flight efﬁciency in european airspace · gotz, craig holloway, janis klaise, james mathews,...

Flight Efficiency in European Airspace

Martin Hawley and Karol Gotz, Winsland Consultancy

Chris Cawthorn, Gemma Cupples, Eoin Devane, Mel Devine, KarolGotz, Craig Holloway, Janis Klaise, James Mathews, Faizan Nazar,Cezary Olszowiec, Gunnar Peng, Clarice Poon, Cristina Sargent,

Jan Van Lent, Emily Walsh

Flight Efficiency in European Airspace 27/03/15 1 / 19

Outline

1 The Problem

2 Data analysis algorithms

3 Optimisation strategiesDiscrete approachContinuous problem approach


The Problem

Busy European airspaceCivil aircraft routing inefficiencies:

Military airspaceWaypoints

Investigate optimisation strategiesFlexible time access to military airspaceModification of military airspaceQuantification of benefits associated with each strategy


Data analysis algorithms

Sample data:Over 2,000 European airportsCirca 33,000 flights from a single day (departure airport/time,arrival airport/time, cruising altitude)Military airspace (location, altitudes)



Cost

Costs based on path flownFuel costsDelay costs



Data: Number of intersections

Plot great circle of flight routes, assume uniform speed and heightPlot paths of intervals of half an hourAssume all military airbases are availableWork out number of intersections with each military airbase in thathalf an hourPlot flights paths for a given day: movieTo represent data we colour each airbase according to number ofintersections; see movie!



Moving airbases

Investigate effect of moving one airbase by small amount oflatitude/longitudeCorresponds to moving airbases by about 30km along compasspoints as seen below



Optimal routing using actual waypoints/segments

Flights from LHR avoiding military space (blue):

10 oW

0o 10oE

20oE

30o E

36 oN

42 oN

48 oN

54 oN

60 oN



Optimal routing using actual waypoints/segments

Flights from LHR allowing access to all military space (red):

10 oW

0o 10oE

20oE

30o E

36 oN

42 oN

48 oN

54 oN

60 oN



And now on the whole of Europe . . .

Method explicitly outputs a cost saving of $30 per flight.Flight Efficiency in European Airspace 27/03/15 10 / 19


Discrete path planning

What is the cheapest path from A to B?

10

8

5

2

Start Goal

Dijkstra’s algorithm (or A*)How to calculate gains from removing any one obstacle withouthaving to re-run the search for each case?





10

8

5

2

Start Goal

0 100 110 310






10

8

5

2

Start Goal

0 100 110 310

0200210310



Optimisation strategies Discrete approach

Linear programming

The shortest path problem is

minxi,j,f

∑i,j

Ci,j,f xi,j,f (1)

subject to:

∑j

xi,j,f − xj,i,f =

1, if i = departure airport for flight f ,−1, if i = arrival airport for flight f ,0, otherwise.

∀ i , f . (2)

xi,j,f ≥ 0, ∀ i , j , f . (3)



Shortest Path on Visibility Graph – Toy Examples



Visibility Graph for Europe Data

10°W


Optimisation strategies Continuous problem approach

Continuous pathfinding approach


Optimisation strategies Continuous problem approach

Continuous pathfinding approach

Curve γ : [0,1]→ R2, such that γ(0) = 0, γ(1) = x,Cruise speed vc , Wind velocity field w : R2 → R2.Parametrisation: γ(t) = tx + a(t)x⊥, a(0) = a(1) = 0.

Time[a] = T [a] =∫ 1

0

√1 + a(t)2

v(t ,a, a,w)dt ,

where

v(t) =(|vc |2 + 2(x + a(t)x⊥) ·w(tx + a(t)x⊥)− |w(tx + a(t)x⊥)|2

)1/2.

Euler-Lagrange equation: subject to a(0) = a(1) = 0.

ddt

(a(t)

v(t)√

1 + a(t)2− 2x⊥ ·w(tx + a(t)x⊥)

v(t)3

)

+2(x + a(t)x⊥ −w(tx + a(t)x⊥)) · ∇w(tx + a(t)x⊥) · x⊥

v(t)3 = 0.


Ideas for further investigation

Future ideas

Find the path of several flights at onceInclude sector capacity constraintsInclude scheduling constraintsLast two options require to include time in the optimisation.Optimize overall network efficiency.

Questions?


flight efﬁciency in european airspace · gotz, craig holloway, janis klaise, james mathews,...

Documents