Mach Number Selection for Cruise Phase Using Ant Colony Algorithm

with RTA ConstrainsAlejandro Murrieta-Mendoza, Antoine Hamy, Ruxandra M. BotezUniversité du Québec / ÉTS/ LARCASE

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Motivation

Airline Expenses: 26% - 40%

Fuel

innovation.columbia.edu

- Profit- Financial Planning

- CO2 - Global Share: 2% - NOx- H20- Hydrocarbons

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MotivationCanada: The Green Aviation Research & Development Network (GARDN)

Develop technologies to reduce aircraft noise and emissions.

Governmental Funding + Industrial Funding + University Expertise

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Introduction

How to reduce fuel?

www.turbosquid.com

SA 3.0

Winglets

Engines Improvements

Morphing wings

Trajectories and Airspace

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Introduction

• Conventional 3D Trajectories– Flight Plan.– Voice communication.

• 4D Time based Trajectories: IBO/TBO– Flight Plan– Advanced Systems– Required Time of Arrival

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Objectives

• Combination of Mach numbers that fulfill the RTA.

ETA = RTA• Reduce the fuel consumption

– Reduce CO2, NOx, HC, etc…

innovation.columbia.edu

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Trajectory Studied

• Cruise Phase– Bucharest – Grand Canary

• Constant Altitude

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Methodology

• Flight Cost

   

Performance Database

Experimental Flight Data

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𝐶𝑜𝑠𝑡=𝐹𝑢𝑒𝑙 𝐵𝑢𝑟𝑛𝑒𝑑+𝐶𝑜𝑠𝑡 𝐼𝑛𝑑𝑒𝑥∗ h𝐹𝑙𝑖𝑔 𝑡𝑇𝑖𝑚𝑒

Methodology

𝐺𝑆=𝑇𝐴𝑆±𝑊𝑖𝑛𝑑𝑆𝑝𝑒𝑒𝑑∗ cos(𝑊𝑖𝑛𝑑𝐴𝑛𝑔𝑙𝑒)

h𝐹𝑙𝑖𝑔 𝑡 𝑇𝑖𝑚𝑒=𝐺𝑆

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

        

RTAWaypointTotal FlightTime FlightTime

i

        

RTAWaypointTotal Fuel Burn Flight Burn

i

𝑅𝑇𝐴• Flight Cost

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Methodology

• How to manage the Mach Number?– Mach Number as a grid

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Mach Number Options

Lateral Flight Plan

Methodology

• Ant Algorithm– Ants wander around for food sources.

– Different ants find the food source.

– Over time the shortest path is selected.

– Use pheromone to keep track of the path• The more ants are in a path, the more pheromone there is

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Methodology

• Ant Algorithm– Probability to select a given Mach Number

– Pheromone Evaporation

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_ * _

_ * _

Fije ij Conso ij

PijFik

e ik Conso ik

1 1    F t F t N P Cij ij ij ij

 e Tt Tr

Results

• 2 Turbo-Fan Aircraft

• Real Flight Plan Waypoints were used– Weather obtained from flight plan

• RTA waypoint just before the ToD.

• Arbitrary imposed RTAs.

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Results

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0 200 400 600 800 1000 1200 1400 1600 1800 20000.77

0.78

0.79

0.8

0.81

0.82

0.83

0.84

0.85

Distance (nm)

Mac

h

Mach Progression, RTA: 4h 20min

4h 20min 0sec.

• RTA: 4h20m0s– Tolerance: +/- 30 sec

Tailwind Headwind Hedwind

Tailwind

Results

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0 200 400 600 800 1000 1200 1400 1600 1800 20000.74

0.75

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0.84

Distance (nm)

Mac

h

Mach Progression – Different RTA

4h 20min4h 24min4h 30min4h 34min

• RTA1: 4h20m (blue) RTA2: 4h24min (green)• RTA3: 4h30m (red) RTA4: 4h36min

(magneta)

Results

• Flight Cost

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Flight RTA Flight Time Difference (s) Fuel Burn (T)1 4h20 4h20m00s - 16.0572 4h25 4h24m59s 1 16.8483 4h30 4h30m40s 40 18.6804 4h35 4h34m43s 17 19.431

Flight # Mach Number

Flight Time

Fuel Burn (Ton)

1 0.80 4h29m07s 18.42 0.81 4h25m30s 18.83 0.82 4h22m07s 19.1

NO RTA

RTA

Conclusion

• In almost all cases, the ACO respected the RTAs imposed.

• The algorithm was able to improve fuel burn. – Less fuel burn equals less emissions.

• The algorithm takes local decisions.• A global weather view is required to reduce

the Mach Number variation.

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Thank YouQ & A

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