ൌ ܸா஺ௌඨ ߩ

଴ߩ

ൌ ܸா஺ௌඨܲ଴ܶ

ܲܶ଴

(3-12) 

where 
, P, and T are the atmospheric density, pressure, and temperature respectively and the 

subscript zero indicates the sea-level value. The second formulation allows the insertion of 

functions for temperature and pressure from the US Standard 1976 atmosphere model for 

altitudes below 36,152 ft [NOAA1976]: 

ൌ ܪ

݄ܴ௘

݄൅ܴ௘

(3-13) 

ܮܪ ൅ ൬ͳ଴ ܶൌܶ

ܶ଴

൰ (3-14) 

ܮܪ ൅ ൬ͳ଴ ܲൌܲ

ܶ଴

൰

ି௚Τሺ௅ோሻ

(3-15) 

where, 

 g = the standard acceleration due to free fall, 32.17404 ft/s2 

 h = the geometric altitude, feet 

 L = the lapse rate, -3.56616x10-3 R/ft 

 P0 = sea-level pressure, 2116.22 psf 

 R = the gas constant for air, 1716.55915670803 ft2

/(s2 R) 

 Re = the radius of the Earth, 20855531.5 ft 

 T0 = sea-level temperature, 518.67 R 

 H = the geopotential altitude, feet 

With these equations, the conversion from EAS to TAS becomes: 

்ܸ஺ௌ ൌ ܸா஺ௌඨ൬ͳ ൅ ݄ܮܴ௘

ሺ݄൅ܴ௘ሻܶ଴

൰

ଵା௚Τሺ௅ோሻ

ൌ ܸா஺ௌඨ൬ͳ െ ͳͶ͵Ǥ͵ͻͶ݄

݄ ൅ ʹͲ ͅͷͷͷ͵ͳǤͷ൰

ିସǤଶହହ଼ଽ

(3-16) 
31 

Equation 3-16 computes TAS as a function of geometric altitude. To determine the distance 

traveled over a given time, we recognize that TAS is dr/dt where r is the distance along the 

glideslope. Since the glideslope angle is constant, we can reformulate dr/dt in terms of geometric 

altitude using the relation h = r sin(	). 

்ܸ஺ௌ ൌ ݀ݎ

ܶܭ ߛ ൬ ൌ ݐ݀

൰ݏ݌݂

݄݀

݀ݐ ൌ ܸா஺ௌඨ൬ͳ െ ͳͶ͵Ǥ͵ͻͶ݄

݄ ൅ ʹͲ ͅͷͷͷ͵ͳǤͷ൰

ିସǤଶହହ଼ଽ

(3-17) 

න ݀ݐ ൌ ݐ ൌ ൬ ߛ

ܸா஺ௌ

ܶܭ

݂ݏ݌൰ න ඨ൬ͳ െ ͳͶ͵Ǥ͵ͻͶ݄

݄ ൅ ʹͲ ͅͷͷͷ͵ͳǤͷ൰

ସǤଶହହ଼ଽ

݄݀ (3-18) 

(Note the change of sign for the exponent in Equation 3-18.) The integral for dh does not have a 

closed form solution. However, a closed form approximation can be constructed by converting 

the integrand to a Taylor series and integrating the first two terms: 

ߛ ൌ൬ݐ

ܸா஺ௌ

ܶܭ

݂ݏ݌൰ න ቀͳ െ ͳǤͶ͸͵Ͳͻ ൈ ͳͲିହ݄ ൅ ͷǤ͹Ͷ͵Ͷ͹ ൈ ͳͲିଵଵ݄ଶ ൅ ܱሺ݄ଷሻቁ ݄݀

(3-19) 

ൌ

 ߛሺ݄ െ ͹Ǥ͵ͳͷͶ͵ ൈ ͳͲି଺݄ଶ ൅ ͳǤͻͳͶͶͻ ൈ ͳͲିଵଵ݄ଷሻ

ܸா஺ௌ

ܶܭ

݂ݏ݌ ൌ ܦா஺ௌሺ݄ሻ

ܸா஺ௌ

ܶܭ

ݏ݌݂

Note that removing the second and third order terms reduces the equation to the assumption that 

TAS = EAS. Thus, the second and third order terms represent the effect of accounting for 

EAS→TAS conversion with altitude on the time to reach sea-level. For example, when starting 

at an altitude of 1000 ft, the equation indicates that the EAS→TAS conversion is equivalent to 

reducing the distance traveled by 139 ft. The third order term produces a distance of less than 1 

foot below h = 3738 ft. It could be ignored for KSFO given that the geometric altitude of the trail 

aircraft is expected to be below 2200 ft when the lead aircraft is at the FAF. But the term is kept 

for future use at other airports whose runways are at an elevation of 1500 ft MSL or greater. 

As indicated by the final formulation of Equation 3-19, this equation defines an equivalent 

airspeed distance term (DEAS) that is a function of geometric altitude. We can substitute DEAS for 

the z/sin(	) terms in equations 3-1 through 3-9. For example, the time to travel from SAP to TCH 

(Equation 3-2), becomes: 

ݐௌ஺௉՜்஼ு ൌ ܦሺ݄ǡ ߛሻ

ܸ ൌ ൫ܦா஺ௌሺ݄ௌ஺௉ሻ െ ܦா஺ௌሺ்݄஼ுሻ൯

ܸ௙

ܶܭ

 (3-20) ݏ݌݂

This substitution also works for the deceleration segment when deceleration is assumed to be a 

constant deceleration of the equivalent airspeed because the deceleration term can then be 

evaluated in the time integral: 

்ܸ஺ௌ ൌ ൫ܸா஺ௌ

଴ ൅ ܽா஺ௌݐ൯ඨ൬ͳ െ ͳͶ͵Ǥ͵ͻͶ݄

݄ ൅ ʹͲ ͅͷͷͷ͵ͳǤͷ൰

ିସǤଶହହ଼ଽ ൌ ൬ ߛ ܭܶ

൰ݏ݌݂

݄݀

ݐ݀

(3-21) 
32 

න൫ܸா஺ௌ

଴ ൅ ܽா஺ௌݐ൯ ݂ݏ݌

ܭܶ ݀ݐ ൌ  ߛ න ඨ൬ͳ െ ͳͶ͵Ǥ͵ͻͶ݄݄ ൅ ʹͲ ͅͷͷͷ͵ͳǤͷ൰

ସǤଶହହ଼ଽ

݄݀ (3-22) 

ቀܸா஺ௌ

ଵ ൅ ݐ ଴

ଶ

ܽா஺ௌݐଶቁ݂ݏ݌

ܭܶ ൌ ܦா஺ௌሺ݄ሻ (3-23) 

Equation 3-23 is identical to the kinematic equation for constant acceleration for true airspeed 

with the distance term replaced with DEAS. Finally, equations 3-1 through 3-9, modified to use 

DEAS, are applied to KSFO. KSFO runways RWY28L and RWY28R are 13 ft above sea-level so 

the conversion of height above runway (z) to geometric altitude(h) is h = z + 13. Furthermore, 

RWY28L has a TCH of 57 ft and RWY28R has a TCH of 55 ft. The lead aircraft is placed on 

RWY 28L. The final equations are: 

ݐ௔௘௟ௗ ൌ ቆ

൫୉୅ୗሺͳͲͳ͵ሻ െ ୉୅ୗሺ͹Ͳሻ൯

ܸ௙

൅

ʹ൫୉୅ୗሺͳ ͅͳ͵ሻ െ ୉୅ୗሺͳͲͳ͵ሻ൯

ܸ௙ ൅ ܸ௖

ܶܭ ቇ

ݏ݌݂

(3-24) 

ൌ

ͳͲͷͻͳ

ܸ௙

൅

ͳ͹͹Ͷͳ

ܸ௙ ൅ ܸ௖

ݐூି௧௥௔௜௟ ൌ 

൫୉୅ୗሺͳͲͳ͵ሻ െ ୉୅ୗሺ͸ ͅ ൅ ୡ୭୪୪୧ୱ୧୭୬  ͵ιሻ൯

ܸ௙

ܶܭ

൅ ݏ݌݂

ͳ͹͹Ͷͳ

ܸ௙ ൅ ܸ௖

(3-25) 

ൌ

ͳͲͳ͹Ͳ

ܸ௙

൅

ͳ͹͹Ͷͳ

ܸ௙ ൅ ܸ௖

ܽ௟௘௔ௗ ൌ ൬ οܸ

ݐி஺ி՜ௌ஺௉

൰

௟௘௔ௗ

ൌ ൫ܸ௙ െ ܸ௖൯

ܸ௙ ൅ ܸ௖

ͳ͹͹Ͷͳ ൌ ൫ܸ௙

ଶ െ ܸ௖

ଶ൯

ͳ͹͹Ͷͳ (3-26) 

ݐௗ௘௖௘௟ ൌ οܸ௧௥௔௜௟

ܽ௟௘௔ௗ

ൌ ͳ͹͹Ͷͳ ൫ܸ௙ െ ܸ௖൯

௧௥௔௜௟

൫ܸ௙

ଶ െ ܸ௖

ଶ൯

௟௘௔ௗ

(3-27) 

To compute the X coordinate of the trail aircraft when the lead aircraft is at the FAF, first 

compute the position as a DEAS distance: 

ܦூି௧௥௔௜௟ ൌ ܦா஺ௌሺ݄ி஺ிሻ ൅ ܸ௖ሺݐ௔௘௟ௗ െ ݐூି௧௥௔௜௟ሻ

ݏ݌݂

 (3-28) ܶܭ

ܦ஽ି௧௥௔௜௟ ൌ ୉୅ୗሺ͸ ͅ ൅ ͹ͷͲ  ͵ιሻ ൅ ቀܸ௙ݐ ൅ ௟௔௡௜௙ଵ

ଶ

൫ܸ௖ ൅ ܸ௙൯ݐௗ௘௖௘௟ ൅ ܸ௖ݐௗ௘௟௔௬ቁ

ݏ݌݂

 (3-29) ܶܭ

 ൌ ʹͲͶͻ ൅ ൫ܸ௙ݐ ൅ ௟௔௡௜௙భ

మ

൫ܸ௖ ൅ ܸ௙൯ݐௗ௘௖௘௟ ൅ ܸ௖ݐௗ௘௟௔௬൯ ௙௣௦

௄்

ܦ௧௥௔௜௟ ൌ ቊ

ܦூି௧௥௔௜௟݂݅ሺݐ௔௘௟ௗ െ ୍ି୲୰ୟ୧୪ሻ ൑ ୢୣ୪ୟ୷

ܦ஽ି௧௥௔௜௟݂݅ሺݐ௔௘௟ௗ െ ୍ି୲୰ୟ୧୪ሻ ൐ ୢୣ୪ୟ୷

(3-30) 

Then, solve the DEAS formula to determine the starting geometric altitude: 
33 

 ߛ ሺ݄ െ ͹Ǥ͵ͳͷͶ͵ ൈ ͳͲି଺݄ଶ ൅ ͳǤͻͳͶͶͻ ൈ ͳͲିଵଵ݄ଷሻ ൌܦ௧௥௔௜௟ (3-31) 

ͳǤͻͳͶͶͻ ൈ ͳͲିଵଵ݄ଷ െ ͹Ǥ͵ͳͷͶ͵ ൈ ͳͲି଺݄ଶ ൅݄െܦ௧௥௔௜௟  ߛ ൌ Ͳ (3-32) 

The last term, Dtrail sin	, represents an EAS equivalent altitude, h'. Thus, the resulting solution 

will be a conversion from the EAS equivalent altitude (h') to the geometric altitude (h). The real 

cube root of the cubic formula is a complicated formula. To simplify it, the cube root is expanded 

into a Taylor series and the first four terms of the series are used: 

݄௧௥௔௜௟ ൌ ݄ᇱ ൅ ͹Ǥ͵ͳͷͶ͵ ൈ ͳͲି଺݄Ԣଶ ൅  ͅǤ͹ ͅ ͅ͸ʹ ൈ ͳͲିଵଵ݄Ԣଷ ൅ ͳǤʹͷ͹ͳ ͅ ൈ ͳͲିଵହ݄Ԣସ (3-33) 

The X runway coordinate for the trail aircraft is then: 

ܺ௧௥௔௜௟ ൌ െ  ߛ ሺ݄௧௥௔௜௟ െ ்݄஼ுሻ (3-34) 

Finally, the compression length (dcompression) is: 

݀௖௢௠௣௥௘௦௦௜௢௡ ൌ 

଻ହ଴ ሺܺி஺ி െ ݀௖௢௟௟௜௦௜௢௡ െ ܺ௧௥௔௜௟ሻ (3-35) 

Using the prior example of the lead aircraft with a final approach speed of 120 KT and a trail 

aircraft with a final approach speed of 130 KT, the resulting value of dcompression and intermediate 

terms are: 

 tlead = 147.4 seconds 

tI-trail = 135.5 seconds, (tlead - tI-trail) = 11.9 seconds > tdelay so compute XD-trail

tdecel = 49.3 seconds 

Dtrail = 36891 ft 

htrail = 1959 ft 

Xtrail = -36076 ft 

dcompression = 2029 ft 

In comparison to the earlier example using the assumption that TAS = EAS, the compression 

length grew from 1957 ft to 2029 ft, a difference of 72 ft. So, how can the compression length be 

larger when the time of flight for both aircraft is shorter? The answer is that the trail aircraft 

maintains a higher altitude and, therefore, has a slightly higher true airspeed, even when the 

equivalent airspeed is equal to the lead aircraft. Depending on the initial separation, this effect 

can cause added compression that is greater than the reduced compression from the shorter flight 

time. It is a limitation of the EAS-based model. In the procedure, the trail aircraft uses a speed 

management algorithm that maintains separation through deceleration, effectively causing the 

trail aircraft to track the true airspeed of the lead vehicle. Therefore, until the trail vehicle 

decelerates to its final approach speed as an equivalent airspeed, the trail's equivalent airspeed 

should be slightly lower than the equivalent airspeed of the lead. There is no simple mechanism 

to modify the EAS-based model for this behavior. What is certain is that the compression length 

computed from such a modification would be between those computed by the EAS-based model 

and the TAS=EAS assumption. The EAS-based model often provides the more conservative 

estimate. Furthermore, the EAS-based model remains sufficiently simple to program or to use in 

generating look-up tables; therefore, it can be used in real-time by flight deck or controller 

systems to generate custom values of the front-gate separation for specific pairings. 

This kinematic model has other simplifications that can incrementally affect results. First, the 
34 

model does not account for path deviation (lateral or longitudinal FTE) which can modify the 

flown distance (and therefore time) from FAF to touchdown. However, the longitudinal window 

in which the separation between aircraft is allowed to float (see section 3.4.3) partly accounts for 

the path deviation. The model also does not account for longitudinal deviation in the lead 

initiating the deceleration segment. Late deceleration will shorten the compression distance; 

early deceleration will lengthen it. The equations in this section can be adjusted to examine late 

or early deceleration, and this can be pursued if a future need arises for improved analysis. 

Lastly, the model is limited to the standard day profile for density in the 1976 atmosphere model, 

actual density that departs from the standard day profile will also adjust the compression distance. 

Again, investigating greater diversity in density profiles is left to future work if needed. 

3.3. Front Gate for the Constant Speed Segment 

When the lead aircraft reaches the final approach fix (FAF), the front gate is the minimum of 

1500 ft (see section 3.1) or the sum of the collision-free separation at the threshold (dcollision) and 

the compression distance (dcompression). The previous section details the formulas used to derive 

dcompression but variation of the actual airspeed to the planned airspeed was not addressed. In 

reality, the actual deviation of the airspeed from planned resembles a random walk plus a bias 

about the planned airspeed. The equations for dcompression assume constant speed and cannot 

accommodate the random walk contribution to variation. However, if one assumes the random 

walk is approximately symmetric about the bias, then its effect on front gate position is likely to 

be small enough to negligible. This leaves the bias, which can be added to the planned aircraft 

speed. Comprehensive studies of actual vs. commanded speed over the approach path could not 

be found. However, Helleberg, et al. [Helleberg2006] performed an analysis of actual versus 

planned speed at the threshold. Unfortunately, the quantitative values presented included both 

manual and autothrottle flights though the study also graphically depicts separate distributions for 

autothrottle and manual flights. Moreover, the planned airspeed was derived from a Vref lookup 

table after estimating the aircraft landing weight. This method is necessary to combine the 

manual and autothrottle flights. However, for the paired-approach, the data of interest is 

deviation from commanded speed with autothrottle engaged. In Helleberg's study, flights with 

autothrottle engaged could have commanded speeds that differ from the planned speed. Still, for 

the most automated aircraft models, the Airbus A320 and Boeing 777, the mean deviation of 

actual speed from planned was +3.24 KT and +2 KT respectively with standard deviations of 3.6 

and 2.8 KT. From these numbers, it appears reasonable to assume that the bias in the actual 

versus planned difference in airspeed (V) between the trail and lead aircraft is between 4 and 6 

KT. Since the compression distance expands as the lead aircraft airspeed decreases and the trail 

aircraft airspeed increases, the bias is applied by decreasing the lead aircraft airspeed by half the 

bias and increasing the trail aircraft airspeed by half the bias. 

Table 3-2 and Table 3-3 show the front gate for lead aircraft approach speeds of 100 to 140 

knots equivalent airspeed (KEAS) with the trail aircraft V from 0 to 20 KEAS and with a V 

bias of 0, 4, and 6 KEAS. The values are color-coded based on the length of the front gate: 

 1500 ft ≤ Green ≤ 2500 ft

 2500 ft < Yellow ≤ 3500 ft 

 3500 ft < Red ≤ 4500 ft

 4500 ft < Purple

Table 3-2 presents this data for current generation aircraft and Table 3-3 presents this data for 

next generation aircraft. 
35 

Table 3-2: Front Gate for Current Generation Fleet 

Planned Vapp of 

Lead Aircraft 

Vapp

Variation 

Planned Vapp of Trail Aircraft Final Approach Speed 

+0 

KEAS 

+5 

KEAS 

+10 

KEAS 

+15 

KEAS 

+20 

KEAS 

100 KEAS 

0 KEAS 1500 2315 3242 4204 5201 

+4 KEAS 2166 3104 4076 5083 6125 

+6 KEAS 2557 3518 4513 5542 6606 

110 KEAS 

0 KEAS 1500 2147 2995 3882 4808 

+4 KEAS 2011 2866 3759 4690 5659 

+6 KEAS 2367 3244 4159 5112 6102 

120 KEAS 

0 KEAS 1500 1993 2779 3608 4481 

+4 KEAS 1868 2657 3488 4362 5278 

+6 KEAS 2195 3007 3860 4755 5692 

130 KEAS 

0 KEAS 1500 1851 2588 3376 4214 

+4 KEAS 1735 2471 3256 4090 4972 

+6 KEAS 2039 2799 3607 4463 5366 

140 KEAS 

0 KEAS 1500 1719 2422 3185 4009 

+4 KEAS 1610 2307 3061 3874 4745 

+6 KEAS 1895 2618 3398 4235 5128 

Table 3-3: Front Gate for Next Generation Fleet 

Planned Vapp of 

Lead Aircraft 

Vapp

Variation 

Planned Vapp of Trail Aircraft Final Approach Speed 

+0 

KEAS 

+5 

KEAS 

+10 

KEAS 

+15 

KEAS 

+20 

KEAS 

100 KEAS 

0 KEAS 1500 2120 3060 4035 5045 

+4 KEAS 1963 2914 3899 4919 5973 

+6 KEAS 2357 3331 4339 5381 6457 

110 KEAS 

0 KEAS 1500 1978 2839 3739 4678 

+4 KEAS 1834 2703 3608 4552 5534 

+6 KEAS 2192 3083 4011 4976 5979 

120 KEAS 

0 KEAS 1500 1850 2649 3491 4377 

+4 KEAS 1717 2519 3363 4250 5178 

+6 KEAS 2047 2871 3738 4646 5595 

130 KEAS 

0 KEAS 1500 1734 2484 3285 4135 

+4 KEAS 1610 2360 3157 4004 4899 

+6 KEAS 1916 2690 3511 4379 5296 

140 KEAS 

0 KEAS 1500 1628 2344 3120 3956 

+4 KEAS 1511 2221 2989 3814 4699 

+6 KEAS 1799 2535 3328 4177 5084 

The CONOPS currently identifies a minimum approach speed (Vapp) of 120 KT and a target 

capability to accommodate V of up to 20 KT [MITRE2013]. However, both values are 

identified as to-be-resolved (TBR). The tables show that for parallel, paired approach using 
36 

echelon spacing, a planned V of 20 KT requires a front gate larger than 4500 ft (0.74 NM) for 

all speeds if actual V can vary. Therefore, a planned V of 20 KT appears infeasible for the 

paired approach. For lead aircraft with Vapp ≥ 120 KT, a planned V ≤ 15 KT can be 

accommodated with a front gate of 4500 ft if the bias in actual V can be held below 6 KT. This 

front gate can also accommodate slower Vapp if planned V ≤ 10 KT. A front gate of 3500 ft can 

accommodate Vapp ≥ 120 KT and planned V ≤ 10 KT if the bias in actual V can be held below 

4 KT, which may be feasible for next generation aircraft. A front gate of 3500 ft can also handle 

all Vapp and the maximum V bias if planned V ≤ 5 KT. Overall, a front gate of 2500 feet 

covers 31% of the table cells, a front gate a 3500 ft covers 55% of the cells, and a front gate of 

4500 feet covers 77% of the cells. This study will explore the feasibility of the procedure with 

front gates of both 3500 ft, which might be achievable for planned V ≤ 10 KT with future 

avionics, and 4500 ft, which expands the pairable V to 15 KT.

3.4. The Wake-Safe Distance 

3.4.1. Modeling Wake Transport 

This study uses the wake transport model described in section A.3 of the CONOPS 

[MITRE2013]. The model performs a constant velocity transport of the wake from its generation 

point to the wake encounter zone of the trailing vehicle. The transport velocity is the sum of the 

crosswind velocity and, when below 400 ft AGL, a wake self-transport velocity of 2 knots. 

Figure 3-4 depicts the geometry that defines the distance the wake travels laterally before 

encountering the trailing vehicle.2

 The wake encounter zone is defined as a lateral distance from 

 

2

 Note that Figure 3-4 shows the geometry using the instantaneous true location of each aircraft. Applying 

the model to a given runway separation with aircraft that perform to a given total system error is discussed 

later. 

Figure 3-4: Wake Transport Model 
37 

the centerline of the trailing vehicle. This distance is defined as a safe encounter distance of 100 

feet plus the radius of the wake vortex. 3 The distance for the wake to travel is the lateral distance 

between its generation point and the wake encounter zone. 

The following equation expresses the distance to a wake encounter: 

ୣ୬ୡ୭୳୬୲ୣ୰ ൌ Ȃୱୟ୤ୣȂ୴୭୰୲ୣ୶Ȃ୴୭୰୲ୣ୶ (3-36) 

where, 

Y is the true lateral distance between aircraft, in feet. 

 Dsafe is the safe encounter distance from the trail aircraft’s centerline, it equals 100 ft.

 Rvortex is the radius of the vortex which equals (Dvortex/2). 

 Dvortex is the generation location of the vortex from the lead aircraft’s centerline. It is equal to 

( Dwingspan/8) where Dwingspan is the wingspan of the lead aircraft. 

This study will assume that the lead aircraft is a Boeing 747-400. 4 The Boeing 747-400 has a 

wingspan of 211 ft 5 in. The distance equation, therefore, reduces to: 

ܦ௢௖௡௘௨௡௧௘௥ ൌ ܻȂ ʹʹͶǤͷ݂ݐ) 3-37 (

The next part of the problem is determining the worst-case (i.e. minimum) Y for the closelyspaced parallel runway (CSPR) procedure. This is discussed in the next section. 

Dencounter is then converted to a time-to-encounter (Tencounter) by dividing Dencounter by the wake 

transport velocity (Vtransport). Vtransport is the sum of the maximum allowable crosswind (Vcrosswind) 

and, if under 400 ft AGL, the self-transport velocity (Vself-transport): 

୲୰ୟ୬ୱ୮୭୰୲ ൌୡ୰୭ୱୱ୵୧୬ୢ ൅൜

ୱୣ୪୤ି୲୰ୟ୬ୱ୮୭୰୲  ൏ ͶͲͲ


Ͳ  ൒ ͶͲͲ
 (3-38) 

The CONOPS uses a “worst-case” Vself-transport of 2 knots [MITRE2013]; however, since this study 

is looking at the wake-safe distance at the FAF, Vself-transport will be zero. For Vcrosswind, this study 

uses a worse-case value of 10 knots. 

Lastly, the longitudinal wake-free boundary is the product of the time-to-encounter (Tencounter) 

and the trail aircraft’s true speed (Vtrail). 

ܮ௪௔௞௘ି௙௥௘௘ ൌܶ௘௡௖௢௨௡௧௘௥ כܸ௧௥௔௜௟ ൌܦ௢௖௡௘௨௡௧௘௥ כ

ܸ௧௥௔௜௟

ܸ௧௥௔௡௦௣௢௥௧

(3-39) 

3.4.2. Closest Lateral Separation under Normal Operations 

The closest allowable lateral separation under normal operations (Y) determines the 

 

3

 The safe encounter distance is not the distance that avoids the wake but the distance where a wake 

encounter does not endanger the aircraft. This distance is used to maintain consistency with the analysis 

presented in the CONOPS [MITRE2013]. However, in future studies, replacing the safe encounter distance 

with the half-wingspan of the largest trail aircraft is recommended. This changes the runway separation 

calculated by the difference between the half-wingspan and 100 ft. 

4

 The Boeing 747-400 was chosen to maintain consistency with the CONOPS [MITRE2013]. Prior NASA 

studies have used the wider Boeing 747-8. 
38 

design-to, wake-free boundary for the procedure. The lateral separation between aircraft during 

the procedure is determined by the actual path each aircraft flies. The deviation of the actual path 

from the desired path is characterized by the total system error (TSE). TSE is made of three error 

components: path definition error (PDE), navigation error (NE), and flight technical error (FTE). 

PDE is the difference between the path defined by the on-board avionics and the desired path; it 

is normally negligible and can be ignored. NE is the error between the position of the aircraft 

estimated by the on-board navigation system and its actual position. FTE is the error in the 

autopilot or crew's ability to fly the path. NE and FTE are both modeled by a normal distribution; 

therefore, TSE is also modeled as a normal distribution. The TSE, NE, and FTE values presented 

here are 95% confidence bounds (1.96
). 

To date, comprehensive studies of FTE for aircraft on approach have examined a mixture of 

hand-flown and autopilot approaches using the Instrument Landing System (ILS) as the primary 

navigation aid. Thomas and Timoteo [Thomas1990] and Thomas, Timoteo, and Huang 

[Thomas1993] showed that the FTE of ILS approaches increases with distance from threshold. 

FTE exceeded 200 ft at distances greater than 8 to 10 NM from the threshold and, on final 

approach, FTE was less than 40 ft/NM from threshold. Eckstein [Eckstein2011] also depicted the 

localizer deviation of ILS approaches starting at 7 NM from threshold and computed the FTE at a 

point 3 NM from the threshold. Unlike previous work, Eckstein divided the data between handflown and autopilot approaches. The FTE of hand-flown approaches was an order of magnitude 

greater than autopilot approaches. The FTE of the autopilot approaches was less than 10 feet. 

Eckstein's study keeps open the possibility that it may be possible for the paired approach 

procedure to be performed from start to finish using only the ILS with the autopilot engaged. 

However, until a comprehensive analysis of autopilot only approaches with ILS have been 

conducted, this study will proceed under the assumption that the aircraft pair performs an RNP or 

GPS RNAV approach to the FAF (though each aircraft may transition to the ILS navaid 

afterwards). This study uses two sources of TSE or FTE data for RNAV or RNP approach to 

represent current generation and next generation aircraft. Murphy presented data from Air France 

showing that the TSE of aircraft on RNP approach was 59 m (194 ft) at the time they disengaged 

the autopilot [Murphy2010]. Passerini provides data on the Quantas fleet of Boeing 737-800s 

that measure the FTE of RNP approaches at 0.02 NM (37 m or 122 ft) [Passerini2011]. The TSE 

value of 59 m will be used to represent RNP or RNAV performance in the current generation 

aircraft. The FTE value of 37 m will be used to represent next generation aircraft. 

This study assumes that a GPS-based navigation system or equivalent will be used to estimate 

the position of the aircraft. Current generation aircraft are assumed to have an autonomous GPS 

system. RTCA DO-242A Appendix J.3.3 characterizes the lateral NE of autonomous GPS as 

12.5 m; however, in an unpublished work used for development of the CONOPS, Eftekari 

[Eftekari 2008] identifies the lateral NE of autonomous GPS as 8 m (26 ft) based on observations 

from ADS-B flight tests at the FAA Technical Center in July 2007. This study will use the 

smaller 8 m NE. Next generation aircraft are assumed to have a Wide-Area Augmentation 

System (WAAS) GPS system or better. RTCA DO-242A Appendix J.3.3 characterizes WAAS 

GPS with a lateral NE of 3.5 m (12 ft) [RTCA2002]. 

Table 3-4: Total System Error of Aircraft Fleets 

TSE FTE NE Event Duration Events/Procedure 

Current Generation 59.0 m 58.5 m 8.0 m 70 s 6 

Next Generation 37.2 m 37.0 m 3.5 m 70 s 6 
39 

The final TSE, FTE, and NE values are summarized in Table 3-4. Recognize that these errors 

are defined for a sample. To ascertain their affect on the maximum deviation over the entire 

approach path during normal operations, it is necessary to determine how many samples will 

occur during the course of the procedure. Aircraft do not suddenly jump from one error to the 

next, the error occurs as a random walk with a period in distance or time. Boeing identifies the 

period between independent FTE events at 70 seconds [Boeing2012]. For GPS receivers, the 

period between independent navigation error events is four to eight minutes. However, because 

NE is much smaller than FTE, the period of NE events is made equal to FTE events for 

simplicity. Thus, the period of independent events for TSE, FTE, and NE are each set at 70 

seconds for both current and next-generation aircraft. The paired-approach procedure can have a 

duration of up to six minutes at KSFO based on approach path geometry and speed schedule. 

Therefore, six independent events can occur during the course of the procedure. 

Having established the lateral error characteristics of the aircraft, these characteristics are 

applied to a definition of normal operation in order to determine the bounds on lateral deviation. 

Normal operation is defined by the alert rate and alert integrity for the participating aircraft. 

Independent monitoring of the lead aircraft by the trail is not practical because ADS-B 

uncertainties are large relative to the lateral path separation (see section 3.4.3). Therefore, each 

aircraft is responsible for monitoring its own lateral deviation. Aircraft are capable of monitoring 

their lateral FTE directly. The alert rate is assumed to be 10-4 alerts per aircraft per procedure 

without a blunder. Because lateral FTE is being monitored but lateral NE cannot be monitored. 

The aircraft can exceed its alerting bounds without an alert. Therefore, the containment bound 

for normal operation is also defined by an alert integrity criterion equivalent to RNP integrity 

requirements of 99.999% containment per hour. 

First, the alerting bounds are computed. Part of the per-aircraft, per-procedure alert rate 

(araircraft) is allocated to alerted hardware failure (aravionics) and part of this rate is allocated to 

aircraft performance (arFTE). It is assumed that the hardware will have an alerted failure at a rate 

of 5 x 10-5/hr. This alerted failure rate is taken from the continuity requirement for RNP of 

99.99% per hour and assumes that half the probability of continuity failure is due to alerted 

hardware failure. It is also assumed that the hardware alert rate is linear with time and reduces to 

aravionics = 5 x 10-6/procedure. The remaining alert rate due to aircraft performance is 9.5 x 10-5

per procedure. The equivalent alert rate per FTE sample (arFTE) is given by Equation 3-41 where 

nFTE is the number of FTE samples per procedure. This equation is derived from the probability 

of no alert (1 - araircraft ) being equal to the combined probability of no hardware failure (1 - 

aravionics ) and the probability that the aircraft will not exceed the alerting bound (1 - arFTE) for each 

of the six FTE samples (Equation 3-40). The resulting per FTE sample alert rate is 1.6 x 10-5. 

൫ͳ െ ܽݎ௙௔௥௖௥௜௔௧൯ ൌ ሺͳ െ ܽݎ௔௩௜௢௡௜௖௦ሻሺͳ െ ܽݎி்ாሻ௡ಷ೅ಶ (3-40) 

ܽݎி்ா ൌͳെ൬ͳ െ ܽݎ௙௔௥௖௥௜௔௧

ͳ െ ܽݎ௔௩௜௢௡௜௖௦

൰

ଵ ௡Τ ಷ೅ಶ

(3-41) 

Using arFTE, the FTE bound that triggers an alert is determined from the normal distribution. 

Though deviations to only one side of the aircraft adversely affect the lateral separation between 

aircraft, the FTE bound will be computed for alerting on either side of the aircraft path. This is 

simpler from a procedural perspective. There is no need to identify the aircraft as being on the 

left or right runway and the alerting remains similar to loss of containment alerts for RNP. The 

following equation computes the alerting bound (yalert) where erf-1 is the inverse error function: 
40 

ܧܶܨ ൌ ௧௔௟௘௥ݕ

ͳǤͻ͸ ξʹ݁ݎ݂ିଵሺʹܽݎி்ா െ ͳሻ (3-42) 

Next, the alert integrity bound is computed. This bound is designed to be equivalent to the 

RNP requirement of 99.999% containment per hour per aircraft, i.e. upaircraft = 10-5 / hr. The study 

assumes that integrity loss is divided equally between un-alerted hardware failure (upavionics) and 

position uncertainty (upTSE). Therefore, both contributions have a probability of 5 x 10-6 / hr. 

This probability is further reduced to a probability of upavionics = upTSE = 9.7 x 10-8 per FTE 

sample. The resulting probability of un-alerted containment loss during the procedure 

(accounting for both aircraft) is 1.75 x 10-6. 

The quantity upTSE represents the probability that the true position of aircraft (ytrue) is beyond 

the integrity bound (yintegrity) when the aircraft does not generate an alert. This occurs when the 

navigation error is of a sufficient adverse value to place the estimated position of the aircraft 

(yFTE) below the alerting bound yalert. Because of the symmetry in the normal distribution of 

lateral deviation, upTSE can be formulated as twice the probability, on one side of the path, that 

ytrue will be outside yintegrity when |yFTE| < yalert. Thus, one constructs the combined probability that 

the navigation error (yNE) is greater than yintegrity - yFTE for all yFTE in the range [-yalert, yalert]. This 

is represented by the dual integral below: 

݌ݑ்ௌா ൌ ʹ න න ൮ ݁

ି ௬ಷ೅ಶ

మ

ଶఙಷ೅ಶ

ξʹߨߪி்ா൲ ൮ ݁

ି ௬ಿಶ

మ

ଶఙಿಶ

ோ൲ߪߨʹξ

ஶ

௬೔೙೟೐೒ೝ೔೟೤ି௬ಷ೅ಶ

௬ೌ೗೐ೝ೟

ି௬ೌ೗೐ೝ೟

݀ݕோ݀ݕி்ா (3-43) 

where 
FTE and 
NE are the standard deviation of the FTE and NE errors, respectively. 

Recognizing that the inner integral is equivalent to an integral with the range [-λ, yFTE - yintegrity], 

the double integral reduces to: 

݌ݑ்ௌா ൌ ʹන

ۉ

ۈ

݁ቆۇ

ି ௬ಷ೅ಶ

మ

ଶఙಷ೅ಶቇ ݁ݎ݂ ቆ

ݕ௡௜௧௘௚௥௜௧௬ െ ݕி்ா

ξʹߪோ ቇ

ی ா்ிߪߨʹξʹ

ۋ

೟ೝ೐೗ೌ௬ ۊ

ି௬ೌ೗೐ೝ೟

݀ݕி்ா (3-44) 

where erf() is the error function. This outer integral cannot be further reduced and must be 

resolved numerically. Therefore, the yintegrity value that corresponds with a upTSE value is solved 

iteratively using root-finding methods. 

The design-to lateral separation bounds for each aircraft are the larger of yalert and yintegrity. 

Table 3-5 summarizes the probabilities used to define normal operation in this section. Table 3-6 

shows the values of 
FTE, 
NE, yalert and yintegrity, rounded up to the nearest foot, for current and 

next generation aircraft and how these values affect required path separation. The required path 

separation is computed from Equation 3-37 where Y = 2 x max(yalert, yintegrity), i.e. the worst case 

is when both aircraft deviate toward each other by the design-to separation bounds. The path 

separation values shown here merely depict the spacing at which the wake vortex does not need 

to move to encounter the trail aircraft if both aircraft are positioned at their integrity bounds. A 

feasible runway spacing must be much greater than the value shown. These results show that 

neither current nor next generation aircraft can accommodate 750 ft runway spacing with a 

parallel echelon procedure. The question is how much spacing is needed to enable the procedure. 
41 

To answer this question it is necessary to determine the length of the echelon window based on 

expected longitudinal deviation during normal operation. 

Table 3-5: Summary of Probabilities Defining Normal Lateral Deviation 

Total Alert Rate (araircraft) 10-4 / aircraft / procedure 

 Hardware Alert Rate (aravionics) 5 x 10-6 / procedure 

Position Alert Rate (arFTE) 9.5 x 10-5 / procedure 

1.583 x 10-5 / FTE sample 

Total Un-alerted Lateral Containment Loss (upprocedure) 2.3 x 10-6 / procedure 

Loss due to un-alerted hardware failure (upavionics) 5.8 x 10-7 / procedure 

9.7 x 10-8 / FTE sample 

Un-alerted loss due to position uncertainty (upTSE) 5.8 x 10-7 / procedure 

9.7 x 10-8 / FTE sample 

Number of FTE samples per procedure (nFTE) 6 

Duration of FTE sample 70 seconds 

Table 3-6: Lateral Deviation Parameters under Normal Operation 

Current Generation Next Generation 


FTE 98 ft 62 ft 


NE 13.4 ft 5.9 ft 

yalert 408 ft 258 ft 

yintegrity 438 ft 271 ft 

path separation >> 1100 ft >> 767 ft 

3.4.3. Minimum Longitudinal Window under Normal Operations 

The minimum longitudinal window during normal operations is defined similarly to the 

expected lateral deviation during normal operations in the previous section. Normal operation is 

defined by a desired alert rate and an alert integrity criterion similar to lateral operation. Here, 

the trail aircraft monitors its position relative to the lead aircraft and attempts to maintain a 

desired separation. As with lateral monitoring, the desired alert rate is to be no greater than 10-4

per procedure. Alert integrity due to position uncertainty will also be maintained to the same 

requirement as RNP integrity. 

One difference in the longitudinal monitoring is that the longitudinal separation is subject to 

both ADS-B OUT errors of lead aircraft and the longitudinal TSE of both aircraft. Longitudinal 

TSE and its component FTE and NE are assumed equal to the lateral TSE, FTE, and NE. The 

same similarity holds for the duration of a longitudinal TSE event (70 seconds) and the number of 

longitudinal TSE events in a procedure (6). ADS-B OUT data is assumed to be derived from the 

lead aircraft's navigation solution. Therefore, the variation in ADS-B reported position has three 

components, navigation error (NE), latency compensation error, and uncompensated latency 

error. The latter two are combined into an ADS-B latency error (ALE). The combination of all 

three components is the estimated position uncertainty (EPU) of the ADS-B output. ADS-B EPU 

is normally reported as a 2-D radius uncertainty and is assumed to conform to a Rayleigh 

distribution. Therefore, the standard deviation of uncertainty in longitudinal position (
EPU) is 

EPU/2.447. Current Generation aircraft are assumed to have an EPU of 92.6 m, which conforms 

to the FAA ADS-B rule [FAA2010]. Next Generation aircraft are assumed to have an EPU of 10 
42 

m associated with a Navigation Accuracy Category for Position (NACp) value of 10. These 

errors are used to determine the variation in observed separation to the planned separation. The 

observed separation is the difference in the observed position of the lead aircraft (via ADS-B 

OUT) and the observed position of the trail aircraft (via its navigation system). The ADS-B OUT 

report represents the lead aircraft's observation of its own longitudinal FTE plus the ALE. The 

trail aircraft uses observation of its own position to monitor its longitudinal flight technical error 

(FTE). Therefore, the variation in observed longitudinal separation is a combination of both 

aircraft's FTE and the ALE of the lead aircraft: 

ߪ௕௢௦ ൌ ටሺߪி்ாሻ௟௘௔ௗ

ଶ ൅ ሺߪி்ாሻ௧௥௔௜௟

ଶ ൅ ሺߪ௅஺ாሻ௟௘௔ௗ

ଶ (3-45) 

The standard deviation of ALE is computed by subtracting the contribution of NE to EPU: 

ߪ௅஺ா ൌ ටߪா௉௎

ଶ െ ߪோଶ (3-46) 

The longitudinal alert uses similar probability assumptions to the lateral alert. The 

longitudinal alert rate is 10-4 per procedure with alerted hardware failures occurring with a 

probability of 5 x 10-6 / procedure. Therefore, alerts due to separation performance (arsep) are 9.5 

x 10-5 / procedure or 1.583 x 10-5 / FTE sample. There are two contributors to variation in 

separation performance. The first is the variation in observed separation. The second is the 

response time (tdelay) of the trail aircraft to the lead aircraft. During that time, the airspeed 

difference between the two aircraft can vary. For this study, the longitudinal airspeed difference 

is assumed to vary with a standard deviation (
V) of 3.4 KT (5.7 ft/s or 1.7 m/s); this number is 

derived from an assumed 3 KT standard deviation in the horizontal airspeed of each aircraft. The 

equivalent spacial variation (
x) is the product of tdelay and 
V. For current generation aircraft, 


x is 29 ft and, for next generation aircraft, 
x is 20 ft. Therefore the total variation in 

separation performance (
sep) is: 

ߪ௦௘௣ ൌ ටߪ௕௢௦

ଶ ൅ ߪο௫

ଶ (3-47) 

The longitudinal alerting bound (xalert) is therefore: 

ݔ௥௘௟௔௧ ൌ ߪ௦௘௣ ξʹ݁ݎ݂ିଵ൫ʹܽݎ௦௘௣ െ ͳ൯ (3-48) 

The integrity of the longitudinal alert also uses similar probability assumptions to the lateral 

alert. Un-alerted longitudinal containment loss is 10-5 / hr with the contributions of un-alerted 

hardware failure (upavionics) and position uncertainty (upTSE) both at 9.7 x 10-8 per FTE sample. 

Derivation of the integrity bound (xintegrity) is the same as for the lateral integrity bound with the 

following differences. The two PDFs involved are the PDF of separation performance (and thus a 

function of 
sep) and the PDF of navigation uncertainty. However, the navigation uncertainty in 

this case is the combined navigation uncertainty of the two aircraft. Since the navigation 

uncertainty of the two aircraft is assumed equal, the PDF of the combined navigation uncertainty 

is a function of 2 
NE. The resulting equation for xintegrity is: 
43 

݌ݑ்ௌா ൌ ʹන

ۉ

ۈ

ۈ

ۇ൭݁ି ௫ೞ೐೛

మ

ଶఙೞ೐೛൱ ݁ݎ݂ ቀݕ௡௜௧௘௚௥௜௧௬ െ ݕி்ா

ʹߪோ ቁ 

ی ௣௘௦ߪߨʹξʹ

ۋ

ۋ

ۊ ೟ೝ೐೗ೌ௫

ି௫ೌ೗೐ೝ೟

 (3-49) ௣௘௦ݔ݀

The design-to longitudinal window for the trail aircraft (xwindow) is double the larger of yalert

and yintegrity. Table 3-7 summarizes the probabilities used to define normal operation in this 

section. Table 3-8 shows the values of 
sep, 
NE, xalert, xintegrity, and xwindow, rounded up to the 

nearest foot, for current and next generation aircraft. 

Table 3-7: Summary of Probabilities Defining Normal Longitudinal Deviation 

Total Alert Rate (araircraft) 10-4 / procedure 

 Hardware Alert Rate (aravionics) 5 x 10-6 / procedure 

Position Alert Rate (arFTE) 9.5 x 10-5 / procedure 

1.583 x 10-5 / FTE sample 

Total Un-alerted Lateral Containment Loss (upprocedure) 1.17 x 10-6 / procedure 

Loss due to un-alerted hardware failure (upavionics) 5.8 x 10-7 / procedure 

9.7 x 10-8 / FTE sample 

Un-alerted loss due to position uncertainty (upTSE) 5.8 x 10-7 / procedure 

9.7 x 10-8 / FTE sample 

Number of FTE samples per procedure (nFTE) 6 

Duration of FTE sample 70 seconds 

Table 3-8: Longitudinal Deviation Parameters under Normal Operation 

Current Generation Next Generation 


sep 194 ft 97 ft 


NE 13.4 ft 5.9 ft 

xalert 806 ft 403 ft 

xintegrity 842 ft 418 ft 

xwindow 1684 ft 836 ft 

3.4.4. Calculating the Wake-Safe Distance 

The required wake-safe distance (Lwake-free) is a simple summation of the longitudinal window 

(xwindow) and the front-gate (xfront-gate): 

ܮ௪௔௞௘ି௙௥௘௘ ൌ ݔ௡௢௥௙௧ି௚௔௧௘ ൅ ݔ௪௜௡ௗ௢௪ (3-50) 

3.5. Determining Feasible Runway Separation and Conclusions 

The feasible runway separation can be computed as a function of the required wake-safe 

distance (Lwake-free) and the lateral integrity (yintegrity). First, the required wake transport distance 

(Dencounter) is computed by inverting Equation 3-39: 
44 

ܦ௢௖௡௘௨௡௧௘௥ ൌ ܮ௪௔௞௘ି௙௥௘௘

ܸ௧௥௔௡௦௣௢௥௧

ܸ௧௥௔௜௟

(3-51) 

Before the FAF, the worst-case wake transport velocity (Vtransport) is equal to the maximum 

adverse crosswind of 10 KT. The trail aircraft velocity (Vtrail) is nominally 180 KT but we will 

assume that variation in speed performance can decrease it to a minimum of 177 KT. 

With Dencounter computed, the minimum runway separation (Yrunway) that is feasible for the 

procedure is: 

οܻ௥௨௡௪௔௬ ൌ ʹʹͶǤͷ݂ݐ൅ ܦ௢௖௡௘௨௡௧௘௥ ൅ ʹݕ௡௜௧௘௚௥௜௧௬ (3-52) 

Table 3-9 shows the results, rounded up to the nearest foot, for current and next generation 

aircraft: 

Table 3-9: Feasible Separation Geometry 

Current Generation Next Generation 

xfront-gate 3500 ft 4500 ft 3500 ft 4500 ft 

Lwake-free 5184 ft 6184 ft 4336 ft 5336 ft 

Dencounter 293 ft 350 ft 245 ft 302 ft 

Yrunway 1393 ft 1450 ft 1010 ft 1066 ft 

As the results show, current generation aircraft cannot conduct paired approaches on parallel 

paths using echelon spacing on runways less than ~1400 ft apart and next-generation aircraft 

cannot conduct the paired approach on runways less than ~1050 ft apart. In both cases, the 

minimum spacing increases by about 50 feet if the front gate must be 4500 ft at the FAF. These 

runway separations are the same as in the initial estimates for which passing becomes safe using 

the SAPA procedure (see Section 2.1.3.1). Therefore, for parallel approaches, the pairedapproach with echelon spacing does not offer an increase in airports where the procedure is 

feasible. Furthermore, since the SAPA approach allows passing, SAPA can more easily 

accommodate larger differences in approach speed and lower minimum approach speeds. 

However, the echelon spacing approach should maintain a cost advantage for new or modified 

equipage since it requires only monitoring of lateral and longitudinal bounds while SAPA 

requires an alerting algorithm and an automated escape maneuver. Nevertheless, the above 

analysis used a simple wake transport model and the feasible runway separation for echelon 

spacing may grow if higher-fidelity models further constrict the wake-free distance. Such a case 

would further tilt in favor of SAPA over echelon spacing. 

What aircraft performance would be necessary to enable operation at runways separated by 

750 ft? Runway separation has the most sensitivity to the FTE of the participating aircraft. The 

FTE of the next generation aircraft was reduced until the runway separation fell at or below 750 

feet for both front gates of 3500 and 4500 ft. Table 3-10 shows the results: 
45 

Table 3-10: Performance Required to Enable Paired-Approach for 750ft Runway Spacing 

xfront-gate 3500 ft 4500 ft 

FTE (95%) 63 ft (19.2 m) 50 ft (15.3 m) 

yalert 134 ft 107 ft 

yintegrity 148 ft 122 ft 

xalert 255 ft 228 ft 

xintegrity 271 ft 245 ft 

Lwake-free 4042 ft 4989 ft 

Dencounter 229 ft 282 ft 

Yrunway 749 ft 749 ft 

As the table shows, aircraft FTE must decrease by half in next generation aircraft to open the 

paired approach procedure for 750 foot runway spacing. The feasibility of achieving such 

performance on a straight approach from loss of vertical separation to the threshold is 

questionable. However, aircraft performing CAT IIIB ILS approaches routinely achieve this 

level of performance within the inner marker where the ILS navigation error is similar to the 

assumed WAAS GPS navigation error of 3.5 m lateral. Nevertheless, many aspects of flight 

within the inner marker (including airspeed and winds) are more favorable to controlling path 

deviation than flight beyond the FAF (outer marker). More data on actual straight-in approaches 

using state-of-the-art autopilot and autothrottle systems will be needed to better characterize the 

total system error that can be routinely achieved. 

One final note, the alerting rates in this analysis are cumulative. With each aircraft having a 

10-4 rate of lateral alerts and the trail aircraft having a 10-4 rate of longitudinal separation alerts, 

the total breakout rate for the procedure is approximately 3 in 10,000 procedures. Any further 

decrease in this total will require wider runway spacing or improved aircraft path performance. 
46 

4. Towards Lower Visibility Minima 

The MITRE echelon procedure [MITRE2013] takes advantage of an offset leg that merges 

about 1 NM from the runway threshold. This is necessary so that the final 1 NM parallel landing 

can be achieved using VFR rules. In this section we consider the potential of an IFR landing if 

the ALAS algorithm were used. In our earlier work, we found that the aircraft could not be 

allowed to pass each other for a runway spacing of 750 ft. But there are two reasons why the 

ALAS alerting algorithm may enable lower visibility minima when used in conjunction with the 

MITRE echelon concept: 

1. The total system error (TSE) is significantly smaller for the last 1 NM of the 

approach and therefore the ALAS alerting algorithm will be more effective here. 

2. The MITRE procedure constrains the aircraft to be longitudinally separated at the 

FAF which will provide some longitudinal separation at the merge point even after 

much ground speed compression. 

The tAlas simulation was configured to simulate the parallel landing after the merge point: 

Different simulations were run varying the parameter ClosestInitSepAllowed over range from 

0 ft to 250 ft and varying the parameter maximumGsDifferential over range from 0 KT to 30 KT. 

Because these simualtion runs begin after the turn, they are equally valid for echelon spacing 

on parallel approaches. 

4.1. Experimental Results Using Monte Carlo Simulation Starting 1 NM From Runway 

The tAlas simulation was run in Monte Carlo mode varying runway separations, initial 

separation longitudinally, and the maximum ground speed difference. In all cases the intruder 

and ownship were given starting positions in the range of 1 NM to 1.5 NM. 

We begin with a baseline result obtained by running the tAlas simulation with alerting and the 

escape maneuver disabled. In this simulation, the ownship was always in the rear position. The 

results are given in Table 4-1. Note that acceptable probabilities are indicated in blue font and 

unacceptable probabilities are indicated in red. 

ClosestInitSepAllowed 

1 NM 

Figure 4-1: Parallel landing after the merge point 
47 

Table 4-1: Results for 750 ft Runway Spacing, No Escape Maneuver 

Initial Longitudinal 

Separation (at 1 NM) 

Max GS 

Difference 

Probability 

250 ft 5 2.34E-02  4.78E-05 

250 ft 10 3.65E-02  5.93E-05 

250 ft 15 4.49E-02  6.55E-05 

250 ft 20 5.00E-02  6.89E-05 

500 ft 5 1.63E-03  1.27E-05 

500 ft 10 1.18E-02  3.42E-05 

500 ft 15 2.33E-02  4.77E-05 

500 ft 20 3.15E-02  5.53E-05 

750 ft 5 4.38E-07  1.48E-07 

750 ft 10 7.40E-04  8.60E-06 

750 ft 15 7.01E-03  2.64E-05 

750 ft 20 1.52E-02  3.87E-05 

1250 ft 5 4.38E-07  1.48E-07 

1250 ft 10 4.38E-07  1.48E-07 

1250 ft 15 8.38E-07  2.49E-07 

1250 ft 20 5.87E-04  7.66E-06 

1500 ft 5 4.38E-07  1.48E-07 

1500 ft 10 4.38E-07  1.48E-07 

1500 ft 15 4.38E-07  1.48E-07 

1500 ft 20 3.34E-06  5.58E-07 

The largest ground speed differential for each initial longitudinal separation is given in Table 

4-2. 

Table 4-2: Summary of Results for 750 ft Runway Spacing, No Escape Maneuver 

Initial Longitudinal 

Separation (at 1 NM) 

Largest GS 

Difference that 

meets Target 

Probability 

250 ft --- 

750 ft 5 

1250 ft 15 

1500 ft 20 

Clearly, without an alerting algorithm and an escape maneuver, there must be an initial 

longitudinal separation of at least 1500 ft at the merge point to accommodate ground speed 
48 

differences up to 20 KT. This is achieved procedurally in the MITRE concept of operations by 

constraining the aircraft to be 4000+ ft apart longitudinally at the FAF and disallowing pairings 

with large ground speed differences. 

We next explored the potential of deploying the ALAS alerting algorithm on the final leg of 

the approach that begins 1 NM from the runway threshold. In these runs we have constrained the 

samples so that the ownship was always in the rear position. We note that the ALAS runway 

conformance algorithm could be used during the offset approach, but the full collision algorithm 

would likely generate a large number of false alarms while one aircraft was on the offset leg. 

In Table 4-3 we show the impact of the ALAS algorithm when used on this final leg. 

Table 4-3: Summary of Results for 750 ft Runway Spacing (Final Parallel Leg) 

Initial Longitudinal 

Separation 

Max GS 

Difference 

Probability Minimum Distance (ft) 

0 ft 5 4.38E-07  1.48E-07 287.91 

0 ft 10 5.38E-07  1.79E-07 237.37 

0 ft 15 5.38E-07  1.79E-07 264.17 

0 ft 20 6.38E-07  2.05E-07 291.13 

250 ft 5 4.38E-07  1.48E-07 287.91 

250 ft 10 5.38E-07  1.79E-07 264.17 

250 ft 15 5.38E-07  1.79E-07 246.49 

250 ft 20 5.38E-07  1.79E-07 291.13 

The ALAS alerting system is especially effective here because the total system error is smaller 

nearer the runway. 

The results are very promising but they critically depend upon having both a turn and vertical 

acceleration in the escape maneuver. Also, the analysis assumes that the turn of the ownship 

from the offset path to the centerline doesn't increase the TSE in the final 1 NM. In the next 

section we explore the impact of disabling the turn component of the escape maneuver. 

4.2. A Closer Look at the SAPA Escape Maneuver When Near to the Ground 

In this section we will provide a limited look at the problem of executing the escape maneuver 

when the aircraft is very near to the ground. Because of near ground obstacles, we could imagine 

that below a certain altitude, the aggressive turn component of the escape maneuver must be 

turned off, and only the vertical climb will be allowed to occur. We ran the tAlas simulation for a 

1050 ft runway separation for the SAPA procedure. We turned off the turn component at 

different altitudes and measured the collision probability. 

In Table 4-4 we present the probability of a collision as a function of the cutoff altitude where 

the turn component of the escape maneuver is disengaged. 
49 

Table 4-4: Simulation Runs for 1050 ft Runway using Escape Maneuver with No Turn 

Cutoff 

Altitude (ft) 

ADS-B 

Latency (s) 

Probability (400 ft) Probability (large 

cylinder) 

Minimum 

Distance (ft) 

0 1.5 9.84E-06  9.81E-07 4.38E-07  1.48E-07 316.55

50 1.5 1.99E-05  1.40E-06 1.44E-06  3.49E-07 163.95

100 1.5 2.00E-04  4.47E-06 1.27E-05  1.12E-06 128.78

200 1.5 1.64E-03  1.28E-05 9.71E-05  3.11E-06 123.07

300 1.5 3.72E-03  1.92E-05 2.15E-04  4.64E-06 119.49

The results are drastically different than those obtained with the turn component included. 

The reason for this difference is seen in the following failure case. Here, the blunder occurs near 

the ground (below 300 ft) and the turn component of the escape maneuver was disabled and 

therefore the horizontal view shows the ownship continuing to follow the centerline. 

The vertical view shows that the intruder levels out and by the time the alert occurs and the 

climb maneuver engages, the ownship is well below the intruder. The ownship then climbs back 

through the path of the intruder. 

In this trial, the blunder started at time 117 (marked by circle) and the red alert occurred 3.0 

seconds later. The point of closest approach is colored in orange which occurred at time 131.5. 

The ownship aircraft performed a vertical climb, but no turn because the blundering aircraft was 

Motion 

Motion 

Figure 4-2: Escape maneuver near the ground (Top View) 

Figure 4-3: Escape maneuver near the ground (Side View) 
50 

currently located at 275 ft AGL. In this case the blunder was a level-out blunder and was slightly 

above the ownship. By the time the ownship maneuvers, it descends below the level out altitude 

of the intruder and then climbs back up into a loss of separation: (H: 232.95 ft, V: 86.75 ft). If the 

turn were enabled, a loss of separation would not have occurred here. 

4.3. A First Look at an Intelligent Escape Maneuver 

The escape maneuver examined in the previous subsection is clearly inadequate. However, an 

escape maneuver that is different depending on the available ownship and traffic state vectors 

may be able to remedy the problem. There are many avenues to pursue, but the following two 

approaches may be a part of the solution: 

1. Use the throttle to increase ground speed rather than altitude for a short time. 

2. Delay the vertical climb until sufficient horizontal separation has been achieved. 

This strategy is only used when the intruder is longitudinally close to the ownship and the 

intruder is above the ownship in altitude. We have performed some very preliminary simulations 

where a ground speed acceleration of 4 m/s2

 used in conjunction with a delayed vertical ascent. 

This alternate maneuver was only used when the intruder was longitudinally within 350 ft and at 

least 20 ft above the ownship in altitude. The ground speed acceleration continues until 250 KT 

was reached. The vertical climb was delayed about 8 seconds. 

The table shows that if the turn was not disengaged until 100 ft AGL, then this strategy has a 

good potential of working. In future work, we will look for ways to improve the intelligent 

escape maneuver further and perhaps raise the altitude further where the turn component can be 

turned off. 

Table 4-5: Simulation Runs for 1050 ft Runway using Intelligent Maneuver with No Turn 

Cutoff 

Altitude (ft) 

ADS-B 

Latency (s) 

Probability (400 ft) Probability (large 

cylinder) 

Minimum 

Distance (ft) 

0 1.5 9.84E-06  9.81E-07 4.38E-07  1.48E-07 316.55

50 1.5 1.02E-05  1.00E-06 5.38E-07  1.79E-07 200.30

100 1.5 4.50E-05  2.12E-06 2.44E-06  4.71E-07 150.96

150 1.5 2.63E-04  5.13E-06 1.38E-05  1.17E-06 150.96

200 1.5 7.20E-04  8.48E-06 3.76E-05  1.93E-06 140.87

300 1.5 1.86E-03  1.36E-05 9.65E-05  3.10E-06 134.27

4.4. Modifying the Offset Paired-Approach to Enable Lower Decision Minima 

The offset paired approach in the CONOPS is currently defined at KSFO with a minimum 

descent altitude (MDA) of 363 MSL (350 AGL) and a decision height (DH) of 200 ft (CAT I). 

This work looked at the modifications to the offset paired approach that would enable CAT II or 

CAT III A/B approach minima. The instrument landing system (ILS) remains the only 

operational technology in the near term to enable CAT II or CAT III A/B approaches. Therefore, 

this study examined the path stability of the trail aircraft at heights of 200 ft, 100 ft, and 50 ft 

AGL after the aircraft turned onto the extended runway centerline to capture the localizer. The 
51 

intercept point of the offset path with the extended centerline was varied and set at heights along 

the glidepath of 370 ft, 587 ft, 730 ft, and 833 ft. The first intercept height is 1 NM from the 

threshold and allows the fastest aircraft to turn onto the centerline above the 200 ft DH. The 

heights in between approximately correspond to turns completed by the slowest aircraft at 

distances of 1 NM and 1.5 NM from the 200 ft DH. The 833 ft height is the highest intercept 

height that allows the fastest aircraft to initiate the turn onto centerline after the stabilized 

approach point (SAP). 

The high-fidelity transport-class aircraft simulation in Langley's Cockpit Motion Facility 

(CMF) was used to assess the FTE of aircraft at each of the decision heights. To perform a 

Monte-Carlo analysis with the high-fidelity simulation, it was necessary to configure the flight 

automation differently from the expected procedure design but try to maintain similar lateral 

deviation errors. In the modified offset paired-approach procedure, the trail aircraft is expected 

to fly the offset path as an RNP or RNAV(GPS) leg as described in the CONOPS. This offset 

path is automated by the flight management computer (FMC). The FMC then executes the turn 

from the offset leg onto the centerline. When the turn nears completion, the localizer and 

approach modes will be armed either manually by the crew or automatically by the FMC (which 

may require equipage modifications). The crew will then manage the flight in accordance with 

procedures for CAT I, CAT II, CAT IIIA, or CAT IIIB approach as normal. The CMF simulation 

utilizes a hardware FMC; therefore, it is not practical to include the FMC in a Monte-Carlo 

execution of the simulation. Instead, the offset path was automated using a localizer type 

directional aide (LDA) under localizer mode (LOC) for lateral flight with vertical-speed mode 

(VERT SPD) used to automate flight along the glidepath. The turn was automated using heading 

select mode (HDG SEL). Near completion of the turn, the simulation changed the ILS frequency 

to the runway ILS and armed both localizer and approach mode using delays as if these modes 

were manually armed by the crew. To stimulate flight technical errors in the aircraft, navigation 

errors were enabled for both the LDA and runway localizer. However, to ensure that data was 

collected at the same distance from the runway threshold, errors were not enabled for vertical 

flight. For similar reasons and to isolate the effects of navigation error as the primary cause of 

lateral deviation, winds, atmospheric disturbances, and errors in sensed airspeed were not 

enabled. The signal-in-space error for the runway localizer was set to the navigation error limits 

of a CAT III ILS for all runs. For the LDA, two signal-in-space errors were used. The navigation 

error limits of a CAT III ILS were used to examine path stability when the navigation error is the 

same on both the offset path and extended centerline. The navigation error limits of a CAT I ILS 

were used to examine path stability when the navigation error is larger on the offset path than the 

extended centerline. The numerical parameters for the CAT III and CAT I localizer errors were 

derived from data in table 13.3 of Kayton and Fried [Kayton1997]. 

For each combination of intercept height and localizer navigation error, 6000 runs were 

performed. These runs included six final approach speeds of 122 KN, 130 KT, 138 KT, 145 KT, 

153 KT, and 160 KT, each of which are associated with a 10 ton increase in aircraft landing 

weight. These speed selections were combined with 1000 random seeds for the localizer 

navigation error. The simulation was configured for landings at KSFO RWY28R using the 

published runway and runway ILS geometry. Geometry of the LDA was derived by rotating the 

RWY28R ILS about the intercept point by the offset angle of 3. Flights began at an altitude of 

2600 ft and a commanded speed of 180 KT. Flights decelerated to their final approach speed 

starting at the FAF (1800 AGL). Characteristics of the simulation are summarized in Table 4-6. 
52 

Table 4-6 Simulation Parameters for Modified Offset Approach 

Final Approach Speeds 122 KT, 130 KT, 138 KT, 145 KT, 153 KT, 

160 KT 

Landing weights5 80T, 90T, 100T, 110T, 120T, 130T 

Intercept height of offset path with centerline 

(AGL) 

370 ft, 587 ft, 730 ft, 833 ft 

LDA offset 3

CAT III Localizer Navigation Error (95%) 0.0525

CAT I Localizer Navigation Error (95%) 0.1642

Initial Altitude (AGL) 2600 ft 

Initial Speed (EAS) 180 KT 

Glidepath angle 3

FAF height (AGL) 1800 ft 

Number of runs per trial 6000 

The simulation results are show in Table 4-7. To interpret the results, the maximum safe TSE 

at the 50 ft decision height (CAT IIIB) is ±27 ft, taken from table 13.2 of Kayton and Fried 

[Kayton1997]. The maximum safe TSE for the 100 ft and 200 ft DH is set at ±35 ft and ±50 ft, 

respectively, to accommodate expected increase in TSE with distance from threshold for an ILS 

approach. In all cases, TSE at the 200 ft DH improved as the intercept point moved further away 

from the runway threshold. TSE at 100 ft DH and 50 ft DH reach their minimums at the intercept 

height of 730 ft. For the CAT I LDA to CAT III ILS, which best resembles modification of the 

paired-approach described in the CONOPS, the aircraft cannot achieve sufficient stability on the 

localizer path for landing at any decision height when the intercept height is 370 ft. A couple of 

the behaviors observed in the simulation work against achievement of path stability this late in 

the approach. First, the autopilot of the simulated aircraft takes eight seconds to engage LOC 

mode from the time LOC is armed. Second, once the LOC mode is engaged, the aircraft appears 

to fly two under-damped oscillations about the path before smoothly aligning with the localizer 

beam. With the fastest aircraft, these behaviors require a distance of more than 0.5 NM to 

complete; therefore, the faster aircraft does not complete capturing of the localizer path until after 

the 200 ft DH for an intercept height of 370 ft. However, at the next intercept height of 587 ft, 

TSE does show sufficient stability across all three decision heights to conduct a landing. 

Moreover, the improvement is large enough that it may be possible achieve acceptable results at 

an intercept height between 370 and 587 ft. However, a number of secondary effects that might 

increase TSE or decrease its rate of decay were not enabled in the simulation. Moreover, the TSE 

observed on the offset path in the simulation was half as large for the CAT I LDA as the 40 m 

TSE assumption for the offset path in the CONOPS [MITRE2013]. Therefore, a more 

conservative recommendation is to compare the two scenarios of CAT III LDA to CAT III ILS 

and CAT I LDA to CAT III ILS, and chose the intercept height where sensitivity to TSE on the 

offset path disappears. This occurs beginning in the neighborhood of the 730 ft intercept height. 

 

5

 Landing weights have a one-to-one correspondence with the approach speeds. 
53 

Table 4-7 Observed TSE at Decision Heights for Modified Offset Paired-Approach 

Intercept Height 

(ft AGL) 

Total System Error (ft, 95% bounds) 

CAT III LDA to CAT III ILS CAT I LDA to CAT III ILS 

200 ft 100 ft 50 ft 200 ft 100 ft 50 ft 

370 25 19 18 77 47 37

587 21 18 17 25 20 18

730 20 17 16 21 17 16

833 19 17 16 19 17 16

These results indicate that it is not possible to conduct landing at CAT II or lower minima for 

offset path intercept at or below 1 NM from the threshold. Therefore, the geometry for the offset 

paired-approach currently defined in the CONOPS cannot be extended to lower minima. The 

intercept point must be increased to 1.5 and 2 NM from the threshold. Extending the intercept 

distance, however, also constricts the wake-safe distance throughout the procedure. This 

constriction presents the biggest challenge on the parallel portion of the approach. For a given 

procedure availability, the necessary crosswind tolerance increases with altitude, reaching a near 

asymptote around 10 KT adverse crosswind [Audenaerd2012]. The offset portion of the 

approach provides relief from the increasing crosswind by increasing the distance that the wake 

must travel. However, the parallel portion of the approach must absorb the entire effect of 

increasing crosswind. The CONOPS design was validated, assuming the current fleet of aircraft 

in service, with a maximum near surface crosswind of 5 KT. Similar studies would need to be 

performed to ascertain the feasibility of extending the parallel portion of the approach with the 

current aircraft fleet or to determine the future performance necessary to execute this modified 

approach. The study, however, does suggest that, when the TSE on the offset path and turn 

equals that of a CAT III approach (CAT III LDA to CAT III ILS), then a late turn onto the 

extended centerline at 1 NM becomes possible. However, achieving similar performance on the 

offset path, would require next generation avionics utilizing high accuracy navigation sources like 

ground-based augmentation system approach service type D (GAST-D) GPS or even wide-area 

augmentation system (WAAS) GPS with 5 Hz update rate. 

4.5. Observations 

The ALAS alerting algorithm is especially effective when the aircraft are within 1 NM of the 

runway threshold. This is due to the significantly smaller TSE in this region. Therefore, from a 

collision detection viewpoint, the potential of lowering the visibility minima using a hybrid 

procedure is very promising. However, the high-fidelity simulation indicates that stabilizing the 

approach path on a CAT III ILS is possible for the current generation aircraft fleet only for 

intercept points at least 1.5 to 2 NM from the threshold. Assessing the aircraft capabilities 

necessary to conduct the offset paired-approach with the offset intercept at higher elevations will 

require additional simulation studies. Alternatively, the high-fidelity simulation results also 

suggest it may be possible to retain a 1 NM intercept distance if technology can be developed to 

constraint total system error to the accuracy of a straight-in CAT III ILS approach when flying 

the latter part of the offset path, the turn onto the extended centerline, and the extended centerline 

to touchdown. Such a system may be possible using GAST-D GPS or even WAAS GPS with 5 

Hz update rate. 

We have briefly looked at the issue of executing the escape maneuver while near to the 
54 

ground. It is conceivable that near ground blunders are extremely unlikely and perhaps they can 

be excluded. But if these blunders cannot be excluded, future work will be necessary to develop 

a more intelligent escape maneuver that differs depending on the relative position and velocity of 

the aircraft. 
55 

5. Conclusions 

In this report we present the analytical and experimental results using the ALAS alerting 

algorithm in several variants of a future paired approach concept of operations. We examined the 

SAPA procedure for different runway spacings using a fast-time simulation and found that the 

SAPA procedure can be used at 950 ft separations or higher with next-generation avionics and 

that 1150 ft separations or higher is feasible with current-rule compliance ADS-B OUT. Both of 

these results depend upon the use an aggressive escape maneuver that is automatically 

engaged. The runway separations can be lowered an additional 50 ft if different glideslopes are 

used (i.e. 2.85° and 3.0). We have also conducted high-fidelity simulations at 1050 ft for nextgeneration avionics and 1400 ft separation for the current-rule ADS-B, which confirmed the fasttime simulations. The Joint Planning Development Office (JPDO) recently asked NASA to 

consider whether adding additional aircraft states, like roll angle, to ADS-B OUT could improve 

results; NASA has added expansion of ADS-B state data to its planned FY14 work. 

We have also analyzed the use of echelon spacing for straight in approaches without the use of 

the ALAS alerting algorithm. The statistical analysis shows that current generation aircraft 

cannot conduct paired approaches on parallel paths using echelon spacing on runways less than 

1400 ft apart and next-generation aircraft will not be able to conduct paired approach on runways 

less than 1050 ft apart. These runway separations are greater than the estimates for which passing 

becomes safe using the SAPA procedure (see Section 2.1.3.1). Since the SAPA approach allows 

passing, SAPA can more easily accommodate larger differences in approach speed and lower 

minimum approach speeds. However, the echelon spacing approach has a cost advantage since it 

requires only monitoring of lateral and longitudinal bounds while SAPA requires an alerting 

algorithm and an automated escape maneuver. 

Finally, we looked at the use of the ALAS alerting algorithm in conjunction with the MITRE 

echelon concept. The goal of this work was to lower the visibility minima requirements for the 

MITRE CONOPS. The fast-time simulation found that the ALAS alerting algorithm was very 

effective when deployed starting at 1 NM from the threshold. However, for the offset pairedapproach, the high-fidelity simulation showed that stabilizing the approach path on a CAT III ILS 

was only possible for current generation aircraft at merge points at least 1.5 to 2 NM from the 

threshold. Nevertheless, the high-fidelity simulation results suggest that it may be possible to 

retain a 1 NM intercept distance if technology can be developed to constraint total system error 

on the offset path and final turn. Such a system may be possible using ground-based 

augmentation system approach service type D (GAST-D) GPS or even wide-area augmentation 

system (WAAS) GPS with 5 Hz update rate. Without such technology, this hybrid approach 

using an offset path is not likely to be feasible at a 1 NM merge point. We have also identified an 

issue in using the escape maneuver near ground (e.g. 300 ft or below). Due to airport buildings 

and surrounding terrain, the turn component may have to be disengaged until a sufficient height is 

reached. Preliminary results show that this can have a serious impact on the probability of a 

collision. Nevertheless, the same ground obstacles can also restrict the blunder characteristics of 

the lead aircraft. More analysis is required to determine the limits of both blunder and escape 

maneuvers near the ground. 
56 

6. Future Work 

In FY14, NASA plans to pursue improvements in paired-approach procedure design and the 

ALAS alerting algorithm to increase the availability of the paired-approach procedures while 

improving safety. 

 Evaluate the benefits of adding roll-angle to the ADS-B OUT broadcast. Roll angle often 

leads the observed turn performance of the intruder aircraft. Therefore, it is possible that the 

broadcast of roll angle can provide earlier alerts and reduce the required runway separation 

for safe passing under the SAPA procedure. 

 Evaluate the benefits of adding Traffic Alert and Collision Avoidance System (TCAS) slant 

range data as an input to the ALAS alerting algorithm. TCAS slant range has higher accuracy 

than slant range derived from ADS-B OUT broadcasts. It may be possible to develop alerting 

criteria derived from or blended with TCAS slant range data to improve alerting performance. 

 Refine and enhance the performance of the ALAS alerting algorithm, based on actual aircraft 

position/velocity data for auto-coupled, auto-throttle approaches obtained from FAA data 

sources. 

 Continue hybrid Paired Approach (CAT II/III) development with echelon spacing and ALAS 

alerting to achieve enhanced performance to lower weather minima. For echelon spacing 

with an offset path, assess the capabilities needed to move the merge point an additional 0.5 

to 1.0 NM from the runway. 

 Investigate the problem of executing an escape maneuver near the ground (e.g. 350 ft and 

below). Develop an intelligent escape maneuver that is based on the available positions and 

velocities of the aircraft. 

 Integrate interval management for closely spaced parallel operations (IM-CSPO) and SAPA 

using flight-deck interval management (FIM) to deliver aircraft to the initiation point for 

SAPA and then transition to a SAPA operation. 

The results in this paper and those of future work are subject to the fidelity and uncertainty of 

wake vortex models. Higher fidelity models of wake vortices and better characterization of 

model uncertainties will be necessary to increase confidence in the safety of estimated wake-free 

boundaries. Moreover, improved wake-vortex modeling may also reveal opportunities to 

accommodate closer runway spacing through adjustments in the procedure. For parallel approach 

procedures like SAPA, the need for improved wake-vortex characterization extends across all 

three regions of vortex behavior: in-ground effect (IGE), near-ground effect (NGE), and out-ofground effect (OGE). 
57 

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60 

Appendix A. New Offset Runway Conformance Algorithm 

The previous version of the ALAS Alerting algorithm was designed for fully parallel approaches 

only. However, the latest version of the algorithm and software enables runway conformance 

testing on merged approaches. The algorithm is illustrated in the Figure A-1: 

 

The runway centerlines are solid lines. The dotted red lines show the maximum deviation 

before an alert is issued. The runway centerlines are extended with dashed lines. The algorithm 

measures the perpendicular distance from both runway centerlines. The safe side distance is 

given a negative sign and hence becomes a negative number. The maximum distance is used as 

the runway deviation. This maximum distance is compared to two positive parameters values: 

yellowRunwayDist and redRunwayDist. If the distance exceeds these values an alert is issued. 

If the position vectors are Euclidean the calculation is straight-forward: 

 t = (q – s)v / vv 

 Distance = || s + t v – q || 

If the position vectors are given in geodesic coordinates: 

Compute the “cross track distance” as defined by the Aviation Formulary (v1.44) by Ed 

Williams. This function forms a great circle from two points on the centerline (p1, p2). It 

then computes the shortest distance of another point (off Circle) to the great circle: 

cross_track_distance(p1, p2, offCircle) { 

dist_p1oc = angular_distance(p1,offCircle); 

trk_p1oc = initial_course_impl(p1,offCircle,dist_p1oc); 

trk_p1p2 = initial_course(p1,p2); 

//This is a direct application of the "spherical law of sines" 

return distance_from_angle(asin(sin(dist_p1oc)*sin(trk_p1oc-trk_p1p2)), 

 (p1.alt()+p2.alt()+offCircle.alt())/3.0); 

Figure A-1: Offset runway conformance bounds 
61 

 

Thus far we have not performed any simulations using this new ALAS capability. The 

algorithm has been coded in both Java and C++ and is ready for experimental use in future work. 
62 

Appendix B. tAlas Simulation Validation 

B.1. Results for Cylinder Protection Zone and No Escape Maneuver 

In this section we present the results of a baseline run, executing the tAlas simulation with no 

alerting and no escape maneuver. This is important to insure that the simulation is generating 

blunders that will lead to collisions if not detected. 

Table B-1: Results for Various Runway Spacings with No Escape Maneuver 

Runway 

Spacing (ft) 

Num Los Probability Minimum Distance (ft) 

750 1,863,967 1.86E-01  1.23E-04 0.86

850 1,682,885 1.68E-01  1.18E-04 0.48

950 1,521,025 1.52E-01  1.14E-04 0.87

1050 1,375,997 1.38E-01  1.09E-04 0.26

1150 1,245,431 1.25E-01  1.04E-04 1.13

1250 1,129,458 1.13E-01  1.00E-04 0.41

1350 1,025,597 1.03E-01  9.59E-05 0.25

1450 932,246 9.32E-02  9.19E-05 0.86

Comparing this table with Table 2-5 shows us that the ALAS alerting algorithm provides at 

least 4 orders of magnitude improvement. 

B.2. Impact of maxT2 on Blunder Angle of Incidence 

The T2 parameter controls the duration of the blunder turn. This value will determine the 

maximum angle of incidence of the intrusion onto the ownship’s centerline.

Table B-2: Angle of Incidence of Blunders For Runway 1050 ft, 1.5 s latency as a function of 

MaxT2 

MaxT2 Maximum 

Incidence Angle () 

Average 

Incidence Angle () 

10 30.94 7.90 

11 33.58 8.54 

12 36.17 9.17 

13 41.50 9.86 

14 46.97 10.63 

15 52.47 11.47 

16 56.60 12.37 
63 

Table B-3: Angle of Incidence of Blunders For Runway 750 ft, 1.5 s latency as a function of 

MaxT2 

MaxT2 Maximum 

Incidence Angle () 

Average 

Incidence Angle () 

10 30.78 8.11 

11 33.40 8.73 

12 35.99 9.35 

13 41.32 10.02 

14 46.14 10.78 

15 50.12 11.59 

16 51.63 12.42 

For a given runway spacing there is a maximum angle of incidence onto the ownship’s 

centerline that can be achieved. For a 1050 ft runway the maximum angle of incidence is a bit 

over 30 degrees. Increasing maxT2 increases the frequency of more aggressive maneuvers and 

hence increases the probability of a LoS. 

B.3. Track Rate Threshold Sensitivity 

The performance of the Alas alerting algorithm is strongly dependent upon the 

trackRateThreshold parameter. The collision detection component of the algorithm is engaged 

when the intruder’s averaged turn rate exceeds the value of this parameter. If it is set too low, 

there will be too many false alarms. If it is set too high, then the alert will be delayed longer. In 

Table B-4 the impact of this parameter is shown for the 950 ft runway spacing case and in Table 

B-5 the impact on the 1050 ft runway spacing case is shown. Note that acceptable probabilities 

are indicated in blue font and unacceptable probabilities are indicated in red. 

Table B-4: Simulation Runs for 950 ft Runway using Different Track Rate Thresholds 

Track Rate 

Threshold 

(/s) 

Probability (400 ft) Probability (large 

cylinder) 

Minimum 

Distance (ft) 

1.0 1.40E-04  3.74E-06 3.34E-06  5.58E-07 258.65 

1.1 2.11E-04  4.59E-06 7.84E-06  8.73E-07 218.96 

1.2 3.13E-04  5.59E-06 1.58E-05  1.25E-06 212.68 

1.5 8.50E-04  9.21E-06 7.69E-05  2.77E-06 157.66

2.0 2.96E-03  1.72E-05 4.37E-04  6.61E-06 58.79

Using the large cylinder protection zone, values of this parameter of 1.2 or larger resulted in 

collision probabilities that are beyond our target value of 1E-05/landing. There were some CMF 

runs where false alarms were seen, but the latest version of ALAS used for generating the fasttime results in this paper does not exhibit false alarms for these runs. The trackRateThreshold

parameter was set at 1.0 /s for these runs. 
64 

Table B-5: Simulation Runs for 1050 ft Runway using Different Track Rate Thresholds 

Track Rate 

Threshold 

(/s) 

Probability (400 ft) Probability (large 

cylinder) 

Minimum 

Distance (ft) 

1.0 9.84E-06  9.81E-07 4.38E-07  1.48E-07 316.55

1.1 1.77E-05  1.32E-06 5.38E-07  1.79E-07 292.52

1.2 3.18E-05  1.78E-06 7.38E-07  2.28E-07 292.15

1.5 1.34E-04  3.67E-06 6.24E-06  7.76E-07 240.72

2.0 7.11E-04  8.43E-06 7.96E-05  2.82E-06 141.78

Note that if the trackRateThreshold parameter were increased to 1.5 /s, then the 950 runway 

spacing would no longer be available, but the 1050 runway spacing would still be practical. We 

do not expect that the parameter will need to be this large because in the CMF simulation results 

we very rarely see any track rates above 0.5 /s. We hope to test the behavior of the ALAS 

algorithm on real landing data to tune this parameter to its optimal value. Also, there is potential 

to improve the averaging filter that is used in the algorithm if real landing data becomes available. 
65 

Appendix C. Measuring ALAS False Alarm Rate Using 

MITRE/Boeing TSE Model 

Our fast-time simulation tAlas was used to measure the false alarm rate of ALAS. For this 

experiment, the ownship’s protection zone was defined as a moving quadrant D distance away 

from the ownship’s centerline in the direction of the intruder and X units behind the ownship, as 

illustrated in Figure C-1. The protection zone extends forward from the ownship all the way to 

the runway to account for the possibility of a catastrophic wake encounter if the intruder were to 

cross in front of the ownship. Crossing behind the ownship is considered safe (for the ownship). 

The area to the side of the ownship away from the intruder is included in the protection zone as 

this is where the ownship would escape in case of a red alert. A blunder was defined as any 

intruder trajectory that entered the ownship’s protection zone. A false alarm occurs when ALAS 

issues a red alert on an intruder trajectory that does not carry it into the ownship’s protection 

zone. 

Figure C-1: Top view of the scenario for measuring the false alarm rate 

To measure the false alarm rate, we ran landing trials in which the aircraft followed their 

respective glide paths at constant ground speeds. These trials used a random lateral error model 

tuned for a typical distribution of deviations from the centerline for both the ownship and the 

intruder. This model is described in the next section. There were no blundering trajectories 

during these tests. The aircraft were given initial positions on their glide paths between 7 and 8 

NM from the runways with a longitudinal separation between 1000 and 1500 ft. The ground 

speeds ranged between 114 and 160 KT with a maximum speed difference of 15 KT. The 

protection zone parameters were set to X = 400 ft and D = 230 ft. The landing trials ran for 400 

seconds of simulated time or until the altitude of one or both aircraft dropped below 100 ft above 

ground level. We ran four sets of landings, each with 7,290,000 landing trials. Only the 

TrackRate Threshold of ALAS changed between the sets of landings. All other parameters of 

ALAS and the test trajectories remained constant. Two statistics were collected for each set of 

trials: the number of red alerts issued by ALAS and the number of false alarms. As there were no 

blunders in any of these landing trials, the false alarm rate was equal to the number of red alerts 

divided by the number of trials. 

C.1. Lateral Error Model 

The simulation of the lateral motion of the aircraft used a flight technical error (FTE) model 

from MITRE [Eftekari2008], which was based on a lateral control model for final precision 

IS 

Ownship 

Intruder 

SOSInitial(x, y, z)

SISInitial(x, y, z)

VOSInitial(x, y, z)

VISInitial(x, y, z)

Xprotectio

n 

Dprotectio

n 

SOSRunway(x, y, z)

SISRunway(x, y, z)

OSRunway 

ISRunway 

Ownship 

Runway

Intruder 

Runway 

yIS
66 

approach developed by Boeing [Warren1999]. This parameterized model can be tuned to the 

characteristics of any aircraft and simulates effects of path disturbances due to closed loop 

guidance errors, wind and gusts. The model consists of a pair of differential equations for the 

aircraft lateral deviation y and track angle  relative to the centerline. 

 ߰ כ  ൌ ݐ݀Ȁݕο݀

݀߰Ȁ݀ݐ ൌ  െ݇ଵ כ߰െ݇ଶ כ ȟݕ ൅ ߝ 

The variables y and  are illustrated in Figure C-1 for the intruder aircraft. y is in units of feet 

per second and  has units of radians. Variable v denotes the aircraft airspeed in units of feet per 

second. Parameters k1 and k2 are control gains. The input  is a noise error process representing 

centerline deviations of the track angle. 

This model describes a second order closed-loop system with disturbance . The control gains 

are related to the damping constant  and natural frequency  as follows. 

݇ଵ ൌ ʹߦ߱ 

݇ଶ ൌ ߱ଶȀ 

The natural frequency  in units of radians is related to the frequency f in Hz and the period p 

in seconds. 

߱ ൌ ʹߨ ൌ ʹߨȀ 

For the simulations to measure the false alarm rate of ALAS, the damping constant  had a 

range from 0.3 to 0.5 and the period p had a range from 55 to 65 seconds. 

The input  represents disturbances acting on the aircraft and causing deviations of the track 

angle, which then cause lateral deviations from the centerline. The error model is parameterized 

with the standard deviation of the lateral error 
y. This is derived from the FTE bound defined as 

the 95% containment lateral error. 


y = FTE/1.96 

The FTE can be inferred from the least accurate RNP level for aircraft under consideration for 

the simulation. These aircraft are assumed to be equipped with GPS flight management systems. 

FTE = (minimum RNP)/1.38 

So: 


y = (minimum RNP)/2.705 

The disturbance  is modeled with a Johnson distribution given as a reshaped Normal 

distribution with slight higher probabilities at the extreme ends of the value range. 

 = zj*

67 

zj = e(z/2.18) – e(-z/2.18)

z = x/
 

x = N(0, 
), a Gaussian random process with 0 mean and 
 standard deviation 


 = (2*k1*k2*
y

2

/v)1/2 

For the false alarms runs the FTE was set to 60 ft. 

C.2. Results and Analysis 

Table C-2 shows the measured false alarm rates as a function of the TrackRate Threshold. As 

would be expected, the false alarm rate decreases as the alarm threshold is relaxed. The false 

alarm rate was significant for a threshold of 1.0, which is the current value set through a tuning 

process for the ALAS parameters. 

Table C-2: False alarm rate results 

ALAS TrackRate Threshold False Alarm Rate 

0.7 47.36% 

1.0 24.72% 

1.5 2.20% 

2.0 0.14% 

It is known that the performance of ALAS is sensitive to the value of the TrackRate Threshold 

parameter as this is used to trigger the sweep algorithm that predicts blunder trajectories. Any 

intruder trajectory with a track rate exceeding the set threshold and a predicted potential intrusion 

into the front or back buffer of the ownship triggers a red alert. ALAS has a low pass filter 

intended to reduce the sensitivity to track rate noise, but the attenuation must be balanced with the 

amount of signal lag (i.e., timing delay) introduced by the filter. This lag delays the triggering of 

red alerts and impacts the performance of the ownship’s escape maneuver.

 A quick examination of the lateral error model reveals that the track rate is a direct function 

of the noisy disturbance . Thus, although the model may be representative of actual patterns of 

lateral error deviation, it is our judgment that the track rate is not representative. We know that 

the trajectories generated by the CMF high-fidelity simulations do not contain as much track rate 

noise. Based on this, we decided not to use this lateral error model to measure the performance of 

ALAS or tune its parameters. We will continue to use in tAlas the simple sinusoidal oscillation 

model for the lateral error until a more representative stochastic model is available. 
REPORT DOCUMENTATION PAGE Form Approved

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Technical Memorandum

 4. TITLE AND SUBTITLE

Analysis and Simulation of the Simplified Aircraft-Based Paired Approach 

Concept With the ALAS Alerting Algorithm in Conjunction With Echelon 

and Offset Strategies 

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Torres-Pomales, Wilfredo; Madden, Michael M.; Butler, Ricky W.; Perry, 

Raleigh B.

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NASA Langley Research Center

Hampton, VA 23681-2199

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14. ABSTRACT

This report presents analytical and simulation results of an investigation into proposed operational concepts for closely spaced parallel runways, including the 

Simplified Aircraft-based Paired Approach (SAPA) with alerting and an escape maneuver, MITRE’s echelon spacing and no escape maneuver, and a hybrid 

concept aimed at lowering the visibility minima. We found that the SAPA procedure can be used at 950 ft separations or higher with next-generation avionics 

and that 1150 ft separations or higher is feasible with current-rule compliant ADS-B OUT. An additional 50 ft reduction in runway separation for the SAPA 

procedure is possible if different glideslopes are used. For the echelon concept we determined that current generation aircraft cannot conduct paired approaches 

on parallel paths using echelon spacing on runways less than 1400 ft apart and next-generation aircraft will not be able to conduct paired approach on runways 

less than 1050 ft apart. The hybrid concept added alerting and an escape maneuver starting 1 NM from the threshold when flying the echelon concept. This 

combination was found to be effective, but the probability of a collision can be seriously impacted if the turn component of the escape maneuver has to be 

disengaged near the ground (e.g. 300 ft or below) due to airport buildings and surrounding terrain. We also found that stabilizing the approach path in the 

straight-in segment was only possible if the merge point was at least 1.5 to 2 NM from the threshold unless the total system error can be sufficiently 

constrained on the offset path and final turn. 

15. SUBJECT TERMS

Aircraft Spacing; Airports; Flight Paths; Kinematics; Simulators; System Warnings

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