Takeoff and Landing Performance Optimization Development of a Computional Methodology João Pedro Rodrigues de Lemos Viana Dissertation submitted to obtain the Master’s Degree in Aerospace Engineering Jury Chair: Prof. Fernando José Parracho Lau Supervisor: Prof. António José Nobre Martins Aguiar External examiner: Prof. Pedro da Graça Tavares Alvares Serrão October 2011
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Takeoff and Landing Performance Optimization
Development of a Computional Methodology
João Pedro Rodrigues de Lemos Viana
Dissertation submitted to obtain the Master’s Degree in
Aerospace Engineering
Jury
Chair: Prof. Fernando José Parracho Lau Supervisor: Prof. António José Nobre Martins Aguiar External examiner: Prof. Pedro da Graça Tavares Alvares Serrão
October 2011
i
Acknowledgments
It is a pleasure to thank those who have contributed to the realization of this dissertation:
Daniela Vasco, my girlfriend, who has always supported me, especially in the later stages of
this work. Thank you for your patience.
António Aguiar, Engr., my supervisor, for giving me the chance to take part in such an
interesting project and, also, for the amount of time and close attention to detail he has always
offered when coordinating this project.
Carlos Figueiredo, one of the lead engineers on TAP’s Electronic Flight Bag project, who has
played a major role in this work, never hesitating in grating me some of his valuable time.
António Messias, Engr., Pedro Faria Pereira, Engr., and Paulo Marques, who provided utmost
important feedback during the development of this project.
Notwithstanding all the people that made my experience more enjoyable at TAP during the last
six months, namely Bruno Moreira, David Afonso, Marília Santos, Ana Maria Sousa, Amélia
Santos, Ivo Santos and Belinda Cardoso.
ii
Abstract
During the past decades the global aviation industry has been experiencing a precarious
balance between revenue and costs. Besides, the modern world is living an economic recession
and so crude prices are now higher than ever. Therefore, all over the world, airlines need to
adapt and evolve, finding new ways of struggling through the competitive world of commercial
aviation. Optimization is currently the key to succeed.
Aircraft performance data calculation and optimization reflects through the whole airline
operation. Besides having flight safety as its ultimate concern, data availability and easy
recalculation makes airlines’ operation more safeguarded to operation disruptions due to
external agents. Also, the quality of this data reflects in the airlines’ balance sheets at the end of
the year as the result of possible savings in different areas of operation [1].
The present work focuses in the development of a computational application for takeoff and
landing performance data generation and optimization. The takeoff performance optimization
entails the maximization of the Regulatory TakeOff Weight (RTOW) and the respective
operational speeds (V1, VR and V2). In a similar way, the Regulatory Landing Weight (RLW), the
final approach speed (VFA) and the landing distances (actual and required) are computed during
the landing optimization. The results are to be automatically published in the form of RTOW and
RLW charts. The actual calculations are processed by Airbus’ Operational and Certified TakeOff
and landing Performance Universal Software (OCTOPUS).
The developed application is more than a simple program; it handles a set of TAP’s databases
and external programs with the single objective of providing customized aircraft performance
optimization capabilities, at the distance of one click, to TAP’s personnel.
In opposition, the purpose of leading edge high-lift devices like slats (Figure 4) is not to increase
the lift coefficient for a given angle of attack. Their aim is to delay airflow separation until a
higher angle of attack is reached and this way helping the wing to achieve a higher maximum lift
coefficient than would be otherwise possible [9].
7
Figure 4- Slat [9].
Figure 5 - Flaps lever [13].
The pilot uses the flaps lever (Figure 5) to select simultaneously the slat and flap setting.
Consequently, it is a common practice to refer to the “flap setting” and the “aircraft
configuration” interchangeably. For that reason the author will make no distinction between
these two terms.
For example, considering an Airbus A320, the five positions of the flaps’ lever correspond to the
following surfaces positions:
Lever Position Slats Flaps Flight Phases
0 0° 0° Cruise / Hold
1 18° 0° Hold / Approach
10°
Takeoff
2 22° 15° (14°) Approach
3 22° 20° (21°) Approach / Landing
Full 27° 35°(*) (25°) Landing (*) : 40° for A320 with IAE
3 engine or A319
( ) : setting for A321
Table 1 - A320 family Flap and Slat configurations [14].
Additionally, some aircraft configurations also activate the speedbrakes (e.g. configuration FULL
or configuration 3 for A321 [14]).
3.1.2. Engine Bleeds
Aircraft engine bleeds are required by the Anti-Icing and the Air Conditioning systems. The following figure represents the Environmental Control System (ECS) schematic; its purpose is to highlight the connections between the engines, the Anti-Icing and the Air Conditioning systems (see ATA 21 refers
to Air Conditioning ATA 26 refers to Pneumatic Systems
Figure 6).
From an aircraft performance engineer’s perspective, operation of any of these systems
degrades the performance of the aircraft since the “engine air bleed for de-icing or air
conditioning, implies a decrease in engine thrust” [15, p. 124]. This reflects negatively on the
climb gradients and consequently on the takeoff and landing performance.
Although the air conditioning can be switched on or off (depending on the company policy), the
anti-icing system must be switched on if the environmental conditions demand it (according to
regulation).
3 International Aero Engines (engine manufacturer)
8
ATA
4 21 refers to Air Conditioning
ATA 26 refers to Pneumatic Systems
Figure 6 - Environmental Control Systems for the A320 family [14].
3.1.3. Aircraft Status (MEL/CDL)
Aircraft status is dealt with by the Minimum Equipment List (MEL) and the Configuration
Deviation List (CDL).
“MEL procedures were developed to allow the continued operation of an aircraft with specific
items of equipment inoperative under certain circumstances. The (…) [FAA and the JAA have]
found that for particular situations, an acceptable level of safety can be maintained with specific
items of equipment inoperative for a limited period of time, until repairs can be made. The MEL
document describes the limitations that apply when an operator wishes to conduct operations
when certain items of equipment are inoperative” [16].
Under certain conditions, aircraft may be approved for operations even with missing secondary
airframe and engine parts [16]. The aircraft source document for such operations is the CDL.
Since under these circumstances aircraft performance may be affected, considerations must be
made for the takeoff and landing optimization processes. For this purpose, the developed
computational method takes advantage of a CDL database (provided by the manufacturer) as
will be explained in the 8th chapter of the current work.
In the aircraft’s MEL/CDL manual items are addressed by their ATA code. Table 2 is an
example of the CDL items referenced in the MEL/CDL manual, in this particular case, for an
Airbus A319-111.
4 Air Transport Association of America Spec 100 – A broadly used specification that provides
common reference for all commercial aircraft documentation. It defines a widely-used outline for aircraft parts and systems, according to their characteristics and functions which are referred as ATA Chapters [34].
9
ATA Chapter Items
ATA21 AIR CONDITIONING ATA21-01 Ram air inlet flap ATA21-01 Ram air inlet flap (MOD 26363) ATA21-02 Ram air outlet flap
ATA52-01 Toilet servicing door and drainage 172AR ATA52-02 Access door to hydraulic ground connectors. 197CB - 197EB - 198CB ATA52-04 Access door to opening control of landing gear doors on ground 195BB ATA52-08 Cargo door opening system - Access door of cargo opening system 134AR ATA52-09 Nose landing gear main doors (713, 714) ATA52-10 Nose landing gear aft doors (715, 716) ATA52-12 Main landing gear door (732, 742) (flight with gear up) ATA52-13 Main landing gear door (733, 743) (flight with gear up) ATA52-14 Main landing gear door (732, 742) (flight with gear down) ATA52-15 Main landing gear door (733, 743) (flight with gear down) ATA52-16 Main landing gear door (734, 744) (flight with gear down) ATA52-18 Main landing gear door: Seal on secondary hinged fairing ATA52-19 Pax door upper cover plate ATA52-22 Forward cargo door access cover panel 825AR ATA52-23 Aft cargo door access cover panel 826AR
ATA54 NACELLES/PYLONS ATA54-01 Nacelle Strake
ATA54-03 Pylon pressure relief door 413 (423)BL - 414 (424)BR
ATA57 WINGS ATA57-01 Wing tip fence - Complete wing tip fence ATA57-01 Wing tip fence - Lower part of wing tip fence
Table 2 - A319-111 CDL (data from LPCAirport database).
3.2. Aircraft Limitations
3.2.1. Limiting Speeds
This subchapter is not an enumeration of all the limiting speeds. Since its aim is to provide the
reader with a background for the subsequent chapters, the author will focus on the most
relevant definitions and the ones that have a direct impact on the takeoff and landing
optimizations.
a) Stall Speed
Stall is a loss of lift caused by either the breakdown of airflow over the wing when the angle of
attack passes a critical point, or at a fixed angle of attack, when the speed goes bellow a critical
value.
Air velocity increases over the wing with the angle of attack5, it follows that air pressure
decreases and consequently the lift coefficient increases. This can be seen across the blue
section of the figure below:
5 The angle formed between the relative airflow and the chord line of the airfoil [30].
10
Figure 7- CL versus angle of attack (adapted from [15]).
The lift coefficient increases until it reaches the maximum lift point (CLMAX). From this point on
the lift coefficient suffers a sudden decrease.
This occurrence is called a stall and two speeds can be identified [15]:
VS1g, which corresponds to the maximum lift coefficient, when the load factor is equal to
one.
VS, which corresponds to the conventional stall, when the load factor is already less
than one.
VS1g is the reference stall speed for the airbus fly-by-wire aircraft and consequently for all the
TAP’s aircraft. Consequently, as in Airbus official documentation, in this work VS is referred to
as VS1g.
b) Minimum Control Speed on the Ground (VMCG)
The Minimum Control Speed on the Ground (VMCG) defines the minimum speed that ensures
that the aircraft will remain controllable during the takeoff roll, in the event of an engine failure
on the ground [17].
According to regulations, the lateral excursion must be less than 30 feet after an engine failure
on the ground (see Figure 8) (JAR 25.149 (e)).
Figure 8 - VMCG (adapted from [18]).
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The following conditions are assumed for VMCG determination [18]:
• Most critical takeoff configuration
• Most unfavorable center of gravity
• Most unfavorable takeoff weight
• Aircraft trimmed for takeoff6
• Operating engines on takeoff power
VMCG mainly depends on [15]:
Engine(s) thrust and position
Pressure altitude
For further information on VMCG see Appendix A - JAR 25.149 (e).
c) Minimum Control Speed in the Air (VMCA)
Minimum Control Speed in the Air (VMCA) is the speed at which in case of an engine failure the
aircraft can be controlled either with a 5 degree maximum bank angle (Figure 9 – a), or with
zero yaw (Figure 9 – b) (JAR 25.149 (b) and (c)).
Figure 9 - Sideslip angle (a) and bank angle (b) in a one-engine-inoperative condition (adapted from [17]).
All the conditions for the determination of VMCG are assumed plus [18]:
• The aircraft is airborne and out of ground effect
• Landing gear is retracted
• Inoperative engine windmilling7
Further information on VMCA is presented in Appendix A - JAR 25.149, paragraphs (b) and (c).
6 Trimmers adjusted in order to get the required hands-off pitch attitude prior to the takeoff [30].
7 Turning around by wind force only, without engine power [30].
12
d) Minimum Unstick Speed (VMU)
According to regulation, “VMU is the calibrated airspeed at and above which the airplane can
safely lift off the ground, and continue the takeoff” (JAR 25.107 (d)).
VMU is determined during low speed flight test demonstration (Figure 10). The control stick is
pulled to the limit of the aerodynamic efficiency of the control surfaces, taking the aircraft on a
slow rotation to an angle of attack at which either the maximum lift coefficient is achieved, or the
Table 5 - Takeoff Segments Characteristics (adapted from [15]).
11
Flexible takeoff is explained in chapter 5.4 12
Green Dot speed is the optimum climb gradient speed, one engine out (APT INT A320-214)
24
4.3.2. Obstacle Clearance
Most of the time, runways have surrounding obstacles that must be taken into account prior to
takeoff, to determine that the aircraft is able to clear them with a certain safety margin. This
leads to the definition of gross and net flight paths.
Also, “Some airports are located in an environment of penalizing obstacles, which may
necessitate turning to follow a specific departure procedure” [15, p. 65]. Turning departures are
subject to specific conditions.
a) Gross and Net Flight Paths
The gross flight path is “the takeoff flight path actually flown by the aircraft” (JAR 25.115 (a)),
while the net flight path is the “gross takeoff flight path minus a mandatory reduction” (JAR
25.115 (b)). This mandatory reduction, based on a climb gradient reduction, must grant a safety
margin of 35 ft between the aircraft and every obstacle in its flight path (see Figure 24). Two
engine aircraft have a gradient penalty of 0.8%, while four engine aircraft have their “takeoff
path reduced at each point by a gradient equal to” 1.0% (JAR 25.115 (b)).
Figure 24 - Gross and net takeoff paths [15].
b) Takeoff Turn Procedure
According to regulation, no track changes are allowed before the aircraft achieves a height
equal to one half its wingspan (Table 6) and before reaching at least 50 ft above the end of
TORA.
Aircraft Type Wingspan Minimum height to start a track change
A319/A320/A321 34.10 m (111 ft 10 in) 56 ft A330-200/300 60.30 m (197 ft 10 in) 99 ft A340-200/300 60.30 m (197 ft 10 in) 99 ft
Table 6 - Minimum height to start a track change according to wingspan [18].
25
Also, no bank angle should exceed 15° under a 400 ft height. Above 400 ft, bank angles must
be under 25°. If at any time the banking angle gets over 15°, then the whole net flight path must
clear all obstacles by at least 50 ft (JAR-OPS 1.495 (c)).
Greater banking angles, other than the ones specified, may be applied but are subject to
specific approval by the Authority (JAR-OPS 1.495 (c)).
4.3.3. Departure Sector
The departure sector delimits “an area surrounding the takeoff flight path, within which all
obstacles must be cleared, assuming they are all projected on the intended track” [15, p. 71].
The following figures represent departure sectors with and without heading changes over 15°.
Figure 25 - Departure Sector for track changes under 15° [15].
Figure 26 - Departure Sector for track changes over 15° [15].
“E” stands for the width of the departure sector, which must be equal to 90 m plus 0.125 x D or
60 m plus 0.125 x D, for aircraft with a wingspan of less than 60m. “D is the horizontal distance
the aircraft has traveled from the end of the take-off distance available or the end of the take-off
distance if a turn is scheduled before the end of the take-off” (JAR-OPS 1.495 (a)).
26
The following table represents the semi-width (1/2E0) at the start of the departure sector for
TAP’s aircraft:
Aircraft Type Wingspan 1/2E0
A319/A320/A321 34.10 m (111 ft 10 in) 56 ft A330-200/300 60.30 m (197 ft 10 in) 99 ft A340-200/300 60.30 m (197 ft 10 in) 99 ft
Table 7 - Semi-width ( E0) at the Start of the Departure Sector [18].
In the situation where there are no heading changes over 15°, the maximum width of the
departure sector is 300 m if the pilot is able to maintain the required navigational accuracy and
600 m otherwise (JAR-OPS 1.495 (d)). When the aircraft performs track changes above 15°
these values increase to 600 and 900 m, respectively (JAR-OPS 1.495 (e)).
4.4. Outside Elements
Considerations must be made to account for the external conditions of the day which can vary
considerably on a daily basis.
4.4.1. Wind
For performance purposes, only the wind component that is parallel to the runway (headwind –
HW) is considered (Figure 27). The crosswind component can be safely overlooked in the
takeoff optimization because it has a negligible effect on the aircraft acceleration [9].
Figure 27 - Headwind determination.
The headwind component has a positive effect on takeoff performance by shortening the takeoff
distances (the ground speed is reduced - see Figure 28). In the presence of tailwind the
opposite occurs, the takeoff performance degrades and the resulting takeoff distances increase.
27
Figure 28 - Headwind effect on ground speed [15].
According to regulation, takeoff performance calculations must only consider 50% of the actual
headwind component, or 150% of the actual tailwind component (JAR-OPS 1.490 (c)).
Notice that usually the takeoff software applications perform the 50% 150% corrections
internally, so the wind input is simply the headwind or the tailwind, respectively. This is, of
course, the case with TLP as well.
4.4.2. Pressure Altitude
As was seen before, in chapter 3, engine performance degrades with pressure altitude: engine
thrust decreases so the takeoff distances increase and the climb gradients decreases.
Additionally, when the pressure altitude increases, the corresponding static pressure (PS) and
air density decreases (eq. 14 – adapted from [23]) [15]. Consequently the pressure altitude also
has a direct impact on aerodynamics (eq. 15).
(14)
(15)
To compensate for a decrease in the air density, the true airspeed (TAS) of the aircraft must be
increased and therefore the takeoff distance is also increased [15].
Summing up:
Figure 29 - Pressure altitude effect on takeoff performance [15].
4.4.3. Outside Air Temperature
When the outside air temperature (OAT) increases the air density ( ) decreases (see eq. 14).
Consequently the takeoff performance degrades in a similar way as with the pressure altitude:
TAS must increase, therefore the takeoff distances increase as well (see Figure 29).
28
4.4.4. Runway Condition
The runway condition is utmost important when accounting for the takeoff (and landing)
performance. The runway is, after all, the surface between the aircraft and the ground.
Therefore its state, or condition, defines the interaction between the two and, consequently, can
take major impact in the aircraft acceleration or stopping capabilities, when compared to a dry
runway.
Since this is a topic of great complexity, this subsection can be seen as only a summary of the
major considerations to take into account when evaluating the takeoff performance in a wet or
contaminated runway. For an overall description of the physical processes and regulatory
limitations that lead to the considerations in this sub-chapter see Appendix B – Performance on
Non-Dry Runways.
When it comes to runway condition, the takeoff performance will depend on the depth and type
of contaminant:
Contaminant Wet Contaminated
Water (fluid) < 3 mm 3 – 13 mm (1/2”) Slush (fluid) < 2 mm 2 – 13 mm (1/2”) Wet Snow (fluid) < 4 mm 4 – 25 mm (1”) Dry Snow (fluid) < 15 mm 15 – 25 mm (2”) Compacted Snow (hard) - all Ice (hard) - all
Table 8 - Wet and contaminated runways [15].
Contaminants can be divided into hard and fluid contaminants, which have a different effect on
aircraft performance [15]
Hard contaminants reduce friction forces;
Fluid contaminants reduce friction forces, cause precipitation drag and aquaplaning.
Also, as seen in the Table 8, the runway is considered either wet or contaminated, depending
on the type and depth of the contaminant.
This way, the performance software will consider the specific physical processes (friction forces,
aquaplaning and drags) that apply for each kind of contaminant, as it will account for the
particular regulations that apply for the corresponding runway state (wet or contaminated),
which may also differ from the dry runway condition.
When considering an all engines operating takeoff TOD, TOR and ASD are determined the
same way as described early in this chapter, whatever the runway condition. When accounting
for a one engine inoperative takeoff, however, TOD and TOR are calculated in a different way
[18]:
the use of reverse thrust credit is allowed for ASD determination;
the gross flight path starts at 15 feet.
4.5. Limitation Summary
All in all, the takeoff limitations, resulting from the the former definitions and regulatory
constraints that were presented throughout this chapter can be summarized the following way
(Figure 30 and Table 9):
29
Figure 30 - Takeoff Performance Limitations.
The following table enumerates the resulting limitations:
Code Limitation
1 1st Segment
2 2nd
Segment 3 Runway 4 Obstacle 5 Tire Speed 6 Brake Energy 7 Maximum Weight 8 Final Takeoff 9 - - - - - -
VMU VMCG VMCA V1/VR Acceleration 3
rd Segment
Gross Level-off Height Turn Height
Table 9 - TAP’s takeoff limitations.
The first nine correspond to the original limitations set by Airbus’ official documentation, while
the remaining five are in agreement with the new TAP’s takeoff performance limitations table
(currently implemented in TAP’s EFB project).
30
5. Takeoff Optimization
This section covers the principle/methodology used to optimize the takeoff performance. The
optimization objective is to obtain the highest possible performance-limited takeoff weight –
Maximum Takeoff Weight (MTOW), while fulfilling all the airworthiness requirements seen in the
past sections [15] and, consequently, respecting all the limitations enumerated in the past Table
9 - TAP’s takeoff limitations.
It is necessary to determine which parameters influencing the takeoff (influencing the
limitations) are fixed – Sustained Parameters (cannot be changed) and which offer freedom of
choice – Free Parameters. For instance, the current wind condition cannot be changed or
chosen – this is a sustained parameter.
The influencing parameters are enumerated in the table below.
Sustained Parameters Free Parameters Runway TORA
TODA ASDA Lineup Adjustments Slope Condition
Flaps Setting Air Conditioning V1/VR Ratio V2/VS Ratio
Outside Elements
Wind Pressure Outside Air Temperature
Obstacles and Takeoff Trajectory
Anti-Ice
Aircraft Status (MEL/CDL)
Table 10 - Influencing Parameters (adapted from [15] and [18]).
As seen in the Aircraft Performance chapter, both the chosen flap setting and the engine bleeds
condition take major impact in the aircraft performance, and consequently in the takeoff
performance.
Nevertheless the takeoff speeds represent the most important source of optimization and
MTOW gain [15] [24]. This way, “at a given configuration (and all sustained parameters), takeoff
weight limitations are set as functions of V1/VR and V2/VS” [18].
5.1. Optimization Range
Assuming a given aircraft condition, the takeoff optimization process will take place inside a well
delimited range defined by the maximum and minimum allowed values for both speed ratios.
a) V1/VR Range
As mentioned in chapter 3, the decision speed, V1, must always be less than the rotation speed,
VR. Although VR depends on the weight and the value of V1 is not fixed, the maximum V1/VR
ratio is equal to one (V1/VR 1) [15].
31
Also, the minimum V1/VR ratio is equal to 0.84 (manufacturer value [15]). This way, one can say
that the V1/VR ratio has a well-defined range:
(16)
This proves to be particularly useful since it also grants a well-defined range for the takeoff
optimization process.
“Any V1/VR increase (resp. decrease) should be considered to have the same effect on takeoff
performance as a V1 increase (resp. decrease)” [15, p. 193].
b) V2/VS Range
As seen in chapter 6, the minimum value for V2 imposed for Airbus’ Fly-By-Wire aircraft (all of
TAP’s fleet) is 1.13VS1g. Although V2 does not have a fixed value (since the stall speed depends
on the aircraft weight), the V2/VS ratio is known for a given aircraft type.
This way, having a well-known range, the V2/VS ratio proves to be very helpful for the takeoff
optimization process:
(17)
A maximum value for V2 (and consequently, a maximum V2/VS) is specified by the manufacturer
(see table below), which corresponds to an optimal V2.
Aircraft Family V2/VS range
A320 1.35 1.13 ≤ V2/VS ≤ 1.35
A330 1.40 1.13 ≤ V2/VS ≤ 1.40
A340 1.45 1.13 ≤ V2/VS ≤ 1.45
Table 11 - V2/VS maximum values for the Airbus family (data retrieved from [15]).
“Any V2/VS increase (resp. decrease) should be considered to have the same effect on takeoff
performance as a V2 increase (resp. decrease)” [15, p. 194].
5.2. Free Parameters Influence
This is one of the most significant sections of the present work since it will allow the reader to
understand in detail the variables of the takeoff optimization and this way get a clear picture of
how the weight optimization is actually performed.
a) Flaps Setting
Currently all of TAP’s aircraft have three distinct sets of flaps and slats configurations that are
specially designed for the takeoff procedure: Configuration 1+F, Configuration 2 and
Configuration 3 [14].
Each of these configurations is associated with a set of certified performance, making it suitable
for one specific situation but inappropriate for another (e.g. shorter/longer runway). On account
of this, “the optimum configuration is the one that provides the highest MTOW” [15]. As a
general rule, this is the chosen configuration.
However there are some exceptions, take for example situations that may result in a loss of
comfort by the passengers or that are prone to a tail strike event (e.g. using Configuration 1+F
on extensive runways for long aircraft as the A340) [24] [20]).
32
The takeoff configuration selection also affects the FLEX temperature and consequently the
level of necessary thrust [24]. This will be the focus of attention at the end of the current
chapter.
As a general rule, Configuration 1+F offers better aircraft performance on long runways (better
climb gradients), whereas Configuration 3 provides better performance on short runways
(smaller takeoff distances). Sometimes, other parameters, such as obstacles, can interfere. In
this case, a compromise between climb and runway performance is required, making
Configuration 2 the optimum configuration during takeoff [15].
The resulting takeoff distances and gradients achieved by the different configurations are
illustrated in the subsequent figure:
Figure 31 - Takeoff configurations performance (adapted form [15]).
b) Air Conditioning
Having the air conditioning switched on during takeoff results in a loss of power and
consequently degrades the takeoff performance.
c) V1/VR Ratio
As the purpose of this sub-section is to analyze the impact of V1/VR ratio variation on the aircraft
weight limitations, the V2/VS ratio will be considered a fixed parameter.
Figure 32 translates the influence of the V1/VR ratio on the MTOW, limited by the runway
limitations.
Figure 32 - Runway Limited MTOW (adapted from [15]).
A higher V1/VR ratio (or a higher V1) leads to a higher percentage of the acceleration phase with
all engines operating (remember that despite the value that V1 will take, the engine failure is
33
assumed one second before it is achieved), consequently, it will take less time (and distance) to
achieve V2 at 35 ft. This translates in less restrictive TODOEI and TOROEI limitations. On the
contrary, TODAEO and TORAEO are independent of V1 as there is no engine failure, and thus no
consequence on the acceleration phase and the necessary distance to reach 35 ft. As for the
ASD, it will grow more limiting as V1 increases, since a longer part of the runway is covered
during both the acceleration and the braking phases [15].
Figure 33-a translates the influence of V1 on the climb and obstacle limited MTOW, while Figure
33-b shows its effect on the tire speed and brake energy weight limitations.
Figure 33 – Effect of V2/VS in the (a) obstacles, takeoff segments, (b) brake energy and tire speed
limitations (adapted from [15]).
The V1 speed has no direct influence on climb gradients and consequently on the 1st, 2
nd and
final segment gradients. However, as the takeoff distance is reduced (for higher values of V1),
the obstacle-limited weights are improved since the aircraft requires a lower gradient to clear
the obstacles [15]. “A maximum V1 speed, limited by brake energy (VMBE), exists for each TOW,
this is why it seems to grow more limiting as V1 increases. To achieve a higher V1 speed, it is
necessary to reduce TOW” [15]. V1 has no influence on the tire speed limitation.
Taking into account the preceding limitations it is possible to find the optimal V1/VR which
corresponds to the MTOW for a specific V2/VS ratio:
Figure 34- Optimum V1/VR [15].
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34
d) V2/VS Ratio
In a similar way to the previous sub-section, the V1/VR ratio will now be considered as a fixed
parameter this way allowing to study the influence of the V2/VS ratio on the MTOW limitations.
As a general rule, for a given V1/VR ratio, any increase in the V2/VS ratio translates as an
increase of the takeoff distance (both all-engine-operating and one-engine-out). This reflects the
need to acquire more energy (speed) on the runway in order to achieve a higher V2 speed at 35
feet. Consequently the acceleration phase is longer and the 2nd
segment slope increases [15].
Although the V2/VS ratio does not influence directly the ASD, a higher ratio leads to an increase
in VR which demands a higher V1 (for a given V1/VR) and outcomes in a higher ASD. The
resulting increase in V1 translates as a reduction of the weight by the brake energy and tire
speed limitations (see Figure 33-b) [15].
Additionally, any V2/VS increase results in higher climb gradients and consequently in less
restrictive 1st and 2
nd segment gradient limitations. It does not influence, however, the final
takeoff gradient since this is flown at green dot speed.
V2 does not have a direct impact on the brake energy limitation. Nevertheless any increase in V2
demands an increase in V1, and consequently on VR as well (assuming a fixed V1/VR ratio)
which results in a more restrictive brake energy limitation.
Table 12 summarizes all the previous conclusions on the influence of V2/VR in the MTOW
This section contains transcripts from Joint Aviation Requirements, issued by the Joint Aviation
Authorities. The full document can be purchased from Global Engineering Documents, whose
worldwide offices are listed on the JAA website (www.jaato.com) and Global website
(www.global.ihs.com).
JAR 25.25 (Weight Limits)
“(a) Maximum weights. Maximum weights corresponding to the aeroplane operating conditions (such as ramp, ground taxi, take-off, en-route and landing) environmental conditions (such as altitude and temperature), and loading conditions (such as zero fuel weight, centre of gravity position and weight distribution) must be established so that they are not more than -
• The highest weight selected by the applicant for the particular conditions; or • The highest weight at which compliance with each applicable structural loading and
flight requirement is shown. (b) Minimum weight. The minimum weight (the lowest weight at which compliance with each applicable requirement of this JAR-25 is shown) must be established so that it is not less than -
• The lowest weight selected by the applicant; • The design minimum weight (the lowest weight at which compliance with each
structural loading condition of this JAR-25 is shown); or • The lowest weight at which compliance with each applicable flight requirement is
shown.”
JAR 25.103 (Stall Speed)
(a) The reference stall speed, VSR, is a calibrated airspeed defined by the applicant. VSR may not be less than a 1-g stall speed. VSR is expressed as:
√
where: VCLMAX = Calibrated airspeed obtained when the load factor-corrected lift coefficient
(
) is the first maximum during the maneuver prescribed in paragraph (c) of
this section. In addition, when the maneuver is limited by a device that abruptly pushes the nose down at a selected angle of attack (e.g., a stick pusher), VCLMAX may not be less than the speed existing at the instant the device operates;
nZW = Load factor normal to the flight path at VCLMAX; W = Aeroplane gross weight; S = Aerodynamic reference wing area; and
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Q = Dynamic pressure.
(c) Starting from the stabilized trim condition, apply the longitudinal control to decelerate the
airplane so that the speed reduction does not exceed one knot per second.
JAR 25.107 (Takeoff Speeds)
“(a) V1 must be established in relation to VEF as follows: • VEF is the calibrated airspeed at which the critical engine is assumed to fail. VEF must
be selected by the applicant, but may not be less than VMCG determined under JAR 25.149 (e).
• V1 in terms of calibrated airspeed, is the take-off decision speed selected by the applicant; however, V1 may not be less than VEF plus the speed gained with the critical engine inoperative during the time interval between the instant at which the critical engine is failed, and the instant at which the pilot recognises and reacts to the engine failure, as indicated by the pilot's application of the first retarding means during accelerate-stop tests.”
“(b) V2min, in terms of calibrated airspeed, may not be less than:
VSR for turbo-jet powered aeroplanes […]
1.10 times VMCA (c) V2, in terms of calibrated airspeed, must be selected by the applicant to provide at least the gradient of climb required by JAR 25.121(b) but may not be less than:
V2min; and
VR plus the speed increment attained before reaching a height of 35 ft above the take-off surface.”
“(d) VMU is the calibrated airspeed at and above which the airplane can safely lift off the ground, and continue the takeoff. VMU speeds must be selected by the applicant throughout the range of thrust-to-weight ratios to be certificated. These speeds may be established from free air data if these data are verified by ground takeoff tests.” “(e) VR, in terms of calibrated air speed, must be selected in accordance with the conditions of paragraphs (e) (1) through (4) of this section:
VR may not be less than: - V1, - 105% of VMCA - The speed that allows reaching V2 before reaching a height of 35 ft above the
take-off surface, or - A speed that, if the aeroplane is rotated at its maximum practicable rate, will
result in a VLOF of not less than 1 10% of VMU in the all-engines-operating condition and not less than 105% of VMU determined at the thrust-to-weight ratio corresponding to the one-engine-inoperative condition, except that in the particular case that lift-off is limited by the geometry of the aeroplane, or by elevator power, the above margins may be reduced to 108% in the all-engines-operating case and 104% in the one-engine-inoperative condition. (See ACJ 25. I07(e)( i)(iv).
(…)”
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(f) VLOF is the calibrated airspeed at which the aeroplane first becomes airborne.”
JAR 25.113 (Take-off distance and take-off run)
(a) Take-off distance on a dry runway is the greater of:
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 for a dry runway;or
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 25.1 11. (See ACJ 25.1 13(a)(2).)
(b) Take-off distance on a wet runway is the greater of:
The take-off distance on a dry runway determined in accordance with sub-paragraph (a) of this paragraph; or
The horizontal distance along the take-off path from the start of the take-off to the point at which the aeroplane is 15 ft above the take-off surface, achieved in a manner consistent with the achievement of V2, before reaching 35 ft above the take-off surface, determined under JAR 25.111 for a wet runway. (See ACJ 113(a)(2).)
(c) If the take-off distance does not include a clearway, the take-off run is equal to the take-off distance. If the take-off distance includes a clearway:
The take-off run on a dry runway is the greater of: - The horizontal distance along the take-off path from the start of the take-off
to a point equidistant between the point at which VLOF is reached and the point at which the aeroplane is 35 ft above the take-off surface, as determined under JAR 25.1 1 1 for a dry runway; or
- 115% of the horizontal distance along the take-off path, with all engines operating, from the start of the take-off to a point equidistant between the point at which VLOF is reached and the point at which the aeroplane is 35 ft above the take-off surface, determined by a procedure consistent with JAR 25.111. (See ACJ 25.1 13(a)(2).)
The take-off run on a wet runway is the greater of: - The horizontal distance along the take-off path from the start of the take-off
to the point at which the aeroplane is 15 ft above the take-off surface, achieved in a manner consistent with the achievement of V2 before reaching 35 ft above the take-off surface, determined under JAR 25.1 11 for a wet runway; or
- 115% of the horizontal distance along the take-off path, with all engines operating, from the start of the take-off to a point equidistant between the point at which VLOF is reached and the point at which the aeroplane is 35 ft above the take-off surface, determined by a procedure consistent with JAR 25.111. (See ACJ 25.113(a)(2).)
JAR 25.149 (Minimum control speed)
“(b) VMC[A] is the calibrated airspeed, at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with that engine still inoperative, and maintain straight flight with an angle of bank of not more than 5 degrees.
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(c)VMC[A] may not exceed 1.2 VS with: Maximum available take-off power or thrust on the engines;
• The most unfavourable centre of gravity; • The aeroplane trimmed for take-off; • The maximum sea-level take-off weight”
JAR 25.149 (Minimum Control Speed)
“(e) VMCG, the minimum control speed on the ground, is the calibrated airspeed during the take-off run, at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with the use of the primary aerodynamic controls alone (without the use of nose-wheel steering) to enable the take-off to be safely continued using normal piloting skill. In the determination of VMCG, assuming that the path of the aeroplane accelerating with all engines operating is along the centreline of the runway, its path from the point at which the critical engine is made inoperative to the point at which recovery to a direction parallel to the centreline is completed, may not deviate more than 30 ft laterally from the centreline at any point.”
JAR 25.149 (Minimum Control Speed)
“(f) VMCL, the minimum control speed during approach and landing with all engines operating, is the calibrated airspeed at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with that engine still inoperative, and maintain straight flight with an angle of bank of not more than 5º. VMCL must be established with:
• The aeroplane in the most critical configuration (or, at the option of the applicant, each configuration) for approach and landing with all engines operating;
• The most unfavourable centre of gravity; • The aeroplane trimmed for approach with all engines operating; • The most unfavourable weight, or, at the option of the applicant, as a function of
weight. • Go-around thrust setting on the operating engines
(g) For aeroplanes with three or more engines, VMCL-2, the minimum control speed during approach and landing with one critical engine inoperative, is the calibrated airspeed at which, when a second critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with both engines still inoperative, and maintain straight flight with an angle of bank of not more than 5 degrees. VMCL-2 must be established with [the same conditions as VMCL, except that]:
• The aeroplane trimmed for approach with one critical engine inoperative • The thrust on the operating engine(s) necessary to maintain an approach • path angle of 3 degrees when one critical engine is inoperative • The thrust on the operating engine(s) rapidly changed, immediately after • the second critical engine is made inoperative, from the [previous] thrust to:
- the minimum thrust [and then to] - the go-around thrust setting
(h) In demonstrations of VMCL and VMCL-2, … lateral control must be sufficient to roll the aeroplane from an initial condition of steady straight flight, through an angle of 20 degrees in the direction necessary to initiate a turn away from the inoperative engine(s) in not more than 5 seconds.”
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A2. AMJ 25-13 Transcripts
AMJ 25-13
"(4)(c) Reduced takeoff thrust, for an aeroplane, is a takeoff thrust less than the takeoff (or
derated takeoff) thrust. The aeroplane takeoff performance and thrust setting are established by
approved simple methods, such as adjustments, or by corrections to the takeoff thrust setting
and performance.”
“(5)(a) The reduced takeoff thrust setting
Is based on an approved takeoff thrust rating for which complete aeroplane
performance data is provided
Enables compliance with the aeroplane controllability requirements in the event that
takeoff thrust is applied at any point in the takeoff path
Is at least 75% of the maximum takeoff thrust for the existing ambient conditions”
“(f) The AFM states that [reduced thrust takeoffs] are not authorised on contaminated runways
and are not authorised on wet runways unless suitable performance accountability is made for
the increased stopping distance on the wet surface.”
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APPENDIX B – Performance on Wet
and Contaminated Runways
This appendix on performance on wet and contaminated runways has the purpose of providing
a better understanding on the physical processes that take place on non-dry runways.
Different runway conditions will have different effects on the acceleration and deceleration
characteristics of an airplane. Wet and slippery runways will affect the aircraft’s deceleration
capability without affecting its acceleration. Standing water, slush and loose “compactible” snow
will affect an airplane’s acceleration capability as well as its deceleration. For that reason,
runway contaminants are divided into two different categories: solid contaminants and loose
contaminants [9].
Solid contaminants affect deceleration but have no effect on acceleration. This category
includes ice and compact snow.
Loose contaminants add a component of drag, retarding the aircraft’s motion and thus
affect both acceleration and deceleration. This includes loose snow and slush or
standing water with more than 0.125 inches deep
.
7.2 Solid Contaminants
Solid contaminants have a direct impact on aircraft braking coefficient. In general a wet runway
has less friction available for stopping an aircraft in an emergency. How much the runway
friction is reduced by moisture on the surface of the runway is a function of the material and
techniques of runway construction [9].
JAR 25.109, paragraph (c) provides equations for the wet runway “maximum braking coefficient
(tire-to-ground)” as a function of tire pressure and airplane ground speed:
Tire Pressure (psi) ( ) Maximum Braking Coefficient (tire-to-ground)
50 (
)
(
)
(
)
100 (
)
(
)
(
)
200 (
)
(
)
(
)
300 (
)
(
)
(
)
Where V is the true ground speed in knots; note that linear interpolation is allowed for tire
pressures other than the listed above.
As an example, for a tire pressure of 200 psi the maximum friction coefficient defined by the
equation will be as shown in Figure 58.
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Figure 58 - Aircraft braking coefficient for a 200 psi tire pressure on a wet runway [9].
For its determination of the aircraft maximum braking coefficient on wet runways aircraft
manufacturers use a tire pressure which is approximately at the top of the range of tire
pressures for a given aircraft [9].
The maximum tire-to-ground wet runway braking coefficient of friction ( ) must be
adjusted to take into account the efficiency of the anti-skid system on a wet runway. Anti-skid
system operation must be demonstrated by flight testing on a smooth wet runway, and its
efficiency must be determined [9].
Based on the equations and the results of flight testing, then, aircraft manufacturers are able to
find a definition of the wet runway airplane braking coefficient for each aircraft, as shown in
Figure 59.
Figure 59 - Aircraft braking coefficient on a wet runway [9].
Because aircraft braking coefficient is a function of ground speed, the calculation of the stopping
distance on wet runways does not use a single constant value of as for dry runways.
Instead, the step integration of stopping distance will use a changing value of as the speed
decreases [9].
For solid contaminants other than wet or wet skid-resistant there is no universally accepted
relationship between runway description, reported braking action, and airplane performance.
The airplane’s actual performance may well be different for the same description of the runway
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surface or the pilot-reported braking action. Aircraft manufacturers have been choosing, based
on experience, a relationship of reported braking action to airplane braking coefficient. This
relationship has been used to create the published data [9].
7.3 Loose Contaminants
The physics of takeoff on a runway having loose contaminants (see Figure 60) are similar to
those on a dry runway, with one notable exception: the addition of the drag on the airplane
resulting from the material which is covering the runway, be it standing water, slush, or wet
snow [9].
Figure 60 - Physics of contaminant drag [9].
Contaminant drag actually has two elements: displacement drag and impingement drag.
As illustrated in Figure 61, displacement drag results from the energy required for the landing
gear tires to displace the contaminant – that is, to move it out of their way as the airplane rolls
along the runway [9].
Impingement drag results from the airplane kinetic energy lost due to the impact of contaminant
on parts of the body (see Figure 62). The passage of the wheels through the contaminant
causes a very powerful spray to be thrown up; due to its density and the velocity at which it
strikes the airplane, it creates considerable impact force on the airplane. Since this impact force
is in an aftward direction, it subtracts from the airplane’s kinetic energy [9].
Figure 61 – Displacement Drag [9].
Figure 62 - Impingment Drag [9].
The contaminant impact can actually cause physical damage to an aircraft. As a result of this,
and because of the increasingly adverse effect of loose contaminants on takeoff performance
as depth increases, the FAA and JAA both state specifically that takeoff is prohibited on
runways having more than ½ inch (FAA) or 12.7 millimeters (JAA) of loose contaminant. The
latest EASA regulations on non-dry runways, however, permit up to 15 millimeters instead of the
earlier 12.7 mm (or ½ inch) [9].
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Additionally, hydroplaning, or aquaplaning, is a dynamic condition encountered by an aircraft’s
tires when operating on runways covered with loose contaminant. At low speeds on a runway
having loose contaminant there is adequate time for the contaminant to move away from an
aircraft’s tires as it accelerates down the runway for takeoff, allowing the tires to remain in solid
contact with the runway surface. The presence of the contaminant does result in an increase of
the airplane’s drag, as discussed above, but there are no other adverse effects. However, as an
aircraft accelerates in loose contaminant, the tires cause an increase of pressure in the
contaminant in the area immediately ahead of them. When that pressure becomes sufficiently
great, it forces a wedge of fluid underneath the tires’ leading edges, thus lifting the tires out of
contact with the runway surface resulting in a loss of traction [9]:
Figure 63 – Hydroplaning effect [9].
The speed at which hydroplaning commences during an acceleration is known as the
hydroplaning speed VHP. It’s a function of tire pressure.
The EASA’s accepted equation for the hydroplaning speed is:
The following figure illustrates the repercussions that the different contaminants have on the
takeoff distance, for the same weight (292.97 tons) and V1 (160.6 kt), on a dry runway with
3352.8 meters long (11,000 ft):
Figure 64 - Effect of contaminants on takeoff distances [9].
The following graphics were obtained in Excel. The corresponding data points were calculated by the Flight Path function of PEP’s certified FM module. Position (0,0) corresponds to brake release.