Requirement 1: Landing Field Length (LFL)

Background

landing distance, landing field length, landing distance available

The landing distance (LD) is defined in the aviation regulations:

JAR 25.125 Landing.
(a) The horizontal distance necessary to land and to come to a complete stop from a point 50 feet above the landing surface must be determined ... as follows:
(1) The aeroplane must be in the landing configuration.
(2) A stabilised approach, with a calibrated airspeed of not less than 1.3 VS, must be maintained down to the 50 foot height.

For jet powered aircraft, the landing field length (LFL) is 1/0.6 = 1.667times the landing distance and must not be more than the landing distance available (LDA). This follows from JAR OPS 1.515:

JAR - OPS 1.515 Landing - Dry Runways
(a) An operator shall ensure that the landing mass of the aeroplane ... allows a full stop landing from 50 ft above the threshold:
(1) Within 60 % of the landing distance available at the destination aerodrome and at any alternate aerodrome for turbojet powered aeroplanes ... .

The landing distance available has to be less or equal than the safety landing field length.

Figure 1: animation of landing field

typical landing field lengths
next: equations for calculation

Equations

The landing field length requirement determines an upper limit for the wing loading. The equation for the wing loading is calculated from four basic equations.

1. equilibrium (weight = lift):

2. Loftin'statistic:

3. minimum approach speed:

4. mass ratio:

These equations combined and solved for the wing loading m_MTO /S_W yields
result equation

with a factor k_L = 0.107 kg/m³, the density at sea level = 1.225 kg/m³.
Lift-coefficient c_L,max,L, landing field length s_LFL
and mass ratio m_ML/m_MTO are chose from statistics.

A click on a variable/equation informs about the background.

Data

Maximum landing lift-coefficient:

The maximum landing lift-coefficient depends on the type of the high lift systems. Several systems were developed to increase the lift coefficient with the intention to decrease the approach velocity. The values of the lift coefficient range from 1.3 for a clean profil and to 3.0 for a profil with Fowler flaps and slats. Today's aircraft have maximum landing lift-coefficients of around 2.6. For details see e.g. Dubs 1987 or Roskam 1989.

statistics of lift-coefficient

next: calculation of wing loading and approach speed

Calculation

With given values of landing field length, maximum landing lift-coefficient and mass ratio it is now possible
to calculate the wing loading an the approach speed. The following assumptions are made:
- the density at the airport is the density at sea level
- the aircraft is a jet.
Typical start values are already entered in the table. The graph is presented in Figure 2.

landing field length s_LFL : [ m ]		maximum landing lift-coefficient c_L,max,L : [ - ]	landing to takeoff mass (range): 0.91 (short) 0.82 (middle) 0.73 (long) custom:

results :	approach speed : [ m/s ]		wing loading : [ kg/m² ]

The result can be saved for the matching chart.
Figure 2: chart for calculated results

The wing loading of the aircraft must be on the left of the blue line above to fulfil the requirement for the landing condition. Bear in mind: The aircraft's weight is limited due the landing requirements.

Results compared

The wing loading and approach speed calculated above may be compared and checked against existing aircraft.

wing loading and approach speed of selected aircraft Jane's 1995-98

Aircraft	Airbus A 300-600B	A 310-300	A 340-300	Antonov AN 124	Boeing B 737-600	B 777	Learjet 60	McDonnell Douglas MD11	Tupolev TU 204
Wing loading [kg/m²]	634.6	684.9	707.8	644.9	520.7	567.2	433.8	806.4	518.6
Approach speed [m/s]	69.2	69.4	N/A	63.8-72.2	64.7	71.1	71.4	N/A	61.1

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Thomas Perthel, thomas.perthel@gmx.de