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Numerical and Analytical Takeoff Field Length Calculations for Jet Aircraft

Dennis Lucht

Abstract
Purpose – The greater of two distances (Balanced Field Length or Takeoff Distance +15%) results in the Takeoff Field Length (TOFL). The TOFL is a takeoff distance with safety margins according to Certification Standards for Large Aeroplanes by EASA (CS-25) and FAA (FAR Part 25). Simple analytical approximations for the TOFL are checked against more demanding numerical simulations to determine the validity of the simple solutions and to implement adjustments for them as necessary. --- Methodology – The differential equation of the aircraft's acceleration is solved in MATLAB together with varying engine failure speeds. Analytical calculations of the Balanced Field Length by Torenbeek, Kundu, and Loftin are investigated. This includes the evaluation of statistical data. --- Findings – Analytical approximations deviate by 0.1% to 28.2% from the numerical solution. The most accurate analytical approximation is the simple method proposed by Loftin based on statistics. It shows deviations of less than 5.4%. The results confirm that the TOFL for jets with four engines is determined by the Takeoff Distance +15%, while for jets with two engines, the Balanced Field Length is decisive for TOFL. --- Research limitations – Simplifying assumptions had to be made e.g. regarding rotation time and speed, flap geometry, and asymmetric drag. While ground distances were solved numerically from acceleration and deceleration, air distance and rotation distance had to be determined analytically. --- Practical implications – A reliable and tested analytical procedure is useful for quick aircraft performance estimates and to include an inverse TOFL method into aircraft preliminary sizing. --- Originality – This seems to be the first report to provide a systematic check of available analytical approximations for the TOFL in comparison with a numerical solution.

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Date:2022-06-15
Type of work: Bachelor Thesis
Advisor / Examiner:Dieter Scholz
Published by:Aircraft Design and Systems Group (AERO), Department of Automotive and Aeronautical Engineering, Hamburg University of Applied Sciences
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Persistent Identifier: https://doi.org/10.48441/4427.2886
 
PERSISTENT IDENTIFIER:
URN: https://nbn-resolving.org/urn:nbn:de:gbv:18302-aero2022-06-15.018 (to reach this page)
DOI:https://doi.org/10.15488/20694
ARK:https://n2t.net/ark:/13960/s2t1cc38jkg
Associated research data:https://doi.org/10.7910/DVN/QX3MAH    (Program and Data)
URLs registered with URN: Show all links associated with this text!
 
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Keywords, German (GND): Luftfahrt,   Flugzeug,   Flugleistung,   Flugzeugentwurf,   Start
Keywords, English (LCSH): Aeronautics,   Airplanes,   Airplanes--Performance,   Electronic spreadsheets
Keywords, free: Luftfahrttechnik, Verkehrsflugzeug, Flugmechanik, Zulassung, Airbus, Boeing, Computersimulation, Tabellenkalkulation, Aeronautical engineering, Jet transports, take-off, aviation, aircraft, balanced field length, BFL, TOFL, take-off distance, TOD, MATLAB, EXCEL, Abflug, acceleration, deceleration, EASA, FAA
DDC: 629.13,    629.132,    629.1323,    629.1325212
RVK: ZO 7250

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Any further request may be directed to:
Prof. Dr.-Ing. Dieter Scholz, MSME
E-Mail see: http://www.ProfScholz.de

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LUCHT, Dennis, 2022. Numerical and Analytical Takeoff Field Length Calculations for Jet Aircraft. Bachelor Thesis. Hamburg University of Applied Sciences, Aircraft Design and Systems Group (AERO). Available from: https://nbn-resolving.org/urn:nbn:de:gbv:18302-aero2022-06-15.018 [viewed YYYY-MM-DD].

Major results / graphical abstract:
Balanced Field Length (BFL) and Take-Off Distance (TOD) with All Engines Operative (AEO)

Balanced Field Length (BFL) and Take-Off Distance (TOD) with All Engines Operative (AEO) factored with 1.15 to give TOD1.15 . Aircraft with 2 engines are sized from BFL. Aircraft with 4 engines are sized from TOD1.15 .

 

Modified analytical solution from Loftin to estimate Take-Off Field Length (TOFL)

Modified analytical solution from Loftin to estimate Take-Off Field Length (TOFL).

 

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LAST UPDATE:  20 February 2026
AUTHOR:  Prof. Dr. Scholz
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