On Improving Eﬃciency of Flight Using Optimization

On Improving Efficiency of Flight UsingOptimization

Marianne JacobsenAeronautical and Vehicle Engineering

Kungliga Tekniska hogskolan

SE-100 44 Stockholm, Sweden

TRITA/AVE 2009:45

ISBN 978-91-7415-399-6

TRITA/AVE 2009:45 KTH Farkost & Flyg

ISSN 1651-7660 Teknikringen 8

ISBN 978-91-7415-399-6 100 44 Stockholm

Akademisk avhandling som med tillstand av Kungliga Tekniska hogskolan

framlagges till offentlig granskning for avlaggande av teknologie doktorsexamen

i flygteknik tisdagen den 22 september 2009 klockan 10.15 i Kollegiesalen F3,

Lindstedtsvagen 26, Stockholm.

Typsatt i LATEXTryck: Universitetsservice US AB, Stockholm 2009c© Marianne Jacobsen 2009

On improving efficiency of flight using optimization 1

Preface

The work presented in this thesis was performed at the Department of Aero-

nautical and Vehicle Engineering at the Royal Institute of Technology (KTH)

in Stockholm, Sweden. The financial support provided by the Swedish Defence

Materiel Administration (FMV) is gratefully acknowledged.

Without my supervisor Ulf Ringertz this thesis would not have happened.

Ulf, thank you for always challenging me with difficult questions and ideas, and

teaching me never to give up. Despite our differences, I really appreciate youralways optimistic view on everything from noisy wind tunnel measurements to

flutter instabilities.

I would also like to thank both former and present colleagues in the Flight

Dynamics group, Dodde, Carin, Martin C, David and Gloria. Sebastian, thanks

for being a great room mate and for always taking time helping me with ev-

erything from wind tunnel hardware to theoretical arguments, and for being a

really good friend. Martin Norsell, thank you for introducing me to life as a

PhD student and for all your great advice even after you left.

I would not have had such a good time at KTH if it weren’t for all my

friends at the department. Fredrik, thank you for taking me skiing in the

Alps, Chris thanks for carrying my skis! Anders, thank you for all the fikabreak discussions, Markus thanks for bringing some European culture into the

department. Kalle P, thank you for making sure that Flyg beats LattK in pool.

Ylva, last but not least, you are a true friend and I hope you really know how

much you mean to me. Having you next door has helped a lot!

My friends outside the department should also be acknowledged for their

support during these years. Kristina and Kattis, thank you for understanding

what it is like to be a PhD student, and Jenny, thank you for all your kind

words when I have needed it the most.

Also, to my family, you are the most important ones in my life. Thank you

for your open arms when confronted with doubts. Finally, Erik, the recent years

have been the happiest of my life. Thank you for always believing in me, even

when I don’t believe in myself. ’Det loser sig’!

Stockholm, August 2009

Marianne Jacobsen


Abstract

In this thesis, optimization is used to improve the performance of aircraft. The

focus is on operating current generation aircraft more efficiently rather than

designing new aircraft. Drag minimization and aircraft trajectory optimization

is used to increase efficiency. Optimization methods are implemented and

evaluated on different problem formulations.

The first part of the thesis presents a drag minimization strategy using multi-

ple control surfaces distributed across the span of an elastic wing. Aeroelasticityis exploited to reduce drag for a wide range of flight conditions. A method

to minimize drag during a long distance flight is developed and tested in a

wind tunnel environment. The method is based on continuously changing the

control surface deflections to obtain a more beneficial load distribution from

a drag point of view for the current flight condition. In a second study, the

method is extended to include the angle of attack as a variable together with the

control surface deflections in the drag minimization algorithm. Extensive wind

tunnel testing demonstrates the possibility to reduce drag significantly with the

presented method for a wide range of flight conditions.

The second topic in the thesis is optimizing the aircraft trajectory. The

emissions from the aircraft engine are modeled as smooth functions suitable foroptimization using published certification data. These emissions are combined

in different environmental indices and used as objective functions in the air-

craft trajectory optimization problem. The optimization problem is formulated

by discretizing the trajectory in time. The resulting large scale nonlinear opti-

mization problem is solved using a sequential quadratic programming method.

The trajectory optimization problem is first studied using a model of the Boe-

ing 737 and the results show that the optimal trajectory depends significantly

on the definition of the environmental objective function. A method to treat

restricted airspace is also presented and evaluated using a model of the Swedish

Air Force trainer SK60. The results show that the method for imposing airspace

constraints on the flight path works well, especially when the initial point for

the optimization is feasible.


Dissertation

This doctoral thesis is based on a brief introduction to the area of research and

the following appended papers:

Paper A

M. Jacobsen. Real time drag minimization using redundant control surfaces.

Aerospace Science & Technology, 10(7):574-580, 2006.

Paper B

M. Jacobsen and U. Ringertz. Performance optimization of flexible wings using

multiple control surfaces. Presented at the International Forum on Aeroelasticityand Structural Dynamics, Seattle, USA, June 2009.

Paper C

M. Jacobsen and U. Ringertz. Reducing emissions using aircraft trajectory opti-

mization. TRITA/AVE 2009:43, Department of Aeronautical and Vehicle Engi-

neering, KTH, May 2008. Submitted for publication.

Paper D

M. Jacobsen and U. Ringertz. Airspace constraints in aircraft emission trajectory

optimization. TRITA/AVE 2009:44, Department of Aeronautical and Vehicle

Engineering, KTH, May 2009.


Contents

Preface 1

Abstract 3

Dissertation 5

Introduction 9

Aviation and the environment 10

Aviation today and in the future . . . . . . . . . . . . . . . . . . . . . 11

Impact on the environment . . . . . . . . . . . . . . . . . . . . . . . 12

Objective 15

Drag 16

Drag reduction strategies . . . . . . . . . . . . . . . . . . . . . . . . . 17

Emissions 18

Modeling of emissions . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Optimization 22

Optimization with wind tunnel measurements . . . . . . . . . . . . . 23

Trajectory optimization . . . . . . . . . . . . . . . . . . . . . . . . . 25

Summary of appended papers 27

Drag minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Emission optimized trajectories . . . . . . . . . . . . . . . . . . . . . 28

Discussion 29

References 31

Division of work between authors 37

Appended papers


Introduction

Flying has in all times been intriguing to man. Early evidence of this desire

is illustrated in ancient Greek mythology about Icarus and Daedalus. In the

beginning, people tried to imitate birds by making wings tied to themselves or

machines copying the birds flapping motion, as Leonardo da Vinci’s famous

flying machine in Figure 1. Several strategies have since then been tested and in-

Figure 1: Drawing by Leonardo da Vinci of a flying machine.

vestigated to make flying possible, such as kites, hot air balloons etc. Eventually,

aviation developed into powered aircraft with the possibility to carry hundredsof passengers, and today, transportation may be the main reason for flying.

For long distance transports, especially with passengers, aviation is the only

reasonable alternative today. The transatlantic crossing by ship takes at least six

days (approximately 140 hours), even with the most modern ships [1]. Aviation

reduces this time with at least 130 hours. Considering that aviation is a large

part of the transportation system today and in the future makes it essential toreduce the environmental impact as much as possible, and to fly efficiently from

an environmental perspective.

There are several means of transportation available today, such as trains,

ships, cars and buses. These all have different benefits and drawbacks. The

main advantage with air transport is the possibility of traveling long distances

at high speed and also taking the shortest path passing above mountains or waterinstead of going around. The only infrastructure needed is the airport, a local

facility, to be compared with trains in need of tracks for the entire distance to

be covered, or roads for cars. The modest need of required infrastructure makes

it possible to avoid bad weather that may prevent other forms of transportation.

10 M. Jacobsen

It is also possible for an aircraft to store energy in altitude and use it to glide

long distances if designed properly.

With all forms of transportation, environmental issues need to be addressed.

For aviation, climate change and stratospheric ozone depletion are the mainissues discussed today. With increasing fuel prices, much has already been

done on the efficiency of aircraft. Modern jets are relatively fuel efficient with

approximately 0.035 l per passenger km [2], which is comparable to cars despite

the much higher speed.

Aviation and the environment

During the last decades, there has been a significant growth in air traffic. The

annual growth rate is estimated to continue with around 5% for the coming

years [3, 4, 5]. Since the beginning of flight, a constant development has been

ongoing, but even the most modern aircraft of today are very similar in shape

and operations to the aircraft developed in the 1950’s, see Figure 2.

Figure 2: Boeing 707 from the 1950’s and Airbus 380 from the 2000’s.

Since the jet engine was introduced and became widely used in the early

1960’s, the tendency in the development of air transport has been an increase in

both range and the number of passengers. With the introduction of jet engines,

the speed also increased significantly. However, large aircraft flying at high

speeds in the transonic regime with a Mach number around 0.85 at an altitude

of 10-13 km may not be the most efficient way of flying.

Due to the international characteristics of aviation, taxes and fees are diffi-cult to implement and this has led to aviation being excluded from taxes on fuel

for many years. This is about to change, and policy makers must come together

and put pressure on airlines and manufacturers to improve the environmental

efficiency of flying.


Aviation today and in the future

Before the 1980’s, aircraft were designed mainly with range as the objective [6],

which in turn gave a lower fuel consumption without being the primary tar-

get. This is most likely due to the historically very low fuel costs. Now, thishas started to change, and fuel efficiency and emissions are considered impor-

tant parameters when designing new aircraft. The environmental awareness has

increased dramatically during the last years, even though Arrhenius described

what is today known as the greenhouse effect already in 1896 [7]. Nevertheless,

it is difficult to connect a certain human activity to climate change, but it is

now rather well understood and accepted that burning fossil fuels emits carbon

dioxide that contributes to climate change.

The amount of fuel used in aviation is approximately 2-3% of the total

amount of fossil fuels burnt today [8]. The transportation sector uses about

20-25% of all fossil fuels, which means that aviation uses about 13% of all fuels

used for transportation. To reduce these figures, new technology development

is of importance. The intergovernmental panel on climate change (IPCC) has

considered several different scenarios for air traffic in the future, but common to

all these scenarios is a continuous growth in air traffic. During the last decades

of development, a clear trend has been that propeller has changed to jet, but also

that the specific fuel consumption is becoming smaller and smaller, which is a

good trend. Aerodynamics has been refined, and new light-weight materials, like

carbon fiber composites, are already being used to a large extent in new aircraftdesigns, such as the Boeing 787.

Today, design of new aircraft is driven by cost. Operators are interested in

the operating cost, and this does not only include fuel cost, but also different fees

and taxes. Manufacturers also have to consider airport requirements. According

to Peeters et al. [6], the Airbus 380 would have a different design if the aircraft

was designed only for fuel efficiency. The wings would have had larger span, but

due to airport handling constraints of a maximum span of 80 m, the planformwas designed for this requirement. Without those restrictions the aircraft could

have been 12% more fuel efficient. In future designs, foldable wing tips could

be used to combine the airport requirements with more fuel efficient designs.

This would increase the manufacturing cost, but may lower the fuel cost.

There is a continuous development of aviation. In 1999, IPCC summarized

technology improvements to future aircraft in the special report on aviation and

the global atmosphere [8]. The main topics were laminar flow technology, newdesigns like a Blended Wing Body (BWB), see Figure 3, and also new engine

technology. This year (2009), the EU initiative Clean Sky [9] is starting up and

several of these concepts, especially the laminar flow technology, will be studied.

Air traffic management is also important to improve, and IPCC estimates the

12 M. Jacobsen

Figure 3: Blended wing body design.

reduction in fuel consumption only due to increased efficiency in air traffic

management to be between 8 and 18%.

Many of the concepts in the IPCC report and also in the Clean Sky project

are small adjustments to already existing aircraft designs. It may, however, be

essential for aviation in the future to make larger changes. Considering the

great efficiency development in high performance gliders, it may be possible to

use knowledge from this area even in commercial aircraft. Larger aspect ratios

and using aeroelasticity to optimize performance over a wider range of flight

conditions may be possible in the future. Long slender wings on smaller aircraftand lower speeds may be the future for environmentally friendly air transports

rather than the large high speed aircraft in use today. The same principles allow

the Global Flyer [10] to fly nonstop around the world without refueling, see

Figure 4.

Impact on the environment

In 1990, 3.5% of all greenhouse gas emissions were related to air traffic [6].

Even though modern jet engines have been developed over several decades, and

lately with fuel efficiency as a primary target, a piston engine from the 1950’s is

almost as fuel efficient as a modern jet today [6], if computed per seat kilometer.

The early jets, however, consumed almost twice as much fuel per seat kilometer

as the piston engines at that time. This comparison is performed without any

consideration of the much higher speeds possible with the jet engine.

The emissions from an aircraft engine have an impact on the environment.

There are several different emissions in the jet engine exhaust, but carbon diox-ide (CO2) may be most frequently discussed. Other emissions include nitrogen

oxides (NOx), hydrocarbons (HC), carbon monoxide (CO), sulfur oxides (SOx),

water vapor (H2O), and particles in the form of, for example, soot [11].

In any combustion process with fossil fuels, even if it is complete, carbon


Figure 4: The Virgin Atlantic Global Flyer (courtesy of Jim Sugar).

dioxide and water vapor will be produced. These have, therefore, not always been

considered pollutant emissions, but in recent years the climate effects caused by

greenhouse gases have been better understood. Carbon dioxide and water vapor

can only be reduced by burning less fuel. Both carbon monoxide and unburned

hydrocarbons are toxic to humans and can, in large concentrations, even causedeath. Hydrocarbons also contribute to photochemical smog when combined

with nitrogen oxides.

Some of the direct effects of the emissions on climate change are summa-

rized in Table 1. Here, the complexity of discussing climate change due to

different emissions is shown. Several indirect effects of the different emissions

are excluded from Table 1. Some of this complexity is mentioned in the fol-

lowing. Emissions have different effects on the environment and on humans.

Carbon dioxide, for example, stays in the atmosphere approximately 100 years

after the actual emission, which should be compared to the more limited res-

idence times for other emissions. Water vapor is also a greenhouse gas whenemitted at altitude and should not be completely neglected when discussing the

impact of emissions on the environment. However, it only stays around 9 days

when emitted in the troposphere, and a little longer in the stratosphere. Green-

house gases contribute to climate change, mainly warming, and so does soot

14 M. Jacobsen

Emission Effect

CO2 Direct radiative forcing → warming

H2O Direct radiative forcing → warmingIncreased contrail formation → radiative forcing → warming

Modifies ozone (O3) chemistry → O3 depletion

NOx O3 formation in the upper troposphere → warming

Decrease in methane → cooling

SOx Enhanced sulfate aerosol concentrations

Direct radiative forcing → cooling

Contrail formation → radiative forcing → warming

Increased cirrus cloud cover → radiative forcing → warming

Modifies O3 chemistry

Particles Direct radiative forcing → warming

Contrail formation → radiative forcing → warming

Increased cirrus cloud cover → radiative forcing → warmingModifies O3 chemistry

Table 1: Emissions and their environmental impact [8].

and other particles mainly through increased cloud formation. Gases absorb in-

frared radiation and alter the natural flow of energy through the climate system,but the system is complex and difficult to have a complete understanding of. To

make it even more complex, the earth’s temperature does not respond instantly

to emissions, but instead the effects can be seen several years after the emissions.

Several attempts have been made to model the effect on the climate from

different emissions. One such measure, or index, is known as the global warm-

ing potential, GWP. This is a way to compute the actual heating impact of a

specific gas. The relevance of GWP has been questioned due to its inability to

include contrails since they are not directly connected to a greenhouse gas. It

is, therefore, not enough as an index for measuring the effect of aviation on the

global climate [8]. Another measure is the radiative forcing, RF (Wm−2). This

is a measure of climate change computed from a change in greenhouse gases,

aerosols and clouds. If the RF is positive, it means that the terrestrial cooling

is decreased, i.e. the climate will be warmer. Radiative forcing is built on theconcept of assuming an approximately linear relation between global-mean RF

and a change in equilibrium global mean surface (air) temperature.

Contrails from aviation are also connected to climate change through in-

creased formation of cirrus clouds. Cirrus clouds, or even contrails them-

selves, influence the radiative forcing by reducing the outgoing thermal radi-


ation (warming) more than the incoming solar radiation (cooling) giving a net

positive RF and, therefore, a warmer climate or earth surface temperature. Con-

trails consist of water vapor that condensates under specific thermodynamic

conditions and freezes to water/ice particles leaving a condensation trail as inFigure 5. If the humidity is low, or if the air is cold enough, the contrails

Figure 5: Contrails (courtesy of Martin Boschhuizen).

disappear rapidly, but otherwise they can stay for a long time and after a while

turn into man-made cirrus clouds [12, 13, 14]. Contrails can be of two main

types; jet exhaust contrails directly from the engine or aerodynamic contrails

from mainly the inner parts of the wings. The aerodynamic contrails can have

different colors and are formed due to large variations in pressure and tempera-

ture. Aerodynamic contrails can form even in layers of air that are generally too

warm for jet exhaust contrails, and can be controlled by choosing flight altitude

and route.

Objective

The aircraft flying today will continue to fly for many years to come. There-

fore, it is of great importance to make sure that they are used as efficiently as

possible. The objective with this thesis is to show that today’s aircraft can be

used in a more environmentally preferable way. Two different case studies areperformed; minimizing drag during flight and optimizing aircraft trajectories

with environmental objective functions. Both studies are related to increased

efficiency of the operation of current generation aircraft, but are also applicable

for future generation aircraft.

16 M. Jacobsen

The objective of the drag minimization concept in this thesis is to develop

a method that exploits the already existing control surfaces on the aircraft to

reduce drag while maintaining the current state. Less drag requires less thrust

for propulsion, which also means less fuel consumed. The aircraft trajectoriesare studied to decrease emissions during a flight. The objective with this part

of the thesis is to be able to model aircraft emissions to make them suitable for

optimization. The main goal is to optimize the aircraft trajectories to minimize

environmental impact. Before describing the contributions and results of this

thesis, some background will be given on drag, emissions and optimization,

which is the main tool for the studies.

Drag

Aerodynamic forces on a body, such as lift and drag, can be described as com-

ing from two sources, namely surface pressure p and surface shear stress τ , asillustrated in Figure 6. Both the surface pressure and the shear stress will vary

over the surface. The pressure is always perpendicular to the surface and the

shear stress acts tangential to the surface. The aerodynamic force on a body can

be found by integrating the pressure and the shear stress over the entire surface

of the body. This, of course, assumes that the pressure and shear stress distribu-

tions are known. The total aerodynamic force on the body can be divided intoone component perpendicular to the relative wind u∞, the lift force, and one

component parallel to u∞, the drag force.

u∞

p

τ

Figure 6: Pressure and shear stress on an airfoil.

The drag of an aircraft is commonly divided into different components,

such as parasite drag and induced drag. The parasite drag exists on a body even

if no lift is created. This is due to both pressure imbalances as well as friction.

The induced drag, however, refers to the drag due to the spanwise lift distribu-tion [15]. At some conditions, the parasite drag is larger than the induced drag,

but the situation may also be the opposite. If the flow, for example, separates

from the body, the parasite drag is increased substantially. This is referred to as

pressure drag due to separation. Adding a wing to a body creates interference at the


intersection between the parts. This can cause interference drag on the body. At

transonic speeds, shock waves appear and this creates wave drag due to the total

pressure loss across the shock wave [16].

There are different approaches when investigating the drag of an object. The

oldest approach is to use experimental facilities, such as wind or water tunnels,

to investigate different fluid phenomena. Another approach is to use numerical

techniques and solve the fundamental governing equations. This is commonly

referred to as computational fluid dynamics, CFD. Both approaches are fre-quently used today together with ’handbook methods’, such as Hoerner [17].

Drag reduction strategies

Reducing drag has always been of great interest for many different applications.

Lower drag generally means lower required thrust for an aircraft. Early on in

the design process drag is considered an important parameter and much work

is put on reducing drag in the aeronautical industry.

Much work is also put on weight reduction today to allow for more payload

or reducing the required lift giving less induced drag. Structural weight reduc-

tion often leads to more flexible wings, and a European research program called

Active Aeroelastic Aircraft Structures (3AS) [18], studied concepts that exploit

the increased aeroelastic effects in a beneficial way. As part of this project, dif-

ferent techniques for drag minimization, or drag reduction, were studied. Theconcept of using distributed control surfaces across the span to change the lift

distribution depending on the flight condition was used in a study by Eller and

Heinze [19]. Here, the induced drag was minimized on a slender wing with 20

control surfaces. It was also shown that significant drag reduction was possi-

ble using only a few of these control surfaces making it more realistic from a

manufacturing point of view. This study was performed using both numerical

predictions and experimental validation of the drag. A similar study, although

only numerical, was performed recently by Kolonay and Eastep [20] also reduc-

ing the induced drag for different flight conditions and for two different wing

configurations.

Using multiple control surfaces distributed across the span to change geom-

etry can be compared to the constant changes of the wings of a bird. Consider

an eagle slowly soaring the skies, as in Figure 7. The wings hardly move. It

can stay in the air soaring for hours. The eagle makes small adjustments to

the shape and size of its wings to optimize performance. Depending on theflight condition, birds change both the wingspan and the wing area [21]. This

constant optimization makes the eagle’s flight very efficient. A migrating bird

needs to cover large distances, while a bird circling in the air trying to locate

prey may benefit more from endurance.

18 M. Jacobsen

Figure 7: Soaring eagle.

Two comprehensive studies by Stanewsky [22, 23] show the potential of

using control surfaces to make the structure adapt to different flow conditions.

This concept was taken one step further when NASA performed flight tests on

a modified Lockheed 1011 [24, 25, 26, 27]. In this work, only one redundant

control variable, namely symmetric deflections of the outboard ailerons, wasused. The optimization consisted of performing a sweep with the outboard

ailerons, testing all possible deflections, while gathering data. This was then used

to make a decision on the optimal deflection for the current flight condition.

The drag of the L-1011 was shown to be reduced by approximately 1% [24],

which in the case of aeronautics is considered a significant drag reduction,

especially when considering that only one control surface on a rather small

part of the wing was used for this purpose. In the studies by NASA, drag

was evaluated during flight by measuring the changes in speed for given thrust.

This was shown to be possible and the results were reliable enough to locate

the optimal control surface deflection. In these studies, the total drag was

minimized. Note that no computational model of the drag dependence on thecontrol surface deflections was used to perform the optimization.

Emissions

Today, pollutant emissions are frequently discussed and due to their health and

environmental effects, emissions are a public concern. Emissions affect the

environment differently, but to decide what is good and bad an index defining

the total environmental impact is needed. In the subject of life cycle impact


assessment (LCIA), different environmental indices are defined depending on the

objective. This is widely used when determining the environmental impact of a

product’s life cycle. The emissions during the life cycle are weighted together to

form an index as illustrated in Figure 8. There are several indices describing the

etc.

P

etc.

CFCs

etc.

NOx

NH3

CO 2

CH

eutrophication

global warming

etc.

index

ClassifiedInventoryresults

Characterizationresults

SO2

NOx

HCl

acidification

4

resultsWeighing

Figure 8: Weighing emissions to a scalar index.

environmental impact of a process, such as the Ecoindicator’99 [28], EDIP [29]

and EPS [30]. There are also other categories that describe the environmental

effects like acidification, eutrophication, and human toxicity. None of theseindices are, however, designed for aircraft emissions and no altitude dependence

on the impacts is available.

Modeling of emissions

When discussing aircraft engine emissions, an emission index is commonlydefined as the amount of emission in grams per kilogram of fuel consumed.

This is denoted EIHC for hydrocarbons, EICO for carbon monoxide, etc. A

constant emission index means that the emission is proportional to the fuel

burn.

20 M. Jacobsen

Today, certification of aircraft engines with respect to noise and emissions

is required. The engine manufacturers perform measurements of the emissions

under sea level static, standard day conditions for different power settings. The

certification data is built on these measurements, but to compute the emissionsduring an entire flight a more comprehensive model is needed.

There are different methods available for using sea level measured emission

data and correcting it for altitude and Mach number. Two methods are described

here, the T3-P3 method [31] and the fuel flow method 2 [32]. The T3-P3 method

requires much knowledge of the engine internal parameters and this informationis rarely made publicly available. The fuel flow method 2, developed by the

Boeing Company, is derived from the T3-P3 method but only requires an engine

model that predicts the fuel flow. In the studies in this thesis, the Boeing fuel

flow method is used.

The T3-P3 method The T3-P3 method is a way to estimate the emission

indices, EI, for CO, HC and NOx using sea level emission indices and a pressure

correction for altitude. This method requires the temperature and the total

pressure at the combustor inlet, T3 and P3 , as well as the emission indices at

sea level as function of T3, that is EICOsl(T3), EIHCsl(T3) and EINOx,sl(T3).The emission index at altitude is determined by running a simulation with an

aircraft performance model to obtain thrust and fuel flow together with pressure

altitude, flight speed and ambient temperature. These data are then used asinput to the engine performance model, giving P3 and T3 for the current flight

condition. A pressure correction is used to transfer the sea level emission indices

to the correct altitude.

The fuel flow method 2 The T3-P3 method requires much knowledge about

the engine internal parameters, but the fuel flow method 2 is developed to model

the emission indices from more readily available data, such as the engine fuel

flow. A model of the sea level static emission indices is also needed as function

of the fuel flow. To obtain the emission indices for CO, HC and NOx at al-

titude, an aircraft performance model is used to compute the fuel flow for the

flight condition of interest. The corresponding pressure altitude, flight speed

and ambient temperature should also be computed. The fuel flow at altitude

is then corrected for temperature, pressure and Mach number to give a corre-

sponding fuel flow at sea level. The corrected fuel flow at sea level is used tofind the emission indices at sea level and these are then corrected for altitude

and humidity. A more extensive review of both methods is found in DuBois

and Paynter [32].


The international civil aviation organization, ICAO, is an agency of the

United Nations that, among many other things, certifies commercial jet engines

for noise and emissions. Almost all countries in the world are members of

ICAO making it rather powerful. The ICAO engine standards are constantlyrevised to drive engine technology forward. The data for the certified engines is

collected in the comprehensive ICAO engine exhaust emission data bank [33].

The certification data consists of four data points where emissions are measured

at different thrust levels, which can be correlated to different fuel burn levels.

These four data points can be used to determine a model of the emissions as

function of fuel burn at sea level.

A method for using these four data points to model the emission indices

as function of fuel flow is described in [31, 32, 34]. The four data points are

first corrected to account for installation effects according to [32]. The base-10-

logarithm of the emission indices is then plotted as function of the 10-logarithm

of the corrected fuel flow. For HC and CO, a piecewise linear logarithmic fit ismade to model the behavior of EIHC and EICO as function of fuel flow. The

piecewise linear fit is shown in Figure 9(a), and it consists of the straight line

between the two lower fuel flow values and a horizontal line at the mean of the

two highest fuel flow values. The straight line is extended until it intersects the

horizontal line, as shown in Figure 9(a). For EINOx, the curve fit is simply a

linear fit of the logarithmic values as shown in Figure 9(b). The fitted curves

log(fuel flow)

log(

EIC

O o

r E

IHC

)

(a) Piecewise linear logarithmic curve fit forEIHC and EICO.

log(fuel flow)

log(

EIN

Ox)

(b) Linear logarithmic curve fit for EINOx.

Figure 9: Emission indices as function of fuel flow.

represents the model of the emission indices at sea level as function of fuel flowand may be used in the fuel flow method 2.

The method described above does not work for all engines, as discussed

in Dubois and Paynter [32]. The fuel flow method 2 requires a model of the

emission indices as function of the fuel flow, but it does not have to be on

22 M. Jacobsen

the logarithmic form as described above. Another approach, which has been

used in this thesis, is to model the emission indices as function of fuel flow as

smooth functions using polynomial B-splines [35, 36]. The advantage with this

representation is that the model is continuously differentiable to any chosenorder and there are efficient methods to evaluate both the function and its

derivatives once the splines have been defined. Approximating a spline to only

four data points from the certification data may, however, not give a correct

representation of the function. More data points would be beneficial to obtain

better insight to the function behavior.

An extensive study by NASA has been performed in order to investigate

the aircraft emissions, the aircraft particle emissions experiment (APEX) [37].

Here, a DC-8 aircraft equipped with four General Electric CFM56-2-C1 engines

is used as the test platform. This study investigated different fuel types and

the effect of thrust on the engine exhaust. The engine studied here is rather

similar to engines on several commercial aircraft of today, and it is assumed

that the general trends shown through the measurements in this study shouldhold for most commercial jet engines of similar type. This data can, therefore,

be used to approximate the splines to obtain a model of the emissions suitable

for optimization.

Optimization

The main tool in this thesis is optimization. When used correctly, it can be a

powerful tool, and often the solution is far from expected. When defining an

optimization problem, good and bad must somehow be defined. This is com-

monly referred to as the objective function, which should either be minimized

or maximized. Also, the variables usually have to satisfy some constraints that

can be linear or nonlinear functions. This can be expressed mathematically as

minx

f(x) (1)

subject to g(x) ≤ 0,

where x denotes the variables, f(x) the scalar valued objective function, and

g(x) the vector of constraints. Solving the optimization problem means find-ing the variables x that minimize the objective function while satisfying the

constraints.

There are several different types of solution methods for any given opti-

mization problem. Depending on the characteristics of the problem, such as the

number of variables and the differentiability of the functions, different methods


are suitable. In this thesis, two rather different problems have been studied and

the optimization techniques used are described here.

Optimization with wind tunnel measurements

The problem of minimizing drag during flight is discussed here. The objective

function is in this case the drag coefficient CD, which is defined as the drag

force, D, normalized with the dynamic pressure, q∞, and the aerodynamic

reference wing area, S, i.e. CD = D/(q∞S). The dynamic pressure is defined

as q∞ = ρu2∞

/2 with ρ as the density of the air and u∞ as the freestreamvelocity. The dynamic pressure is essentially a measure of the kinetic energy of

the airstream. The constraints in the optimization problem include keeping the

lift coefficient, CL, constant as well as keeping the control surface deflections,

δi, and the angle of attack, α, within some given bounds. The lift coefficient is

defined in the same way as the drag coefficient but with the lift force L instead

of D. The optimization problem can be written as

minα, δ

CD(α, δ) (2)

subject to CL(α, δ) = CLset,

αl ≤ α ≤ αu,

δl ≤ δ ≤ δu,

where αl, δl and αu, δu are the lower and upper bounds on the angle of attackand the control surface deflections. The constant lift coefficient, given by CLset,

is essentially defined by the altitude at which the aircraft is flying, the mass and

the airspeed. The solution to a problem of this form is given by the optimal

angle of attack α∗ and the optimal control surface deflections δ∗ that minimizes

the drag coefficient while satisfying the constraints.

Solution strategy

In the drag minimization studies in this thesis, the objective is the measured

drag. Hence, no computational model of the drag coefficient is used. Using

measured or numerically computed drag is a choice, and several studies mini-

mizing the numerical drag have been performed, as discussed previously. Here,

the focus is similar to the concept studied and tested by NASA [24], but focusingon a more sophisticated optimization technique and using more variables.

Many gradient based techniques for solving constrained optimization prob-

lems are available today and they are generally very effective. Gradients can be

determined from measurements by finite differences, but measured data contains

24 M. Jacobsen

noise that may give inaccurate and unreliable results. Therefore, a derivative-free

approach is desired. However, solving (2) without the explicit use of gradients is

not straightforward.

The optimality conditions involve derivatives of both the objective functionand the constraints [38]. Hence, the question is if it is even possible to find

an optimal solution without the use of derivatives. Several methods exist that

try to do just this. The wide class of optimization techniques that does not use

derivatives are referred to as derivative-free methods [39, 40, 41, 42]. There are

two main groups of derivative-free methods; methods that construct approxi-

mations of different kinds to the objective function, and direct search methods

that only compare function values. The distinction between these two groups

is not always clear. Many of the derivative-free methods are practical only for

unconstrained optimization, but it is possible to generalize some of the methods

to include constraints.

A widely used method for solving unconstrained optimization problemswithout explicit use of gradients is the response surface methodology (RSM) [43].

This is a method that samples the objective function, or response function, at

designated points close to the current iterate and performs regression analysis to

approximate a local linear (or quadratic) model of the response function. This

method has been used in many engineering applications [44, 45, 46]. If RSM

is to be used successfully, it is of great importance to choose the sample points

with care. Using a full quadratic model may give a rather good picture of the

actual objective function, but it is also costly since it requires many function

evaluations to approximate the response surface accurately if the number of

variables is large.

Another method is the popular Nelder-Mead simplex algorithm [47]. It isa direct search method and it works well in many cases. Unfortunately, it may

also fail [39]. This has led to a lot of work analyzing the asymptotic behavior of

the Nelder-Mead method [48]. It can be shown that the algorithm is robust and

will converge to a stationary point in R1, but in higher dimensions convergence

has not been proven.

There are, however, other direct search methods that are known to be robust.

A review on a class of methods known as generating set search methods (GSS)

is found in Kolda et al. [40]. These methods can be shown to be reliable in the

sense that convergence results can be obtained, local rates of convergence can be

established as well as how the performance is affected by the dimension of the

problem. To solve the drag minimization problem in this thesis, a GSS methodhas been used that can be generalized to take linear inequality constraints into

account, see [49, 50, 51].

Direct search methods are, although robust, still slow and should only be


used when necessary. The solution can generally be found more efficiently if

gradients can be computed or approximated. The performance is also degraded

quickly when the number of variables is increased or when the problem is badly

scaled [52].

Trajectory optimization

The second part of the thesis is related to the trajectory of the aircraft when

flying from one location to another. There are infinitely many ways of per-

forming this flight, see Figure 10, where some are better than others. When the

Figure 10: Examples of different trajectories.

trajectory optimization problem is considered, the difficulties are not lack of

gradients since the problem can be defined using smooth functions. The objec-

tive function may be the fuel burn or an index defining the integrated emissions

for the flight. The constraints in the trajectory optimization must describe the

equations of motion for the aircraft and these are commonly written as a system

of ordinary differential equations on the form

x = h(x, u). (3)

Here, x and u are continuous variables of time, x(t) and u(t). The vectorx contains the state variables, for example the speed and the altitude of the

aircraft, and u is the vector of controls such as the throttle setting. To this set

of equations, algebraic constraints, like a limiting load factor, are added. The

problem is to determine u such that the best trajectory is found given a specific

objective function and not violating the constraints.

Nonlinear optimization problems can be quite large and efficiency of the

solution method is of great importance. Methods for solving optimal control

problems are discussed in Betts [53], and two main classes of methods can

26 M. Jacobsen

be identified, direct and indirect methods. The indirect methods are generally

more difficult to implement and good theoretical knowledge about the problem

formulation is required in order to obtain good results.

To use a direct method, on the other hand, the equations are discretized

and formulated as one large optimization problem. Here, the equations of mo-

tion (3) are discretized in time using collocation, as first suggested by Hargraves

and Paris [54]. This gives a problem described as a set of nonlinear algebraicequations on the form

maxy

f(y)(4)

subject to l ≤

c(y)Cyy

≤ u,

where f is the objective function and the variables y consist of the discretized

state and control variables. The constraints c(y) are the discretized equations

of motion and algebraic constraints for the aircraft. The matrix C may de-fine linear continuity constraints, if the problem is defined using a multi stage

formulation [55]. The vectors containing the lower and upper bounds of the

constraints are denoted l and u respectively.

To solve the nonlinear optimization problem (4), several different optimiza-

tion techniques may be used. However, the problem is usually rather large and

nonconvex, making it difficult to solve and the method should be chosen with

care. In general, it is not possible to find a unique global minimizer to a non-

linear optimization problem. It is, therefore, of great importance to use already

known information about the solution. For example, using a feasible starting

guess may speed up the solution process quite drastically.

Due to the collocation technique used to discretize the equations, sparsity

could be exploited when solving the optimization problem (4). In the trajec-

tory optimization studies included in this thesis, SNOPT by Gill et al. [56] is

used. This is a sequential quadratic programming (SQP) algorithm that solves

a quadratic subproblem at each major iteration. The algorithm uses Quasi-

Newton approximations to the required second derivative information, and itefficiently exploits sparsity in the constraint Jacobian when solving the quadratic

subproblem. This formulation and solution strategy has been used successfully

in previous studies at the Department of Aeronautical and Vehicle engineering,

see for example Ringertz [57] and Norsell [58].


Summary of appended papers

The aircraft flying today will keep flying for several years to come. This means

that it is of great importance to use the already existing aircraft in a way that

reduces the environmental impact. This can be performed through various new

technology concepts that can be incorporated into existing aircraft, and one such

improvement, drag minimization during flight, is studied in the first part of the

thesis. This is covered by papers A and B. An approach to optimize trajectories

for increased environmental efficiency is presented in papers C and D.

Drag minimization

It will always be beneficial to reduce drag of an aircraft. Less drag results in less

thrust needed to keep the aircraft at a certain speed. The first two papers in

this thesis, papers A and B, discuss a drag reduction scheme that can be used

on existing aircraft with only minor changes to the hardware, or for fly-by-wire

aircraft, only software changes. The concept presented is built on the hypothesisthat the aircraft is not optimized for all flight conditions during a long flight.

For example, as mass is reduced when fuel is burnt, the lift coefficient changes

and if the wings are elastic, so does the deformation. This may result in a less

beneficial load distribution from a drag perspective.

To affect the drag during flight, the control surfaces that already exist on any

transport aircraft today can be used. Since only two variables are theoretically

required to maintain altitude and speed, there will be several redundant control

surfaces available on most modern aircraft. If all control surfaces are used

continuously, lift can be kept constant while drag is minimized.

The work presented in this thesis does not focus on the implementation in a

real aircraft, but instead the main focus is on using a more advanced algorithm

to solve the optimization problem. Already when using two variables, testing

all possible combinations becomes very time consuming and the need for a

more sophisticated algorithm is obvious. Emphasis is also put on satisfying

constraints while minimizing drag.

Paper A discusses the drag minimization problem and how to formulate

it. Different strategies for choosing an appropriate optimization technique are

discussed and a derivative-free approach is implemented. The implementationof the method is described in detail, and some preliminary wind tunnel tests

are performed to investigate the performance of the algorithm on the specific

problem. Wind tunnel tests are performed on a wing with 16 individual control

surfaces distributed across the span on both the leading and trailing edges, see

Figure 11.

In paper B, the drag minimization algorithm is enhanced to include the

28 M. Jacobsen

Figure 11: Wind tunnel model.

angle of attack of the wing as a variable. This small change made a large im-

pact on the lift constraint, which no longer could be approximated as linear.

This changes the problem significantly and some algorithmic changes are in-

corporated to deal with the nonlinearity. The paper describes this algorithmicimprovement and more extensive wind tunnel tests at different flight conditions

are performed with the same wind tunnel model as used in paper A.

The two studies show that a derivative-free optimization approach works

well on the drag minimization problem, and that it is difficult to quantify the

actual drag reduction due to measurement uncertainties.

Emission optimized trajectories

The second part of the thesis discusses methods for modeling emissions that can

be used in the trajectory optimization problem. Finding an emission optimized

trajectory is a large scale nonlinear optimization problem. The problem is solved

using the optimization software SNOPT.

Paper C discusses the modeling of emissions in detail using only ICAO data

and the Boeing fuel flow method 2. An aircraft model of a B737-600 is imple-

mented using the BADA database [59, 60]. This model is enhanced with the

emission model. The trajectory optimization problem is studied using a longi-

tudinal model on a distance of approximately 700 km, a typical domestic flightin Sweden. Different emissions are used as objective functions, minimizing for

example carbon dioxide or nitrogen oxides. In this paper, different methods for

weighing emissions together into an environmental index are also studied and

used as objectives in the trajectory optimization.


In paper D, a three-dimensional model of the SK60 is used. Here, the

approach to an airfield is studied from an environmental perspective. In this

case, a new type of constraint is added to account for no-fly zones, for example

avoiding flying directly above urban areas to avoid noise and emissions tooclose to human beings. The airspace constraints are also treated on a more long

distance flight with the SK60 from Stockholm to Visby, where a large restricted

airspace is encountered on the way.

The results from the two studies show that it is possible to model the

emissions to make it possible to include them in trajectory optimization. The

optimal trajectories differ significantly when different emissions or indices are

minimized. Minimizing emissions of carbon dioxide is the same as minimizing

the fuel burn during the flight. Generally the solution shows that lower speeds

may be better from an environmental perspective, as well as flying at higher

altitudes.

Discussion

The concepts presented in this thesis are related to the operations of aircraft.

This technology can be used on the aircraft of today, but it is not restricted in

any way and would most likely be useful on future aircraft as well.

The drag minimization technique presented in the first part of this thesis

takes advantage of control surfaces that are available on most aircraft. The test

object is a rather nonconventional wing with 16 control surfaces that may lookrather different from a typical aircraft wing. However, the wing of the Airbus

340 has at least 20 control surfaces distributed across the span that could be used

to minimize drag during flight. The results from the experiments performed

in the wind tunnel at KTH show a potential for drag reduction when using

only a few control surfaces. This is coherent with the results from the NASA

test flights with the Lockheed 1011 where a one percent drag reduction could

be achieved using only one redundant control surface. The NASA reports also

show that it is, in fact, possible to evaluate drag during a flight with a real

aircraft. In the wind tunnel environment where the experiments presented in

this thesis are performed, drag is evaluated using measurement techniques that

are not available in real flight.

The validation experiments performed in the wind tunnel show drag reduc-

tion possibilities. However, more accurate measurements would be required toquantify the actual increase in performance using the proposed drag minimiza-

tion technique. Problems with repeatability and drift in the measured signals

make these tests difficult. A larger wind tunnel model with larger forces would

make the measurements more reliable. Some of these problems are directly re-

30 M. Jacobsen

lated to the low Reynolds numbers in the wind tunnel tests. A study by Selig

and McGranahan [61] shows that drag measurements on a clean airfoil varies

significantly for low Reynolds numbers making measurements difficult.

The wind tunnel model used in these studies has a low absolute value ofthe drag force, and trying to resolve changes in this already small force has been

a challenge. With a larger wind tunnel model, or more accurate measurement

equipment, several other optimization techniques could be tested and compared.

It would, for example, be of interest to compare the derivative-free GSS method

to a more standard gradient based technique.

As for the aircraft trajectories, including other emissions than carbon diox-

ide may be premature [62]. The focus here has been to show the possibility of

modeling the emissions to make them useful in trajectory optimization. There

are already taxes or landing fees at some airports depending on how much hy-

drocarbons the engine emits according to the certification data. This shows the

importance of also including other emissions in the optimized trajectories. Theresults presented here are not to be seen as environmentally preferred trajectories

since a more accurate aircraft model would be required as well as more aircraft

related environmental indices. The question about what is good and bad should

be answered by climatologists involved in atmospheric studies.

It is difficult to put fees or taxes on aircraft emissions due to its global

nature. Today, many such fees are regulated only with the help of engine

certification data. This strategy will not, however, put any pressure on making

the airlines operate the aircraft in a more environmentally friendly way. Without

economic policies related to the actual emissions of the regulated substances

chances are small that much will be done. Airlines operate in a way to minimize

the total cost, and if emissions are not directly included, it will not be takeninto account. A future strategy could, for example, be to use simple GPS data

and reverse engineering to compute the actual aircraft trajectory [63] and from

that how much emissions have actually been produced during the flight.

Taking one step back, aviation may not be the most fuel efficient way of

traveling today, but on long distances and across large oceans, it is the only

reasonable means of transportation. It is, therefore, essential to keep working

toward improved efficiency of flight. Great benefits could also come from

optimizing aviation as a whole including everything from engine, airframe and

operations, rather than looking at just one part.


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Division of work between authors

Paper B

Jacobsen and Ringertz jointly developed the optimization method. Jacobsenimplemented the method and performed the experiments. The paper was written

by Jacobsen with support from Ringertz.

Paper C

Ringertz developed the trajectory optimization method. Jacobsen and Ringertz

jointly developed methods for modeling emissions. Jacobsen implemented the

computations of the emissions and the objective functions related to emissions.

The paper was written by Jacobsen with support from Ringertz.

Paper D

Ringertz developed the trajectory optimization method. Jacobsen and Ringertz

jointly developed methods for airspace constraints. Jacobsen implemented theairspace constraints in the trajectory optimization. The paper was written by

Jacobsen with support from Ringertz.

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