effect of lnav and vnav equipage on time-based scheduling...the tapss system consists of four...

American Institute of Aeronautics and Astronautics

1

Effect of LNAV and VNAV Equipage on Time-Based

Scheduling

Sai Vaddi1, Xiaoli Bai

2, and Monish Tandale

3

Optimal Synthesis Inc., Los Altos, CA, 94022

This paper evaluates the effect of Lateral NAVigation (LNAV) and Vertical NAVigation

(NAV) equipage on the performance on time-based scheduling. The paper relies on two

companion papers: (i) the first paper develops a high-fidelity simulations model of LNAV +

VNAV, and (ii) the second paper develops a realistic spatio-temporally correlated model of

wind uncertainty. Two different Monte Carlo simulation frameworks are used to evaluate

the effect of LNAV + VNAV equipage on time-based-scheduling. The first Monte Carlo

simulation framework is used to evaluate the time-of-arrival uncertainty for flights equipped

with LNAV + VNAV capability. This Monte Carlo simulation uses a point-mass simulation

model of the aircraft equipped with LNAV + VNAV and flying through spatio-temporally

correlated wind uncertainty fields. The second Monte Carlo simulation evaluates the effect

of LNAV + VNAV equipage on the performance of time-based scheduling. NASA's

Stochastic Terminal Area Scheduling and Simulation (STASS) software is used for time-

based scheduling and terminal area traffic simulations. Terminal-area traffic Monte Carlo

simulations are conducted for 1.0x, 1.5x, and 2.0x demand ratio at San-Francisco

International Airport (SFO), Los Angeles International Airport (LAX), and Dallas Fort

Worth International Airport (DFW). Results illustrating the effect of LNAV + VNAV

equipage level (0%, 25%, 50%, and 75%) on delay, throughput, and the number of

separation violations are presented in the paper.

I. Introduction

ASA and the FAA have been involved in extensive efforts to develop advanced concepts, technologies, and

procedures for the Next Generation Air Transportation System (NextGen)1. The objective of these research

efforts has been to improve the capacity, efficiency, and safety in the next-generation National Airspace System

(NAS). Improvements can come in the form of more accurate and autonomous onboard navigational capabilities

based on the Global Positioning System, more accurate surveillance capabilities such as Automatic Dependent

Surveillance-Broadcast, advanced communication capabilities such as datalink, improved vehicle designs, and

improved air-traffic operations realized through advanced automation systems. A significant portion of the NextGen

research is aimed at (i) developing ground-side automation systems to assist controllers in strategic planning

operations, (ii) developing controller decision support tools to separate and space the traffic, and (iii) developing

flight-deck-side automation to assist pilots in accomplishing airborne merging and spacing operations.

Reference 2 describes a concept for future high-density terminal air traffic operations that has been developed by

the Airspace Super Density Operations (ASDO) researchers at NASA Ames Research Center. The concept

described in Ref. 2 includes five core capabilities: 1) Extended Terminal Area Routing, 2) Precision Scheduling

Along Routes, 3) Merging and Spacing, 4) Tactical Separation, and 5) Off-Nominal Recovery. The first two

capabilities are strategic planning tools and the remaining three are tactical decision support tools.

Successful implementation of precision scheduling requires an understanding of the following:

The range of flight times feasible for an aircraft to transit between two points along its flight path (e.g., Top

of Descent to a Meterfix & Meterfix to Runway)

The accuracy with which an aircraft can realize a Scheduled Time of Arrival (STA)

The accuracy with which an aircraft can maintain self-separation with respect to a leading aircraft?

1 Senior Research Scientist, 95 First Street, AIAA Member.

2 Research Scientist, 95 First Street, AIAA Member.

3 Senior Research Scientist, 95 First Street, AIAA Member.

N

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232

2013 Aviation Technology, Integration, and Operations Conference

August 12-14, 2013, Los Angeles, CA

AIAA 2013-4232

AIAA Aviation


2

The feasible flight time depends on the following:

Aircraft performance characteristics

Cruise and descent speeds selected by the Flight Management System (FMS)

Terminal area route geometry

Atmospheric conditions such as temperature and winds

The Time-of-Arrival (TOA) accuracy and self-separation accuracy depend on the following:

Uncertainty associated with the atmospheric predictions.

Advisories from ground-side controllers assisted by automation tools such as Controller Managed Spacing3

(CMS).

Current-day and NextGen FMS automation capabilities which are the focus of current research.

Current-day and NextGen FMS capabilities that affect the TOA accuracy at a Meterfix or runway are listed

below:

1) Lateral NAVigation (LNAV) & Vertical NAVigation (VNAV)4-10

features of that enable 3D-path

tracking capability.

2) Required Time-of-Arrival11-14

(RTA) feature of FMS that enables an explicit TOA specification at

waypoints such as the Meterfix and runway .

3) Interval Management15-19

(IM) tools that enable the capability to maintain spatial and temporal spacing

with another aircraft.

4) 4Dimensional FMS (4DFMS)20-23

capability that enables full 4D-trajectory tracking.

The objective of the research in this paper is to evaluate the impact of LNAV + VNAV equipage on the

performance of time-based scheduling in the terminal airspace, specifically for arrival flights. Section II introduces

overall framework to realize the afore mentioned objective. Section III describes the time-based scheduling concept.

Section IV presents the TOA uncertainty results associated with LNAV + VNAV capability. Section V presents the

predicted delay and throughput benefits for SFO, LAX, and DFW airports as a function of LNAV+VNAV equipage

level and demand.

II. Introduction

The overall approach to evaluate the effect of LNAV + VNAV equipage on time-based scheduling can be split

into two sub-objectives:

Objective 1: Characterizing the TOA accuracy of a flight equipped with LNAV + VNAV at the

Meterfix and runway. This objective is pursued in detail in Reference 33.

Objective 2: Characterizing the effect of equipping arrival flights with LNAV + VNAV on delay,

throughput, and separation violation metrics at different airports.

Figure 1 depicts a dual Monte Carlo simulation approach for evaluating the above mentioned objectives. The

first Monte Carlo simulation uses a high-fidelity simulation of a single aircraft equipped with LNAV + VNAV

capability. High-fidelity aircraft simulation in the context of the current work includes point-mass simulation of an

aircraft - with 7 states , speed, heading, flight path angle, and mass of the aircraft; auto-pilot models; engine

lag model; and an atmospheric uncertainty model. The first Monte Carlo simulation evaluates the TOA uncertainty

of an aircraft equipped with LNAV + VNAV subjected to realistic atmospheric uncertainties. The simulation

consists of the following components: (i) NextGen FMS Capability models, (ii) aircraft simulation, (iii) atmospheric

uncertainty models, and (iv) terminal airspace route data. Reference 33 provides a detailed description of this first

Monte-Carlo simulation.

The second Monte Carlo simulation uses a time-based scheduling software and a lower fidelity terminal area

traffic simulation. The TOA uncertainty models resulting from the first Monte Carlo simulation framework are

treated as inputs to the time-based scheduler. The current research uses Stochastic Terminal Area Scheduling

Software31

(STASS) developed at NASA Ames Research Center. STASS serves the dual purposes of time-based

scheduling and terminal-area traffic simulation. The outputs from the STASS scheduler are the STAs for each flight

in the demand data set. The robustness of the STASS schedule when subject to the TOA uncertainty models is tested

using another set of terminal-area traffic Monte Carlo simulations also by STASS. Outputs from this second set of

Monte-Carlo simulations are the statistics of average delay, throughput, and number of separation violations.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


3

Figure 1. Block Diagram of the Overall Approach

III. Time-Based Scheduling

Time-based scheduling refers to the process of sequencing and scheduling flights at the Meterfix and runway in

order to maximize throughout, or minimize delay while respecting the inter-aircraft separation constraints. The

Traffic Management Advisor (TMA)24

is one of earliest scheduling tools developed at NASA Ames Research

Center. The TMA supports en route controllers and managers with scheduling, spacing, and arrival flow

management and is currently deployed at multiple Air Route Traffic Control Centers. The TMA uses a timeline

graphical user interface to display schedule and sequence constraints at the traffic management position. Terminal

Area Precision Scheduling and Spacing (TAPSS) 25,26

is an integrated set of trajectory-based automation tools

providing precision scheduling, sequencing, and controller merging and spacing functions. It is a strategic and

tactical planning tool that provides Traffic Management Coordinators, En Route and Terminal Radar Approach

Control air traffic controllers with the ability to efficiently optimize the arrival capacity of a demand-impacted

airport, while simultaneously enabling fuel-efficient descent procedures. The TAPSS system consists of four-

dimensional trajectory prediction, arrival runway balancing, aircraft separation constraint-based scheduling, traffic

flow visualization, and trajectory-based advisories, to assist controllers in efficient metering, sequencing, and

spacing.

Among other terminal area scheduling research, Reference 27 proposed a decision support tool for high-density

departure and arrival traffic management. Saraf et. al28

developed a dynamic scheduling algorithm using

optimization techniques. Capozzi et al.29

developed a mixed-integer linear programming formulation for optimal

routing and scheduling of Metroplex operations. In Reference 30 Saraf et al. compare different scheduling

algorithms for Metroplex operations.

The terminal-area scheduling tool used in the current research is STASS. It is a massively parallel advanced

scheduling software created at NASA Ames Research Center. STASS was designed as a time-based scheduling

simulation tool that models aircraft arrivals in the terminal area. The scheduling is performed in two steps using (1)

the Center Scheduler to schedule aircraft from the freeze horizon to the meter fixes and runways and (2) the

TRACON Scheduler to schedule aircraft to the runways upon their arrival at the meter fixes. Uncertainty in arrival

times is modeled at the freeze horizon, meter fixes, and runways. STASS uses two types of constraints: inter-aircraft

13

NextGen FMS Automation Capabilities 1. Lateral & Vertical Navigation (LNAV+VNAV)2. Mode Control Panel (MCP)3. Required Time-Of-Arrival (RTA)4. Interval Management (IM)5. 4D Flight Management System (4D-FMS)

Aircraft Simulation

Monte Carlo Sim2

Monte Carlo Sim1 (Single Aircraft)

OBJECTIVE 1 OBJECTIVE 2

Atmospheric Uncertainty Model

TOA Uncertainty at Runway

TOA Uncertainty at Meterfix

Terminal Area Simulations (STASS

Sim.)

STASS Scheduler

Terminal Airspace Route Data

Flight Schedule

Metrics1. Throughput2. Delays3. Traffic Flow Efficiency

STAs

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


4

separation, and transit time bounds. The required inter-aircraft spatial separations, mandated by the FAA, are

converted in STASS to time constraints using nominal aircraft speeds at the meter fix and runway. Transit time

constraints are derived from the minimum and maximum transit times for aircraft traveling through the center and

TRACON airspaces. Advanced versions of STASS consider time-advance and constrained position shift to realize

better performance. Figure 2 shows a schematic of the terminal area scheduling problem for arrival flights.

Scheduling and sequencing is done at two points: (i) Meterfix (indicated by MF in Figure 2) and (ii) Runway

Threshold (indicated by RT in Figure 2). The inputs to the scheduler are typically: (i) list of flights including their

aircraft type, wake classification category and engine type, (ii) TOA at the schedule freeze horizon (19 minutes to

the Meterfix), (iii) TOA uncertainty at the meterfix, (iv) transit-time from Meterfix to runway (all combinations

permitted by the runway configuration), and (v) transit-time uncertainty. Figure 3 further illustrates the TOA and

transit-time uncertainty.

Figure 2. Schematic of the Terminal Area Scheduling Problem

Figure 3. Time-of-Arrival and Transit-Time Uncertainty

MF1 MF2

MF3MF4

(AC1, t1)

(AC2, t2)

(AC6, t6)

(AC7, t7)

(AC8, t8)

(AC3, t3)(AC4, t4)

(AC5, t5)

(AC9, t9)

(AC11, t11)

(AC10, t10)

TRACON

RT1 RT2

MF1

(AC1, t1)Time-of-Arrival

Uncertainty

Transit-Time Uncertainty

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


5

The transit-time matrix file consists of the following pieces of information: (i) number of feeder fixes and their

name, (ii) number of runways and their names, (iii) transit-time from each feeder fix to applicable runways

characterized as a function of the engine type. Three engine types are considered: (i) Jet, (ii) Turboprop, and (iii)

Piston.

The following aircraft data is required by STASS: (i) tail number, (ii) flight id, (iii) aircraft type, (iv) appearance

probability, (v) feeder fix name, (vi) engine type, (vii) wake vortex category, and (viii) TOA at freeze horizon. The

aircraft data set is randomly segregated by STASS into two groups one unequipped and the other equipped which in

the current paper refers to LNAV/VNAV capability.

STASS also uses additional parametric settings that specify the temporal buffer to be used both at the Meterfix

and runway. These buffers are required to accommodate the uncertainty associated with the times-of-arrival. These

uncertainties are a function of the aircraft equipage. STASS permits the use of two different equipage levels. In this

research equipped flights are treated as those with LNAV + VNAV equipage. Unequipped flights are those without

any of the following capabilities: LNAV, VNAV, RTA, IM, and 4DFMS.

IV. Time-of-Arrival Uncertainty Models

The current section describes the methodology used to estimate the TOA uncertainty associated with LNAV +

VNAV capability. Reference 33 provides a detailed description and results from the Monte-Carlo simulation to

characterize the TOA uncertainty associated with LNAV/VNAV flights. A summary of the overall approach and

key results are presented here for the benefit of the reader.

A. LNAV + VNAV Closed Loop Simulation

Figure 4 shows the closed-loop simulation used to evaluate the TOA performance of the LNAV + VNAV

capability.

Figure 4. Closed Loop Simulation Setup of LNAV+VNAV

The simulation consists of a reference trajectory generator which generates the horizontal and vertical plane

reference paths. Together the horizontal and vertical plane reference paths constitute the 3D-reference path.

Reference 32 describes the algorithms used for reference trajectory synthesis. The LNAV and VNAV modules take

in as input the horizontal and vertical reference paths and compare it with the navigation state of the aircraft.

Reference Trajectory Generator

VNAV

LNAV

Thrust Control

Spoiler Control

Aircraft Point Mass Dynamics

Bank Angle Auto-Pilot

Pitch-Axis Auto-Pilot

Engine

Navigation & Aircraft Sensors

AC FMS State

AC Actual State

Reference Trajectory

AC FMS State

AC FMS State

AC FMS State

AC FMS State

Hor. Ref. Traj

Ver. Ref. Traj

Speed. Ref. Traj

Speed. Ref. Traj

Bank Angle Command

Lift Coefficient Command

Thrust Command

Spoiler Drag

Thrust

Lift

Co

effi

cien

t

Bank Angle

BADA + Spoiler Aerodynamic

Model

Speed. Ref. Traj

Aerodynamic Drag

Aerodynamic Lift

Wind-DisturbanceNorth & East Wind Components

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


6

Depending on the observed deviations between the 3D-reference paths and the current state of the aircraft LNAV

and VNAV generate corrective actions in the form of a bank angle command and lift-coefficient command

respectively. Actual VNAV is expected to generate either pitch-attitude command or an angle-of-attack command.

However, developing such a model would require an aerodynamic model more sophisticated than the Base of

Aircraft DAtabase BADA drag-polars assumed under the current research. It should be noted all aircraft

performance data used in this paper is based on BADA 3.9.

Whereas, LNAV and VNAV track the 3D-reference path the thrust control module and spoiler control modules

maintain the reference airspeed within limits without any regard to groundspeed or the TOA. Thrust and drag

commands are generated depending on the observed deviation between the reference and the actual airspeeds of the

aircraft. Reference 33 describes the algorithms used for LNAV, VNAV, thrust control, and spoiler control.

In an actual aircraft the bank angle, lift coefficient, and thrust commands are realized by the auto-pilot and

engine. This paper uses second-order response models for bank angle and pitch axis auto-pilot models. A first-order

model is used to model the lag from the throttle. The outputs from the bank angle auto-pilot and engine models are

input to an aircraft point mass simulation. The lift coefficient and the spoiler drag command are processed through

the BADA drag-polars and a spoiler aerodynamic model to produce the aerodynamic lift and drag forces acting on

the aircraft. The lift and drag aerodynamic forces are in turn used to drive the point-mass simulation model. Detailed

equations relating to the simulation are presented in a companion paper (see Reference 33).

B. Wind Uncertainty

In addition to the aerodynamic forces, thrust, and bank angle the point-mass simulation also takes in as inputs the

North and East wind components of wind. In this paper the wind is modeled as the sum of two components: (i)

deterministic forecast component and (ii) a random forecast error component. The random forecast error represents

the uncertainty in the wind. This paper uses a realistic wind uncertainty model that is based on the observed

deviations between forecast atmospheric data and actual atmospheric data. It is assumed that the FMS uses forecast

atmospheric data. National Oceanic and Atmosphere Administration's (NOAA's) 1hr RAPid Refresh Data (RAP) is

used as the wind forecast. Actual wind data is extracted from Aircraft Communications Addressing and Reporting

System (ACARS) data which in turn is obtained from Meteorological Assimilation Data Ingest System (MADIS).

RAP provides North and East components of wind at 13 km horizontal plane resolution, and 50 vertical levels.

The forecasts are available 1 through 18 hours in advance. A bi-linear interpolation scheme is used to generate wind

data for arbitrary latitude, longitude, and altitude specification. The ACARS data is actual aircraft recorded wind

data and is considered true wind for the purpose of characterizing the wind forecast errors. ACARS also provides the

North and East components of the wind. However, this data is only available at spatial locations along a flight’s

path.

Figure 5 shows a block diagram of the wind-uncertainty characterization framework.

Figure 5. Wind Uncertainty Characterization Framework

Overall, the wind uncertainty model used in the current paper has the following features:

ACARS Data

RAP Data

RAP Parser

ACARS Parser

+-

Ro

ute

s &

Tim

es Error/Uncertainty Characterization

Algorithms

North & East Wind Components

North & East Wind Components

Fore

cast

Tim

e

Wind Uncertainty ModelD

ownl

oade

d by

UN

IVE

RSI

TY

OF

CA

LIF

OR

NIA

- B

ER

KE

LE

Y o

n Ju

ne 2

5, 2

014

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/6

.201

3-42

32


7

Wind is modeled as a function of latitude, longitude, altitude, and time.

Wind uncertainty is characterized by the standard deviation of the errors as a function of altitude. The

standard deviation is observed to increase with altitude.

The wind errors are correlated both spatially and temporally.

A more detailed description of this is available in an accompanying paper (see Reference 34).

C. Monte Carlo Simulation

The previous sub-sections described the closed loop simulation environment used to evaluate the LNAV +

VNAV capabilities and the wind-uncertainty model. This section describes the Monte Carlo simulation framework

used to establish the TOA uncertainty for aircraft equipped with LNAV/VNAV capability and subject to wind

uncertainties. The Monte Carlo simulations are conducted in two stages: (i) from Freeze Horizon (about 120nmi

away from the Meterfix) to Meterfix, and (ii) from the Meterfix to the runway. Each Monte Carlo simulation uses

the same aircraft. flying along the same route. The aircraft uses the same reference trajectory and experiences the

same deterministic wind forecast component. However, each simulation experiences a different random forecast

error component.

The reference trajectory used in the simulations is generated for a A320 aircraft flying along the BIGSUR route

at SFO. The Meterfix is chosen as the BOLDR waypoint along the route, and the runway is chosen as the 28R

runway. Figure 6 show the standard deviation of the errors as a function of path length from Freeze Horizon to

Meterfix. In Figure 6 the initial path length equal to zero represents the Freeze Horizon and final path length close to

120nmi represents the Meterfix. It can be inferred from this figure that the uncertainty in TOA at the Meterfix for

this aircraft example is 6.5seconds.

Figure 7 shows standard deviation of the errors as a function of path length from Meterfix to Runway. In Figure

7 the initial path length equal to zero represents the Meterfix and final path length close to 30nmi represents the

Runway. It can be inferred from this figure that the uncertainty in TOA at the Runway for this aircraft example is

3.75seconds.

Figure 6. STD of TOA Errors from Freeze

Horizon to Meterfix

Figure 7. STD of TOA Errors from Meterfix

to Runway

V. Time-Based Scheduling Simulation Results

Details of the time-based scheduling experiment conducted using STASS at SFO, LAX, and DFW airports are

presented in this section.

The following simulation scenarios are considered:

Demand Ratios: 1.0x, 1.5x, 2.0x

Equipage Fractions: 0, 25%, 50%, and 75%

Number of Monte-Carlo Iterations: 500

Outputs: Average Delay, Makespan, and Runway Separation Violations

A total of 12 Monte-Carlo simulation scenarios (3 Demand Ratios x 4 Equipage Ratios) are chosen to evaluate

the impact of LNAV/VNAV equipage on time-based scheduling at each of the three airports SFO, LAX, and DFW.

0 20 40 60 80 100 1200

1

2

3

4

5

6

7

Path length(nmi)

ST

D o

f T

OA

Err

or(

se

c)

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4

Path length(nmi)

ST

D o

f T

OA

Err

or(

se

c)

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


8

Each Monte-Carlo simulation represents a 4Hr traffic scenario (at 1.0x demand). Each Monte-Carlo scenario

involves 500 simulations of the terminal area traffic using randomly generated times-of-arrival and transit-times.

Table 1 shows STASS parametric settings related to time-of-arrival accuracy resulting from LNAV + VNAV

(equipped aircraft) and unequipped aircraft. It also shows the spacing buffers used for equipped and unequipped

aircraft. The TOA standard deviation of the equipped (LNAV/VNAV) aircraft are based on Figure 6 and Figure 7 in

Section IV. The LAX terminal area routes are longer than the SFO routes. Hence, the TOA uncertainty at the

Runway for LAX is chosen (by extrapolation) slightly higher than that of the SFO routes. The TOA standard

deviations for unequipped aircraft are assumed to be slightly higher than the LNAV/VNAV equipped

aircraft. This is an important assumption because the benefits expected from equipped aircraft depend

strongly on the TOA uncertainty values relative to the unequipped aircraft.

Table 1. STASS Parametric Settings

SFO, DFW LAX

Unequipped (s) LNAV/VNAV

Equipped (s) Unequipped (s)

LNAV/VNAV

Equipped (s)

Time-of-Arrival

Standard Deviation

@ Meterfix

10 7.5 10 7.5

Time-of-Arrival

Standard Deviation

@ Runway

8 4 10 5

Spacing Buffer @

Meterfix 10 7.5 10 7.5

Spacing Buffer

@Runway 8 4 10 5

A. SFO Time-Based Scheduling Results

Figure 8 shows the TRACON route model for San Francisco used in current simulations. Five Standard Terminal

Arrival Routes (STARs) and one arrival runway 28R are used for this experiment.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


9

Figure 8. SFO TRACON Airspace

Table 2 labels the five different routes and their Meterfixes.

Table 2. SFO TRACON Routes and their Meterfixes

S. No Route Name Meterfix

1 BIGSUR BOLDR

2 MODESTO CEDES

3 PIRAT HOMKA

4 GOLDN LOZIT

5 RISTI CEDES

Table 3 lists a synopsis of the benefits resulting from equipping 75% of the flights with LNAV/VNAV capability

at SFO. The benefits are with respect to 0% LNAV/VNAV equipage scenario. It should be noted that the results are

rounded to the nearest integer value.

Table 3. Expected Benefits from 75% LNAV/VNAV Equipage at SFO

Demand Ratio

No. of Flights Change in Avg. Delay % Change in

Makespan

% Change in

Separation

Viols. Actual %

1.0x 112 2.85 seconds -12% 0% -11%

1.5x 168 48 seconds -25% 0% -6%

2.0x 224 210 seconds -17% -3% -1%

Whereas Table 3 lists the benefits for 75% equipage ratio the figures below illustrate the benefits for different

equipage levels between 0%-75%. Figure 9, Figure 11, and Figure 13 illustrate the effect of LNAV/VNAV equipage

on the average delay at 1.0x, 1.5x, and 2.0x demand ratios respectively. The x-axis represents the fraction of flights

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


10

equipped with LNAV/VNAV capability. Figure 10, Figure 12, and Figure 14 illustrate the effect of LNAV/VNAV

equipage on Makespan at 1.0x, 1.5x, and 2.0x demand ratios respectively. Figure 15, Figure 16, Figure 17 illustrate

the effect of LNAV/VNAV equipage on Runway Separation Violations at 1.0x, 1.5x, and 2.0x demand ratios

respectively.

Figure 9. Average Delay at 1.0x Demand

Figure 10. Makespan at 1.0x Demand



Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


11



Figure 15. Separation Violations at 1.0x

Demand


Demand


Demand

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


12

B. LAX Time-Based Scheduling Results

Figure 18 shows the LAX terminal airspace route geometry used for the current experiment. Six STARs and two

arrival runways 25L and 24R are used in this experiment.

Figure 18. LAX TRACON Route Geometry

Table 4 shows the Meterfixes chosen along each of the six arrival routes in Figure 18.

Table 4. LAX TRACON Routes and their Meterfixes

S. No Route Name Meterfix

1 RIIVR GRAMM

2 SEAVU KONZL

3 SADEE PIRUE, VTU

4 SHIVE SHIVE

5 KIMMO LHS

6 LEENA SXC

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


13


at LAX. The benefits are with respect to 0% LNAV/VNAV equipage scenario. It should be noted that the results are


Table 5. Synopsis of Expected Benefits from 75% LNAV/VNAV Equipage at LAX

Demand Ratio


Makespan

% Change in

Separation

Viols. Actual %

1.0x 182 3.6 seconds -14% 0% -19%

1.5x 273 33 seconds -19% 0% -12%

2.0x 364 156 seconds -20% -3% -10%

Figure 19, Figure 21, and Figure 23 illustrate the effect of LNAV/VNAV equipage on Average Delay at LAX

for 1.0x, 1.5x, and 2.0x demand ratios respectively. Figure 20, Figure 22, and Figure 24 illustrate the effect of

LNAV/VNAV equipage on Makespan at LAX for 1.0x, 1.5x, and 2.0x demand ratios respectively. Figure 25, Figure

26, and Figure 27 illustrate the effect of LNAV/VNAV equipage on Runway Separation Violations at LAX for 1.0x,

1.5x, and 2.0x demand ratios respectively.





Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


14



Figure 25. Separation Violation at 1.0x

Demand


Demand


Demand

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


15

C. DFW Time-Based Scheduling Results

Figure 28 shows the DFW TRACON route model used in this paper. Three arrival Meterfixes and four runways

are used in this experiment.

Figure 28. DFW TRACON Route Geometry


at DFW. The benefits are with respect to 0% LNAV/VNAV equipage scenario. It should be noted that the results are


Table 6. Synopsis of Expected Benefits from 75% LNAV/VNAV Equipage at DFW

Demand Ratio


Makespan

% Change in

Separation

Viols. Actual %

1.0x 276 7.5 seconds -13% 0% -16%

1.5x 414 170 seconds -15% -2% -9%

2.0x 552 280 secods -9% -3% -9%

Figure 29, Figure 31, and Figure 33 illustrate the effect of LNAV/VNAV equipage on Average Delay at DFW

for 1.0x, 1.5x, and 2.0x demand ratios respectively. Figure 30, Figure 32, and Figure 34 illustrate the effect of

LNAV/VNAV equipage on Makespan at DFW for 1.0x, 1.5x, and 2.0x demand ratios respectively. Figure 35,

Figure 36, and Figure 37illustrate the effect of LNAV/VNAV equipage on Runway Separation Violations at DFW

for 1.0x, 1.5x, and 2.0x demand ratios respectively.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


16







Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


17


Demand


Demand


Demand

D. Summary

Table 7 summarizes all the STASS Monte-Carlo simulation results presented in the previous sections.

Table 7. Synopsis of Expected Benefits from NextGen Capabilities at 75% Equipage Level

Airport Demand

Ratio

No. of

Flights

Change in Avg. Delay % Change in

Makespan

% Change in Runway

Separation Violations Actual %

SFO 1.0x 112 2.85 seconds -12% 0% -11%

SFO 1.5x 168 48 seconds -25% 0% -6%

SFO 2.0x 224 210 seconds -17% -3% -1%

LAX 1.0x 182 3.6 seconds -14% 0% -19%

LAX 1.5x 273 33 seconds -19% 0% -12%

LAX 2.0x 364 156 seconds -20% -3% -10%

DFW 1.0x 276 7.5 seconds -13% 0% -16%

DFW 1.5x 414 170 seconds -15% -2% -9%

DFW 2.0x 552 280 seconds -9% -3% -9%

In summary this paper has illustrated that increasing the ratio of high-equipage aircraft will result in reduced

TOA uncertainty, which in turn will lead to delay reduction benefits. The benefits are not uniform and seem to differ

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


18

for different airports and demand ratios. The above benefits portray a beneficial impact of LNAV/VNAV Capability

on Time-Based Scheduling especially at higher demand ratios. However, it is important to recognize the

assumptions of the benefits evaluation process. Some of the assumptions and caveats are listed below:

Concept:

o The overall concept assumes the ability to predict the aircraft's TOA in the absence of

uncertainty. For this purpose it is important to know the weight, cruise altitude, cruise CAS,

descent Mach, and descent CAS of the aircraft. Datalink capability may be required for

transmitting this information from the flight-deck to the ground-side.

o It is assumed that the aircraft’s reference trajectory is based on a 1hour RAP forecast. For

long duration flights this might require some form of communication from the Airline

Operations Center to receive these forecasts before the initiation of descents.

Uncertainty:

o The TOA uncertainty is based on Monte-Carlo simulation of one aircraft (A320 flying along

BIGSUR Route at SFO). Further Monte-Carlo simulations need to be conducted to better

evaluate this uncertainty for a wider range of aircraft, routes, and wind conditions.

o TOA uncertainty is currently estimated along one route at SFO using one wind uncertainty

model generated using 15 days of ACARS and RAP data. In case, the uncertainty is not

constant over the entire year the TOA uncertainty as well as the NextGen Capability benefits

will vary.

o Whereas the TOA uncertainty associated with flights equipped with NextGen Capabilities has

been rigorously estimated, the TOA uncertainty associated with unequipped aircraft is not

known. In this work it was assumed that the TOA uncertainty associated with unequipped

aircraft is slightly higher than those aircraft equipped with LNAV/VNAV capability. This is a

crucial assumption with significant impact on the results obtained.

Simulation:

o The STASS simulation environment uses a single transit-time for all flights along a route. In

reality the transit-time depends on the aircraft type and the descent speeds.

o The STASS simulation environment uses a single TOA uncertainty model for all flights. The

actual TOA uncertainty depends on the length of routes and distance from Meterfix to

Runway which could vary for different routes. The longer the distance the higher the

uncertainty.

Conclusion

The paper presents a rigorous framework for evaluating the benefits of LNAV + VNAV equipage on the

performance of time-based scheduling. Preliminary results indicate average-delay reduction benefits ranging from

3seconds to 280seconds. These benefits correspond to a fleet-wide LNAV+VNAV equipage level of 75%. The

benefits are more relevant for higher demand ratios (1.5x and 2.0x) than the current 1.0x demand ratio. The effect of

LNAV/VNAV equipage on throughput seems very modest. The number of separation violations seem to reduce and

overall benefit from LNAV/VNAV equipage. The results are based on a high-fidelity LNAV + VNAV model

developed in house and also a realistic wind uncertainty model. There exists some scope for refinement of these

models. Whereas the TOA uncertainty associated with flights equipped with NextGen Capabilities has been

rigorously estimated, the TOA uncertainty associated with unequipped aircraft is not known. In this work it was

assumed that the TOA uncertainty associated with unequipped aircraft is slightly higher than those aircraft equipped

with LNAV/VNAV capability. This is a crucial assumption with significant impact on the results obtained.

However, the paper establishes a realistic expectation of benefits from LNAV/VNAV equipage.

Acknowledgments

The work under the current research was sponsored by NASA Research Announcement NNA12AA49C. The

authors would like to thank Mr. Daniel Mulfinger, Mr. Leonard Bagasol, Mr. John Robinson, and Mr. Doug

Isaacson for their inputs and feedback to this research.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232


19

References 1“Concept of Operations for the Next Generation Air Transportation System, Version 3.2,” Joint Planning and Development

Office, September 30, 2010. 2Isaacson, D. R., Swenson, H. N., and Robinson III, J. E., “A Concept for Robust, High Density Terminal Air Traffic

Operations,” Proceedings of the 10th AIAA Aviation Technology, Integration, and Operations Conference, Fort Worth, TX, Sep.

13-15, doi: 10.2514/6.2010-9292, 2010. 3Kupfer, M., Callantine, T.J., Mercer, J., and Palmer, E., “Controller Support Tools for Schedule-Based Terminal-Area

Operations,” Ninth USA/Europe Air Traffic Management Research and Development Seminar, 2011. 4Sam Miller, “Contribution of Flight Systems to Performance-Based Navigation”,

www.boeing.com/commercial/aeromagazine/articles/qtr_02_09/article_05_1.html, Accessed Feb 25, 2013. 5Randy Walter, “Flight Management Systems”, in Avionics Elements, Software, and Functions, 2nd edition, edited by Cary R.

Spitzer, CRC Press, 2007, Chapter 20, pp. 20-1 to 20-26. 6Federal Aviation Administration, Advanced Avionics Handbook, FAA-H-8083-6, 2009, chap. 3. 7Honeywell, Avionics Pilot Guides & Familiarization Se ries. 8Rockwell Collins, Rockwell Collins Flight Management System, 2005. 9Spiro P. Karatsinides, “Flight Management VNAV-Approach Paths”, AIAA Guidance, Navigation, and Control Conference

and Exhibit, 5-8 August 2002, Monterey, California, AIAA 2002-4926. 10Alan C. Tribble and Steven P. Miller, “ Software Safety Analysis of A Flight Management System Vertical Navigation

Function – A Status Report”, 22nd Digital Avionics Systems Conference (DASC). 11Balakrishna, M., Becher, T. A., MacWilliams, P. V., Klooster, J. K., Kuiper, W. D., and Smith, P. J., “Seattle Required

Time-of-Arrival Flight Trials,” IEEE/AIAA 30th Digital Avionics Systems Conference (DASC), 16-20 Oct. 2011. 12Klooster, J. K., Wichman, K. D., and Bleeker, O. F., “4D Trajectory and Time-of-Arrival Control to Enable Continuous

Descent Arrivals,” Proceedings of the Guidance, Navigation, and Control Conference and Exhibit, August 2008, Honolulu,

Hawaii. 13Klooster, J. K., Amo, A. D., and Manzi, P., “Controlled Time-of-Arrival Flight Trials,” Proceedings Eighth USA/Europe

Air Traffic Management Research and Development Seminar (ATM2009). 14Wichman, K. D., Carlsson, G., and Lindberg, G. V., “Flight Trials: Runway-to-Runway Required Time of Arrival

Evaluations for Time-Based ATM Environment,” in Proceedings of the IEEE/AIAA 20th Digital Avionics Systems Comference

(DASC), vol 2. pp 7F6/1 - 7F6/13, Oct 2001. 15Krishnamurthy, K., Barmore, B., Bussink, F., Weitz, L., and Dahlene, L., “Fast-Time Evaluations of Airborne Merging and

Spacing in Terminal Area operations,” AIAA Guidance, Navigation, and Control Conference and Exhibit 15 - 18 August 2005,

San Francisco, California. 16Barmore, B. E., “Airborne Precision Spacing: A Trajectory-Based Approach to Improve Terminal Area Operations,” 25th

Digital Avionics Systems Conference, Portland OR. 15-19 October 2006. 17Barmore, B. E., Abbott, T.S., Capron, W. R. Baxley, B.T., “Simulation Results for Airborne Precision Spacing along

Continuous Descent Arrivals,” 8th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Anchorage,

AK, 14-19 September 2008. 18Verhoeven, R.P.M, de Gelder, N., “Time-based navigation and ASAS interval managed CDA procedures,” NLRTP-2009-

477, September 2009. 19Houston, V. E., and Barmore, B., “An Exploratory Study of Runway Arrival Procedures: Time-Based Arrival and Self-

Spacing,” 9th AIAA Aviation Technology, Integration, and Operations Conference (ATIO) 21 - 23 September 2009, Hilton

Head, South Carolina. 20Garrido-Lopez, G., D’Alto, L., and Ledesma, R. G., “A Novel Four-Dimensional Guidance for Continuous Descent

Approaches,” in Proceedings of the IEEE/AIAA 28th Digital Avionics Systems Conference, Oct. 2009, pp 6.E.1-1 - 6.E.1-11. 21Ballin, M., Williams, D., Allen, D. B., and Palmer, M. T., “Prototype Flight Management Capabilities to Explore Temporal

RNP Capabilities,” in Proceedings of the IEEE/AIAA 27th Digital Avionics Systems Conference (DASC), Oct. 2008, pp 3.A.6-1

- 3.A.6-12. 22De Prins, J., Ledesma, R. G., and Mulder, M., “Towards Time-based Continuous Descent Operations with Mixed 4D FMS

Equipage,” DOI: 10.2514/6.2011-7018, September, 2011. 23Vaddi, S. S., Sweriduk, G. S., and Tandale, M. D., “Design and Evaluation of Guidance Algorithms for 4D-Trajectory-

Based Operations,” Aviation Technology, Integration, and Operations (ATIO) Conference, Indianapolis, IN, Sep. 2012. 24H. N. Swenson, T. Hoang, S. Engelland, D. Vincent, T. Sanders, B. Sanford, and K. Heere, "Design and operational

evaluation of the traffic management advisor at the Fort Worth Air Route Traffic Control Center," 1st USA/Europe Air Traffic

Management R&D Seminar, Saclay, France, 1997. 25Swenson, H.N., Thipphavong, J., Sadovsky, A., Chen, L., Sullivan, C., and Martin, L., "Design and Evaluation of the

Terminal Area Precision Scheduling and Spacing System," 9th USA/Europe ATM R&D Seminar (ATM2011), Berlin, Germany,

14-17 June 2011. 26Thipphavong, J., Swenson, H., Lin, P., Seo, A.Y., and Bagasol, L.N., "Efficiency Benefits Using the Terminal Area

Precision Scheduling and Spacing System," AIAA-2011-6971, 11th American Institute of Aeronautics and Astronautics (AIAA)

Aviation Technology, Integration, and Operations (ATIO) Conference, Virginia Beach, VA, 20-22 Sep. 2011. 27Taylor, C., Masek, T., and Bateman, H., “A Decision Support Tool for High Density Area Departure and Arrival Traffic

Management,” AIAA-2011-6531, August 2011.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232

http://www.boeing.com/commercial/aeromagazine/articles/qtr_02_09/article_05_1.html


20

28Saraf, A. P and Slater, G. L., “Optimal Dynamic Scheduling of Aircraft Arrivals at Congested Airports,” Journal of

Guidance, Control, and Dynamics, Vol. 31, No. 1, Jan-Feb 2008, pp.53-65. 29Capozzi, B.J., Atkins, S.C., Choi, S., “Towards Optimal Routing and Scheduling of Metroplex Operations,” DOI:

10.2514/6.2009-7037, September 2009. 30Saraf, A. P., Clarke, J-P., and McLain, E., “Discussion and Comparison of Metroplex-Wide Arrival Scheduling

Algorithms,” DOI: 10.2514/6.2010-9258, September 2010. 31Mulfinger, D., and Sadovsky, A., “Design and Evaluation of a Stochastic Time-Based Arrival Scheduling Simulation

System,” 11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, 20 - 22 September 2011, Virginia

Beach, VA. 32Zhao, Y and Vaddi, S. S., “Algorithms for FMS Reference Trajectory Synthesis to Support NextGen Capability Studies,”

AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Los Angeles, CA, August 2013. 33Bai, X., Vaddi, S. S., and Zhao, Y., “Design and Evaluation of LNAV/VNAV Guidance Algorithms for Time-of-Arrival

Error Characterization,” AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Los Angeles, CA, August

2013. 34Tandale, M., Vaddi, S., Sengupta, P., and Lin, S., “Spatio-Temporally Correlated Wind Uncertainty Models for Simulation

of Terminal Airspace Operations,” AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Los Angeles,

CA, August 2013.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

AL

IFO

RN

IA -

BE

RK

EL

EY

on

June

25,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

013-

4232

effect of lnav and vnav equipage on time-based scheduling...the tapss system consists of four...

Documents