Multi Disciplinary Object Oriented Design Analysis of High Altitude

Transcription

Multi Disciplinary Object Oriented Design Analysis
of High Altitude Platforms
Von der Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik
der Universität Stuttgart
zur Erlangung der Würde eines
Doktors der Ingenieurwissenschaften (Dr.-Ing.)
genehmigte Abhandlung
Vorgelegt von
Dipl.-Ing. Mohammad Ataul Manan Haq
aus Rawalpindi
Vorsitzender:
Hauptberichter:
Mitberichter:
Tag der Einreichung:
Tag der mündlichen Prüfung:
Prof. Dr.-Ing. Arnold Kistner
Prof. Dr.-Ing. Dr. h.c. Alexander Verl
Prof. Dr.-Ing. habil. Bernd Kröplin (i.R.) (Fak. 6)
03.11.2011
14.05.2012
Institut für Steuerungstechnik der Werkzeugmaschinen
und Fertigungseinrichtungen
der Universität Stuttgart
2012
III
I dedicate this work to
Hadhrat Mirza Masroor Ahmad
and
my parents
Mirza Abdul Haq and Amtul Waheed
I have been really blessed and encouraged by their prayers.
V
Acknowledgments
Die vorliegende Arbeit begann während meiner Tätigkeit als wissenschaftlicher Mitarbeiter am Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen der
Fakultät Luft- und Raumfahrttechnik. Später wurde die Arbeit am Institut für Steuerungstechnik der Werkzeugmaschinen der Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik fortgesetzt und vollendet. Während der Promotionsphase war ich bei der Firma
TAO-Trans Atmospheric Operations GmbH Stuttgart tätig.
Besonders danken möchte ich Herren Professor Dr.-Ing. Dr. h.c. Alexander Verl. Durch
seine breite Unterstützung und Vertrauen ermöglichte er die Fortsetzung und Fertigstellung meiner wissenschaftlichen Arbeit an seinem Institut ISW. Herren Prof. Dr.-Ing.
Arnold Kistner danke ich für die Übernahme des Vorsitzes des Promotionsausschusses.
Ganz herzlich möchte ich mich beim verehrten Herren Professor Dr.-Ing. Bernd Kröplin
bedanken, der mir die Möglichkeit gab an seinem Institut ISD mit den Entwurfssprachen
zu arbeiten und anschließend in seiner Firma TAO-Trans Atmospheric Operations GmbH
Stuttgart die Entwurfssprachen für den Entwurf von Luftwürmern anzuwenden.
Allen Kollegen der damaligen Pi-Gruppe am ISD gilt ein herzliches Dankeschön für die
stets gute Zusammenarbeit und den vielen interessanten Diskussionen.
Ganz besonders erwähnenswert sind für mich zwei Personen, nämlich Frau K. Finken
und Herr A. Finken aus Prüm. Für ihre Hilfe und Unterstützung möchte ich mich ganz
herzlich bedanken. Sie erbrachten sehr viel Mühe und Geduld mir die deutsche Sprache
und Latein zu lehren. Ihre Selbstlose Hilfe öffnete mir meinen Weg zum Studium.
Besonders bedanke ich mich bei meiner Familie insbesondere meinen Eltern und meiner
Frau Madiha. Ihre Unterstützung und ihr Verständnis für meine Arbeit gaben mir stets
den nötigen Rückhalt.
Einen herzlichen Dank an all diejenigen, die zum Erfolg dieser Arbeit beigetragen haben.
Ich konnte sie zwar hier namentlich nicht erwähnen aber ihre Unterstützung wird mir stets
Verbunden mit dieser Arbeit in Erinnerung bleiben.
Stuttgart, Oktober 2012
Manan Haq
Contents
VII
Contents
Abstract
IX
Kurzfassung (german)
XI
Nomenclature
XIII
List of figures
XXIII
1 Introduction
1.1 Motivation . . . . . . . . . . . . .
1.2 Concept of Chain Body LTA-HAP
1.3 Objectives/ Method Application .
1.4 Scope of the Thesis . . . . . . . .
1.5 Outline of the Thesis . . . . . . .
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1
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2 Background
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2.1 High Altitude Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Design Languages and Grammars . . . . . . . . . . . . . . . . . . . . . 18
3 Decomposition and Model Development
3.1 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Model Development of Individual Disciplines . . . . . . . . . . . .
3.2.1 Envelope Structure . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Aerostatics and Aerodynamics . . . . . . . . . . . . . . . .
3.2.3 Operational Environment . . . . . . . . . . . . . . . . . . .
3.2.4 Power and Propulsion System . . . . . . . . . . . . . . . .
3.2.5 System Integration and Power Network . . . . . . . . . . .
3.3 Model Development of Couplings and Patterns . . . . . . . . . . .
3.3.1 Design Characteristic: Parametrical and Topological Design
3.3.2 Multi Disciplinary Parameter Variation . . . . . . . . . . .
3.3.3 Balance Equations and Constraints . . . . . . . . . . . . . .
3.3.4 Mission Scenarios . . . . . . . . . . . . . . . . . . . . . .
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Contents
VIII
3.3.5
Multi-Objective Optimization of Power Network . . . . . . . . .
4 Building Design Variants and Alternatives
4.1 Envelope Configurations . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Design Variants by Topological Modifications . . . . . . . . . .
4.1.2 Design Variants by Parameter Modifications . . . . . . . . . . .
4.2 Layout of Energy System . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Energy system based on accumulator . . . . . . . . . . . . . .
4.2.2 Power system based on photovoltaic . . . . . . . . . . . . . . .
4.2.3 Energy system based on hydro-solar fuel cell system . . . . . .
4.3 Layout of Propulsion System . . . . . . . . . . . . . . . . . . . . . . .
4.4 Systems Integration and Multi Criteria Optimization of Power Network
5 Examples of Multi Disciplinary Mission Analysis
5.1 Short Duration Mission;
Energy Source: Battery . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Mission Scenario 1 . . . . . . . . . . . . . . . . . . . .
5.2 Mid Duration Mission;
Energy Source: Photo Voltaic + Batteries . . . . . . . . . . . .
5.3 Long Endurance Mission;
Energy Source: Solar-Fuelcell System . . . . . . . . . . . . . .
5.4 Comparison and Discussion of the Results . . . . . . . . . . . .
5.4.1 Discussion of the Constraint Lines . . . . . . . . . . . .
5.4.2 Comparison and Discussion of Design Space
variation of solar cell efficiency ηSA for duration t ≥ 24h
5.4.3 Comparison with Conventional Airship Design . . . . .
5.4.4 Summary of the Results . . . . . . . . . . . . . . . . .
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6 Conclusion
155
Bibliography
159
Abstract
IX
Abstract
The growing demand for telecommunication and other applications has led to rapid deployment of satellite wireless networks. Signal delay is caused because of their geostationary orbit of 36,000 km and terrestrial relay stations have to be installed to convert their
long range communication signal into a short range signal for instance for mobile phones.
Satellites in lower orbits of 200 km permit rather short phases of few minutes. Apart from
these problems the operational costs of satellite communication are very high.
Within the last decades another alternative research field has been carried out in parallel to
the well established technology of satellite communication. It is based on quasi-stationary
aerial platforms, so called High Altitude Platform (HAPs), operating in the lower stratosphere about 20 km altitude. Their distinct advantages compared with satellite systems
are reduced cost, relatively close range, flexibility in terms of rapid deployment, ease
of re-configuration, possibility for frequent take-offs and landings for maintenance and
upgrading and very favourable path-less characteristics.
Thus a mission within the lower stratosphere would allow multi cast and broadband
telecommunication, remote sensing, environmental monitoring, disaster recovery, meteorological measurements, real time monitoring of seismic regions, agriculture support and
many more. Therefore the HAPs should be capable of quasi geostationary long endurance
mission. Because of tough environmental conditions within this flight region, such as low
density of air, only 7% of that on ground surface, and the seasonal wind speeds up to
35m/s there exist no flight vehicles so far with endurances of more than 48h. In the past
airplanes, balloons and airships where designed for flight within the stratosphere. But
soon it became evident that these concepts have major difficulties to fulfill the operational
requirements.
For this reason an aerostatic segmented chain body was designed at the Institute for Statics and Dynamics of Aerospace Structures (ISD; University Stuttgart) to overcome the
limitations of stratospheric flight of conventional air vehicles. Such chain body air vehicles are very complex and require a multi disciplinary design analysis of their envelope,
structure, propulsion, energy system and control.
X
Abstract
For this purpose we introduce the method of design languages within this work to facilitate an overview of the mission characteristics of such chain body air vehicles from
various perspectives. Design languages allow to describe the involved disciplines in a
very precise way and subsequently enable evaluating them. The mightiness of this approach is illuminated within this work and verified with help of layout examples. It is
demonstrated that by this method a huge amount of design variants can be generated semi
automatically and thus allows to explore the design space very efficiently. The design
space is investigated in regard to the borders and the borderlines and corresponding parameters of the used technology are identified. Furthermore strategies are developed how
these border lines can be moved in a favourable area of the design space.
Abstract
XI
Kurzfassung
Der wachsende Bedarf an Telekommunikation und weiteren Anwendungen hat zur raschen Ausbreitung der auf Satelliten basierenden Drahtloskommunikation geführt. Aber wegen deren geostationären Orbits von 36.000km wird eine Signalverzögerung verursacht.
Außerdem müssen terrestrische Relaisstationen installiert werden, um deren Langstreckensignal in ein Kurzstreckensignal z.B. für Mobilfunkanwendungen umzuwandeln. Satelliten in niedrigeren Umlaufbahnen von ca. 200km erlauben leider nur ein kurzes stabiles
Sichtfenstern von wenigen Minuten. Abgesehen von all diesen Problemen stellen Operationskosten von satellitenbasierter Kommunikation einen erheblichen Faktor dar.
Während den letzten Jahrzehnten wurde parallel zu der etablierten Satelliten basierter
Kommunikation ein weiteres Forschungsfeld eingeführt. Es basiert auf quasi stationären
Antennen-Plattformen, die so genannten Höhenplattformen (High Altitude PlatformsHAP), welche in der niedrigen Stratosphäre in einer Höhe von ca. 20km operieren. Deren
eindeutige Vorteile gegenüber Satellitensysteme sind reduzierte Kosten, relativ nahe Entfernung, Flexibilität in Hinsicht auf Einsatzbereitschaft, einfache Neukonfiguration, beliebige Lande- und Startfähigkeit im Hinsicht auf Wartung und Ausbau und eine günstige
pfadlose Charakteristik.
Demzufolge hat der Einsatz von Höhenplattformen in der niedrigen Stratosphäre seine
besonderen Vorteile, wie Breitband Telekommunikation, Fernerkundung, Umweltüberwachung, Katastrophenschutz, meteorologische Messungen, Echtzeitüberwachung von
seismischen Aktivitäten, Unterstützung der Agrarwirtschaft und viele weitere Anwendungen. Daher müssen Höhenplattformen in der Lage sein quasi Geostationäre und Langzeiteinsätze durchzuführen. Wegen den rauen Umgebungsbedingungen in dieser Einsatzhöhe
wie der geringen Luftdichte von nur 7% als der auf Meereshöhe und jahreszeitlich bedingten Windgeschwindigkeiten von bis zu 35m/s, existiert bisher kaum ein Fluggerät
welches eine Ausdauer von mehr als 48 Stunden besitzt. Für diesen Einsatzzweck wurden in der Vergangenheit Flugzeuge, Ballone und Luftschiffe konzipiert, aber es wurde
bald offensichtlich, dass all diese Konzepte in dieser Umgebung ihre schwerwiegenden
Probleme haben.
XII
Abstract
Aus diesem Grund wurde am Insitut für Static und Dynamic der Luft- und Raumfahrtkonstruktionen der Universität Stuttgart ein Leichter als Luft Gliederkörper entwickelt, um
die Probleme der konventionellen Fluggeräte zu bewältigen. Solche mehrgliedrige Fluggeräte sind sehr komplex und bedürfen einer multidisziplinären Entwurfsanalyse aller
Disziplinen, wie der Hülle, Struktur, Antrieb, Energiesystem, Regelung etc.
Für diesen Zweck wird in dieser Arbeit die Methode der objektorientierten graphenbasierten Entwurfssprachen eingeführt, wodurch ein Überblick über die Missionscharakteristik von solchen Gliederkörpern von unterschiedlicher Perspektive ermöglicht wird.
Entwurfssprachen erlauben die involvierten Disziplinen in einer sehr präzisen Art und
Weise zu beschreiben und diese auch anschließend zu evaluieren. Die Mächtigkeit dieses
Ansatzes wird in dieser Arbeit hervorgehoben und wird mit Hilfe von Entwurfsbeispielen verifiziert. Es wird demonstriert, dass mit dieser Methode eine sehr große Anzahl an
Varianten in relativ kurzer Zeit generiert werden können und ermöglicht somit den Entwurfsraum sehr effizient zu durchsuchen. Der Entwurfsraum wird auf seine Grenzen hin
untersucht, und die für Grenzlinien verantwortlichen Parameter der verwendeten Technologie werden identifiziert. Außerdem werden Strategien erarbeitet, wie diese Grenzlinien in einem bevorzugten Bereich des Entwurfsraumes verschoben werden können.
Nomenclature
XIII
Nomenclature
Formula symbol
Symbol
α
ax
A
Aenv
ASA
ASA_vis
ASA_real
Aenv_i
a, b, bz, bzn
CG
Cw
Cw,f
Cw,p
Cbat
d, D
dblade
ESA
Ehydro
EF Z
Description
day angle
longitudinal axis of ellipsoid
surface area
surface area of envelope
surface area of solar array
visible surface area of solar array
real surface area of solar array
surface area of envelope segment i
axis of ellipsoid
center of gravity
drag coefficient
friction drag coefficient
pressure drag coefficient
capacity of battery
HAP diameter
diameter of propeller blade
eccentricity: 0.017
energy of solar array
energy of solar hydro system
energy of fuel cell
Unit
[Rad]
[−]
[m2 ]
[m2 ]
[m2 ]
[m2 ]
[m2 ]
[m2 ]
[m]
[−]
[-]
[-]
[-]
[Ah]
[m]
[m]
[−]
[W h]
[W h]
[W h]
Nomenclature
XIV
Symbol
Ebat
Ebat_F Z
ESA_12h
Epowersystem
f1
Fi
FB
FG
FD
FT
Fz
Fx
g
H
Hs
I
I(F )
l, L
LR
Lif tnet
Lif ttotal
τ
mi
mSA
mEL
mF z
menv
mbat
menv_i
mgc
mgc_i
mengine
msp
Mf
Mair
MHe
Description
energy of battery based system
energy of battery fuel cell system
energy of solar cells during 12h daylight
total energy of power system
distance of total mass from middle axis
force i
buoyancy force
weight force
aerodynamic drag force
thrust force
force in z-direction
force in x-direction
gravitational constant: 9.81
altitude
altitude of 11km, begin of stratosphere
electrical current
function of surface calculation of ellipsoid
HAP length
laps rate: 0.0065
net lift
total lift
torque, momentum
sub mass i
mass of solar array
mass of electrolyzer
mass of fuel cell
mass of LTA HAP envelope
mass of batteries
mass of LTA HAP envelope segment i
mass of gas cell
mass of gas cell segment i
mass of engine
specific mass
molar mass of fluid
molar mass of air: 0.0287
molar mass helium: 0.004
Unit
[W h]
[W h]
[W h]
[W h]
[m]
[N]
[N]
[N]
[N]
[N]
[N]
[N]
[m/s2 ]
[m]
[m]
[A]
[m2 ]
[m]
[K/m]
[N]
[N]
[Nm]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
kg
kg
[ kW
]
m2
[mol]
[kg/mol]
[kg/mol]
Nomenclature
Symbol
nBl
∆p
P
Pcons
Pdisp
Pcons_daytime
Ppowersystem
PSA_12h
Pconsumer_12h
Ptotal
Pshaf t
Pengine
PP L
ps
pair
pHe
q
r
rorb
rorbm
Rprop
R
air
ρ
ρair
ρHe
Re
sp, spn
SI
SIm
SIevr
t
tmission
trequirement
tbat
tSA
tSA_hydro
XV
Description
number of propeller blade
over pressure
power
constant power
dissipation power of cable
constant power consumption during 12h daylight
power of power system
power of solar cell during 12 h
power consumption of consumer during 12h
total power consumption
power of shaft
power of engine
power of payload
air pressure at Hs=11km with 22633
air pressure
helium pressure
dynamic pressure
radius
earth orbital radius
mean earth orbital radius
propeller radius
Universal gas constant: 8.3143
special gas constant for air: 287
density of flow
density of air
density of helium gas
Reynolds number
reference point of origin for ellipsoid
solar intensity
mean solar intensity
everage solar intensity
time duration
time mission duration
required mission duration
duration of a mission with battery
duration of a mission with solar cell
duration of a mission with hydro fuelcell system
Unit
[-]
[P a]
[W ]
[W ]
[W ]
[W ]
[W ]
[W ]
[W ]
[W ]
[W ]
[W ]
[W ]
[P a]
[P a]
[P a]
[P a]
[m]
[m]
[m]
[m]
[J/molK]
[m2 /s2 K]
[kg/m3 ]
[kg/m3 ]
[kg/m3 ]
[-]
[m]
[W/m2 ]
[W/m2 ]
[W/m2 ]
[h]
[h]
[h]
[h]
[h]
[h]
XVI
Symbol
T
T0
Ts
THe
Tair
U
v
V, Vx
Vtotal
Vi
Xhnight
z3
zCG
η
Nomenclature
Description
Unit
gas temperature
[K]
sea level air temperature: 288.15
[K]
constant air temperature of stratosphere at 11km altitude: 217 [K]
helium gas temperature
[K]
air gas temperature
[K]
voltage
[V]
velocity, speed
[ ms ]
volume
[m3 ]
total volume of LTA HAP
[m3 ]
volume of segment i
[m3 ]
night flight duration
[h]
displacement of mass
[m]
stable position of center of gravity
[m]
efficiency
[-]
Nomenclature
Abbreviations
Symbol
Agr
Apr
acu
BC
EA
LTA
HAP
HTA
GPS
UAV
CAD
MDO
SPG
Vnt
Vt
PR
S
UV
H2
O2
FC
H2 O
PEM
Seg
Cell
elip
zyl
PL
Description
aggregate, system device
apron
accumulator
on board computer system
evolutionary algorithm
lighter than air
High Altitude Platform
heavier than air
global positioning system
unmanned air vehicle
computer aided design
multi disciplinary design optimization
solution path generator
nonterminal vocabulary
terminal vocabulary
set of production rules
set of starting symbols
ultra violet
hydrogen molecule
oxygen molecule
fuel cell
water molecule
proton exchange membrane
segment
cell
ellipse
cyllinder
payload
XVII
List of Figures
XIX
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
Wind speed diagram for summer and winter months for 20◦ E-50◦ N [59] .
Comparison of conventional airship concept and chain body LTA HAP . .
Concept and design domains of a chain body LTA HAP . . . . . . . . . .
Multi disciplinary object oriented design graph with embedded design
domains, such as functional, geometry, electrical and controll software . .
Data structure of a vocabulary with several domains integrated within it .
Components of a graph grammar based object oriented design language .
Decomposition for modelling of the individual disciplines (vocabulary)
and their relations (grammar rules) within the method of graph grammar .
Decomposition of continuum to discontinuum and aggregation of discontinuum to novel continuum . . . . . . . . . . . . . . . . . . . . . . . . .
Decomposition of envelope structure in its essential elements for modelling of vocabulary with geometrical CAD information . . . . . . . . .
Discretization of the geometry for numerical calculation and CAD modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Library of geometrical objects; vocabulary of envelope structure with discretization and CAD model . . . . . . . . . . . . . . . . . . . . . . . . .
Parametrical description of the envelope vocabulary for partial volume
and surface area calculation . . . . . . . . . . . . . . . . . . . . . . . . .
A curve described by a function f (x) for rotation around the x-axis . . . .
Aerostatics and aerodynamic partial dependancy graph of LTA HAP . . .
Condition of helium gas at different altitudes: ground surface H = 0km
and H = 20km . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Structure of earths atmosphere including troposphere and stratosphere . .
Wind chart of weather soundings Stuttgart Schnarrenberg; All profiles of
whole month are presented within one chart . . . . . . . . . . . . . . . .
Solar radiation spectrum at top of atmosphere and sea level [34] . . . . .
Solar radiation in different altitudes and time of year for directional as
well as undirectional radiation [59] . . . . . . . . . . . . . . . . . . . . .
3
4
6
7
8
9
23
24
28
29
30
31
32
35
37
39
40
42
43
List of Figures
XX
3.14 A schematic of power and propulsion system of a LTA-HAP . . . . . . .
3.15 Contour map of an electrical engine with regulator [37] . . . . . . . . . .
3.16 Comparison of single junction solar cells and triple junction solar cell
with solar spectrum graph presenting which part of the wavelength is used
by each technology [134] . . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 Integration of photo voltaic arrays on the upper surface of LTA HAP segment by considering the issue of CG-position for reducing roll moment .
3.18 Energy and power density of rechargeable batteries [102] . . . . . . . . .
3.19 Cell voltage and current density characteristic curve of a regenerative fuel
cells in operation with O2 and air [93] . . . . . . . . . . . . . . . . . . .
3.20 Voltage-current density characteristic curve of electrolyzer [129] . . . . .
3.21 Comparison of mass distribution problem of a conventional airship and
chain body LTA HAP . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.22 Building of system component model, cable model and battery model . .
3.23 Multi disciplinary network of domains involved within design of LTA HAP
3.24 Graph of multi disciplinary couplings for sizing the envelope structure . .
3.25 Topological design of envelope structure with corresponding rules . . . .
3.26 Topological design of propulsion system with corresponding rules . . . .
3.27 Partial graph for energy system design with flow of variable and parameters
3.28 Topological design of energy system with corresponding rules . . . . . .
3.29 Topological integration of system components with corresponding rules .
3.30 Filling of gas cells and sloshing behaviour of helium gas in segments at
ground surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.31 Iteration algorithm for calculation of optimal designs by multi disciplinary
parameter variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.32 Principle contour map diagram of a design space with constraint lines as
boundary lines. All valid design points are lying in the design space and
the invalid design points are out of the design space. . . . . . . . . . . . .
3.33 Graph model of energy and mass balances of multi disciplinary HAP design
3.34 Optimization rules involved within rule based multi objective optimization of cable diameter and type . . . . . . . . . . . . . . . . . . . . . . .
3.35 Process chain for rule based multi objective optimization of power network
4.1
4.2
4.3
4.4
Programs (groups of rules) within production system of a graph grammar
based design model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Structural configuration of LTA HAP: distribution of buoyancy forces and
aerodynamical drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Programs P1 for structural layout of a LTA HAP . . . . . . . . . . . . . .
Topological variation of envelope of a LTA HAP . . . . . . . . . . . . .
43
45
49
50
51
53
55
56
58
59
61
62
63
64
65
67
68
71
74
76
86
87
90
92
93
94
List of Figures
4.5
XXI
4.6
Result of sizing the envelope structure by varying parameters of altitude
and payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Graph of dependency for design of power system . . . . . . . . . . . . .
4.7
4.8
4.9
4.10
4.11
4.12
Concept of energy system based on accumulator batteries . . . . . . . .
Schematic of designing energy system based on accumulator batteries .
Energy system based on photovoltaic arrays and accumulator batteries .
Energy system based on photovoltaic hydrogen energy system . . . . .
Comparison of Re-Number of 70m and 23m LTA HAP, figure from [52]
Topological variants of propulsion system of various LTA HAPs . . . .
.
.
.
.
.
.
96
97
98
99
100
101
103
105
4.13 CAD model of a HAP system demonstrating configuration of power, propulsion and system components . . . . . . . . . . . . . . . . . . . . . . . . 106
4.14 Systems integration strategy 1: one power network for overall supply of
electrical energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.15 Systems integration strategy 2: two different power networks for system
components and propulsion unit . . . . . . . . . . . . . . . . . . . . . . 108
4.16 Abstraction electrical model of circuit plan of HAP configuration . . . . . 109
4.17 Graph based representation of electrical circuit plan for multi criteria optimization of wiring harness . . . . . . . . . . . . . . . . . . . . . . . . 111
4.18 Optimization result of wiring harness of power cables . . . . . . . . . . . 112
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Wind speed values for three different months for altitude of 20 km . . . .
Energy system concept based on accumulator batteries for a short duration
mission with batteries as energy source for electrical devices. The mission
duration is limited by the amount of electrical energy of the batteries. . . .
Design of LTA HAP with 7m diameter in operational altitude of 20km
and a maximum flight duration of 4.3 h . . . . . . . . . . . . . . . . . .
Results of HAP configurations with batteries as energy source and varying
payload and duration in 20 km altitude for mean wind velocity of 12m/s .
Energy system concept for a mid duration mission based on photo voltaic
Solar Radiation in 2500m altitude for summer and winter [59] . . . . . .
Solar Radiation in 20000m altitude for summer and winter [59] . . . . . .
HAP-Mission in 2500m altitude with solar cells and accumulators for different payloads PL, wind speeds v and durations t . . . . . . . . . . . . .
115
116
117
118
120
121
121
123
HAP-Mission in 2500m altitude with solar cells and accumulators for
varying payloads PL, wind speeds v and a duration t ≥ 24h . . . . . . . . 124
5.10 HAP-Mission in 2500m altitude with solar cells and batteries as energy
source for varying payloads PL, wind speeds v and a duration t ≥ 24h;
diagrams displaying area and mass of solar arrays as well as mass of batteries for same mission . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
XXII
List of Figures
5.11 HAP-Mission in 20000m altitude with solar cells and batteries as energy
source; solar array: η=19% and 1.5 kg/m2 ; battery: 156 Wh/kg . . . . .
5.12 Diagrams of mass and area of solar array and battery mass for HAPMission in 20000m altitude with solar cells and battery as energy source .
5.13 Energy system concept with photovoltaic arrays to produce electrical energy and electrolyzer fuel cell combination for storing electrical energy
for usage during the night phases . . . . . . . . . . . . . . . . . . . . . .
5.14 HAP-Mission in 2500m altitude with a regenerative solar fuelcell system;
solar arrays: 1.5kg/m2, fuelcell: 1866 Wh/kg and duration t ≥ 24h . . .
5.15 Diagrams of area and mass of solar arrays and fuelcell mass for a HAPmission in 2500m altitude with a regenerative solar fuelcell system and
duration T ≥ 24h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.16 HAP-Mission in 20000m altitude with a regenerative solar-fuelcell system; solar arrays: 1.5kg/m2 and fuelcell: 1866 Wh/kg . . . . . . . . . .
5.17 Diagrams of area and mass of solar arrays and fuelcell mass for a HAPmission in 20,000m altitude with a regenerative solar fuelcell system with
T ≥ 24h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.18 Comparison of design windows for description of the CG-constraint line
for both energy storage concepts: batteries and hydro fuel cell; for flight
in 2.5 km and 20km altitude and solar arrays with 1.5kg/m2 and 19%
efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.19 Crossection of segment to illustrate the D/4 stable area of total mass mtotal
of segment; while mtotal lying in this area occures that the segment is
atable against roll moments . . . . . . . . . . . . . . . . . . . . . . . . .
5.20 Principle development of areas of solar array and segment upper surface
dependent from velocity, for flight in 20km altitude and specific payload,
solar array efficiency, specific mass of solar array and electrical storage
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.21 Comparison of design space for flight in 2.5 km altitude with a duration
t ≥ 24h and variation of solar array efficiency; right diagram is top projection of the left diagram . . . . . . . . . . . . . . . . . . . . . . . . . .
5.22 Comparison of design space for flight in 20 km altitude with a duration
t ≥ 24h and variation of solar array efficiency; right diagram is top projection of the left diagram . . . . . . . . . . . . . . . . . . . . . . . . . .
5.23 Comparison of diagrams of mass of solar arrays and fuelcell corresponding to the design surfces presented in figure 5.22 for flight in 20 km altitude and variation of solar array efficiency . . . . . . . . . . . . . . . . .
5.24 Variation of solar array efficiency and corresponding intersection points
of segment surface area and solar array area for maximum wind velocities
of the area constraint line . . . . . . . . . . . . . . . . . . . . . . . . . .
126
127
129
130
131
132
133
136
138
139
142
143
144
146
List of Figures
XXIII
5.25 Shape of conventional airship HALE-D [78] which is scaled and morphed
for further investigation . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.26 Conventional airship configuration 1: H=20km; duration T ≥ 24h; solar
array material: 1, 5kg/m2; Cw=0.08; η = 19%; energy density of battery:
156W h/kg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
156W h/kg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
156W h/kg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.29 Conventional airship configuration 4: H=20km; duration T ≥ 24h; solar array material: 0, 25kg/m2; Cw=0.05; η = 19%; energy density of
battery: 1866W h/kg . . . . . . . . . . . . . . . . . . . . . . . . . . . .
148
149
150
151
152
1 Introduction
1
1 Introduction
The aim of this work is a multi disciplinary object oriented design analysis of chain body
lighter than air high altitude platforms (LTA HAP). These HAPs are airship similar chain
body air vehicles for operation in an altitude of about 20km. Their main task amongst
many others is to provide telecommunication services. The design of chain body HAPs
is inherently a complex problem by incorporating a large amount of sub systems and
disciplines which are interacting with each other within a network.
For this purpose an object oriented design language [42] based on the method of graph
grammars is developed for generation of a large number of design variants of HAP’s that
reflects practical design goals. The number of alternatives within the design space defined by the graph grammar based design language is quite large. Thus, the objective of
this work is to develop an object oriented design language which is capable of building
up a complex design space and then searching it for plausible designs. Moreover it incorporates the rule based approach and provides insight into feasibility and performance
of multidisciplinary chain body HAP design. This method allows designs by considering both design paradigms, top-down and bottom up, respectively [70]. The top-down
paradigm allows designing from an abstract level to a detailed level. With every design
step in the next deeper design level the apriori abstract design model is concretized until
the design model is implemented. The bottom-up paradigm has a backward design direction as the top-down paradigm. It starts with an informal specification of the lowest
design level. With every design step in the next design level the basis components are put
together to even complexer ones until the final design is achieved. The method of graph
grammars allows a mix of both paradigms [63]. e.g. by starting with top-down and building an abstract specification of design object. At the same time by performing bottom-up,
a detailed model component library of each discipline is generated. Thus a design can be
performed by integrating all known details of known disciplines and the level of detail of
those disciplines with unknown details remain abstract. With every iteration step the level
of detail increases until the final design is achieved.
2
1 Introduction
1.1 Motivation
The worldwide demand for broadband mobile telecommunication and other applications
has led to rapid deployment of both terrestrial and satellite wireless networks. Additionally the necessity for further services such as internet or GPS-satellite navigation is
permanently growing. Therefore large efforts are done for the development of new infrastructure within the field of mobile telecommunication.
One possibility for long range communication is the application of fiber optic cables
which are used for data transfer of telephone, broadcasting and internet, respectively.
An alternative is a satellite based communication which is able to cover an area of up to
9000km radius. They are positioned in a geosynchronous orbit of about 36,000km [65].
Signal delay of about 0,5s is caused because of their geostationary orbit and terrestrial
relay stations have to be installed to convert their long range communication signal into a
short range signal for instance for mobile phones. Satellites in lower orbits of 200 km permit rather short phases of few minutes. Apart from these problems the development and
operational cost of satellite communication presents a major factor. About 80 Mio. Euros
are invested for the development of a telecommunication satellite to ensure maintenance
free service during lifetime. This is necessary since there is no possibility of repairment
of satellite in the orbit. Also the transportation cost of a satellite into their orbit count for
a large share of total budget, whereby an Ariane-5 start costs about 120 Mio. Euros.
Within the last decades another alternative research field has been carried out in parallel to
the well established technology of satellite communication. It is based on quasi-stationary
aerial platforms, the so called High Altitude Platform (HAPs). They are operating in quasi
geostationary positions in the lower stratosphere of about 20 km altitude. Such a solution
preserves many advantages of both terrestrial and satellite systems but also provides special advantages of its own. There distinct advantages compared with satellite systems
are reduced cost, relatively close range, flexibility in terms of rapid deployment, ease of
re-configuration, possibility for frequent take-offs and landings for maintenance, reprogramming and upgrading and very favourable path-less characteristics. There coverage
radius is about 500km.
Thus a mission within the lower stratosphere would allow multi cast and broadband
telecommunication, remote sensing, environmental monitoring, disaster recovery, meteorological measurements, real time monitoring of seismic regions, agriculture support and
many more. Therefore the HAPs should be capable of quasi/geostationary long endurance
missions. Because of tough environmental conditions (figure 1.1) within this flight region
such as low density of air (only 7% of that on ground surface) and the seasonal wind
speeds up to 35m/s there exist no flight vehicles so far with endurances of more than 48h.
1.1 Motivation
3
Figure 1.1: Wind speed diagram for summer and winter months for 20◦ E-50◦ N [59]
In the past airplanes, balloons and airships where designed for flight within the stratosphere. But soon it became evident that these concepts have major difficulties to fulfill
the operational requirements.
For Heavier Than Air (HTA) vehicles the main issue in high altitude flight is generating
lift within this low atmospheric density environment. The majority of vehicles that can
operate at high altitudes do so by flying very fast to compensate the low-density air.
For instance U2 has a cruising speed of 692 km/h in about 21km altitude. The Global
Hawk is the latest in high altitude UAV development. It is capable of flights at 20 km
altitude with a cruise speed of 643 km/h and endurances of about 35 hours [21].
Until now none of the HTA aircrafts can carry a large payload at high altitudes and remain aloft for long endurances. For this purpose the concept of Lighter Than Air (LTA)
-aircraft is considered. An airship has the ability to meet these needs, while it does not
need to be in motion to generate lift. It is not nearly as power intensive as an HTA-aircraft
while carrying the same payload.
In addition, the limitations of an airship such as weather sensitivity are not factors for
station-keeping missions at altitudes well above the active weather regions. The active
weather occurs below 11km altitude where clouds and associated weather appearances
such as rain, jet streams and turbulences are formed because of the moist air. Above this
region in about 20 km altitude the air is almost dry and therefore free of such weather
activities.
1 Introduction
4
An operation in the very low dense air of 20 km altitude demands very large and very light
weight structures with a good relation of flight mass to dead mass. Moreover they should
be very fragile with a very small absolute mass in relation to the size just like gossamer
structures [9]. Considering the strength there are mainly four problems which an LTA
airship has to face [65]:
1. buckling of structure,
2. differential load,
3. munk load and
4. static load.
The construction of an airship can be stabilized against buckling by using non rigid or
blimp type structures which can also survive an overloading without being destroyed.
This can not be said for any rigid structure. The differential loads are caused by the
lifting forces of the buoyancy gas column within an inclined airship which consists of
only one large gas compartment. For high altitude flight large volume of buoyancy gas
are necessary, which means an increase of gas column. The higher the gas column, the
larger the part of constructive mass connected with differential pressure.
Figure 1.2: Comparison of conventional airship concept and chain body LTA HAP
Thus structural mass can be reduced by dividing the gas chamber into smaller independently suspended gas compartments (figure 1.2). To compensate the destabilizing moments (munk load) of a conventional airship large empennages are necessary which create their self bending moments. Also the static mass of the loads and the empennage
generates a static bending moment. These loads are almost zero for a sphere like bodies.
From this follows that a conventional blimp airship leads to an unfavourable scaling and
increasing part of dead mass for high altitude operations.
5
To overcome all these problems and limitations of stratospheric flight of conventional air
vehicles an alternative structural design was introduced at the Institute for Statics and Dynamics of Aerospace Structures (ISD; University Stuttgart) [65] by clustering spheres in
a chain which seams to be the most light weight blimp design. This would allow using
the thinnest possible material for the chain body in order to minimize the Munk load and
the empennage mass.
This innovative concept provides unique benefits and opportunities and presents a significant step towards the scientific and economic exploitation of this section of the stratosphere.
Such chain body air vehicles are very complex and require a multi disciplinary optimization for the design of their structure, propulsion, energy system and control. These sub
systems of different domains can be considered as a network of nodes. The nodes are
interacting with each other by exchanging information. In case of modifications in one
node these information can propagate through all other nodes of the network and vice
versa. Therefore digital model of each domain of such a multidisciplinary chain body air
vehicle has to be developed in a sufficiently precise way, so that simulation and analysis
can perform to multitude of designs of the air vehicle. For this purpose we introduce the
method of rule-based design languages within this work which facilitate modelling and
describing the involved disciplines of such a complex air vehicle.
In this section we will present the multi segment chain body concept of a LTA High
Altitude Platform (LTA HAP) which will be an object of study within this work.
As compared in figure 1.2 both airship concepts can carry loads by the buoyancy lift
generated by the helium gas containing therein. But the buoyancy lift of a chain body
HAP is distributed over the individual segments which allows a slender and light weight
construction and leads to reducing the overall weight and size of an LTA HAP as well as
the bending moments which occur by manoeuvres and weight distributions. Furthermore
several other problems such as buckling, differential load, munk and static load as well as
large empennage which an airship with very large volume for high altitude flight has to
face are significantly reduced by this innovative design.
1 Introduction
6
Figure 1.3: Concept and design domains of a chain body LTA HAP
Figure 1.3 presents the chain body air vehicle with incorporating sub systems and disciplines:
• Envelope and structure design
• Propulsion system
• Operational environment
• Aerostatics and aerodynamics
• Energy system
• Systems integration
The chain body HAP is driven by the propulsion system integrated in the head segment.
It is able to overcome the velocity of winds prevailing at target altitude. The velocity
of wind varies in different altitude and time of year. There exists even no description
model of velocity and direction of wind over the year. But wind speed is one of the
major factors which influence the design of LTA HAP significantly. For buoyancy lift
generation the gas cells are filled with helium gas. Each segment consists of its own gas
cell. Dependent from target altitude a gas cell can be completely filled or only partially
which can cause gas sloshing. The chain body LTA HAP consists of no skeleton structure
but uses a pressure level in excess of the surrounding air pressure to retain its shape during
flight. Several energy storage concepts are conceivable for operating in high altitudes.
The conventional one are rechargeable batteries. The alternative concept is of a fuel cell
system. Solar cells are used for energy generation during the daylight. The rate of solar
radiation varies during the year and altitude. For instance the duration of day light in
summer is double in comparison to day light duration in winter and also the rate of solar
radiation is in summer much higher than in winter.
7
Figure 1.4: Multi disciplinary object oriented design graph with embedded design domains, such as functional, geometry, electrical and controll software
There are several other disciplines which have to be considered during the design of LTA
HAP. To understand their influence on the LTA HAP and their interrelationship to each
other is very important. The platform dimensions are determined as functions of several
parameters, such as: solar radiation, mass and efficiency of solar cells and of fuel cells,
altitude, aerodynamic performance, electric motors; propeller efficiency, payload mass
and required payload power. The design procedure is based on the energy balance equilibrium between the available solar power and the required power, the former depending
on the solar cell area, the latter depending on the velocity and total drag of the platform.
In particular, the available power must not only be sufficient for the daylight equilibrium,
but also regenerate the fuel cells for night flight power.
As mentioned before all these domains are coupled with each other and are building a
network of nodes (figure 1.4). The nodes are interacting with each other by exchanging
information. In case of modifications in one node these information can propagate through
all other nodes of the network and vice versa. For the modelling of such a complex network the method of graph grammar based object oriented design language is introduced
and is presented in the next section.
1 Introduction
8
1.3 Objectives/ Method Application
In this section we will present the method for development of multi disciplinary object
oriented model of chain body LTA HAP. Subsequently the model is then applied for generation of multitude of HAP designs to provide a foundation for design space analysis.
As mentioned before the method is based on graph grammar based object oriented design
language and is implemented with help of the computational framework "Design Compiler 43"[53], which was developed at the Institute for Statics and Dynamics of Aerospace
Structures (ISD; University Stuttgart). It is used as a design tool for developing a multi
disciplinary design model, which incorporates most of the domains involved within the
design of LTA HAP and facilitates performing a detailed investigation of the design space.
Figure 1.5: Data structure of a vocabulary with several domains integrated within it
By this way a large amount of variants can be generated for an effective analysis of the
design space. Furthermore by applying parametrical and topological variations allow constraining the design space in a feasible way.
As mentioned before, an engineering design model can be developed with help of a design compiler. The whole purpose of such a design model is to enable the design engineer
to define a formal graph-based but domain independent representation of a design space.
Within the rule-based design process the design graph of a LTA HAP is generated by executing a specific sequence of rules which represents a building plan of a design object.
This means that the first step in developing a graph grammar based object oriented design
model is to define the rules and the vocabulary of the grammar. In comparison to object
oriented programming vocabulary are the class/objects and the rules are the functions and
1.3 Objectives/ Method Application
9
methods of the language.
The vocabulary are abstract containers which represent (equations, parameters, variables,
physical, functional etc.) components of the HAP (figure 1.5). The rules are the design
patterns consisting of the building instructions (figure 1.6). In a production system, a
specific set of design rules is composed together which represents a building plan of LTA
HAP. Thus by executing a set of design rules a new design graph can be generated or an
existing design graph can be further manipulated. In a first translation step, a design graph
Figure 1.6: Components of a graph grammar based object oriented design language
is created by executing the production system. Such a design graph contains the complete
information of the disciplines of the LTA HAP.
It is a very high abstraction level of a design object. Therefore it is one common representation for all domains, such as the geometrical, the physical or the functional model
domain and enables to maintain the design model consistency between them through constraint processing techniques.
This method allows designs by considering both paradigms, top-down and bottom up, respectively. The top-down paradigm allows designing from an abstract level to a detailed
level. With every design step in the next deeper design level the apriori abstract design
model is concretized until the design model is implemented. The bottom-up paradigm
has a backward design direction as the top-down paradigm. It starts with an informal
specification of the lowest design level. With every design step in the next higher design
1 Introduction
10
level the basic components are put together to even complexer ones until the final design
is achieved. The method of graph grammars allows a mix of both paradigms [63]. e.g.
by starting with top-down and building an abstract specification of design object. At the
same time by performing bottom-up, a detailed model component library of each discipline is generated. Thus a design can be performed by integrating all known details of
known disciplines and the level of detail of those disciplines with unknown details remain
abstract. With every iteration step the level of detail increases until the final design is
achieved. An overview and detail introduction to graph grammar based design language
is given in [4], [5] and [44].
Main advantages of graph grammar based object oriented design language can be summarised as following:
• formalization of design knowledge
• computational model implementation and therefore design automation
• multidisciplinary design language can incorporate a huge amount of design domains
at the same time
• design graph as a domain independent representation of design object
• rule based design
• multidisciplinary consistency of models
• step by step building of the design model
• design automation at the stage of conceptual design
• time saving by generation of multitude of design objects
• reuse of standards and libraries, thus avoidance of mistake and error repetitions
• support and relief the design engineer from tedious routine tasks
• thus enhance the creativity and insight of the design engineer
1.4 Scope of the Thesis
11
1.4 Scope of the Thesis
The focus of this thesis is to develop a graph grammar based object oriented design language for purpose of design analysis of Lighter Than Air (LTA) Chain Body High Altitude
Platforms (HAP). The design language enables to span a complex design space of a large
amount of variants of chain body HAPs and then search it for plausible designs.
The design language allows incorporating almost all known domains of the design object.
In this work following subsystems are being modelled:
• Envelope/ structure/ gas cell
• Energy system
• Propulsion system
• Systems integration
• Payload
• Operational environment
• Aerostatics and aerodynamics
All other sub-systems are not the primary topic of this thesis.
The design evaluation is based on the energy balance equilibrium between the available
on board power and the required power mainly by the propulsion unit, because the energy
system is the main limiting factor for airship design. The couplings between the individual disciplines are modelled as known from the literature.
In regard to energy and propulsion system contemporary technology is used which is already developed or is in an advanced stage of laboratory testing. This concern to all sub
systems such as fuel cell, electrolyzer, photovoltaic arrays and battery system. As soon as
any new developments are available, the energy model within the design language can be
upgraded.
It is assumed that the used structure has a sufficient mechanical strength and is able to
carry all the loads without destruction. The model can be upgraded for delivering strength
verifications as known from the computational mechanics.
The environmental model includes known data of the ISO-Atmosphere. It can be extended
to a dynamic environmental model. The same concerns to the wind model at target altitude. We assume to meet during the operation dry and laminar weather and turbulences
are not taken in consideration.
Also ascent and descent manoeuvres can be integrated for a simulation model. Within
this work flights in constant altitudes with stationary horizontal flight conditions are taken
1 Introduction
12
into consideration. It is assumed that the trimming of the air vehicle allows such flight
conditions and therefore only the aerodynamic resistance is considered in the model. The
model can be extended to consider further necessary aerodynamic forces.
1.5 Outline of the Thesis
Considering the complexity of the design task the outline of this work is as following:
• Chapter 2 gives a review of related work in both High Altitude Platforms and design
languages.
• Chapter 3 describes the decomposition and modelling process of the disciplines.
For developing such a model the individual disciplines necessary for design of
LTA-HAP has to be identified. This is done by combing through the literature
and collecting data of existing variants of LTA HAP and comparing them with each
other. By doing so there commonalities and differences are identified and can be
used for abstracting and formalising the individual disciplines and their couplings.
At next the decomposition process begins by extracting the commonalities within
them. The purpose is to define basic building blocks for a HAP-system which are
called vocabulary of the graph grammar. The couplings between them are defined
as basic building instructions which are called the rules of graph grammar.
• Chapter 4 describes how the developed model is used to generate sub models of
each discipline. Parametrical and topological modifications are applied to the sub
models and huge amount of variants and alternatives are generated within each
discipline.
• In chapter 5 the developed model is applied for multi disciplinary object oriented
design analysis of chain body LTA HAP. Dependent from respectively utilized energy system three different type of missions are investigated by means of five different kind of mission scenarios. Although a wide range of parametrical and topological variation to the base model of a LTA HAP is applied. The design analysis
is done for basically two different altitudes: 2,500m and 20,000m. Main parameters considered for each altitude and mission are the carry able payload, velocity of
wind, mission duration and the size of LTA HAP as well. This extensive analysis
is done to search the design space for reasonable configurations of High Altitude
Platform. However design windows within the design space were identified, which
contain feasible designs in regard to the mission scenarios.
• Chapter 6 concludes the work by summarizing and discussing the results and giving
an outlook.
2 Background
13
2 Background
2.1 High Altitude Platform
High Altitude Platforms (HAP) are quasi-stationary aerial platforms operating in geostationary positions in the lower stratosphere of about 20 km. Instead as a competitor
surrogate technology it is conceived rather as an alternative research field in parallel to
the well established technology of satellite communication. Such a solution preserves
many advantages of both terrestrial and satellite systems and also provides special advantages of its own [36].
Their distinct advantages compared with satellite systems are:
• reduced cost,
• relatively close range,
• flexibility in terms of rapid deployment,
• ease of re-configuration,
• possibility for frequent take-offs and landings for maintenance, reprogramming and
upgrading and
• very favourable path-less characteristics.
High Altitude is usually defined as been greater then 18km (∼60000ft), which is much
higher than most conventional aircraft can fly. This is an altitude that has been proposed
to facilitate solar-powered station-keeping, which requires a fairly benign environment.
The wind speed and turbulences are relatively minimal within this spot of the surface. It
is an area of the atmosphere that is above the jet stream and below the upper layers of
the stratosphere (between 20 and 30km, because the actual boundary of the troposphere
varies with season and latitude). The jet stream can exist between 7.6 to 12 km with winds
that can exceed 130 knots.
The main issue in high altitude flight is generating lift within this low atmospheric density
environment. The majority of vehicles that can operate at high altitudes do so by flying
2 Background
14
very fast. High-speed vehicles compensate for the low-density air in this manner [21],
[96]. Thus a mission within the lower stratosphere would allow
• multi cast and broadband telecommunication,
• remote sensing,
• environmental monitoring,
• disaster recovery,
• meteorological measurements,
• real time monitoring of seismic regions, agriculture support and many more.
Application Spectrum
Research: The field of research provides a wide spread opportunity for application of
HAPs. One of them is the field of environmental protection. Great efforts are undertaken
for effective measurement of harmful emissions in order to overview the actual state of
environment. These can be helpful to undertake right steps in favour of environmental
protection. Further fields of research are for instance weather research or oceanography.
Surveillance: There are many possible applications of HAPs for purpose of surveillance.
In area of energy supply it could be for instance a monitoring of oil or gas pipe lines. A
HAP could fly along the pipe line trajectory which could be of many thousands of kilometers. Camera systems with night vision capabilities can be used for a non stop monitoring
of pipe lines for early diagnoses and maintenance. An other application is traffic supervision in regional conurbations. Thus an effective traffic jam prediction can be made to
assist GPS-navigation systems. Furthermore HAPs can be used for surveillance of borders, disaster areas, forest fires as well as animal protection areas.
Telecommunication: For long range communication glass fiber cables are used for data
transfer of telephone, broadcasting and internet, respectively. An alternative is a satellite based communication which is able to cover an area of up to 600km radius. They
are positioned in a geosynchronous orbit of about 36,000km. Between there long range
communication signal and the consumer a relay station is installed to transfer this signal
into a short range communication signal for instance for mobile phones. As an alternative
to these kind of fixed relay stations High Altitude Platforms can be used as mobile relay
stations for providing a constant signal for the whole covering area which can be of 60km
to 400km radius. Considering the increasing number of mobile phone consumers during
the last ten years (from 500 Mio. to about 5 billions) a HAP can be used to build a tailored
communication solution for each region to overcome their needs of growing demand of
15
mobile telecommunication. Their feasibility of short range communication is therefore
well suited to cover wider ranges of big cities with less contermination of health harmful
electromagnetic smog.
Heavier Than Air High Altitude Platform (HTA HAP)
Research in the area of High Altitude Flight began within the area of manned military
Heavier Than Air (HTA) flight vehicles. Most of the known high altitude aircrafts are
the military’s U2 and SR71. The U2 is capable of flight to altitudes up to 21 km at a
cruising speed of 692 km/ hr and an endurance of approximately 7 hours [21]. The SR71
is capable of flight to altitudes of 27 km with a cruising speed of 3,380 km/hr (Mach 3.2)
and a flight endurance of approximately 1.5 hours [22]. The Strator 2C G850 from Grob
reached in 1995 an altitude of about 18.5km although a target of 24km were claimed. Difficulties were caused by the cooling problem of the turbo for the piston engine. Therefore
the successor is equiped with a turbofan engine.
Name
Company
U2
SR-71
Condor UAV
Strato 2C
Globel Hawk UAV
Halo Protheus UAV
Boeing (1988)
Boeing (1988)
Boeing (1988)
Grob (1995)
Boeing (1988)
Angle Tech. (1988)
Pathfinder
Pathfinder Plus [48]
Centurion
Helios
Global Observer
Solitair
Zephyr
Helinet
Aerovironment (1997)
DLR
QuinetiQ (2010)
ESA (1999) [36], [128]
Propulsion
Altitude
conventional HTA HAP
Turbo
21 km
Turbo
27 km
Prop.
20.4 km
Turbo
18.5 km
Turbofan
20.4 km
Turbo
21 km
ultralight UAV HTA HAP
electro
electro
electro
electro
electro
electro
electro
electro
21.3 km
24.5 km
30.5 km
19.8 km
20 km
20 km
18 km
20-25 km
Duration
Payload
Remarks
7h
1.5 h
58 h
48 h
35h
8h
1179kg
manned
manned
UAV
manned
UAV
manned
14 h
15 h
15 h
300 h
7 days
months
14 days 21 min
months
11 kg
31 kg
45kg
225 kg
900 kg
1000 kg
862 kg
5 kg
some kg
concept
flight
in development
in development
in development
in development
flight
concept
Table 2.1: Overview to the development of HTA HAP
Due to the fact that these aircrafts are capable of high altitude flight the endurance of these
vehicles is insufficiently limited. Thus recent efforts were done in development of Unmanned Air Vehicles (UAV) to increase flight endurance of such aircrafts. Two examples
are the Condor and Global Hawk. There main task was based on surveillance and to loiter
over a particular area. The Condor (1980’s) was propeller driven and capable of flights up
to 21 km. The global hawk is the latest in high altitude UAV development with turbofan
engine. It is capable of flight at 20 km with a cruise speed of 643 km/hr and endurance of
35 hours. To extend the duration beyond fuel driven aircrafts, a renewable power system
16
2 Background
has to be considered.
Within the field of regenerative energy systems Aerovironment developed the solar powered aircraft with a regenerative fuel cell system as a means for energy storage. It was
claimed that the aircraft would be capable of flight at altitudes up to 21 km for durations
on the order of months. But during test flights in 2003 the prototype was destroyed. However, its main drawback is in its limited payload capacity, estimated to be on the order
of 250 kg, and the requirement to have the payload somewhat distributed along the wing
plan form. This payload capacity should be sufficient for certain types of science and
observational missions. However, if a centralized, more massive payload were required,
such as a radar system, this type of air vehicle would not be applicable.
Lighter Than Air High Altitude Platform (LTA HAP)
Although most of the HTA vehicles discussed above are capable of high altitude flight, the
problem of carrying large payloads at high altitudes and remain aloft for long endurance
persists, however. To achieve this, a different type of air vehicle needs to be considered.
An airship a LTA High Altitude Platform (LTA HAP) has the ability to meet these needs.
Airship, unlike aircraft, generates lift through the buoyancy effect instead of through aerodynamics. This means that the airship does not need to stay in motion to remain aloft.
An airship has also the ability to carry heavy payloads with minimal volume constraints.
These characteristics, compared to that of a conventional aircraft are what make airship a
unique candidate for a long endurance high altitude flight vehicle.
Since an airship does not need to be in motion to generate lift, it is not nearly as power
intensive as an aircraft. In addition, the limitations of an airship, such as slow speed and
weather sensitivity, are no longer existed at altitudes well above the active weather. On
the other hand, LTA vehicles introduce their own set of unique technological and operational difficulties. Worse, many of these difficulties fall into the category of "unknown
unknowns"[136].
Free Floating Balloons: Weather Balloons are one kind of lighter than air vehicles which
routinely operate at high altitudes. There construction is very easy and the launch is very
inexpensive and uncomplicated but they lack of station-keeping capabilities. These balloons can carry heavy payloads to altitudes upwards of 36 km. They are mainly used for
scientific research and weather data collection and typically operate for short durations.
Free-floater systems have already demonstrated commercial viability as communications
platforms. An example of a high altitude balloon is the Air Force’s High Altitude Balloon
Experiment (HABE)
To overcome the problem of control, a balloon can be tethered (aerostat) and thereby held
in a fixed location. Aerostats are common devices and have been used for both military
and civilian applications. An example of an aerostat is Lockheed Martin’s Tethered Aero-
17
stat Radar System [7]. It is capable of flights up to 5 km for durations of up to a week.
Like balloons, aerostats can be used for science data gathering, weather data, communications and surveillance.
Manoeuvring Airships: The next class of vehicles capable of achieving high altitude
flight is the airship. Although they generate lift in the same manner, an airship has a
means of propulsion and a means of control. Propulsion can relay on fossil fuel, nuclear
or solar energy. Control can be attained through both aerodynamic and aerostatic means.
Operating at high altitudes for extended durations requires a renewable based power system. The leading choice for this type of system is a photovoltaic array coupled to an
electromechanical energy storage system such as a fuel cell or battery system [139].
The Lockheed Martin High Altitude Airship (HAA) program is an elliptical shaped airship with three conventional tail fins for stability and four side mounted engine pods for
propulsion and control. This type of layout has good drag characteristics and has heritage
with low altitude airship designs.
There are some variations on the elliptical airship layout that have also been proposed.
Name
Company
HABE [72]
Aerostat [33]
balloon and tethered LTA HAP
USAF
30 km
Lockheed Martin
5 km
Propulsion
Altitude
days
weeks
Sky Station
High Altitude Airship
Sky Net
Strat Sat
Korean HAA [71]
steer able LTA HAP
Sky Station
electro
Lockheed Martin
electro
Wireless Innovation Group
electro
Advanced Tech. Group
electro
Korea
electro
months
months
months
months
months
20 km
20 km
20 km
20 km
20 km
Duration
Remarks
in development
in development
in development
in development
in development
Table 2.2: Overview to the development of LTA HAP
These include the designs from the European Space Agency (ESA) performed through
their contractor Lindstrand Balloons Ltd.
The ESA design is a half elliptical body with a modified tail section. The airship will
have a single 8-meter diameter propeller. Fuel cells will store the sun’s energy during
the day and produce 90 kW at night to drive the propeller and provide 15 kW to power a
communications base station payload. The fuel cells have a mass of 1.1 tons as compared
to 16 tons for batteries of equivalent energy storage. At the present level of fuel cell efficiency, 8 percent, the Lindstrand airship will have enough daylight sunshine in the winter
to provide yearlong coverage only between 45◦ latitude north and south.
JP Aerospace is also designing shapes that can rise to 30 to 42 km. The Dark Sky Station
would drift at an altitude above 30 km buoyed by helium-filled cells stretching out as far
as two miles.
Other more non-conventional configurations have also been proposed for a high altitude
airship. These are mostly symmetrical designs either spherical or saucer shaped. An
18
2 Background
example of this is the Techsphere Systems International’s spherical high altitude airship
concept [15].
An other alternative is a multi segmented high altitude airship concept (Airworm) for operations in 20 km altitude [65]. The hull of the airship is divided into smaller segments
connected with each other. The loads are distributed equally to the segments dependent
from the individual lift of the segments. This leads to reduce the higher bending moments,
reduction of higher stresses and with that the use of significant lighter envelop materials.
2.2 Design Languages and Grammars
The formalism of grammars is both quite general and powerful technique for a very compact and formal representation of possible infinite set of alternatives. Furthermore, the
transformational paradigm inherent in grammars allows for a wider variability than is
possible with other types of procedural formalisms. In this chapter we give an overview
of various grammatical formalism and their characteristics upon which to discuss the
complexity of engineering design.
The Chomsky-Hierarchy: The properties of various grammatical formalisms were first
explored by Noam Chomsky [20] in the 1950s. When he first formalized generative grammars in 1956, he classified them into types now known as the Chomsky hierarchy. Besides
the one non restricted basic grammar of type-0 the other three types have increasingly
strict production rules and can express fewer formal languages within the computer science [87].
String grammars: A string grammar prescribes transformations on and therefore relation among symbols in a string. String grammars are used to specify the syntax of natural
languages and of most programming languages. Other types of languages, such as shape
grammars, structure grammars and graph grammars are extensions to the string grammar
formalism [86]. As presented above, every string grammar G consists formally of four
elements, also called 4-tupl:
G = {Vnt , Vt , PR, S}
where Vnt is a set of non terminal symbols of the vocabulary and Vt is a set of terminal
symbols of the vocabulary. PR is a set of production rules with S as a set of starting
symbols, which is a special set of non terminal symbols. The representational power of
a string grammar depends strongly on the form of the allowable production rules in the
grammar. In [87] bridge structures were generated with a context sensitive, context free
and a context sensitive grammar with its string graph derivation tree. All three grammars
result in a same bridge structure.
19
L-Systems: The L-systems were introduced and developed in 1968 by the Hungarian
theoretical biologist and botanist Astrid Lindenmayer (1925 - 1989) [98]. An L-system is
a formal grammar used to model the growth processes of plant development, but also to
model the morphology of variety of organisms, as well as to generate self-similar fractals
such as iterated function systems. The rules of the L-system grammar are applied iteratively starting from the starting symbol. The distinguishing feature between the L-system
grammar and the formal Chomsky grammar are that by the L-system grammar as many
rules as possible are applied per iteration whereby a formal grammar allows only one rule
per iteration. Depending on the production rules, an L-system can be context free, context sensitive, deterministic or even stochastic. Well-known L-systems are: space-filling
curves (Hilbert curve, Peano’s curves), median space filling curves (Levy C curves, Harter hirhway dragon curve), tillings, trees, plants and the like.
Shape grammars: Geometric shapes can be generated by shape grammars. The formalism of shape grammars in architecture design was first defined by Georg Stiny and James
Gips in 1971 [121], [124]. A shape grammar consists of shape rules which are written in
terms of shapes rather than in terms of strings or graphs representation. So that the rules
combine shape elements with each other and give rise to other shapes which were not explicitly created. The formalism of shape grammars consist of a set of Shapes S and a set
of labels L. By their meaningful combination a set of labeled shape rules (S,L)+ can be
generated. Therefore a rule of shape grammar transforms a labeled shape α into a labeled
shape β, where as α is a labeled shape in (S,L)+ [99].
The widespread use of grammars in a design context has been the use of shape grammars
in architecture and pattern design [123], [122], [2]. The focus was on describing and
recreating architectural styles including Chinese lattice design [120], Palladio-style villas
[125] and Mughul Gardens [126].
Application of shape grammars in engineering design was initiated by the work of Agarawal
and Cagan 1998 as they presented a shape grammar for the design of coffeemakers [3].
The grammar consist of 100 parametric shape rules which allow the designer to generate
an infinite number of coffee makers including a majority of those on the market today [1].
Shea et al. [115] uses a simulated annealing algorithm with a shape grammar to design optimal truss and frame structure configurations as well as three dimensional domes [116].
Several other examples are found in the literature concerning application of shape grammars in engineering design: Brown et. al. [13] introduce the lathe grammar; McCormak
and Cagan [84] the inner hood panels shape grammar; Pugliese and Cagan the Harley
motorcycle grammar [99]. There are many more engineering applications of shape grammars for design and a comprehensive discussion on the many aspects of grammars can be
found in [7].
20
2 Background
Graph grammars: The formalism of graph grammars is an extension to string grammars
which allows representation of non serial component arrangements and functional relationship. Whereby the string grammar formalism requires a string like serial arrangement
of the components, since not all devices of engineering design are configured of serial
wise arranged components. Therefore graph grammars are well suited to express a wide
range of mechanical configurations with their complex functional and structural relations.
The nodes of a graph are used as vocabulary for a formal representation of engineering
components of design artefacts and the edges are then able to represent relationships between nodes.
Several extensions and augmentations were made according rules and vocabulary definition of graph grammars in order to improve automation in computational design synthesis
and machine design [110]. Schmidt et. al. introduces a graph grammar based algorithm
named Assembler for automated generation of geometrically valid models of carts made
of Meccano Erector Set components [107], [111]. Another example is the graph grammar
approach for structure synthesis of mechanism [108] for design of Epicyclic Gear Trains
[74], [73]. Whereby Sridharan and Campbell [119] combined the two methodologies
namely graph grammars and function structures to provide a systematic language for creating function structures. According to design management Baldwin and Chung [8] used
graph grammars for designing and selecting suitable processes for planing and executing
design activities. Since product configuration has been well recognized for the implementation of mass customization Du et. al. use the graph grammar approach for platform
based product configuration [30] and product family modeling [29] from both customer
and technical viewpoint. Westfechtel [131] applies the approach of graph grammars for
dynamic development processes for supporting the coordination of engineers through integrated management of products, activities and resources. In [89] the method of graph
grammar is applied for assistance in conceptual building design. In order to overcome
the limitation of consistency between function and form, Finger and Rinderle [31] used
the formalism of graph grammars [38] for form and function configuration of mechanical
systems.
Concerning design of structural products such as vehicle truss structures, Saitou et al.
[88], [135] generated the so-called topology graphs for decomposition-based assembly
synthesis. Within this context design for manufacturing and design for assembly were investigated in order to obtain optimized structural configurations [18]. The product topology graph [16] is decomposed into subgraphs by using genetic algorithm [15], which
results in a decomposition of the actual product with optimal joint attributes [17]. By
reducing the number of structural joints [81] with respect to structural strength, assemblability and modularity criteria, the issue of cost optimization is introduced in connection
with structural optimization [82].
21
In the context of the development of the design compiler 43 at ISD (Institute for Statics and Dynamics of Aerospace Structures at Stuttgart University) Alber and Rudolph
[5] introduced the approach of a generic graph grammar where a so-called design graph
is generated as an intermediate domain-independent representation. Subsequently, this
graph representation is translated into the various object domains and multiple domaindependent models of the design object can be generated [4]. On the basis of this approach
a design language was developed to generate truss structures such as transmission towers
[6]. By using same framework several graph grammars were developed for conceptual
design of space stations [55], aircraft surface[61], multi disciplinary airship design [10],
automated design process of satellites [105] and space-frames of automobile structures
[44], [43]. Haq and Kröplin developed a graph grammar based design language for design of chainbody LTA HAP (High Altitude Platform) [42]. Kormeier investigated the
application of design languages for optimization of fiber composite structures [62].
23
3 Decomposition and Model
Development
This chapter presents modelling of individual disciplines of the LTA HAP based on method
of graph grammar. As usual within object oriented modelling approaches at first the design object has to be decomposed into its most important components which represent a
general set of component library and their relations (figure 3.1). Thus our object of desire, the multi chain LTA HAP is decomposed for modelling of the individual disciplines
within the method of graph grammar.
Figure 3.1: Decomposition for modelling of the individual disciplines (vocabulary) and
their relations (grammar rules) within the method of graph grammar
24
Accordingly, figure 3.1 presents the main steps of this modelling approach and the organization of this chapter:
1. Decomposition of the LTA HAP into its important building blocks.
2. Modelling of the individual disciplines, so called vocabulary objects.
3. Modelling of the interactions, interfaces and couplings between the sub systems, so
called aggregation rules.
3.1 Decomposition
Decomposition is performed in almost every phase of the engineering design process. It
is one of the main concepts in engineering design and contributes to the simplification of
the system or problem considered so that the resultant outcome is easier to handle [66].
We will decompose the overall LTA HAP to provide a basis for identifying basic building
blocks for vocabulary and aggregation rules in order to develop an object oriented graph
grammar based design language [44].
Figure 3.2: Decomposition of continuum to discontinuum and aggregation of discontinuum to novel continuum
3.1 Decomposition
25
The aim is to obtain a minimum number of vocabulary and rules which enable the generation of a wide range of LTA HAP variants. Since a design from a known set of designs
is considered as continuously the design of LTA HAP is compared to an abstract representational form of a continuum (figure 3.2). Whereby a set of known continuum is
decomposed to a minimum number of discontinuum [60], [97], which on their turn allow
by aggregation to generate not only the set of already known continuum but also a set
of novel continuum [132]. In case that the discontinuum could not satisfy aggregation
of desired variants, the decomposition process is repeated in iteration loops until a set
of discontinuum is obtained which facilitate generation of all desired variants. Applying
this thought experiment to decomposition of LTA HAP means that a known quantity of
different LTA HAP designs incorporating all their disciplines is decomposed in order to
obtain a minimum number of vocabulary and rules of the graph grammar. This initial
grammar should be able to generate not only already known LTA HAP designs but also
novel unknown designs considering diverse design aspects of parametric, topology, function etc. The grammar is then proved whether it is able to satisfy generation of desired
variety of designs. In case of inaccuracy the generateable and not generateable designs
are compared with each other by adapting the decomposition concept and incorporating
the difference into the set of vocabulary and rules, so that the improved grammar can
generate a wide range of all desired novel designs [63].
However several systematic concepts of decomposition are described in the literature,
which can be adopted for decomposition within each discipline of LTA HAP. Within conceptual design a functional basis is introduced in [127]. Whereby the flows of energy,
material and signal (information) need to be consistent at each stage of the functional decomposition [94]. In order to reduce the dimensionality and complexity of complex and
large design problems a decomposition method based on incidence matrix is introduced
in [66]. With an incidence matrix coupling information of the functional dependency between the components and attributes of a design artefact can be expressed [19].
Product modularity refers to the decomposition of the architecture of a product family into
distinct building blocks, also called modules [66]. An interaction and suitability matrices
for the representation and analysis of product modularity is introduced. In [50] a method
for identifying common modules for product platform design is presented. There exist
three different type of modularity: component-swapping modularity, component-sharing
modularity and the bus modularity.
Structural decomposition is captured in a hierarchical model of the product or system
[88], [135], [81]. The system is first decomposed into subsystems and those, on their
turn, are decomposed in components [66]. One major aspect in engineering design is the
appropriate decomposition of the entire product in components concerning production
costs, manufacturability, and assembly by using design rules. The manufacturing rules
may include minimization of total number of parts, assembly directions, material, and
26
part handling. Furthermore maximization of compliance is as necessary as the usage of
standard pats. The design parts should be multi functional and multi useable [18], and has
to fulfill the criteria of modular design [16]. Thus by this way of applying manufacturing
rules for modular product development cost functions [15] can be incorporated in order
to obtain both structural as well as cost optimized structures [17], [82].
For purpose of model development decomposition is applied in order to obtain vocabulary
and rules of the object oriented graph grammar. Therefore the decomposition process for
vocabulary definition and the aggregation process for rules definition are not performed
one after another, but they proceed hand in hand and are complementing each other in
iterative steps. The right level of granularity in the decomposition gives the direction of
quality of design model [44].
On one hand the aim is to decompose the complete system in general building blocks
which can be commonly used for the whole system. On other hand the aim is to define
a minimum number of general rules or building instructions, which facilitates a syntactically correct arrangement of the vocabulary to their neighbours within a graph.
The higher the level of granularity of decomposition of vocabulary and corresponding
rules the larger is the number of variants generated by the aggregation of design process.
Since graph grammars have the ability to formalize all involved disciplines and represent
them at same level of design. Therefore geometrical, physical, mechanical, mathematical, structural, electrical and all necessary domains of each discipline can be decomposed
simultaneously to be represented within a graph which is a domain independent representational form of our LTA HAP.
The vocabulary and rule library achieved by decomposition should be as fine as possible
but the number of vocabulary and rules should be as minimum as possible. Because they
should be very general and reuseable to build a large variety of LTA HAP designs.
3.2 Model Development of Individual Disciplines
27
This chapter presents the modelling of the individual disciplines and their sub systems
related to the method of graph grammar. The objective is to contribute to the formation
and development of vocabulary which are the basic building blocks of the grammatical
approach. Thereby the modelling should be as precise as possible so that any significant
influences must not be disregarded for the modelling. On the other hand this modelling
approach provides the ability dependent from the accuracy of the results to refine the level
of detail of modelling in recursive steps.
The involved disciplines within the modelling process are:
• envelope structure,
• aerostatics and aerodynamics,
• operational environment,
• power and propulsion system and
• system integration and power network.
3.2.1 Envelope Structure
Mainly there exist three different types of conventional airship envelope structures [80]:
• rigid airship structure,
• semi-rigid airship structure and
• non-rigid airship structure (blimp).
Non-rigid airships are airships which, like balloons, keep their exterior shape through
the pressure of the lifting gas inside the envelope: e.g. Santos Dumont, Goodyear-Blimp
and GEFA-Flug Hot Air- Airships [33]. There is no interior skeleton or supporting structure. The gondola, tail unit and propulsion are mounted on the envelope structure. They
are also equipped with ballonets to keep their envelope pressure constant.
The semi rigid airships include a rigid keel structure beneath the flexible airship envelope. e.g. Zodiac Kielluftschiff E9 and Cargolifter [33]. The rigid structure helps
to ensure even distribution of force to the envelope and as a reinforcement of the entire
system. Ballonets are used to ensure constant envelope pressure.
28
With rigid type airship the exterior form is determined by its rigid skeletal structure. e.g.
Zeppelin and Schütte-Lanz-Airships [136]. Within the skeletal structure of large rings
fastened to longitudinal girders there are gas bags filled with lifting gas. The skeleton
structure is covered with a textile material that gives the airship a smooth surface and
protects the gas bags. These are suspended from the structure in a way that compensates
for any volume fluctuations of the lifting gas with increasing or decreasing altitude i.e.
for any expansion or contraction of the gas bags. Thus, rigid airships do not need any
additional ballonets.
The envelope of Chainbody LTA-HAP is derivation of flexible blimp type airships, however with the difference that the structure is divided into many segments [65] and consists
of no ballonets. The multi segment concept is chosen in order to reduce strength problems, such as buckling, differential loads, munk loads and static loads. By this way very
light LTA-HAP structures can be designed for the high altitude flight. As mentioned before there are no ballonets necessary for such a blimp type construction. The structure
of the Chainbody LTA-HAP mainly consists of envelope structure and separate gas cells.
A radiator is integrated to produce enough pressure, only 50 Pa overpressure, to keep the
segments in their shape inflate. During ascent and descent the lifting gas can expand or
contract within the gas cells and the blower can be regulated and keep the overpressure in
order to keep the exterior shape.
Figure 3.3: Decomposition of envelope structure in its essential elements for modelling
of vocabulary with geometrical CAD information
29
Envelope Decomposition: For purpose of model development we will concentrate here
on decomposition of envelope structure and gas cells (figure 3.3). Where by the gas cells
have the same shape and size as the envelope structure.
As afore mentioned the multi segmented concept is a derivation of blimp airships. Which
means that the envelope is the entire carrying structure of the LTA-HAP instead of a rigid
frame for giving shape to the airship. The gas cell contains the helium gas for buoyancy
lift generation.
Decomposing the envelope structure for purpose of modelling within design language
Figure 3.4: Discretization of the geometry for numerical calculation and CAD modelling
we can recognise that the one segment has an alignment connection to another one (figure
3.3). Thus segments are similar and have a parametrical derivation. Two segments are
connected with each other by an apron. Each segment can be decomposed into an elliptical and cylindrical segment part (figure 3.3). The elliptical part is modelled by rotating a
quarter ellipse to its symmetry axis, just as well the cylindrical part is modelled by rotation
a line of a quarter rectangle to its axis (figure 3.4). These two geometrical components
are the basic building blocks for modelling a HAP envelope within design language. By
joining these two components together and varying the parameters even every variant of
HAP envelope can be created. Each vocabulary has its communality consisting of parameters, variables and equation systems. Further more geometrical information are encoded
within vocabulary in form of equations and CAD-scripts. The CAD- model is generated
within three steps:
• At first a contour is created by setting a row of points (Step 1).
• These are over laid by a spline (Step 2) and
• at last rotated to their symmetry axis (Step 3).
Figure 3.5 represents possible parametrical variations of envelope geometry parts. The
vocabulary for elliptical segment part facilitates generating even every possible derive
30
able elliptical body. Further more the cylindrical segment parts, gas cells and aprons
are generated by applying the same modelling method. Material information embedded
within the vocabulary in combination with geometrical information enables calculating
mass, surface and volume of every geometrical part of the LTA HAP.
Figure 3.5: Library of geometrical objects; vocabulary of envelope structure with discretization and CAD model
Volume calculation: The volume calculation is done in order to determine the amount
of buoyancy gas for aerostatic calculation and at the same time the volume is required for
the calculation of aerodynamic drag. Whereas the surface area is used for calculation of
mass of envelope and gas cells.
As presented in figure 3.6 the geometry of the envelope can be described by partial ellipsoid and cylinder shapes, therefore the equation of an ellipsoid is presented as:
Vellipsoid =
4
· π · a · b2
3
(3.1)
With a as rotational axis and b as the vertical axis.
The volume of a cylinder is calculated by the equation:
Vcylinder = π ·
D2
·L
4
(3.2)
With D as the diameter and L as the length of the cylinder.
Simple geometrical shapes can be calculated by these equations, but geometry of the
31
Figure 3.6: Parametrical description of the envelope vocabulary for partial volume and
surface area calculation
rear segments of LTA HAP is much more complicated. They consist of partial parts of
ellipsoids, thus an equation which can describe any kind of ellipsoid has to be developed.
It is then integrated within the general vocabulary of ellipsoid geometry.
The equation of contour of an ellipse is given as following [85]:
f (x) :
(x − x0 )2 (y − y0 )2
+
=1
ax2
bzn2
with y0 = 0 follows:
f (x) =
(x − x0 )2
1−
a2x
b2zn
For the calculation of the volume of the ellipsoid we use the formula:
β
V =π
f 2 (x)dx
α
(3.3)
(3.4)
(3.5)
32
Here the surface under the curve of an elliptical curve segment is rotated around the x-axis
with the values α = 0◦ and β = 360◦. Inserting equation 3.4 in 3.5 and dissolving the
equation according to V symbolically occur:
V =
π
((a − b) · b2zn · (a2 − 3 · a2x + b2 + a · (a − 3 · spn) − 3 · b · spn + spn2 )) (3.6)
3 · a2x
Equation 3.6 can be embedded within the vocabulary for calculating the gas volume enclosed by the elliptical part of the segment.
Vtotal =
Vi
(3.7)
i=1→n
As cognizable in the equation there are several input variables and parameters. Some of
them are given parameters and others are variables dependent on other parameters and
variables.
Surface Area: Determing the surface areas of the segments is necessary for calculation
of total mass of the envelope structure and the gas cells.
Atotal =
Ai
(3.8)
i=1→n
The surface area of a blunt ellipsoid with a curve describing a part of an elliptical curve
segment.
Figure 3.7: A curve described by a function f (x) for rotation around the x-axis
y = f (x) ≥ 0
with
a≤x≤b
Rotating the curve around the x-axis we receive a surface with I(F ):
b
I(F ) = 2 π
f (x) 1 + f´2 (x)dx
a
(3.9)
(3.10)
33
The equation of an ellipsoid with variables and parameters described in figure 3.6 is:
(x − spn )2
f (x) =
(3.11)
1−
b2zn
a2x
The first derivation of equation 3.11:
f´(x) = −
a2x
b2zn (x − spn )
(x−spn )2
2
bzn 1 − a2
(3.12)
x
Simplification of the term occur:
T1 = f (x) 1 + f´2 (x)
=
b2zn 1 −
(x − spn
a2x
)2
1+
I(F ) = 2 π
b2zn (spn − x)2
a2x (a2x − (sp n − x)2 )
(3.13)
b
T1 dx
(3.14)
a
The surface area of a partial ellipsoid is calculated with the same equations as 3.10 and
we obtain the equation:
√
(3.15)
I(F ) = π 1 + m2 d2 (d2 m + 2 n)
With m = (2z − 1z)/(2x − 1x) and n = 1z and d2 = 2x − 1x.
3.2.2 Aerostatics and Aerodynamics
The interaction forces and moments between the LTA HAP body and the surrounding air
are called aerostatics and aerodynamics [106]. The former is due to the static air pressure
and is independent of the motion of the body while the latter is related to its motion [76].
LTA airships, unlike aircrafts, generates lift through the buoyancy effect (aerostatics) by
the carrying gas e.g. helium included within the envelope. In contrast HTA aircrafts
generates lift mainly by moving their body e.g. wings through the surrounding air (aerodynamics). This means that the airship does not need to stay in motion to remain aloft.
For purpose of analysis of flight behaviour and control design several dynamic models
of conventional airships have been developed within the last decades. In [109] nonlinear
equations of motions were developed for design and simulation of airship aerodynamics.
In [58] a dynamic simulation program was developed to analyse the flight characteristics
of Skyship-500. In [75] wind effects were incorporated into nonlinear equation of motions for stability analysis of airships. Further dynamics models were introduced within
34
several literature, however most of these models have not been validated by actual flight
test results.
Following interaction forces and moments caused by aerodynamics are introduced in the
literature [75]:
• added-mass forces and moments
• fluid viscous forces on the envelope
• forces acting on the finns and on the envelope due to the finns
• axial drag
• forces and moments due to control surface deflection
Since most of these forces and moments concern to dynamic motion analysis of conventional airship and their control system design, we will incorporate those aerostatic and
aerodynamic forces in this work which have to be considered for multi disciplinary design
and analysis of LTA HAP missions.
Decomposition for Model Development: For this purpose a network diagram is presented in figure 3.8.
It represents a design graph partially by focusing aerostatics and aerodynamic couplings
between the nodes and their neighbourhood relations. The blocks within the diagram
are models of individual disciplines. Main nodes in this diagram are [AST LIFT] for
aerostatic buoyancy calculation and [Aerodyn DRAG] for aerodynamic drag calculation.
The environmental node [ENV] dictates the wind speed v[ ms ] and further environmental
parameters such as density ρ and temperature T at operational altitude H[m]. These parameters are determined with the equations 3.16 and 3.17 and are fed to [AST LIFT]. In
this node the necessary gas amount is calculated for generating enough aerostatic buoyancy to carry the LTA HAP with all its loads and mass m in desired altitude.
Aerostatic Calculation: It works after the Archimedes’ principle which means that the
net upward buoyancy force is equal to the magnitude of weight of fluid displaced by the
volume V of the body:
(3.16)
FB = V (ρair − ρHe ) · g
the density of air (ρair )
ρair =
pair · Mair
R · Tair
(3.17)
pHe · MHe
R · THe
(3.18)
and the density of helium gas (ρHe ):
ρHe =
35
Figure 3.8: Aerostatics and aerodynamic partial dependancy graph of LTA HAP
are also calculated within [ENV].
Parameter pair is pressure of surrounding air and pHe is the pressure of helium gas in the
gas cell which can be described by the following equation:
pHe = pair + ∆p
(3.19)
∆p is the over pressure of the segment towards surrounding air in order to keep the segments in their shape inflate. Pressure p is dependent from operational altitude, thus it
is calculated by the environmental model as well as the temperature and other physical
properties.
The aim is to determine the volume V of helium gas for the generation of enough buoyancy lift to carry all loads mtotal such as system components, propulsion system, energy
system and entire structure, respectively:
V =
FG /g
mtotal
=
ρair − ρHe
ρair − ρHe
(3.20)
36
mtotal is the sum of all mass within the HAP:
mtotal =
(3.21)
mi
i
As we can recognize that the total mass contains also the mass of the envelope and gas
cell which depends from the volume of the helium gas. Thus assertion of gas volume and
total mass is an iterative process. The calculation is done for every segment separately.
The partial design graph in figure 3.8 clears the complexity of dependencies between
aerostatics and aerodynamics and to their neighbour domains of a LTA HAP. It shows
that aerostatics and aerodynamic calculations are done iteratively after one an other in
combination to the neighbour domains. The aerodynamic drag and the buoyancy lift are
coupled with each other over the envelope volume V.
Aerodynamic Drag Calculation: The bigger the aerodynamic drag the bigger is the mass
of propulsion system and therefore occur a bigger size and buoyancy of LTA HAP. On the
other hand the bigger the size and volume of LTA HAP the bigger is also the aerodynamic
drag (see figure 3.8).
The aerodynamic drag is determined by the following equation:
FD =
ρair 2
· v · Cw · V
2
2
3
(3.22)
ρ is the density of air depending on the operational altitude, v the velocity and V the
volume of the HAP, respectively. Cw is the drag coefficient which is assumed to be an
empirical value of Cw = 0.1. Whereby Cw is a function of Reynolds Number Re which
is in detail investigated in [52]. The calculation of aerodynamic drag is necessary for
sizing the propulsion and energy system, which are the main components in defining the
total mass. Thus the domain of aerostatic and aerodynamic are interactively coupled with
each other within a network of equations.
Figure 3.9 presents the conditions of helium within two different segment shapes at two
different altitudes: ground surface H = 0km and at operational altitude of H = 20km. For
generating buoyancy lift in these two altitude same mass of helium is necessary but the
volume is significantly different. At the ground surface it contains only 7% of the volume
in comparison to 20km, and yields a displacement of center of lift force by which a torque
(moment) τ occurs:
τ = FB · a
(3.23)
This phenomenon can cause special effects such as sloshing of helium gas and provoke
that the HAP have an angle of incline up to 80◦ and cause difficulties in handling at the
ground surface.
37
Figure 3.9: Condition of helium gas at different altitudes: ground surface H = 0km and
H = 20km
3.2.3 Operational Environment
Atmosphere
The atmosphere of earth is the environment in which the LTA HAP will operate. It has a
large influence on its performance and capabilities and has therefore to be considered as a
main domain during the design phase. Main physical properties of the earth are presented
in table 3.1 which influences the environment significantly. We will use the US-Standard
atmosphere for over modelling [92], since it is almost same as the standard atmosphere of
ISO-2533 [27].
The earths atmosphere can be divided into two main sections: the troposphere and the
stratosphere as presented in figure 3.10. The HAP will operate in altitudes approximately
20 km, thus the regions of the atmosphere from the surface to 20 km altitude are of mainly
interest for HAP design. The atmospheric data are for average northern latitudes of about
48 degree and reflect ideal annual average values calculated by the ideal gas equations. A
detailed investigation of the atmosphere is done within [95] and [59].
The troposphere ranges from the surface approximately up to 11 km, and the lower 1/3
portion of the stratosphere ∼11 km to about ∼20 km. The troposphere is the critical
38
Inclination of Equator to Orbit
Orbital Eccentricity
Day Period
Solar Radiation intensity
Gravitational Constant
Siderial Year
Surface Temperature Extremes
Diameter
23.45◦
0.01673
23h 57.8min
Mean: 1352W/m2
Perihelion: 1399W/m2
Aphelion: 1307W/m2
9.81m/s2
365.26 (Earth Days)
130 K to 300 K
12,756 km
Table 3.1: Earth’s physical properties
region in the atmosphere where all the active weather occurs. The majority of cloud
formations of the atmosphere occurs in the troposphere. There is a gradual change from
troposphere to the stratosphere. The temperature in the lower stratosphere is extremely
stable and cold at −56.5◦ C and is mostly free from significant weather patterns.
Figure 3.10 gives an overview of the main physical properties of the earth atmosphere. In
following we will present the physical equations describing the pressure p, temperature T
and density ρ for both regions of interest:
For the Troposphere:
T = T0 − L · H
(3.24)
With surface temperature T0 = 288.15K at H = 0km and the laps rate L = 0.0065K/m.
The pressure is described as following:
p = p0 ·
T
T0
L·g
air
(3.25)
With the special gas constant of air air = 287m2 /(s2 K) and gravitational constant
g = 9.81m/s2 .
39
Figure 3.10: Structure of earths atmosphere including troposphere and stratosphere
Stratosphere: The stratosphere has the following parameters:
Ts = const = 217K = 56.5◦ C and Hs = 11km
(3.26)
The pressure within the stratosphere is described as following:
g
p = ps · e Ts ·air
·(Hs −H)
(3.27)
Thus the density of air and helium gas is calculated by the following equations for both
regions:
p · Mf
(3.28)
ρ=
R·T
With the universal gas constant R = 8.3143J/(molK) and the mol mass of helium
MHe = 0.004kg/mol and the mol mass for air Mair = 0.0287kg/mol.
Winds
The wind on earth is one of the main factor which significantly influences the LTA HAP
design. It is highly variable and depends on the location, time of year and altitude.
40
There is no existing uniformed wind speed model, which can describe the wind speed
dependent from location, time of year and altitude. In [56] we found wind profiles for all
geographic longitudes and latitudes. Further detailed investigations of wind speed effects
on performances of high altitude flight were done in [95]. The outcome was that in more
than 95% of the cases it is possible to perform station keeping tasks.
The wind speed effects the design of propulsion components such as electrical motor and
the propeller blades. Also the mission duration is effected by the wind speed. For instance
power consumption of a station keeping mission depends on the wind speed. Higher wind
velocity cause huge aerodynamic drag hence higher power consumption accure by the
propulsion system and therefore reduce the mission duration.
Figure 3.11: Wind chart of weather soundings Stuttgart Schnarrenberg; All profiles of
whole month are presented within one chart
Figure 3.11 presents wind charts of weather soundings in Stuttgart (Schnarrenberg) [133].
Each curve in the diagram is a profile of wind speed recorded by balloon born sensor ascending twice a day from ground surface to 25km altitude. The chart presents curves of
30 days and therefor 60 wind profiles of the whole month are presented at the same time
in one chart. Two charts are for winter (march and october) and two for summer (july and
august). It is clear that wind speed is much higher in winter than in summer. As presented
in figure 3.11 in winter there is a maximum wind speed of about 100km/h and in summer
41
the wind maximum wind speed is about 45km/h.
Furthermore the higher wind speed in the altitude around 11000m restricts also the operational altitude of a LTA HAP. This is a activity region for jet streams. Thus the operational
altitude of LTA HAP lie in an altitude about 18km to 20km or below the jet streams of up
to 5km. For each region of interest e.g. 20 km altitude the peak wind speeds as presented
in figure 3.11 and are interesting for design of propulsion system, since the propulsion
system must be able to overcome the maximum wind speeds for purpose of station keeping tasks. The mean wind speed is interested for layout of energy system and estimation
of maximum mission duration, since higher mean wind speed would require higher power
consumption and thus reduce thereby the mission duration.
Solar Radiation
In addition to the winds, the solar radiation environment is the second significant environmental factor that drives the design and capabilities of the LTA HAP. The solar radiation
environment is constantly changing and influences the power generation of the solar arrays. Figure 3.12 presents the solar radiation of direct sun light over the wave lengths for
top of the atmosphere and at ground surface. The visible part of the sunlight is relevant
for the photo voltaic generators.
As sunlight passes through the atmosphere, some of it is absorbed, scattered, and reflected
by the following:
• air molecules
• water vapor
• clouds
• dust
• pollutants
• forest fires
• volcanoes
This is called diffuse solar radiation. The solar radiation that reaches the Earth’s surface
without being diffused is called direct beam solar radiation. The sum of the diffuse and
direct solar radiation is called global solar radiation. Since the LTA HAP will fly above
the active weather region, we can assume a clear sky without clouds for the modelling of
the global solar radiation.
As the solar elevation angle changes throughout the day the available output power from
42
Figure 3.12: Solar radiation spectrum at top of atmosphere and sea level [34]
the solar array will vary. This change in elevation angle is also dependent on the time of
year as well as the latitude. The solar intensity also changes throughout the year due to
slight variations in the distance of the earth from the sun. However, unlike the winds, the
incident solar radiation is very predictable and can be modelled with significant accuracy.
The actual solar intensity (solar flux) in W/m2 for a specific day of the year is determined
by the equation:
2
2
SI = SIm (rorbm
/rorb
)
(3.29)
SIm is the average of solar intensity at earth’s orbital location: 1352W/m2 [138]. Because
of the earth’s elliptical orbit the actual solar intensity varies throughout the year. The
dependency between the actual and mean orbital radius is given by the eccentricity =
0.017. The mean orbital radius of the earth is: rorbm = 1.496E8km. The actual earth
radius is then given by the following equation:
rorb =
(1 − 2 )
1 + Cosα
(3.30)
The day angle α is defined as 0◦ on january 4th (perihelion of Earth’s orbit) and increases
by 0.98◦ per day. Detailed investigations to solar radiation were done in [59] and [54].
However figure 3.13 shows charts of mean global solar radiation for summer and winter
months and for different altitudes for 48◦ northern latitudes. The duration of day time
for winter months (8h) is half as much as in summer (16h). Also the mean intensity of
maximum solar radiation is about three times less: 1200W/m2 in summer and 400W/m2
in winter. It will become soon apparent that variation of global solar radiation will have
43
Figure 3.13: Solar radiation in different altitudes and time of year for directional as well
as undirectional radiation [59]
a deep impact on design of LTA HAP. Since less solar radiation means that a larger solar
area is required to generate enough electrical energy and this subsequently leads to an
even greater size of LAT HAP than a HAP design for flight during summer months.
3.2.4 Power and Propulsion System
Figure 3.14 represents a schematic of power and propulsion system as implemented within
design of LTA HAP in this work.
Figure 3.14: A schematic of power and propulsion system of a LTA-HAP
A power and propulsion system consists of all the components that collect, generate,
44
and store energy and convert that energy into use able power and thrust. The propulsion
system is the main power consuming system on the LTA HAP and its design is intimately
dependent from several domains as presented in figure 3.14. The solar arrays collect solar
energy and store it in batteries or in a electrolyzer-fuelcell-system. The energy system
then provides system components and propulsion system with required electrical power.
In the following we will present in detail the components of power and propulsion system.
Electrical Motors
The main part of the propulsion system are the electrical motors which drives the propeller for thrust generation. The motors have to be designed for a reliable functionality
for a mean load over the mission duration. They should also be able to overcome maximum loads for a specific time caused by higher wind speeds. The aim of the layout is to
achieve an electrical motor design with a maximum propulsion efficiency as well as minimum engine mass. High propeller efficiencies are obtained for low rotational velocities
and big diameters [77]. High power densities are achieved by high rotating engines. For
adjusting different rotational speed ranges transmission gears are required. The mass of
gearboxes increases with higher reductions ratios and the efficiency decreases simultaneously [37]. Thus however an overall optimum engine gearbox configuration depends on
the application scenario and presents a well comprehensive and complex task. There exist
a number of different electrical engines interesting for high altitude flight. Since the costs
of engine plays a minor role, permanent magnet (PM) engines will be preferred because
of their high power densities and efficiencies [103].
The operational behaviour of a motor and regulator can be described by a contour map as
presented in figure 3.15 . Both should be aligned to each other. The propulsion efficiency
dependent from load case can also be determined by such contour maps by considering
the torque-revolution-speed curves. This is in turn dependent from type of propeller. Thus
the aim is to achieve an engine configuration with an almost constant high efficiency up
to a specific load case, e.g. 20%. This means that an electrical engine with corresponding
contour map as in figure 3.15 has a high efficiency ≥ 90% by about 6000RpM. At this
level it has a torque about 60 to 65Nm by a power of about 40kW.
Out of mission duration and environmental conditions such as wind speed necessary thrust
can be calculated by:
2
1
(3.31)
FT = · ρair · v 2 · Cw · V 3
2
The power consumption of propulsion system can then be initially estimated:
Ptotal =
FT · v
1
=
· ρair · v 3 · Cw · V
ηtotal
2 · ηtotal
2
3
(3.32)
45
Figure 3.15: Contour map of an electrical engine with regulator [37]
The mass of an electrical motor is calculated by:
mmotor =
Ptotal
(3.33)
msp−motor
msp−motor is the specific mass of the motor. Table 3.2 presents available light weight
Electrical motor type
Mass
Power
Ratio (msp−motor )
Canopy Tech. Cypress 32 MW 15 kV AC PM [23]
Toyota Brushless AC NdFeB PM motor [57]
Himax HC6332-250 Brushless DC motor [47]
Hi-Pa Drive HPD40 Brushless DC wheel hub motor[46]
ElectriFly GPMG4805 Brushless DC [104]
Lange EA-42 series engine [68]
Lange EA-42 series engine + electronics [68]
33,557 kg
36.3 kg
0.45 kg
25 kg
1.48 kg
29.12 kg
38.7 kg
32 kW
50 kW
1.7 kW
120 kW
8.4 kW
42 kW
42 kW
0.95 kW/kg
1.37 kW/kg
3.78 kW/kg
4.8 kW/kg
5.68 kW/kg
1.45 kW/kg
1.09 kW/kg
Table 3.2: List of electrical motors with power to mass ratio
electrical engines used for UAVs. Their power to mass ratio (msp−motor ) varies from each
other significantly. There are many factors which play a major roll for design of electrical
engines, such as durability and reliability. Compromises have to be made between the
aforementioned qualities and light weight. Since a durable and reliable motor is much
heavier than an engine with less durability. However a lot of development efforts are
46
done to increase the power to mass ratio of electrical engines. For modelling purposes
within this work we use a power to mass ratio of 1kW/kg whereas the mounting structure
of the motor is also considered within this value.
Propeller design
The design of propeller is one of the more critical elements of the propulsion system.
There primary function is to produce enough thrust to fulfill the mission requirements.
As mentioned before the majority of the power production and consumption within the
airship is for the production of thrust. From the solar array to energy storage system
to motors, the main function of all these systems and their components is to drive the
propeller. Thus the optimal design of propeller have a great impact on the overall LTA
HAP design and performance.
In order to achieve flight performances for different flight conditions it is necessary to
determine the propeller behaviour within it. The operational altitude of the LTA HAP lies
about 20 km and the main function of the propulsion system will be of station keeping.
Thus it can be designed for this operational environment. The main design parameters
of a propeller are [49]:
• operational altitude H [m]
• wind speed v [m/s]
• number of propeller blades [n]
• power of propeller [W]
• thrust of power [N]
• propeller diameter [m]
• propeller speed [1/min]
• lift coefficient of profile over the radius
• profiling
These parameters can be used as an input for several propeller design software tools for
layout of propeller of a LTA HAP of a specific mission. One of the tools is e.g. PROPPY
from M. Hepperle [45] which is based on the SAE technical paper of Larrabee [69] and
use the blade element theory with mean-value-factor-correction of Prandtl in combination
with a hydrofoil technique [49]. An other tool is XRotor [28] which functions similar as
47
Proppy and is suitable for calculation of free incident flow as well as shrouded flow.
The thrust performance of a propeller is
P =
FD · v
ηges
(3.34)
and the aerodynamic drag of a body in a flow is
ρ 2
· v · Cw · V
2
FD =
2
3
(3.35)
Considering equilibrium of forces between aerodynamic drag and thrust the maximum
performable speed is defined by
v=
3
2 · P · ηges
ρ · Cw · V
(3.36)
2
3
We can now proceed with the derivation of the diameter of the propeller. This can be
achieved by considering the equation of the ideal efficiency factor of a propeller [32]:
η =
=
2
1+ 1+
F
q·π·R2
2
1 + 1 + ρ·π·v2·η·P
3 ·R2
(3.37)
prop
With help of the ideal efficiency the propeller efficiency can be obtained by introducing
a real factor. By comparing a number of propellers in [102] a value between 85% to
90% is obtained. Normally these values are in fact limited to specific flight condition,
however a variable pitch propeller is considered, so that losses are at minimum. The so
ascertained propeller efficiencies are valid for flows without compressibility losses. Since
the velocities are below 0.8 Ma these can be ignored, while the rotor blade tip velocities
should be investigated separately [67].
Transforming equation 3.37 to Rprop (Radius of the propeller), we achieve [51]:
Rprop
=
2·π·η
ρ · π · v 3 · η42 − η4
(3.38)
For purpose of modelling it is not possible straight away to obtain the propeller mass out
of its characteristic parameters such as diameter, shaft power and number of blades. Since
the mass is furthermore dependent from the type of construction, degree of optimization as
well as respective application. Therefore it is reasonable to orientate to practically realized
48
propellers as mentioned within the literature [59]. Here we will not further investigate this
topic in detail and use empiric equations found in the literature [40], [41].
PShaf t
0.391
(3.39)
· 2 · RP rop ·
mprop = 0.12 · nBl
1000
Dependent from flight altitude and load case different aerodynamic blade pitch is required
in order to achieve maximum efficiencies. Therefore an active pitch control is considered
[51] for design of LTA HAP in high altitudes.
Solar Array
One main natural power source for LTA HAP is the sun light and the solar arrays are
the means of converting this incoming energy to electrical power. There design is very
critical, because a LTA-HAP needs to operate for extended periods of time and perform
tasks throughout the day and night time periods. This means that enough electrical energy
has to be produced and stored during the day light hours so that a continuous power supply
for operation of the LTA HAP during both, day and night hours is guaranteed.
The required visible area of solar arrays is calculated by:
ASA,vis =
Ptotal
SIm · ηcell
(3.40)
W
Ptotal is the total power consumption of the LTA HAP and SIm [ m
2 ] is the mean solar
intensity which varies for altitude, day time and season (see figure 3.13). ηcell is the
efficiency of the solar array. As mentioned Aarray,visible is the visible surface of the solar
arrays, whereby the surface of the segments where the solar arrays has to be integrated
is a curved surface which is factor π/2 greater than the visible surface. Therefore the
integration surface of the solar arrays is calculated with:
ASA =
π
· ASA,vis
2
(3.41)
kg
With the specific mass msp [ m
2 ] the total mass of the arrays can be determined with:
mSA = ASA · msp
(3.42)
There exist a lot of different types of solar arrays [100], [101]. In order to fulfill the design
target of minimizing the overall mass of the LTA HAP, we desire to select monocristalline
solar arrays with 1.5kg/m2, which have been already tested reliable in wide spread areas
of applications. An other possibility is amorphous silicon thin film array with an approximately specific mass of 0.2kg/m2 [21], [72]. Both have an efficiency of about 19%,
whereas also 21% are also mentioned in [35].
49
Thin film arrays have a number of characteristics that are desirable for an airship application. One main advantage is that they are very light weight. The active material is that
makes up the array material is only 1 to 2 microns thick and can be deposit on various
light weight substrate materials even directly on the envelope during the manufacturing
process. An other characteristic of thin film arrays is that they are also very flexible.
This is a major benefit due to the curved surface of an airship and leads to increasing the
fragility.
Figure 3.16: Comparison of single junction solar cells and triple junction solar cell with
solar spectrum graph presenting which part of the wavelength is used by each technology [134]
Modern research in the area of photovoltaic technologies has lead to development of high
efficiency solar arrays [39], [130], [11]. Several approaches were followed parallel, in particular with the multi-junction (tandem) solar cells efficiencies up to 41% were achieved
in laboratory conditions.
Figure 3.16 presents a comparison of a single junction and triple junction solar cell:
Single-junction solar cells are composed of a p-n-junction. The photons that hit the top
of the solar cell have the potential to give their energy hν to an electron, if their energy
50
is greater than the band gap. The band gap, also called energy gap, refers to the energy
difference (in eV) between top of the valence band and the bottom of the conduction band.
It is equivalent to the energy required to free an outer shell electron to become a mobile
charge carrier within the solid material.
Triple junction solar cell consist of three layers of single junction solar cells stacked
upon each other. The top cell has a greater band gap than the mid one and the bottom
cell has the smallest band gap [12]. Thus the layers going from top to down absorbs and
converts the photons that have energies greater than the band gap of that layer. All photons with less energy are transmitted to the next layer below for going through the same
process. As presented in figure 3.16 the multi-junction solar cell can use a wide range of
the solar spectrum, than the single-junction solar cell. By combining more junctions the
efficiency can be raised to a theoretical limit value of 86.83% [26].
Thermodynamical problems such as heating of solar arrays in 20km altitudes could lead
to decrease the solar cell efficiency [59], however this issue will be neglected within the
modelling process.
Figure 3.17 presents an integration problem of solar arrays on the upper surface of a
segment of LTA HAP. Because of their shifted centre of mass mSA at 2/3r the centre of
gravity lies above the centre of lift and therefore a roll moment can occur so that the HAP
segment could incline 180◦ up side down.
Figure 3.17: Integration of photo voltaic arrays on the upper surface of LTA HAP segment
by considering the issue of CG-position for reducing roll moment
In order to reduce roll moments some of other mass mSC are shifted downwards z3 to
move the total centre of gravity CG below the centre of lift.
51
Thus z3 is deduced by the following equations:
mSC = mtotal − mSA
2
mSA · · r − mSC · (r + z3 ) = −0.5 · mtotal · r
3
2
z3 · (mSA − mtotal ) = −mtotal · 0.5 · r − mSA · · r + mtotal · r − mSA · r
3
r · (0.5 · mtotal − 53 · mSA )
z3 =
(mSA − mtotal )
(3.43)
(3.44)
(3.45)
(3.46)
This value is then used within the balance equations, where z3 ≤ 0.1 · D. This means that
for each HAP design z3 can be up to a value of 10% of the HAP diameter.
Accumulator Battery
Rechargeable batteries are used within high altitude flight either as a primary provider of
electrical energy or compensator of fluctuations caused by propulsion and other system
components. Since the propulsion system is the main energy consumer on board, it is a
difficult task to find an appropriate battery system which meets the requirements well.
There exist a lot of rechargeable battery systems (table 3.3) in the market and a lot of
Figure 3.18: Energy and power density of rechargeable batteries [102]
efforts are under taken for their further development. The aim is to enhance the energy
density and the power density, respectively. However it is still valid, that battery systems
for high energy density can only cope with low power densities (figure 3.18).
Also the handling and recharge cycle become generally more inconvenient with increasing energy density. Since the optimum chemical reaction of a battery is dependent from
52
the temperature, a regulation of the operation temperature should be integrated.
The type of batteries (table 3.3) available in the market are well tested for usage at ground
surface, thus there is still need of testing these battery systems of operation in high altitudes with low densities and temperatures.
Type
Energy Density
h
[W
kg ]
Cell
Voltage
Charging
efficiency
Life
Time
self
discharging
Lead-Acid
30-40
2,0V
60-70 %
5-10%
NiCd
40-50
1,2V
70%
NiMH
60-80
1,2V
70%
NiMH LSD
60-80
1,2V
70%
LiIon
120-180
200 (in 2020)
30-40
3,6V
90%
-
85%
4-8
300-600 Z
15
800-1500 Z
7-10
350-500 Z
7-10
350-500 Z
10-15
500-800 Z
40-80
Redox-Flow [113]
10-15%
15-20%
1-2%
1-2%
≈ 0%
Table 3.3: Comparison of different accumulator battery types [140]
Until now the development of LiIo batteries is very promising concerning energy density. Until 2020 energy densities of higher than 200 Wkgh could be achieved (Fraunhofer
Institute). An alternative research field is the development of Redox-Flow-Battery system [118]. Energy densities comparable to Lead-Acid batteries were obtained [86]. In
the near future, a breakthrough in the development of Redox-Flow systems is anticipated.
Energy densities much more higher than LiIo batteries are awaited and it is assumed that
the development trend could lead to a fluid Redox-Flow-system with an energy density
h
.
near to that of gasoline with about 12.8 kW
kg
Fuel Cell System
One possibility of electrical power generation is the hydrogen/oxygen fuel cell system. In
stead of oxygen, air can be used as oxider for the fuel cell. An additional compressor will
be necessary for compressing the low dense air of the high altitudes to nominal pressures
for the fuel cell.
A fuel cell function such as an electrochemical device which produces electricity through
catalytic combination of oxygen and hydrogen:
OverallReaction : 2H2 + O2 → 2H2 O + Electricity + Heat
(3.47)
53
Figure 3.19: Cell voltage and current density characteristic curve of a regenerative fuel
cells in operation with O2 and air [93]
The overall electrochemical reaction occurs on a catalytic reactor where oxygen and hydrogen gas reacts to water and heat whereby electricity is produced at the cathode and
anode. The energy density of a fuel cell depends not only on the technology but also on
the application. High energy densities are obtained while the electrolyzer and fuel cell are
operated within the optimum design point. Also a regenerative fuel cell is conceivable,
since the stack fulfills both functionalities of fuelcell and electrolyzer at the same time.
Considering the Faraday law the voltage for the fuelcell reaction can be determined:
= 1.48V
thermonutral voltage Uth = −∆H
n·F
For instance PEM (Proton Exchange Membrane) fuel cells are proposed to be well suited
for high altitude flights [21]. These fuel cells are usually equipped with platinium catalyst
on both the anode and cathode. In this type of fuel cell electricity is produced by flowing
hydrogen over an anode and oxygen over an cathode. It can be operated by using oxygen
or air as an oxydizer, which leads to reducing the weight of the O2 -tank. Because of less
air density in high altitudes the efficiency decreases significantly, however. An air compressor leads also to a reduction of the overall efficiency.
Figure 3.19 shows a characteristic curve of a fuel cell. It is expected that new developments would lead to an increase of the current density and voltages [64]. It is well
recognizable that from 10% to 90% the voltage decreases linear with the the current density. This depends mainly on losses during transport, resistance loss and the polarization
of the electrode. With ever-growing temperature the cell voltage also increase.
Within the last decades, a lot of efforts are undertaken for industrial development of fuelcell technology. PEM fuel cell where developed by Daimler-Benz [24], Honda [90],
54
Toyota [112] and several other [114] companies for automotive needs. This subject area
was also investigated in detail within the solitair project of DLR [59]. All these investigations and developments were made for the automobile industry. For an HAP application
a lot of technological obstacles have to be overcome. These are within the area of thermodynamical problems concerning increasing of voltage and current densities. Also the
less density in operational altitude enforces to use oxygen instead of air and therefore
cause high mass through heavy oxygen tanks. In case of using air instead of oxygen a
compressor is required which, in turn, causes decreasing the over all efficiency. However
there exist a lot of problems concerning operation of fuel cell on a HAP which we are not
going to discuss here in detail.
The modelling of the fuel cell is one of the difficult tasks, because on one hand the flight
Component
Scaling Factor
fuel cell stack
sensors (pressure, temperature, flow
valve (check, flow control)
power converter and controller
lines, fittings, wiring, phase
regulator (hydrogen, oxygen)
heat exchanger, filter
total
1.00 kg/kw
0.09 kg/kw
0.12 kg/kw
1.08 kg/kw
0.63 kg/kw
0.14 kg/kw
0.56 kg/kw
3.62 kg/kw
Table 3.4: Fuel cell system components scaling factors [21]
performances of the LTA HAP are highly dependent from its design, and on the other
hand the characteristic curves of new developed fuel cells are not available. However the
modelling is performed by means of available data of fuel cells.
The weight of the peripheral is assumed to be linearly dependent on the maximum fuelcell power. For the maximum fuel cell power 120% of the necessary flight power are
permitted [59].
kg
kg
· PF C,max = 2 kW
· 1.2 · PF C,erf
mF C = 2 kW
Considering that current developments are not focusing light weight fuel cell construckg
tions, we choose a stack specific weight of 1 kW
(table 3.4).
The use of a fuel cell system for electrical power generation on a LTA HAP requires
a continuous flow of oxygen and hydrogen gas. To ensure a continuous functionality
of a fuel cell system over a long duration either enough hydrogen reserve stock has to
be provided from the ground station or a continuous production of hydrogen gas can be
ensured by the usage of an electrolyzer system.
55
Electrolyzer
An electrolyzer works according to the same principle as the fuel cell described previously
except for the functionality which is the reverse of that what a fuel cell does. The input
of a fuel cell is hydrogen and oxygen gas and the output is electricity and water, where
as the input of an electrolyzer is electricity and water and output is hydrogen [H2 ] and
oxygen [O2 ] gas. A lot of efforts are undertaken to develop electrolyzer system with high
efficiencies. Fraunhofer ISE developed an electrolyzer system with 20kW power for their
energy autarkic house [117].
Although the overall process or mechanism is complex, its sum or balance is simply
Figure 3.20: Voltage-current density characteristic curve of electrolyzer [129]
Component
Scaling Factor
electrolyzer
valves (flow control and check)
controller
sensor (flow, pressure)
water pump, filter
water tanks and heater
heat exchanger, lines, fittings
1.00 kg/kw
0.12 kg/kw
0.08 kg/kw
0.04 kg/kw
0.33 kg/kw
0.48 kg/kw
0.76 kg/kw
total
2.81 kg/kw
Table 3.5: Electrolyzer system components scaling factors [21]
equivalent to producing two molecules of hydrogen and one molecule of oxygen from
56
two molecules of water:
2H2 O → 2H2 + O2
(3.48)
The electrolyzer will be used to fill and maintain the hydrogen and oxygen storage tanks
with a sufficient amount of reactants to maintain continuous operation of the LTA-HAP
for long durations.
The PEM-electrolyzer seems to be very promising and assessable [59]. Therefore both
systems the fuel cell and electrolyzer are very similar systems with same basic principles.
Thus the values of mass for modelling of the peripheral are almost as same as those of
PEM fuelcell (table 3.5).
3.2.5 System Integration and Power Network
The aspect of system integration deals with the integration of all necessary electrical devices on a HAP which are necessary to fulfill a specific HAP-mission [91]. For this pur-
Figure 3.21: Comparison of mass distribution problem of a conventional airship and chain
body LTA HAP
pose the HAP is equipped with payload and some further electrical devices for purpose
of navigation, communication with ground station, control of station keeping, power control system, network for on board communication and power supply of integrated system
components as well as further necessary sensors and actuators required for the mission.
57
Figure 3.21 presents a comparison of mass distribution problem of a conventional airship
and a chain body LTA HAP used within this work. The mass on an conventional airship
are spot concentrated and cause therefore special structural and further problems which
we are not going to discuss in detail. In turn the chain body LTA HAP provides the opportunity to distribute the loads in order to overcome the problems of conventional airship.
The disadvantages we purchase by this strategy is that e.g. the payload of a satellite (e.g.
iridium) should be decomposed into uniform pieces so that they can be distributed over
the segments of a LTA-HAP. Thus decomposition of a satellite cause its own problems,
since the decomposed parts have to be linked with each other, e.g. with fiber optic cables.
There are different strategies of system integration of a High Altitude Platform for a specific mission. Each of them depends on the desired mission. The main task of systems
integration depends on the missions target to ensure internal communication of on board
electrical devices, the communication of HAP with the ground station, payload functionality, as well as providing power in feasible way through out the mission duration.
Different aspects of system integration are redundancy, synergetic, security, efficiency,
etc.
Considering the multi segment airship concept one way of system integration is that each
segment has its independent system integration and is able to function autarkic from other
segments. This means that each segment has its own propulsion, power supply, GPS-, and
control system, as well as communication system.
Depending on mission targets there may be also multiple redundancy of all system components. Equipping each segment with separate propulsion means on the one hand a high
flexibility of manoeuvring the LTA HAP, and on the other hand huge masses, increasing
size and costs of the LTA HAP. An other configuration is to have only a single propulsion
on the head segment of the HAP and to reduce also the amount of other system components to a minimum.
58
Figure 3.22: Building of system component model, cable model and battery model
An other aspect of system integration is the power supply and wiring problem. One can
decide to have only one central power supply circuit and an other solution is to separate
the power supply circuit of propulsion from other system components. Another solution
is to configurate the power supply for a fail safe strategy, where in case of failing accu
batteries the communication and positioning system is still supplied by enough power for
rescue operation of the LTA HAP.
Figure 3.22 describes the discretization model of the system component model, cable
model and the energy storage model of for instance a battery system. A system component
is similarly modeled as a cable, because both consume electrical power in a similar way.
Thus both have properties of a resistor and have resistance R[ohm] a voltage U[V ] and
currant I[A]. A battery is modeled with properties of an energy storage system and has a
constant voltage U[V ] and a variable current I[A]. The numerical analysis of the Power
network is done with the front end software system "LT-Spice"[79].
3.3 Model Development of Couplings and Patterns
59
In this chapter we will identify and develop couplings, the so called graph grammar rules,
between the individual disciplines and their sub-systems of the LTA chain body HAP by
analyzing following issues:
• Design Characteristic: Parametrical and Topological Design
• Multi Disciplinary Parameter Variation
• Balance Equations and Constraints
• Mission Scenarios
• Multi Objective Optimization of Power Network
Figure 3.23: Multi disciplinary network of domains involved within design of LTA HAP
60
Figure 3.23 presents a schematic of such patterns and couplings. Almost every domain
has a link to its neighbour domain and sub system and they are all building a network
of complex dependencies (a). By applying decomposition to the dependency network
graph grammar rules are achieved for computer aided design analysis (b). Executing
these rules within a set of program a design graph is generated including graph nodes and
their couplings (c). The nodes are interacting with each other by exchanging information.
In case of modifications in one node these information can propagate through all other
nodes of the network (design graph) and vice versa.
The design graph is a formal domain independent representation of the LTA HAP by
incorporating information of all domains involved simultaneously within the design of
LTA HAP. These information are of physics, geometry (CAD), propulsion, energy system, electronics, structure, aerostatics, aerodynamics, topology, optimization (multidisciplinary and multi criteria) etc. Thus the design graph is inherently a multi disciplinary
design model and is therefore well suited for object oriented design analysis of LTA HAP.
Since the design graph can be manipulated by the graph grammar rules, the model development by graph grammar based design language represents a dynamic modelling
approach. Dependent from the mission and design requirements the graph as a model
can grow dynamically in order to meet design goals. This is achieved by manipulating
not only the design parameters but also the topology of the design graph by the grammar
rules. Hence optimal designs are obtained for purpose of design analysis of LTA HAP.
3.3.1 Design Characteristic: Parametrical and Topological
Design
Topological Design of Envelope Structure
Topological design is one of the main design characteristics of designing by rule based
methods. Topological variations are applicable by the design rules everywhere on a graph
based representation of LTA HAP. As mentioned in chapter before nodes of a graph can
be manipulated, exchanged or even deleted, and further nodes can be added to the design
graph by the rules, respectively.
Figure 3.24 presents a part of decomposed graph of LTA HAP which mainly incorporates
graph nodes involved within envelope layout. It describes how a LTA HAP [HAP] is decomposed into segments [SEG] and each segment is related with other domains. Such a
dependency graph is detailed for each segment until the complete envelope structure can
be determined. The envelope structure is one of the main components of LTA HAP which
includes the buoyancy gas and thus carries all the loads to the target altitude.
61
Figure 3.24: Graph of multi disciplinary couplings for sizing the envelope structure
The graph presents complex flows of parameters and variables of buoyancy gas volume
V, overall surface area A and in accordance therewith the mass of envelope m. It allows
calculation of
• partial volume V by given LTA HAP geometry,
• the size of LTA HAP by given volume, or
• the surface area A by given volume and geometry of LTA HAP.
Whereas
• V is used → for aerostatics and aerodynamic calculations, and
• A is used → for mass calculation of envelope and aerodynamics.
Figure 3.25 presents topological design of envelope structure [SD]. Its analytical description was presented in section before. Here we present how a segment [Seg] is aggregated
by combining different geometrical parts. The graph model shows that every single segment of a LTA HAP consists of a cylindrical segment part [zyl] enclosed by two elliptical
62
Figure 3.25: Topological design of envelope structure with corresponding rules
parts [elip]. Each segment is represented by its own node, so that every node can be manipulated or even exchanged by applying corresponding design rules. Two segments are
bonded with each other by an apron [Apr] which is also represented by its own node as
well as gas cells [Cell] in each segment. This representation model facilitates topological
design of envelope structure of LTA HAP by manipulating the graph model by design
rules. Furthermore almost every design stage of envelope structure can be visualized by
exporting geometrical data to a CAD modeler.
63
Topological Design of Propulsion System
Design of propulsion system has also its own characteristics within multi disciplinary design of LTA HAP. Here the representational form is also a graph model. As presented in
Figure 3.26: Topological design of propulsion system with corresponding rules
figure 3.26 the graph node [prop] the size of propulsion system is calculated. As mentioned in chapters before it is an iterative process within multidisciplinary design and the
electrical motors [motor] and propeller blades [blade] have discrete size. So that with corresponding rules the graph of propulsion system can be manipulated by adding or deleting
nodes of discrete electrical motors and blades. Each motor node presents a discrete motor
size out of the motor library which is connected to a propeller node. With corresponding
rules propeller blades can be changed. Each propeller has its discrete size and character-
64
istic such as number and form of blades and diameter.
The rules allow distributing the thrust to the number of electrical motors. More number
of motors means reducing size of each motor and propeller blades.
Topological Design of Energy Storage System
The function of energy system within a LTA HAP is to collect, generate and store energy
and provide it as necessary. Corresponding design graph is presented in figure 3.27.
The blocks are the individual disciplines and the edges are couplings between them and
their neighbourhood relations. The [Energy Generation] block is responsible for generation and collection of electrical energy via solar cells and the [Energy Storage] block
stores the energy for buffering purposes and during night phases. Energy storage may be
done by batteries or hydro-solar storage system in form of electrolyzer fuel cell combination. The propulsion system [Propulsion], system components [Sys-Comp] and payload
[Payload] are the energy consumer whereby the electrical propulsion motors are the main
energy consuming components on board. Dependent from the design problem, whether
Figure 3.27: Partial graph for energy system design with flow of variable and parameters
65
the size of LTA HAP is specified and mission duration has to be determined, or mission
duration is the given parameter and the size of LTA HAP is a function of time.
In each case required amount of energy has to be determined in purpose of fulfilling mission requirements. The wind speed influences the design of LTA HAP significantly:
• high wind speed leads to big size and mass of energy system
• high wind speed leads to reduction of mission duration
• low wind speed leads to small size and large duration
Figure 3.28: Topological design of energy system with corresponding rules
We can choose between three different types of energy storage systems:
• batteries
• solar cells
• solar-fuelcell combination or regenerative fuelcell
66
Battery and fuelcell systems are the energy storage systems whereas the solar cells are
converters of solar energy to electrical energy. Dependent on mission requirements one
of these energy systems or a combination of these systems is chosen (figure 3.28).
The batteries are preferable for short duration less than 12h because of there simplicity
in handling. But they may be problematic for longer endurances because of increasing
mass.
Therefore a mission of about 12h during day time may use solar arrays. But for longer
durations a combination of solar cells and fuelcell system (regenerative fuelcell) may be
preferable because of their higher energy density than batteries and could also be used as
regenerative energy systems.
By designing the energy system with corresponding rules one of the energy system component can be chosen. The [Energy] node collects the required power with which the
energy system is designed. The size of solar array depends beside the power and duration
also on the factor how long the night flight period is.
In case of a regenerative system the HAP will fly throughout day and night time, thus the
solar arrays have to be laid out so that they generate enough electrical energy for actual
use and for storage for night time. The electrical storage should be able to cover the night
time until sun rise, so that the solar array start charging the battery again.
67
Topological Integration of System Components
Figure 3.29: Topological integration of system components with corresponding rules
System integration is one of the main tasks within multidisciplinary HAP-design. Its particular characteristic is the topological integration of system components as well as multi
criteria optimization of wiring harness in combination with electrical simulation program
LT-Spice [79]. System integration is done by maintaining a graph based model where
graph nodes are manipulated by design rules (figure 3.29). Graph nodes represents system components, which have discrete mass and power consumption. Thus graph model
representation facilitates performing system integration by considering different aspects
of mission requirements.
System integration also includes the design of wiring harness, which is also done by rule
based manipulation of graph model by doing the electrical simulation in LT-spice. The
68
aim is to determine a tailored solution of wiring harness for a specific HAP mission. By
using thick cable within the harness it would reduce power dissipation and therefore reducing loss of electrical power, but would cause high mass of harness. By reducing the
cable diameter, would in fact reduce the mass but it would cause huge loss of electrical
power in the harness. Therefore a graph model facilitates performing multi criteria optimization of wiring harness. Where each cable model has its discrete model parameters
such as specific mass, ohmic resistance and further parameters.
Filling of Gas Cells and Sloshing Behaviour
Every segment contains a gas cell for generation of enough buoyancy to fulfill entire mission. The filling procedure is one of the critical aspects of a HAP mission. As mentioned
Figure 3.30: Filling of gas cells and sloshing behaviour of helium gas in segments at
ground surface
in chapters before the density of air at target altitude of 20 km is about 15 times less
densed than at ground surface, which means that same mass helium gas has 15 time more
volume than on ground surface and has therefore only 7% of the volume as in 20 km
altitude. Because of this less volume on ground surface the gas sloshes in every segment
and therefore changes its angle of incline from an horizontal position of 0◦ to about 65◦ .
69
The simulation process of sloshing behaviour is presented in figure 3.30. After determining the gas amount [Aerostatic] a stability analysis [stability] is done where equilibrium of
moment is done. These information are fed for numerical analysis to CATIA [14] where a
simulated annealing algorithm is applied to simulate the slosh behaviour of every segment
separately. At least the results are visualized within the CAD modeller of CATIA [14].
3.3.2 Multi Disciplinary Parameter Variation
Searching the design space for feasible designs: An ordinary engineering design task
is to investigate the performance of a LTA HAP with a predefined empirical size. Mostly,
only one design point is investigated and as a result maximum values of some relevant
mission related parameters are achieved, such as maximum wind velocity, maximum carry
able payload, maximum mission duration etc. However, the calculation gets more complex, when in particular a lot of disciplines are involved at the same time.
In contrast to the above mentioned design approach, where the mission performance of
LTA HAP with predefined size is investigated, the inverse approach is to calculate an optimal size of LTA HAP and configuration for a specific mission requirement. The design
task with this kind of approach is solved within the method of graph grammars.
The mission requirements are defined as following: The mission is to carry a specific
payload PL to the target altitude where the LTA HAP has to overcome prevailing wind
speed v for a given mission duration t.
Design Task: The design task is to calculate
• the optimum size of envelope,
• aerostatics and aerodynamics,
• propulsion system,
• solar arrays,
• electrical energy storage system,
• electrical power network,
so that the requirements and the constraints can be fulfilled sufficiently.
The optimum size of an LTA HAP is that which enables to carry the total mass of all aggregates to the target altitude and where the buoyancy and weight forces are in equilibrium.
The optimum propulsion system generates enough thrust to overcome the aerodynamic
70
drag of the envelope. To provide the propulsion system and all other devices with electrical energy the power system is designed optimally, which includes the layout of the solar
arrays and the batteries for energy storage.
Steps of the iteration algorithm: The calculation of the optimal configuration of LTA
HAP in regard to the mission requirement is an iterative process and is performed by the
following iteration algorithm (see also figure 3.31):
1. Step: Graph grammar generates a design graph.
2. Step: Determination of start value for L1 , the initial size of LTA HAP.
3. Step: Defining the state of the technology parameters of various disciplines, such
as specific mass and efficiency of solar arrays, power density of electrical engine
etc.
4. Step: Extracting all equations out of the design graph.
5. Step: All equations are resorted within the SPG (Solution Path Generator) [137].
6. Step: After resorting, all equations are in right order for solving the variables with
the linear equation system.
7. Step: The linear equation system is send to equation solver: mathematica [83].
8. Step: Calculation of all equations with the following order:
a) At first, out of L (length), D (diameter) and envelope geometry the total gas
volume of the LTA HAP is calculated.
b) Calculation of the optimal envelope and out of this the envelope mass.
c) Calculation of gas cells and the corresponding mass.
d) With the size and aerodynamic drag the thrust and engine power is calculated.
e) Dimensioning of the propulsion system and determining the mass.
f) Calculation of the power balances and determing the total power consumption
of all electrical devices.
g) With total power and mission duration the size of solar array area and the size
of electrical energy storage is calculated.
h) Calculation of solar array mass and energy storage mass is determined.
i) Calculation of area for solar array integration.
j) Calculation of center of gravity.
k) Calculation of entire LTA HAP mass.
71
Figure 3.31: Iteration algorithm for calculation of optimal designs by multi disciplinary
parameter variation
72
9. Step: After solving the equations, the result of design variable vector is returned to
the graph model.
10. Step: In the graph model the constraints are proved for satisfaction (see chapter
3.3.3):
a) Constraint: Mass (weight force) balances: Equilibrium of buoyancy force and
the entire LTA HAP weight.
b) Constraint: Area balances for integration of solar array: the available area on
segment 2, 3 and 4 should be equal to the necessary area of solar array.
c) Constraint: Prove of stability against roll moments. The center of gravity of
each segment should be below the center line of segment, so that roll moments
are avoided.
d) Constraint: Buoyancy balances: the segment should be able to carry the integrated solar arrays
11. At the beginning always the 1. constraint is proved for satisfaction. If the first
constraint is fulfilled than the second one is proved and so on, until all constraints
are proved to be satisfied. If this is the case the abort criterion is fulfilled and
no further iteration steps are performed, thus an optimal size and configuration is
achieved. All involved disciplines are laid out optimally.
12. If one of the constraints is not fulfilled the next iteration is performed with L =
L + ∆L and the iterations are repeated until all constrained are satisfied.
13. The result is an optimal configuration of LTA HAP for the predefined parameter
combination. This is a one optimal design point for given parameter configuration
in the design space.
14. However, now the parameters of state of technology can be varied to calculate optimum of another design point. However, all parameter combinations are calculated
systematically and the results of all optimum design points are entered into one
diagram (see figure 3.32).
For searching the design space for feasible designs, however, the parameters can now be
varied systematically. The permissible range of the parameters is released, because the
value range is discontinuous for most of the system components, such as the efficiency of
the solar arrays. The same shell applies for the dimensioning of the electrical engines.
73
Parameter range: The following parameter range is used for the state of technology
parameters:
• Altitude: 2,5km & 20km
• Wind velocity: v> 5m/s
• Payload: 3kg<PL<2000kg
• Specific mass solar arrays: msp1 = 1, 5kg/m2 &msp2 = 0, 125kg/m2
• Efficiency of solar arrays: η1 = 19% η2 = 26% η3 = 41%
h
• Energy density battery: msp = 156 Wkgh ; regenerative fuel cell: 1.866 kW
kg
• Envelope material: 36g/m2 ; 50g/m2; 100g/m2
• Power density engine: 1kW/kg
• Electrical cables: various AWG cables
• Mission duration: 1h < t < 12h and 12h < t < 24h and t > 24h
As a result a multidimensional design space is obtained which is discretised into surfaces
for further investigation of the design space boundaries. For this purpose a contour map
of the discretised surface is presented into a L-PL diagram for various wind velocities
(figure 3.32).
We will apply this approach in chapter 5 for purpose of multi disciplinary mission analysis. There we will investigate 5 different type of mission scenarios and achieve the above
mentioned diagrams with design space delimited by constraint lines. The principle of
such kind of diagram is presented in figure 3.32. There we have such a surface with clear
boundary lines, the so called constraint lines. All design points lying within the design
space are feasible design points and all other points out of this surface are not valid points,
because for these design points not all constraints are satisfied.
As presented in the diagram the design space is restricted by five type of constraint lines.
The purpose of this investigation is to find out the parameters which influence the form
and position of these constraint lines and how these parameters can be varied to move
the design space in the desired direction. By this way, however, the performance of a
LTA HAP which is defined by the parameters of state of technology can be investigated.
Furthermore the investigation could be done to find out which kind of technology has to
be further developed to enhance the performance of the LTA HAP.
74
Figure 3.32: Principle contour map diagram of a design space with constraint lines as
boundary lines. All valid design points are lying in the design space and the invalid
design points are out of the design space.
Constraint Lines: In brief the constraint lines are described as following, the details will
be presented in chapter 5:
• Constraint line of minimum payload.
• Constraint line of minimum wind velocity.
• Constraint line of maximum payload.
• Area constraint line.
• CG (center of gravity) constraint line.
75
3.3.3 Balance Equations and Constraints
Within multidisciplinary design of LTA HAP balance equations are applied in iteration
process of parameter variation. At the end of the iteration algorithm as presented in figure
3.31 these equations are dealt as constraints of the termination criterion. If all constraints
are satisfied then the iteration process is terminated and an optimum solution is obtained.
In the following the balance equations are presented in detail.
Balances of weight and forces: Weight force balance is a sum of static forces equal
to zero in z-axis direction:
F zi ≤ 0 → FB ≤ FG
(3.49)
i
Which means that upward forces generated by buoyancy FB is equal to the weight
of all components of LTA HAP: entire weight FG .
Buoyancy Force: As mentioned before buoyancy is generated by the helium gas
containing within the gas cells and therefore a sum of buoyancy total gas is done.
FB = FB1 + FB2 + ... + FBi
(3.50)
And this sum has to be equal with the sum of the weight of all the components of
LTA HAP.
Weight Force FG :
FG = FG1 + FG2 + ... + FGi
(3.51)
These are the weight of
• envelope structure: Fenv ,
• gas cells: Fcell ,
• propulsion system: Fprop ,
• energy system: FE ,
• system components: FSC ,
• payload: FP L , etc.
Figure 3.33 presents a principle graph of mass (weight force) and energy balances
of a LTA HAP. All mass flows are presented as red edges. The mass of all involved
disciplines flow to the mass balance node and also the value of total buoyancy force.
In this node the mass balance is performed. In case of disequilibrium the amount
of gas has to be increased until an equilibrium is gained. This has in turn effect on
all involved nodes of the network.
76
Figure 3.33: Graph model of energy and mass balances of multi disciplinary HAP design
Also weight force (mass) balances of each segment are performed individually,
otherwise it may be that the entire LTA HAP can carry all the loads into target
altitude, but the segments are not loaded in equilibrium and some of them have an
angle of incline greater than 0◦ and this could lead to a non horizontal position and
therefore a bad Cw factor.
F zi = 0 → FB1 = FG1
(3.52)
i
Some of the components have there fix position on a LTA HAP. For instance the
LTA HAP is driven by the propulsion system integrated on the head segment. The
solar cells are integrated on the back (top surface) of the segments. Then the rest of
the masses are distributed over the segments.
Installation of the payload is also a comprehensive task for doing mass balances.
It depends on the payload whether it can be subdivided into smaller modules for
distributing it to the individual segments respectively. Or the payload presents a fix
module which can not be subdivided and has to be integrated in a one-piece. Thus
the whole weight of the payload must be carried by only one segment. This leads
to drastic increase of the size of LTA HAP.
77
Thrust balances: The next balance equation is the sum of forces along X-axis (longitudinal axis), which is an equilibrium of aerodynamic drag and thrust of propulsion
system:
F xi ≤ 0 → FD ≤ FT
(3.53)
i
The aerodynamic drag is a function of dynamic pressure q and total airship volume
2
V: FD = q · Cw · V 3 , whereby the dynamic pressure q is in turn a function of wind
velocity: q = 12 · ρ · v 2 . Which means that a change in any one of these factors cause
that the thrust balance is not satisfied. These factors are also influencing each other,
e.g. a change of velocity v means a change of aerodynamic drag and this means
increasing of engine size and mass. A change of overall mass means a change
of airship volume V. An this variable influences in turn the aerodynamic drag in
equation 3.53. In case of not satisfaction of thrust balances the iteration algorithm
of figure 3.31 is performed until this constraint is fulfilled.
Energy balances: The energy balance is done by balancing the amount of required
energy for all electrical devices and the amount of energy provided by the energy
system.
Ei ≥ 0 → Epowersystem ≥ Pconsumer · tmission
(3.54)
i
The electrical components with constant power usage are the system components
Psys and the payload PP L . The main energy consumer is the propulsion system
Pprop with variable power load over the time.
consumerpower : Pcons = Psys + PP L + Pprop
(3.55)
On the one hand enough energy has to be provided over the mission duration. On
the other hand enough power has to be provided at the moment of load.
Pcons_i
(3.56)
Ppowersystem ≥ Pcons with Pcons =
i
In case of batteries as energy provider the energy is limited to the capacity of the
batteries. Thus dependent to the power load the mission duration t is limited from
the battery capacity.
case 1 Battery:
case 2 Solar 12 h:
case 3 Solar+Battery:
day time 12 h
night time X h
case 4 Solar Hydro:
day time 12 h
night time 12 h
→ Ebat ≥ Pcons · t
→ Esolar_12h ≥ Pcons_daytime · 12h
12h day time and X h night time
→ Esolar ≥ Pcons · (12h + Xh)
→ Ebat ≥ Pcons · Xh
regenerative system 24h
→ Esolar ≥ Pcons · (12h + 12h)
→ Ehydro ≥ Pcons · 12h
78
In case of solar arrays as power provider the mission duration is limited to the
duration of solar radiation over day time. For the night phases batteries or similar
energy storage system has to be used. Is the storage system big enough to cover the
whole night time, then the system can be designed as a regenerative system. Thus
the solar arrays can provide the systems with electrical energy over the whole day
and at the same time charge the energy storage system for the night phases.
Area balances for solar arrays: The area balances is done for ascertainment of the
area of solar arrays. Which means that it is proved whether the upper surface area
of segments is enough to integrate the solar arrays. For this purpose, both solar
array area and segment surface area are calculated.
The segment surface area is the sum of half cylindric area of the three mid segments.
Aseg = 12 Aseg2 + 12 Aseg3 + 12 Aseg4
(3.57)
The solar array area is dependent from the power consumption Ptotal of all electrical device, mission duration, solar intensity, solar efficiency, etc. With this the
necessary solar array area is calculated with:
ASA_vis =
Ptotal · t
SIevr
(3.58)
m
. The factor t
SIevr is the average solar intensity which is defined as: SIevr = η·SI
2
is the mission duration and SIm the maximum solar intensity. With equation 3.58
we calculate the visible surface of the solar arrays. As we can see the segment surface is curved, thus the visible surface area of the solar arrays has to be transformed
to the curved surface area of the segments:
ASA_real = 0.5 · π · ASA_vis
(3.59)
Thus the balance equation for solar array area balances is defined as:
ASA_real ≤ Aseg
(3.60)
The necessary solar array area for the desired mission ASA_real should be smaller
than the available surface area of the segments Aseg .
Balance of mission duration: Balance of mission duration is done for ascertainment
of the duration of a mission by given size of LTA HAP. The nominal mission duration must be greater than mission duration given in the requirements.
tmission ≥ trequirement
(3.61)
The main limiting factor of a HAP-mission is the energy system and the power
consumption of the propulsion system. Thus follows for the duration of a HAP
mission with a specific energy system:
case 1: Batteries
→ tmission =
case 2: Solar Cell 12h → tmission =
case 3: Solar Cell
Ebat
Pconsumer
PSA_12h ·t
Pconsumer_12h
12h + Xhnight
→ tmission =
case 4: Solar Cell
79
ESA_12h
Pconsumer_12h
+
Ebat_F Z
Pconsumer_Xh
regenerative system 12h + 12hnight
→ tmission =
ESA_12h
Pconsumer_12h
+
Ebat_F Z
Pconsumer_12h
In case 1 the duration is dependent from the capacity of the batteries and the entire
power consumption. In case 2 the mean power of solar system has to be equal to
the mean power consumption. Thus the duration of the mission is equal to the day
time length. Case 3 is a combination of case 1 and 2, thus the solar system provides
electrical energy during the day time and the batteries are used for the night time.
In case 4 electrolyzer and fuelcell is used instead of batteries. The energy system is
designed as a regenerative energy system, therefore the duration is greater than 24
h even up to unlimited.
Balance of stable position of center of gravity: Balance of stable position of center of gravity is done to prove whether the center of gravity of each segment is in
a stable position. This is in particular necessary for the segments where the solar
arrays are installed at the upper surface of the segment. The mass of the solar arrays
cause that the center of gravity (CG) moves upwards. In case of that the position
of CG is above the center line roll moments are caused, so that the segment rolls
upside down. Thats why it is important to avoid roll moments and therefore the CG
should be in the area of 1/4 D (segment diameter).
zCG ≤
1
·D
4
(3.62)
Balance of electrical current: For optimization of wiring harness a power network
is generated. The task is to calculate the right size of cable diameter to provide all
electrical devices with electrical energy, whereby the batteries and all other electrical devices are distributed all over the HAP segments. If the diameter is too small,
then the mass of wiring harness is less but the power dissipation is too large, so that
a huge amount of electrical energy is lost which would have a negative effect on
the mission duration. If the cable diameter is too thick, then the power dissipation
is less, but the cable mass is too large, so that less batteries can be integrated in the
HAP and this has in turn a negative effect on the mission duration.
80
For the calculation of dissipation loss of electrical energy in each cable of the power
network the electrical current in each nod and the voltage of each loop are calculated. This calculation is actually used for the multi objective optimization of the
wiring harness (see also chapter 3.3.5 and 4.4). Therefore the junction rule and the
loop rule are applied.
Ii = 0
→ i Iin = i Iout
junctionrule
(3.63)
i
Ui = 0 →
i
Usource =
i
Uconsumer looprule
(3.64)
i
The calculation of the individual currents and voltages are done in the simulation software
"LT-Spice"[79].
3.3.4 Mission Scenarios
There are mainly three kind of missions we will assay for validation of the graph grammar
based design model. There is
1. the short duration mission,
2. the mid duration mission during the day light and
3. a long duration mission.
Each mission is characterized on behalf of the mission duration and the power system.
The main limiting factor of a mission is the on board energy system and the energy consumption of the propulsion system. Whereby the propulsion system is the main energy
consumer on board of the LTA HAP. In case of a station keeping mission and less wind
speeds, the duration can be increased of many times than by higher wind conditions.
1. Short Duration Mission
The short duration mission is characterized by using rechargeable batteries as energy
source. As the name implies the duration is limited to some hours up to 12 h.
tbat ≤ 12h
(3.65)
The mission may be in lower altitudes of about 2500m or in higher altitudes of 20km.
Dependent from velocity of wind and payload the size of LTA HAP vary but the main
limiting factor is the capacity of the battery system.
81
2. Mid Duration Mission
The mid duration mission is characterized by using solar cells as main energy source.
Since the solar arrays convert solar energy into electrical energy the mission takes place
during day time and is also dependent from the sun light.
energy source: solar arrays
tSA ≤ 12h
energy source: solar arrays and batteries 12 ≤ tSA ≤ 24h
(3.66)
A mission only with solar arrays is restricted to a duration of 12 h. To extend the duration
batteries are add to the power system, so that during the day time the solar arrays provide
the propulsion system and system components with electrical energy and at the same time
the batteries are charged to compensate the shadow and night phase.
Therefore high altitudes within the stratosphere are preferable for a mission with solar
arrays, because in these regions of the atmosphere there are almost no weather happenings
because of the very dry air. Thus there are no clouds which could cause shadow phases.
Also lower altitudes are conceivable but batteries have to be used for compensating the
shadow phases. Thus the size of solar arrays are layouted for average power consumption
throughout the mission, therefore the size of LTA HAP for all missions up to 12h is almost
the same.
3. Long Duration Mission
The long duration mission is characterized by using solar cells for energy generation from
solar radiation and regenerative fuelcell system for energy storage.
The solar arrays convert the solar energy to electrical energy and provide all devices with
current. At the same time the current is used to operate a fuelcell to separate water into
oxygen and hydrogen and use this during the night time to produce electrical current.
tSA_hydro ≥ 24h
(3.67)
With this combination a regenerative energy system is aggregated which allows durations
of no limit due to energy capacity. Also the energy density of fuelcell system is much
higher than batteries, thus less size of LTA HAP can be achieved.
Factors for Defining a Mission Scenario
In following we will point out some factors which are relevant for defining each mission
of a LTA HAP mentioned above:
• Point of time: Point of time means time of year for instance summer or winter as
well as time of day which can be a combination of day or night time. This factor
82
has a great influence on energy generation because of variation of solar radiation
during different time periods. In winter the duration of day light is less then 8 hours
and maximum solar radiation is also less than half as it is during summer.
Time of year: Ty (δ)
Time of day: Td (θ)
summer or winter
day or night time
(3.68)
On the other hand speed of wind is greater than in summer time. Which means that
in winter because of less solar radiation less solar power is available and because of
higher wind speeds a larger propulsion system is required. In contrast to winter the
summer time requires a smaller propulsion system because of less wind speed and
delivers a greater solar radiation for power generation.
• Altitude: From ground surface to high altitudes such as 20 km the density of air
decreases continuously. Less density means less aerodynamical drag, but the volume for carrying load in 20 km is about 15 times larger than on ground surface and
therefore larger volume means larger aerodynamical drag.
Altitude : Hmission
(3.69)
Also wind speeds varies in different altitude. Wind speed increases from ground
surface to about 10 km altitude and gains maximum and decreases again. Thus for
High Altitude Platforms a flight zone above 16 km is tolerable. For mid altitude
flight a zone below 5 km is relevant.
Because of atmospheric decay the solar radiation is less in lower altitudes than in
higher altitudes. Also weather influences such as cloud shadings are less in higher
altitudes.
• Mission duration: Mission duration is one of the main parameters of a mission
scenario. One possibility is to calculate the mission duration for a given mission
requirements and a specified size of LTA HAP. The other one is to determine the
size of LTA HAP for given mission parameters and duration.
Mission duration : tmission
(3.70)
Dependent from this parameter the size of LTA HAP in particularly the size of
energy system is ascertained. The longer the mission the larger is also the amount
of energy necessary to fulfill the mission target. Is the mission during the daytime
period solar cells provide directly electrical energy and therefore a less amount of
buffer batteries are necessary. But for a longer mission enough quantity of batteries
are necessary to compensate the night phase. For a mission duration more then 24
h then a regenerative energy system design has to be considered.
83
• Location: Location is also one of the most effecting mission parameter. Regions
with less weather activities presents beneficial conditions for a HAP mission than
regions with raw weather activities. Preferred location is with less wind activity and
a maximum of solar radiation.
Location : Llatitude (φ)
(3.71)
Less wind activity means a smaller size of propulsion system and less energy consumption and therefore reduced mass of propulsion and energy system. A maximum solar radiation means that smaller solar array area is enough to collect required quantity of electrical energy and therefore leads to reducing mass of solar
system.
• Payload: Payloads are the core of a mission which have to be carried to a specific
altitude for a predefined duration.
P ayload : P Lmission
(3.72)
There mass influences sizing of LTA HAP. Also the mission location is defined
dependently from task of payload.
• Percentile distribution of wind velocity: One main factor which influences designing LTA HAP is the wind velocity within operational environment.
Mean wind speed : vmean (H, δ, θ, φ)
(3.73)
As mentioned before the wind speed varies over the time during a mission. Which
means that a design can be made for a maximum wind velocity during the whole
mission or a mean wind velocity of percentile distribution over the mission duration
is ascertain. First approach leads to a huge HAP size where by the second one
allows a flexible design with less size of HAP.
• Energy storage system: There are three kind of energy storage systems that will
be considered for the missions:
1. battery system
2. solar system with batteries
3. solar hydro fuelcell system
A mission is characterized based on the type of energy storage system. Since the
energy storage system is that which restricts the duration of a mission to a ceratin
period. A mission based on batteries has a very short duration. For a mid duration
mission with a duration up to 12 or more hours solar arrays are preferred. For a
long duration mission a regenerative energy system based on regenerative fuel cell
or electrolyzer fuelcell combination is used.
84
For each mission scenario the above mentioned factors have to be defined for a successful
design of a LTA HAP. Some of the factors are defined within the mission requirement
and other are environmental factors, such as wind speed and solar radiation. All of them
influence each other within a network. The wind speed for instance depends on location,
time of year and day and operational altitude. Thus the aim of each mission scenario is
to fulfill mission requirements by designing a LTA HAP with an optimized minimum size
which leads reducing handling problems and overall mission costs.
3.3.5 Multi-Objective Optimization of Power Network
Multi-objective optimization also known as multi-criteria optimization is the process of simultaneously optimizing two or more conflicting objectives subject to certain constraints
[25]. In our case of optimization of the cable diameter of wiring harness is such a problem
with two objectives which has to be optimized simultaneously, namely
• Objective 1: the mass of the cables and
• Objective 2: the power dissipation of the cables.
Both objectives have to be minimized at a same time by searching for the optimized cable
diameter.
The conflict is that on one hand a thick diameter for the cable means less power dissipation
but a huge mass, on the other hand a less diameter means also less mass but a huge power
dissipation. However an extremum of each leads reducing mission duration. Thus an
optimum of the cable diameter is a desirable goal.
The problem can be formulated as following:
Objective f unction :
minx [µ1 (x), µ2 (x)]
(3.74)
Where µi (x) is the objective function with the constraints g(x) ≤ 0 and h(x) = 0 and x
is the vector of optimization. The solution of the above problem is a set of Pareto Points
[25].
first objective
: µ1 (x)
second objective : µ2 (x)
the vector to optimize:
cable diameter current
d1
I1
x1
x2
d2
I2
x3
d3
I3
x4
d4
I4
x5
d5
I5
= mass of cable
= power dissipation
power
P1
P2
P3
P4
P5
85
An Evolutionary Algorithm (EA) developed by DEB [25] is used as an approach to solve
the multi objective optimization problem.
The setting parameter for the Evolutionary algorithm are described as following:
General Parameters
Populations
Individuals per population
Generations
Cross over probability
Parents selection
:
:
:
:
:
Mutation probability
Repetition
Application
Parameter
Add rule
Remove rule
remark
probability of repetition of rules per individual
probability of application of rules
probability of parameter mutation of a node
probability of adding a rule to program
probability of removing a rule from a program
:
:
:
:
:
Mutation parameters
Max. repetition
Max. Application
Parameter variation
Add rule at end of program
Migration
Migration intervals :
Migrants
:
remark
number of population per generation
number of individuals per populations
number of total generations
cross over probability between populations
parent selection for next generation
:
:
:
:
remark
number of max. repetition of a rule
number of max. application of a rule
parameter variation
rule can add anywhere in a program
remark
number of migration intervals
number of migrants per interval
The main characteristic of the multi objective optimization of our case is that the optimization approach of the evolutionary algorithm is performed by usage of some optimization
rules. Two of them are presented in figure 3.34. These rules of multi-objective optimization facilitates modification of cable types of a circuit plan by replacing already existing
cables by other one. Since the replacement procedure is enabled by the four quadrant
schematic [5] of the graph based rule representation, a rule is executed until the IF part of
the rule is fulfilled then the THEN part is executed subsequently. Which means to modify
an existing circuit plan one of the rules is executed to replace a cable by an new one with
different parameters, and gains by this way a novel circuit plan design.
The process chain for rule based multi objective optimization is presented in figure 3.35.
• Input Parameters: At the beginning the input parameters are defined with all initial design information, such as initial circuitplan configuration for the desired LTA
86
Figure 3.34: Optimization rules involved within rule based multi objective optimization
of cable diameter and type
HAP design, the set of available cable type, setting parameters for the EA (evolutionary algorithm) and the evaluation criteria. The evaluation criteria are the mass
of cable and the power dissipation of the cable.
• Design Language: The input parameters are fed to the design language which
includes the vocabulary, rules and evaluation criteria for the multi objective optimization. As an optimization tool, as mentioned before an evolutionary algorithm
[25] is used.
• Design Graph: By executing the design language a design graph is generated and
at the same time the optimization algorithm is initiated. Within this, optimization
cycles are performed in order to gain the Pareto solutions. In each cycle a complete design of a circuit plan is established in form of a design graph representation.
Which includes data of a HAP with all involved disciplines, especially the information concerning the power network. The electrical cables are also presented in form
of graph node, which can be replaced by alternative cable type by executing cable
replacement rules (figure 3.34).
• Electrical Analysis: The circuit plan information are then derived out of such a
design graph representation and are sent to an external circuit plan analysis tool
named LT_Spice [79] for calculation purposes. There the power dissipation of each
cable of entire circuit is calculated and the result are fed back to the design language
87
Figure 3.35: Process chain for rule based multi objective optimization of power network
in form of design variable vector. The calculation of the mass is performed within
the external solver mathematica [83]. Both parameters are subsequently fed to the
evolutionary algorithm toolbox [25] for purpose of evaluation. Out of the evaluation
results the EA specify a modification strategy for further improvement of the results
by choosing modification rules for the next iteration.
• Output Result: At the end of the optimization process all results are presented in
a diagram in form of a Pareto quantity. The design points lying on the pareto curve
are optimum results and all other result points below the curve are non optimal
points. Out of the Pareto curve the favour designs can be picked out. The amount
of optimization cycles can be of many hundreds to some thousands.

Multi Disciplinary Object Oriented Design Analysis of High Altitude

Transcription

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