Requirement 2: Takeoff Field Length (TOFL)

Background

Three different takeoff cases are described in the regulations:

1. One engine inoperative (OEI) before decision speed (V1)

In this case of an engine failure before decision speed V1, the aircraft must come to a full stop. The covered distance is called accelerate-stop distance (ASD):

JAR 25.109 Accelerate-stop distance.
(a) The accelerate-stop distance (...) is the greater of the following distances:
(2) The sum of the distances necessary to -
(i) Accelerate the aeroplane from a standing start to V1 and continue the acceleration for 2·0 seconds after V1 is reached with all engines operating; and
(ii) Come to a full stop from the point reached at the end of the acceleration period prescribed in sub-paragraph (a)(2)(i) of this paragraph, assuming that the pilot does not apply any means of retarding the aeroplane until that point is reached and that all engines are still operating.

2. One engine inoperative after decision speed

The speed of the aircraft is now higher than decision speed (VEF > V1), the aircraft has to takeoff:

JAR 25.111 Take-off path.
(a) ...
(2) The aeroplane must be accelerated on the ground to VEF, at which point the critical engine must be made inoperative and remain inoperative for the rest of the take-off; and
(3) After reaching VEF, the aeroplane must be accelerated to V2.
(b) During the acceleration to speed V2, the nose gear may be raised off the ground at a speed not less than VR. However, landing gear retraction may not be begun until the aeroplane is airborne.
(c) During the take-off path determination in accordance with sub-paragraphs (a) and (b) of this paragraph -
(2) The aeroplane must reach V2 before it is 35 ft above the take-off surface ... .

If accelerate-stop distance is equal to takeoff distance OEI, then the takeoff field length is called balanced field length.

3. All engines operating (AOE)

If all engines operating the takeoff distance has to be 115 % of the horizontal distance from start point to a point 35 ft above the takeoff surface. (JAR 25.113)
The safety takeoff field length is the greatest of all 3 cases.

JAR 25.113 Take-off distance and take-off run
(a) Take-off distance is the greater of -
(1) The horizontal distance along the take-off path from the start of the take-off to the point at which the aeroplane is 35 ft above the take-off surface, determined under JAR 25.111; or
(2) 115% of the horizontal distance along the take-off path, with all engines operating, from the start of the take-off to the point at which the aeroplane is 35 ft above the take-off surface, as determined by a procedure consistent with JAR 25.111.

typical landing field lengths
next: equations for calculation

Equations

The takeoff field length consists of two parts: takeoff ground roll and takeoff path to 35 ft height.
The equation for takeoff ground roll is:
The ground roll distance depends on several measures:

speed (lift-off v_LOF, stall v_S, wind v_W)
thrust T_TO
lift L_TO and drag D_TO
rolling friction
weight m_MTO
runway slope

To get an estimate equation, which can be used in aircraft design it is necessary to make certain simplifications:

The lift-off speed is equal to 1.2 × stall speed v_S.
The wind speed is zero.
Drag and roll friction are not calculated in detail but taken care of only by a correction factor.
The takeoff field length s_TOFL is assumed to proportional to the takeoff ground roll s_TOG.

The final result is an equation for the ratio takeoff thrust to weight over wing loading:
result equation

Factor k_TO = 2.34 m³/kg is taken from LOFTIN 1980. The density at sea level is given to = 1.225 kg/m³.
The lift-coefficient c_L,max,TO is selected from design statistics (see below). The takeoff field length s_TOFL is a known requirement.

A click on a variable informs of their origin.

Data

Maximum takeoff lift coefficient

The coefficient is around 80 % of the maximum landing lift coefficient. Today's aircraft have maximum takeoff lift coefficient around 2.0. For detailed values it is recommend to consult statistics, e.g. DUBS 1987 or ROSKAM 1989.

statistics of lift coefficient
next: calculation of takeoff thrust to weight over wing loading

Calculation

Figure 2: chart for calculated results

The wing loading of the aircraft has to be to the left of the red line in order to fulfil the takeoff requirement. (Bear in mind: The thrust has to increase if the weight increases.)

Results compared

Takeoff thrust to weight over wing loading ratio of selected aircraft JANE'S 1995-98

Aircraft	Airbus A300-600B	A310-300	A340-300	Antonov AN124	Boeing B737-600	B777	Learjet 60	McDonnell Douglas MD11	Tupolev TU204
TO- thrust / weight wing loading [m²/kg]	0.000485 - 0.00051	0.000424 - 0.00052	0.000311 - 0.000339	0.000358	0.000589	0.000515 - 0.000536	0.000902	0.000371 - 0.000383	0.000658 - 0.000797

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Thomas Perthel, thomas.perthel@gmx.de