The BTF model computes the ground distance between the origin and destination airports, derives the flight’s cruise altitude, and by integrating two institutional data sets calculates the duration and the fuel consumed for the whole of taxi-out, take-off, climb, cruise, descent, approach, landing, and taxi-in phases. The statistical analysis of the results consists of comparing the BTF’s results with those from the ROADEF Challenge 2009, the ones retrieved from FlightAware, considering the same origin and destination airports and aircraft model. Statistical results are reported for percentile and root mean square error and it is demonstrated that the BTF's results for block time are in a lower percentile and have a lower root mean square error than the block times used by the ROADEF 2009 Challenge.

1. Jens
Martensson
CALCULATING
BLOCK TIME AND
CONSUMED
FUEL FOR AN
AIRCRAFT
MODEL
Francisco de Lemos
https://doi.org/10.1017/aer.2020.137

2. Jens
Martensson
THE BLOCK TIME AND FUEL (BTF)
MODEL
Introduction
What is block time?
What is necessary for flight planning?
Flight phases
The bearing (Magnetic Trajectory)
Coordinates for the departure and arrival airport
Cruise altitude
2

3. Jens
Martensson
BTF MODEL
What does the BTF model do?
Computes the ground distance between the
origin and destination airports (Haversine
formula)
Derives the flight’s cruise altitude (Pagoni
2017)
Integrates EMEP/EEA and BADA datasets
Calculates the block time: duration of the trip
gate to gate
Calculates the fuel consumed during block
time
Results 3
 EMEP (European Monitoring and
Evaluation Programme)

4. Jens
Martensson
BTF MODEL – FLIGHT PHASES
Flight phases
taxi-out
take-off
 climb
 cruise
 descent
Approach and Landing
taxi-in
4

5. Jens
Martensson
BTF MODEL – EMEP/EEA DATA
Most-used engine types for each of the most-used aircraft
types flying under Instrument Flight Rules(IFR)(3) in the
European airspace in 2015, source: EMEP/EEA air pollutant
emission inventory guidebook 2019
5

6. Jens
Martensson
BTF MODEL – EMEP/EEA DATA
Aviation 2 LTO emissions calculator 2019
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7. Jens
Martensson
BTF MODEL - BADA
BADA Performance Tables
7

8. Jens
Martensson
BTF MODEL – GROUND DISTANCE
Calculating ground distance, Haversine formula
8

9. Jens
Martensson
BTF MODEL – FLIGHT LEVEL
Defining cruise altitude with the semi-circular rule
9

10. Jens
Martensson
BTF MODEL – CRUISE ALTITUDE
Defining cruise altitude
(Pagoni 2017)

10
Modelling taxi-out,
take-off, approach,
landing and taxi-in
phases

11. Jens
Martensson
BTF MODEL – MOVEMENT
EQUATIONS
Modelling climb descent and cruise phases
11

12. Jens
Martensson
BTF MODEL – EQUATIONS OF
MOVEMENT
Modelling climb descent and cruise phases
12

13. Jens
Martensson
BTF MODEL – RESULTS
Results - A320 aircraft fuel flow vs. time during the
flight CDG-BCN
13
Taxi-out
Take-off
Climb
Cruise
Approach
and landing
Taxi-in
Descen
t

14. Jens
Martensson
BTF MODEL – RESULTS
Results - A320 altitude profile during the flight CDG-
BCN
14
Holding before
landing
Waiting
before take-
off clearness
Difference
between
landing times

15. Jens
Martensson
BTF MODEL – RESULTS
Results - Benchmarking BTF results against ROADEF
2009
15
 Compare the BTF model results for
block time with those supplied by the
ROADEF 2009 Challenge .
 Sample size: 60 distinct flight tuples
consisting of origin airport, aircraft
model and destination airport.
 Real flight block time distribution from
Flightaware between the July 7 and July
23 ,2019.
Source https://uk.flightaware.com/

16. Jens
Martensson
BTF MODEL – RESULTS
Results - Benchmarking BTF results against ROADEF
2009
16
 Percentage of block time retrieved from
Flightaware that are below the block time
values of the BTF model or the ROADEF
2009 Challenge.
 Number of percentile values less than
100 presented in the BTF model exceeds
those presented by ROADEF 2009
Challenge,
 BTF block time can be used as a lower
bound for simulation or validation
procedures.

17. Jens
Martensson
BTF MODEL – RESULTS
Results - Benchmarking BTF results against ROADEF
2009
17
 RMSE
 k is the sample size for each flight f, tn is
the block time retrieved from Flightaware
and t is the block time value either from
the BTF model i = 1 or the ROADEF 2009
Challenge, i = 2
BTF presented a larger set of lower values
than the one presented by ROADEF

18. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results in the
literature review
 Ridvan Oruc and Tolga Baklacioglu. Modelling of fuel flow-rate of commercial aircraft for the climbing flight using
cuckoo search algorithm. Aircraft Engineering and Aerospace Technology, 92(3):495–501, feb 2020.
18
 The work of Oruc
consists in determining a
fuel flow function for the
climb phase, for a
Boeing 737-800.
 BTF model uses the
fuel flow data provided
by BADA, in the
performance table for
the Boeing 737-800.

19. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between the results in the
literature review
 Ridvan Oruc and Tolga Baklacioglu. Modelling of fuel flow-rate of commercial aircraft for the climbing flight using
cuckoo search algorithm. Aircraft Engineering and Aerospace Technology, 92(3):495–501, feb 2020.
19

20. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results in the
literature review
 Alejandro Murrieta-Mendoza, Hugo Ruiz, and Ruxandra Mihaela Botez. Vertical reference flight trajectory
optimization with the particle swarm optimisation. In Modelling, Identification and Control. ACTAPRESS, 2017
20
 In the work of Murrieta-Mendoza there is no explicit reference to which
phases, or aircraft models considered when modeling fuel burn using the
geodesic or the optimal trajectory.
 We assume that authors considered only CCD phases.
 Our assumption, for the aircraft models is based on our research of
Flightaware for the most common aircraft models used on the same flights
namely the Boeing 787-900 for the flights from Montreal to Paris and
Toronto to London.
 As for the flight from Montreal to Vienna, since we were not able to find
any direct flights we aggregate the consumed fuel from two legs , the first
from Toronto to Amsterdam using a Airbus 330-200, and the second one
from Amsterdam to Vienna using a Boeing 737-800.

21. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results in the
literature review
 Alejandro Murrieta-Mendoza, Hugo Ruiz, and Ruxandra Mihaela Botez. Vertical reference flight trajectory
optimization with the particle swarm optimisation. In Modelling, Identification and Control. ACTAPRESS, 2017
21

22. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results in the
literature review
 Sander Hartjes, Marco E. G. van Hellenberg Hubar, and Hendrikus G. Visser. Multiple-phase trajectory optimization
for formation flight in civil aviation. CEAS Aeronautical Journal, 10(2):453–462, sep 2018.
22
 In the work of Hartjes
the authors modeled the
flights, from London to
Atlanta and from Madrid
to New York, using a
Boeing 747-400.
 To compare the results
of the BTF model and
those presented in
Hartjes2018 we used
the same aircraft model
and assumed precise
airport locations for each
of the flights.

23. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between the results in the
literature review
 Sander Hartjes, Marco E. G. van Hellenberg Hubar, and Hendrikus G. Visser. Multiple-phase trajectory optimization
for formation flight in civil aviation. CEAS Aeronautical Journal, 10(2):453–462, sep 2018.
23
 In the work of Hartjes2018
during, the cruise phase, the
fight level increases with time
and true airspeed decreases
with time.
 In the BTF model we assume
that the cruise altitude is FL 380
and that the true airspeed has a
constant value 451 Kts.
Differences between the results
of work of Hartjes2018 and the
BTF model are minimal.

24. Jens
Martensson
BTF MODEL – LIDO FLIGHT PLAN
EXPLAINED
24
Standard Departure
Time
Expected Time of
Departure
Expected Take-off
Time
Fuel On Board
Zero Fuel Weight
Waypoints
Ground Distance
Air Distance
Average Fuel Flow
Take-off Weight
Landing Weight
Reserve Contingency
Alternative Airport
Fuel Reserve
Take-off fuel
Taxi-out fuel

25. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results Lido Flight
Plans
25

26. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results Lido Flight
Plans
26

27. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results Lido Flight
Plans
27

28. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results Lido Flight
Plans
28
 It is possible to verify a significant goodness-of-fit for the linear
regression for block time relative difference vs. BTF block time and,
block time relative difference vs. air distance.
 However, for consumed fuel relative difference vs. BTF block time
and consumed fuel relative difference vs. air distance, the R2 value is
very low, hence the linear regression does not explain the variation
in the consumed fuel relative difference.
 In conclusion the observed relative differences for consumed fuel
cannot be entirely accounted by block time or air distance.
 Future work, the BTF model should consider other factors such as
the change of aircraft weight during the flight.

29. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results Lido Flight
Plans
29

30. Jens
Martensson
BTF MODEL – RESULTS
Results - Comparisons between BTF results Lido Flight
Plans
30
 Percentile results for BTF and Lido are in line with those obtained for
ROADEF.
 RMSE results for BTF and Lido are in line with those obtained for
ROADEF.

31. Jens
Martensson
BTF MODEL – CONCLUSIONS AND
FUTURE WORK
 We conclude that aggregating EMEP/EEA data with BADA PTF data provides a
simple and fast approach for block time and consumed fuel computation and
hence we are able to confirm the conclusion of Alam:
 BADA fuel flow tables are a good approach when computational cost is a
factor.
 Using this method we were able to extend the work of Alam, Murrieta-
Mendoza and Hartjes not only in terms of the number flights evaluated but also
for all the flight phases.
 The BTF model results are compared with Lido, used in commercial flight
planning. They prove to be in accordance.
 The BTF model provides lower bound results for flight planning.
 Future work will introduce the BTF results for block time in the ROADEF
Challenge 2009. The aim is to verify if shorter block times can mitigate flight
disruption.
31

32. Jens
Martensson
Francisco de Lemos
f.j.r.lemos@qmul.ac.uk
THANK
YOU