UNIVERSITÀ DI PISA
FACOLTA’ DI INGEGNERIA
Tesi di Laurea
Studio Preliminare di un velivolo PrandtlPlane
da 250 posti
Preliminary design of a 250 passenger PrandtlPlane
aircraft
Relatori:
Prof. Aldo Frediani
Prof. Dieter Schmitt
Dr. Ing. Eric Maury
Candidati:
Claudio Bottoni
John Scanu
Anno Accademico 2003-2004
Acknowledgements
We wish to express our appreciation to everyone who has aided in this work. Particularly,
to Prof. Ing. Aldo Frediani, for his general support, for his critical revision and for the
constant attention dedicated in every aspect of the thesis; to Ing. Emanuele Rizzo and Ing.
Tommaso Tattesi, for technical support; to Ten. Col. Porcari, for his technical assistance
by collecting information and data, and to the students Marco Boni and “dott.” Giuseppe
Iezzi.
Contents
•
Abstract
iii
•
Introduction
iv
•
Chapter.1
•
•
Chapter.2
Chapter.3
The PrandtlPlane concept
1.1
Unconventional configurations
1
1.2
The Best Wing Systems by Prandtl
5
1.3
A PrandtlPlane aircraft according to Vision 2020
10
Geometry Generation
2.1
Parametric geometry generation
17
2.2
MSD - CATIA® interface
26
2.3
Assembly design in CATIA®
31
PrandtlPlane Conceptual Design
3.1
Introduction and Customer requirements
3.2
Fuselage design
36
3.2.1
Introduction
38
3.2.2
Internal arrangement according
40
to AEA Requirements
3.2.3
Comparisons in term of ergonomics aspects
57
3.2.4
Comparisons in term of skin friction
73
drag at low velocities
i
•
Chapter.4
Preliminary Fluidodynamical Analisys
4.1
Aerodynamical project
4.1.1
Preliminary High speed aerodynamical design
86
4.1.2
Choice of the airfoils
92
4.2
CATIA® model creation optimised for the grid generator
4.3
Fluidodynamical analysis with the software
4.4
99
4.3.1
The aerodynamical field
99
4.3.2
Choice of the computational model
100
4.3.3
Mesh validation
100
Solutions and postprocessing
102
116
Chapter.5
Maximum Take Off Weight Estimation
•
Chapter.6
Longitudinal Flight Stability
Chapter.7
95
FLUENTt®
•
•
86
6.1
Foreword
6.2
Longitudinal equilibrium and stability of the PrandtlPlane 142
6.3
The PrantlPlane stability
Conclusions
137
146
151
ii
Abstract
This graduating thesis aims at showing the potential characteristics of a new aircraft
configuration, named PrandtlPlane in honour of Ludwig Prandtl.
In Chapter 1, the main ideas on the PrandtlPlane concept are presented, starting from the
Prandtl’s problem on the Best Wing System.
Chapter 2 deals with problem of the shape generation of the PandtlPlane aircraft, to be
used to carry out the aerodynamical development of the aircraft.
In Chapter 3 the design of 250 seat PrandtlPlane aircraft is shown.
The aim of this activity is not that of giveing a final design but only to show the potential
benefits of the configuration and to underline the differences between conventional and
PrandtlPlane configuration.
In Chapter 4 preliminary aerodynamical analysis performed on the 250 seat PrandtlPlane
aircraft.
Chapter 5 deals with the assessment of the maximum take off weight.
The relationship between aerodynamical efficiency and the stability of flight appears in
Chapter 6.
Finally some conclusions are presented in Chapter 7.
iii
Introduction
Passenger and cargo traffic are estimated to grow by a factor of three in the next two
decades, especially along medium and long range routes worldwide. The civil aircraft of
the future are requested to improve significantly their performances. Typical required
performances were defined at the beginning of 90’s by the airline companies. More
recent definitions of the required performances in the framework of the European
Community were given in Vision 2020, by the Advisory Council for Aeronautics
Research in Europe, October 2002. This document, starting from the present state of the
art on transport aviation in Europe, defines the future scenarios in fixed wing transport
and indicates the next challenges and goals of the fixed wing air transport in 2020. A
brief analysis of Vision 2020 will be given in this graduating thesis.
Typical requirements for the civil air transport of the future are: more available space and
comfort, 10-12% time reduction for boarding and disembarkation of passengers and
luggage, improvement of cargo capacity, possibility of operating from present runways
and airports, 30% reduction of Direct Operative Costs, improvement of the operative life,
reduction of initial investment and costs for maintenance, 0.85 Mach cruise speed, more
cargo in addition to luggage, reduced approach and landing separations due to wake
vortex turbulence. In addition, new noise and emission requirements are considered to be
a major concern.
The V and VI Framework European Programmes in the field of Aeronautics indicate the
reduction of pollution in the atmosphere and of noise and emissions in the areas around
airports as fundamental requirements for future aircraft.
The problem of reducing Direct Operative Costs and noise and emissions can be faced by
using technology advancements (new materials for structures and engines, reduction of
production and maintenance costs, etc). These advancements can produce only long term
benefits and the trend says that a reduction of about 30% of DOCs (Direct Operative
Costs) is not available in the next decades The increase of aircraft capacity is another way
for reducing the unit costs in the long routes. But, in the short routes, very large aircraft
cannot be used and, in the long routes, the biggest possible aircraft compatible with
existing airports must be included in an 80x80m horizontal square, in order to be
iv
compatible with present airports. So, the advantage of increasing dimensions came to its
end with the A380 aircraft.
The conclusion is that future requirements for DOCs and noise and emission reductions
will not be satisfied, without a significant improvement of aircraft performances.
The improvement of the aerodynamic design against drag is essential for the commercial
success of any transport aircraft programme and for reducing pollution and noise. The
need of improving the aircraft performances is mandatory; a 1% reduction of drag for a
large transport aircraft saves 400.000 litres of fuel and, consequently, 5000 Kg of noxious
emissions per year. Many national and international authorities indicate the dangerous
improvement of pollution due to the aircraft’s share in global emissions. The problems of
noise and noxious emissions during take off and landing produce the worst impact on
people living in the surrounding areas. The improvement of the low speed aerodynamic
efficiency of aircraft is one of the main challenges of the future.
The level of survivability of accidents in take off and landing is a further challenge:
structural design, design against crash and fire, fuel tanks, new materials, evacuation
system, etc., are of major importance in this concern.
The internal noise in cabin and the comfort of passengers have to be enhanced in future
aircraft. In summary, the following main challenges need to be faced in the short and
long term: high reduction of the Direct Operative Costs, cut of noxious emissions,
decrease of the external noise level around the airport areas, improved safety and comfort
in flight, improved survivability of accidents.
In a large transport aircraft during cruise flight, drag is mainly due to friction drag (about
47%, according to Airbus) and induced drag (about 43%), where the induced drag
depends on the lift distribution along wing span. The lift distribution of today large
transport aircraft is so optimised that any further significant reduction of induced drag
cannot be easily obtained.
Ways of reducing friction drag are suction of the boundary layer or use of devices on the
outer surface of the aircraft but, till now, the overall benefits are not well quantified.
A possible jump forward in air transport will come from the introduction of completely
new, non-conventional, aircraft.
The main starting property of this aircraft configuration is a strong reduction of the
aircraft drag, based on an intuition of Prandtl.
According to Prandtl, the lifting system with minimum induced drag is a box-like wing
(named as Best Wing System by Prandtl), in which the following conditions are satisfied:
v
same lift distribution and same total lift on each of the horizontal wings and butterfly
shaped lift distribution on the vertical bulks. When this condition of minimum occurs, the
velocity induced by the free vortices is constant along the two horizontal wings and
identically zero on the vertical bulks. The efficiency increases with the gap between the
wings. The ratio between the induced drag of the Best Wing System and the optimum
monoplane with the same lift and total span was calculated before 1920 and published in
NACA TN 182, 1924. In this paper, Prandtl used an approximate procedure; a closed form
solution of the Prandtl problem was given by Frediani and Montanari, in 1999,
confirming that the Prandtl results, at least in the range of the wing gaps of interest for
applications, were correct. It shows that, in the range of interest of h/b in the present
application (10-20%), the induced drag is reduces from about 20% to 30%. Owing to the
Munk theorems, the induced drag is independent of the sweep angles of the wings and,
therefore, the Prandtl concept can be applied also to transonic transport aircraft.
In honour of Prandtl, the configuration is named as PrandtlPlane.
The problem of friction drag and wave drag is still open and no definite answer is
available at this stage. The PrandtlPlane configuration can be used to design a complete
family of aircraft, ranging from small aircraft to wide bodies, larger than Airbus A380.
All the aircraft of the family are compatible with the present airports. In fact, in the case
of aircraft larger than e.g. A380, the higher efficiency of the configuration can be used to
reduce the wingspan inside 80m, without drag penalty with respect to conventional
aircraft. The possibility of improving the PrandtlPlane capacities beyond the largest
possible conventional aircraft is one of the possible advantages for reducing drag.
The main objective of the present research activity is to develop the preliminary design of
a 250 seat category PrandtlPlane aircraft. This project is also a test case for other
applications of the PrandtlPlane concept
In the European Patent 716978, the PrandtlPlane configuration is similar to that shown
in Figure 1, with the same fuselage of Airbus A380.
The fuselage is a wide body, enlarged vertically with three decks. In the aircraft shown in
Figure 1, the rear negative swept wing shows a low aerodynamic efficiency in the
segment inside the fuselage. So, in order to obtain the static stability of flight, the centre
of pressure of the whole aircraft, coincident with the centre of gravity during the trimmed
flight, must be closer to the front wing, which is more loaded than the rear one. So, the
conditions of best wing system mentioned before are violated and the aerodynamic
efficiency is reduced.
vi
Figure 1
In the period 2000 - 2002, five Italian Universities carried out a national project, financed
by the Ministry of University, to develop the PrandtlPlane configuration with application
to a 600 passenger aircraft. The Universities were Torino, Milano, Roma La Sapienza,
Roma Tre, coordinated by Pisa University. Technical University of Torino carried out
wing tunnel tests together with Alenia Aeronautica; Technical University of Milano
carried out the preliminary design and optimisation of the wing system, Roma La
Sapienza and Roma Tre carried out the overall optimisation of the aircraft. The most
important result of the project was the solution of the conflict between aerodynamic
efficiency and stability of flight and the configuration became completely different as
shown in Figure 2. In the new solution, the fuselage is enlarged horizontally with a single
deck for passenger and with a constant width up to the end. The rear wing is positioned
over the fuselage and connected to it by two fins.
This aircraft is stable in cruise flight, the margin of stability can be controlled and
modified and, at the same time, the lift is equal on the front and the rear wings. This
result is the consequence of the high aerodynamic efficiency of the central wing sector of
the rear wing, (between the two fins), which depends on both the gap and the shape of the
vii
top fuselage or, in other words, on the characteristics of the aerodynamical channel,
defined by top fuselage, bottom rear wing and lateral fins.
The main characteristics of the PrandtlPlane configuration of reference emerge in the
following chapters .
Figure 2. A first possible 600 seat PrandtlPlane with two fins
This thesis analyzes at a preliminary stage an application of the PrandtlPlane concept to a
250 seat aircraft.
A 250-300 seat aircraft of future generation could be interesting to develop the
continental and intercontinental aircraft transportation at lower cost than actually.
At the beginning of this activity the question was: “is the PrandtlPlane concept able to
generate a high efficiency 250-350 seat aircraft ?”
The final answer to this question is not available, because one needs a final design (wich
is not possible now) and a multidisciplinary optimization (wich could be possible only
after some time). Anyway
this thesis shows that the PrandtlPlane configuration is
flexible as far as the passenger accomodation is concerned and, besides, it allows us to
transport a very large amount of containers, say, more then the double of an equivalent
conventional aircraft.
The large cargo deck is possible because of the small height of the front wing box (the
half of a conventional aircraft) wich crosses the fuselage under the same cargo floor and,
viii
also, to the large width of the fuselage, necessary to fulfill the PrandtlPlane
aerodynamical requirements.
The main positive aspects also the possible problems of the configuration are indicated in
this thesis.
ix
The PrandtlPlane concept
CHAPTER 1
The PrandtlPlane concept
1.1
Unconventional configurations
A study by British Airways in 1993 [1], related to the air traffic prediction of the following
decades has estimated an increase rate exceeding 6% per year (Figure 1) with peaks for
international links.
Figure 1. Estimated growth of air traffic on medium and long range routes in the next future
The increase of the dimension of the liners was recommended to the aircraft manifactures
(the Airbus A380 is the result of this strategy).
Future aircraft have to be designed with the following requirements.
Commercial requirements: better control of passenger “status”, much available space, less
vibrations, better choice of on-board activities, less constraints (unpleasant conditions) by
boarding and getting off . The time for loading and disembarcation of passengers should be
reduced by 10-12% with respect to the current mean times (about 120 minutes). The single
bridges must be quickly reset to allow for enhanced operational flexibility.
Economic requirements: reduction by 20% of the direct operative costs (DOC). This can be
achieved by a reduction of the fuel consumption per passenger per km, an increase of the
operational time-span and lesser investment and maintenance costs, etc.
1
The PrandtlPlane concept
Requirements on environmental impact: the noise level must be significantly reduced and the
atmospheric pollution cutted.
The current development of traditional configurations has reached such a level of
optimization that, in spite of enormous technological efforts, only small additional benefits
can be achieved.
These considerations motivate modern aeronautical research towards the study of non
conventional configurations.
Figure 2. Blended wing body
Figures 2 and 3 show one of the non conventional configurations which has been most
intensively studied since World War II, the so-called Blended Wing Body (BWB)
Figure 3. Horten 7 (German experimental prototype).
The advantages of this particular geometry are [2]:
2
The PrandtlPlane concept
-
Saving of 50% of the so-called parasitic drag, because of the lack of a real fuselage.
-
Very high aerodynamical efficiency in cruising conditions, compared with traditional
architectures.
-
Small bending moment along the span in cruise flight, by means of a proper load
distribution.
On the other side disadvantages are:
-
Large aircraft have a span larger than the admissible one (80 m)
-
Engine integration.
-
Stability of flight.
-
Flight controlin pitch.
-
Low structural efficiency due to pressurization.
-
Flight quality in roll.
-
Evaquation problems in emergency, etc.
-
Modest flexibility in the load options especially in low density configurations,
because of heavy restrictions both in axial and side directions;
Figure 4. McDonnell-Douglas Blended Wing Body concept with C-wing tips
Figure 4 shows the addition of C-Wing tips to the McDonnell-Douglas Blended Wing Body
concept [3] . The addition of these wings tips would permit the BWB configuration to
3
The PrandtlPlane concept
improve the stability of flight. Although many details have to be defined the addition of C
wing tips seems to be promising as far as controllability and efficiency are concerned.
A further non conventional configuration, is the Prandtlplane, so called after the German
physicist Ludwig Prandtl (1875-1953) who first tackled the problem of the minimum induced
drag in a lifting system. The results of Prandtl’s studies had no impact on the development of
aviation because the biplane aircraft presented a total drag larger than that of monoplanes,
due to cables and trusses and, at the same time the monoplane configuration made use of the
new aluminium alloys for the box structure.
The PrandtlPlane concept is a practical application of the Best Wing System theory, by
Prandtl in the ‘20s [4].
4
The PrandtlPlane concept
1.2
The Best Wing System by Prandtl
In cruise conditions the induced drag is about 43% of the total drag, the rimaining being due
to friction drag (about 47%) and to the wave drag. In case of a mono-plane configuration it is
well known that the minimum induced drag corresponds to an elliptical distribution of the lift
forces. In modern aircraft the wing span is improved and winlets at wings tips are used to ,
reduce the induced drag. In 1924 Prandtl [4], showed that a lifting system exists (a Best Wing
System) with the minimum induced drag among all the lifting systems with the same span
and total lift. This configuration is a biplane with straight wings, parallel and lying in a plane
normal to the flow direction, with their tips connected by two vertical and properly shaped
surfaces, so as obtaining a boxed shaped wing system. Due to the Munk theorems, the sweep
angles of the two wings do not modify the Prandtl results, so that the PrandtlPlane concept
can be applied to transport aircraft in transonic and supersonic condition too. In the paper of
Prandtl, an approximated procedure was used (without any other information).
Now we recall some useful results on multiplanes, for convenience sake.
The induced drag, Dm, of a monoplane is the following:
(2.1)
Dm =
L2
qπb 2
,
where q is the dynamic pressure, L the total lift and b the wing span. The induced drag of the
biplane can be expressed as the sum of the self-induction drag of both the wings (the same of
Eq. (2.1)) and the mutual induction drag. Denoting the wings with subscripts 1 and 2, and
with obvious meaning of the symbols, the induced drag of the biplane, Db, results:
(2.2)
Db = D11 + D22 + 2 ⋅ D12 =
2
2
1  L1
L
LL 
 2 + 22 + 2 ⋅ σ 1 2  .
πq  b1
b1b2 
b2
The term σ indicates the mutual influence coefficient and depends on the geometry of the
system. A rigorous expression for σ does not exist, but only numerical approximations are
available. In the case b1=b2=b (very important in the practise) Db is minimum and
5
The PrandtlPlane concept
σ =
(2.3)
1
,
1 + 5.3 h b
for values of h/b in the 1/15 to 1/4 interval. In general, denoting L = L1 + L2 the total lift,
r = b2/b1 the ratio of the wing openings (0 ≤ r ≤ 1), letting L2 = Lx, (hence L1 = L(1-x)), one
obtains from the condition dDb/dx = 0:
x=
(2.4)
r −σ
1
r + − 2σ
r
,
and from Eq. (2.2) one finally obtain:
(2.5)
Dbmin =
1−σ 2
L2
⋅
.
πqb12 r  r + 1 − 2σ 


r


Hence the induced drag of a biplane is minimum when r is maximum in the interval [0-1], or
when r=1. In this case, from Eq. (2.4) one obtains x=1/2, or in other words, the minimum is
reached when the lift is equally distributed in the two wings (L1=L2=L/2).
The expression (2.5) for the minimum induced drag of the biplane becomes:
(2.6)
Dbmin =
L2 1 + σ
.
⋅
2
πqb12
The ratio κ = Db/Dm, referred to as efficiency of the biplane is obtained from Eq.s (2.6) and
(2.1) with b1=b and becomes:
(2.7)
Db
1+σ
;
=κ =
Dm
2
Taking Eq. (2.3) into account, one obtains the function Db/Dm = f(h/b) in Figure 1.
6
The PrandtlPlane concept
1
0.9
Db/Dm
0.8
0.7
0.6
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
h/b
Figure 1. Optimum efficiency of the biplane versus h/b.
The optimum biplane is more efficient than the optimum equivalent monoplane and, given
the wing span, the induceddrag decreases for larger spans, h.
An optimum three-plane exists; the efficiency of the optimum three-plane is better than that
of the optimum biplane. And so on up to an infinite-plane. The best infinite-plane is
equivalent to a box plane in wich the vertical wings generate the same tip vortex distribution
of the infinite plane.
Figure 2. Prandtl boxplane
7
The PrandtlPlane concept
This system is the Prandtl Best Wing System when the lift distribution along the vertical
wings is butterfly shaped. The Prandtl result is shown in Figure 3.
1
Biplano
0.9
Best Wing System
Db/Dm
0.8
0.7
0.6
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
h/b
Figure 3. Efficiency of biplane and of Best Wing System versus h/b.
So, in the case of h/b=0.15 the induced drag reduction of the Best Wing System with respect
to the equivalent monoplane is about 27%.
Recent results [6] allowed to gain the following results:
-
On the horizontal wings, the liftdistribution can be split into a constant and an elliptic
contributions.
-
The lift is equally distributed on the two wings.
-
On the bulks the lift distribution is linear, with the load directed outwards in the upper
part and inwards in the lower part.
-
There is an optimum ratio of the value of the lift at the wing extremity (Γmin) to the
peak of the circuitation (Γmax). This optimum value depends on the h/b ratio.
8
The PrandtlPlane concept
Figure 4. Ideal lift distribution on the boxplane
9
The PrandtlPlane concept
1.3
A PrandtlPlane aircraft according to Vision 2020
This thesis aims at showing the preliminary design of a PrandtlPlane aircraft, to be assumed
as the prototype of a new family of medium size aircraft with high load capacity and high
flexibility of use.
The aircraft is made of two swept-wings, with opposite sweep angles, connected at their tips
by aerodynamical surfaces.
The importance of the lateral wings has been already shown from the aerodynamical point of
view. The structural design of the lifting system is well underlined so far.
Infact, the lateral wings transmit internal loads from a horizontal wing to the other and
provide cynematical links between them (Figures 1 and 2).
Figure 1. Detail of the wing bulk
Figure 2. PrandtlPlane’s wing
The fuselage is enlarged horizzontally. The rear wing is positioned over the fuselage and
connected to it by two fins.
The front wing crosses the fuselage under the cargo floor and, the cargo compartment is
wider than in every other conventional civil aircraft.
Figure 3 illustrates the reference configuration which was studied (only at a preliminary
stage) to prove the feasibility of the project.
10
The PrandtlPlane concept
Figure 3. PrandtlPlane
11
The PrandtlPlane concept
The number of parameters wich define this configuration is much larger than in the case of
conventional configurations with the consequence that a wither range of options are available
and the possibility of optimization are improved.
From a structural viewpoint, the PrandtlPlane concept presents many possible advantages
with respect to traditional configurations. The most important are:
-
The total wing span is limited with respect to a traditional configuration without drag
penalty and the aeroelastic problems are less severe, even if the local stiffness is smaller
(however, more research is needed on this topic).
-
The wings of this configuration are characterized by a weight reduction due to the
possible intensive use of composite materials, combined with the absence of the
attachments of the engines (in the configuration with the engines in the rear fuselage)
and of the main landing gears.
-
The transmission of the lift forces to the fuselage occurs through an overconstrained
attachment, with a variety of paths. This property has a great importance on fatigue.
-
The problem of the divergence of the wing with negative sweep angle can be solved by
the stabilizing effect of the wing with positive sweep angle, connected to the first one at
the tip;
-
In cruise conditions, the lift forces are distributed between both the wings, nearly in the
same amount.
-
The fuselage is equivalent to a doulby supported beam, the supports being the front and
rear wing attachments; so the fuselage bending moments are zero in the connection
between fuselage and wings, contrary to conventional aircraft and, during touch down,
the fuselagebending stresses relax the stresses in flight.
In optimum aerodynamical conditions the lift is equally distributed among the two wings
with the maximum advantage in terms of drag . This conditions may be achieved with a
proper ratio of the two lifting surfaces , with a suitable choice of the profiles and links,
and by taking better advantage of the high aerodynamical efficiency of the central wing
sector of the rear wing (between the two fins) due to the aerodynamical characteristic of
the channel defined by the top fuselage, bottom rear wings and lateral fins.
-
A very general kind of longitudinal control can be realized with pure pitching moment or
with a moment associated to lift forces (for example with the elevator positioned on the
front wing as in the canard configuration), by means of opposite rotation of surfaces on
the front and rear wing. Such a control surfaces would be of reduced size, thanks to the
large arm of the couple.
12
The PrandtlPlane concept
Figure 4. PrandtlPlane longitudinal control system
-
The lateral control can be obtained by means of control surfaces set on the two fins and
on the wing bulks.
The lateral stability can be controlled by the presence of diedrical angles of both the
upper and lower wings. The wing bulks give a stabilizing contribution to the sidedirectional dynamic.
The eigenmodes of the aircraft are completely different from conventional aircreft, with
positive effects on the internal comfort, noise on passengers and also on the flight
qualities
-
The ailerons could be positioned on the rear wing; they could be use as flaperons; in
this case both the wings are fitted with high lift devices along the whole span (slats and
flaps), and the condition of Best Wing System coul be obtained also in take off and
landing with lower noise and noxious emissions.
-
The flaps will extend over a smaller fraction of the chord because they will be
distributed for a large opening along the wings. Consequently, the feedback systems of
the control surfaces will be simpler and the low speed configuration more favourable
than in conventional aircraft.
-
The fuel can be loaded in both wings. The control of fuel consumption allows the
control of the attitude of flight of the aircraft.
-
The architecture of the Prandtlplane implies a new design of the main landing gear
which must be positioned in nacelles beside the fuselage. The main landing gear is
13
The PrandtlPlane concept
made of many legs with many wheels of small diameter which can be contained inside
a bay between two subsequent fuselage frames.
The current research stage on the PrandtlPlane aims at studying the large potentialities of the
present configuration.
The present work aims at providing a preliminary scaling for a aircraft configuration for
goods and for 250 passengers or more, as a first step of a future industrial applications to the
civil transport aviation of the next decade, considered of a strategic importance for the next
future market.
The PrandtlPlane configuration has the potential for achieving, all together, the top levels
objectives identified by the European project Vision 2020 :
The challenge of low emissions and noise towards the quite aircraft
The objective of a substantial reduction of pollution and of a decrease by 50% of the noise
perceived at the boundaries of the airfield may be reached with a synergic action in several
domains, which include weight reduction and use of new propellers.
This objective can be obtained for the PrandtlPlane thanks to the pretty high values of CL
which can be achieved with a high lift device system extended on both wings in the take-off
and landing. So smaller propellers can be used with smaller emissions. Besides the vorticity
released by the PrandtlPlane into the field is reduced with respect to a conventional aircraft.
The large hull capacity would allow, in principle, to set H2 or CH4 tanks for the possible
adoption of propellers of advanced conception.
The challenge of safety
The final objective is reducing the frequency of accidents by 80% in spite of a three-fold
intensity of air traffic, operative 24 hours a day and in every meteorological condition.
The following design features of the Prandtlplane make it a good candidate to satisfactorily
reach the objective of:
-
Allocating a rest room for the pilots beside the cockpit.
14
The PrandtlPlane concept
-
Pitch Control by means of pure couple improves safety close to the ground.
-
Control is also guaranteed by large angles of attach, thanks to the large aerodynamical
stability of the rear wing;
The challenge of quality and affordability
The following objectives are linked to such an aspect:
-
Wider choice options for the passenger. Beside the price of the ticket, this depends on
the time necessary to reach destination (including the time spent in the airport), from
the availability of particular services, from the space availability on board and board
activities, from an enhanced comfort index. The larger size of the fuselage and the
enhanced comfort on board of the Prandtlplane reduces the economy class syndrome.
-
Reduction of the flight costs, thanks to the reduction of the costs of the aircraft,
maintenance, crew, fuel and for the flight taxes and parking. Reduction of the latter
ones depends also on reduction of the grounding time. This can be obtained by the
Prandtlplane thanks to the less time spent for boarding and landing operations for goods
and passengers as it will be illustrated in Chapter 3.
15
The PrandtlPlane concept
References
[1]
R.J. Acton, British Airways’ Requirements for a New Large Airliner, presented to
the Royal Aeronautical Society, October 1993.
[2]
Torenbeek E., Synthesis of subsonic Airplane Design, Kluwer Boston Inc.,
Hingham,Maine 1982
[3]
www.desktopaero.it (C-wings design by Ilan Kroo)
[4]
L.Prandtl, Induced Drag of Multiplanes, NACA TN-182, 1924.
[5]
E. Pistolesi, Lezioni di Aerodinamica, Vallerini, Pisa 1924
[6]
A.Frediani, G. Montanari, Problemi di minimo della resistenza indotta in sistemi
portanti chiusi, Graduate thesis in Mathematics, University of Pisa 1998.
[7]
A.Frediani, ThePrandtlPlane, ICCES 4, Madeira 2004
16
Geometry Generation
CHAPTER 2
Geometry Generation
2.1
Parametric geometry generation
The preliminary aerodynamical design of the present aircraft is carried out by means of a
CFD (Computational Fluid Dynamics) code and relies upon the computer to solve the
equations of a flow around a body, with computational volume, made of cells.
The three main phases of a CFD analysis are:
-
Generation of aerodynamical model and the relative computational domain.
-
Generation of the surface volume grid.
-
Computation of the aerodynamical field and analysis of the results.
The generation is made by defining a proper number of parameters to be changed during the
development of the configuration. The grid generation cannot be made automatically but we
need to refine the mashes according to the aerodynamic force gradients.
In the present analisys additional constraint was the limitation of the computational power,
wich limited the number of cells.
In general, the generation of the aircraft shape and that of the grid are consecutive and
distinct processes. This aspect is important due to the need of modifying the configuration; in
these cases it must be possible to generate quickly a new geometrical model and its
conforming grid.
At the At the Department of Aeronautical Engineering of the Pisa University a code named
MSD (Multibody Shape Design) was realized; it was a MATLAB® environment. MSD is a
fully parametric tool, dedicated to geometry generations for CFD simulations. The parametric
features and the flexibility of this tool will allow a remarkable time saving in the realization
and change of geometrical models. The same operations, made with modern CAD (Computer
Aided Design)
packages, like PRO/ENGINEER® or CATIA®, require a high degree of
experience from the operator and, in any case, do not allow the same speed in modifying the
parameters. The MSD package uses a dynamic database of cross sections and profiles. Using
modular functions, geometrical surfaces and links between the several parts with splines of
NURBS type are used. The re-shaping of the geometry with a variation of the parameters
defining the configuration is always possible by means of proper controls. The 3D surfaces
20
Geometry Generation
are constructed simply by stretching the cross sections or the airfoils available in the database
along properly defined directional lines in the 3D space.
MSD allows to export the surface grid both in DAT and IGES formats, so that the same file
can be used both for generating structural meshes and also volume grids for aerodynamic
analyses. The software makes use of some implemented GUI (Graphic User Interfaces) for
handling friendly the design parameters. Axial Symmetric bodies are generated section by
section. The body is also divided into an upper part and a lower part, separated by a side line,
that is the line defining the lateral contour of the body over the XY reference plane. The
center line is the curve of the origins of the local coordinate systems. The control section
lines define the body shape along the longitudinal direction. They are obtained from a
normalised section curve, that is a curve defined in an unit square and stretched, by a proper
choice of parameters, to the selected shape. The basic geometry of the body is obtained by
positioning a set of control section lines along the longitudinal axis in order to fit the
intersections between the support lines, previously defined, and the plane of the control
section line. Once the skeleton geometry has been defined, a set of regions between two
contiguous control sections, called bay, is identified. Now, is possible to generate a
parametric number of intermediate control sections in the bay, by linear interpolation. It can
be pointed out that this kind of body generation allows to define also a primary structured
grid on the body surface, by defining the number of sections and the points in the sections; a
typical result is shown in Figure 1.
Figure 1. Fuselage generation with MSD.
21
Geometry Generation
The generation process of the wings is similar to that for the body. The wing is created by
adding bay to bay, from the first to the last airfoil. The airfoils are defined by: sweep, twist,
dihedron and are referred to the main reference system of the wing itself. All the intermediate
points of the wings are obtained by interpolation between the first and last airfoils of the
bays. Each bay can be generated by extrusion, where the leading edge line, in Figure 2,
defines the direction of extrusion.
Figure 2. Detail of wing generated with MSD.
The holes considered here are defined as intersections between a wing and another wing or a
wing and a body. The hole is generated by a wing, which is considered as the penetrating
object and another wing or body which are the penetrated objects. The first step of the hole
generation process is that of defining the traces of the penetrating object on the structured
grid, on the surface of the penetrated body. This result is a closed curve or profile, relevant to
the projection of a wing over a body. The second step of the procedure is the modification of
22
Geometry Generation
the surface grid of the penetrated object. Once a projection is obtained, the structured grid of
the body surface is locally modified by doubling a body generatrix into the upper and lower
branch of the intersection profile.
Fillet are objects joining wing to body or wing to wing. A wing to wing fillet is simply
created using linear interpolations between the two airfoils to be joined. In the case of wing to
body fillet, the generation is more complex and besides, for aerodynamic reasons, an operator
needs to control the smoothness of the fillet in an accurate way. The shape of a wing to body
fillet can have a remarkable influence on the local aerodynamic field, especially in the
transonic range. The code MSD can allow one to join wing to wing without and with fillet; in
the first case, the hole in the body is introduced by the prolongation of the wing and, in the
second case, a second larger hole is generated on the body surface. This last hole is the fillet
contour on the body and it is obtained by an auxiliary bay. The auxiliary bay is obtained by a
linear interpolation between the wing root airfoil and an auxiliary airfoil positioned inside the
body (in the symmetry plane, for simplicity sake); the trailing edge of the auxiliary bay is the
prolongation of the wing trailing edge. The auxiliary bay allows us to final contour of the
fillet on the body. Of course, the root airfoil of the auxiliary bay is generated independently
of the wing characteristics and it is varied until a satisfactory fillet contour on the body is
obtained by the operator (Figure 3).
Figure 3. Wing auxiliary bay and wing real proyections contolling fillet shape.
23
Geometry Generation
Once the airfoil on the wing and the contour on the body are generated, the fillet surface has
to be defined. For this generation, we use the NURBS. The fillet surface is obtained by means
of the NURBS curves; they are the root wing airfoil, the hole wing/body and the hole
auxiliary bay/body, including inside the previous one. So, for any curve, three points are
defined on the three curves, as shown in Figure 3. The control polygon of each curve is
composed by three points: the start point on the wing root airfoil, central point on wing
intersection profile with body and the end point on the hole generated between wing root
auxiliary bay and the body .
Problems encountered during the present work were:
-
The reconstruction of the structured grid close to the intersection profile is particularly
difficult and a robust interpolation tool is necessary. The standard interpolation tools of
MATLAB® could bring to a bad quality of the grid, owing to the mathematical instability
of the splines, when the interpolation points become too close each other. In order to
solve these instability problems, the NURBS (Non Uniform Rational B-Splines) will be
introduced.
-
The function foreseen by the designers of the code MSD for generating surface grids
turned out in the impossibility of generating interface files IGES compatible with the
GAMBIT® software for generating the computational grid.
The problem is related to the fact that the surface of the solid is transferred from the MSD
as a set of regular rectangular panels and a set of points. This problem has been solved in
the new code release.
Figure 5. First version of MSD IGES imported in CATIA®
24
Geometry Generation
Figure 6. Fuselage tassellation detail in the first version of MSD IGES file
25
Geometry Generation
MSD - CATIA® interface
2.2
The problems found in the geometry generation with MSD software, forced us to use a
different procedure, while awaiting the new release of MSD.
The procedure used consisted into defining the geometry with MSD and importing it into a
modern CAD as a cloud of points.
The generation of the surface was realised by CATIA software through the following
operations (for example limited only to the fuselage).
1.
Reading of IGS file coming from MSD as a cloud of points in Digitized Shape Editor of
CATIA® environment.
Figure 1. Cloud of points comeing from MSD
2. Dissection of the cloud of poits with as many longitudinal cross-sections as the frames
employed in the MSD for the generation of the surface in the environment Quick Surface
Reconstruction
27
Geometry Generation
Figure 2. Clouds sections
3. Generation of new frames as cross-section plot between the crossplanes and the dotclouds
Figure 3. Curves from section
28
Geometry Generation
4.
Generation of surfaces, of holes, and links in environment Wireframe and Surface
Design
Figure 4. Fuselage’s Loft
Figure 5. Entire Aircraft
29
Geometry Generation
Moreover, the above procedure can be made automatically; in fact, it is possible to transfer
the matrixes of dots, which identify geometry, as EXCEL® files from the MSD code. Suitable
tools of CATIA® are able to read these matrixes.
These operations are possible for CATIA® only using EXCEL® files.
30
Geometry Generation
2.3
Assembly design in CATIA ®
The PrandtlPlane aircraft has been assembled in a modular way by CATIA®; this allows us to
modify the single components indipendetly.
The assembley of the whoole aircraft has been realised in Assembly Design of CATIA® and it
is made of the sum of subassembled parts (CATproduct files) which, in turn, are defined by
elementary parts (CATpart files) ) in which the single details are represented.
The complexity of the structure of the general assembled is sumarized by the logical tree in
Figure 1.
Figure 1. Main Assembly’s Logical Tree
Each component is referred to the same co-ordinates system; hence, a file of referenceframes is created in advance for the single component to be transferred into the assembled
aircraft.
36
Geometry Generation
By means of the Existing Component function, the subassembled parts have been correctly
transferred by means of the Snap function, as shown in the example of Figure 2.
3
2
1
Figure 2. Assembling procedure
The final check of a single assembled part is the interference check, an analysis of
interference among the various components has been done.
The total result is a check, with a certain accuracy, of the amount of the space available on
board, also through the introduction of manikins in the most critical areas.
The creation of these models has been made possible in Ergonomic Design and Analysis
environment, exploiting the Human Builder function.
37
Geometry Generation
Figure 3. Manikin Generation
Figure 4. Manikin use for ergonomic analysis
The previus work conducted to the result shown in Figure 5.
38
Geometry Generation
Figure 5. General assembly
39
Geometry Generation
References
[1]
Gasperini M., Lugli R., Saporito G., Strumenti per la generazione semiautomatica di
geometrie tridimensionali e grigle di superficie per l’analisi CFD, (instruments for
tridimensional geometries and surface grid authomatic generation for CFD analysis),
Aerospace Engeneering Department of Pisa.
[2]
Frediani A., Gasperini M., Saporito G., Development of a geometric and
aerodynamic grid generators for innovative aircraft configuration, Department of
Aerospace Engineering of Pisa Oct 2002.
40
PrandtlPlane Conceptual Design
CHAPTER 3
PrandtPlane Conceptual Design
3.1
Introduction and Customer requirements
A civil aircraft is designed to satisfy operative, commercial and safety requirements.
The aeronautical designing process is an interative process with a growing complexity in
which, starting from the requirements, a preliminary definition of a set of possible solutions
is carried out.
The design process can be divided into three phases: conceptual design, preliminary design,
detail design. The conceptual phase is developed by a few people with a deep experience in
different fields of aeronautics and with good ability in planning and management. They
identify the aims to be reached concerning loads and services and obtain the final definition
of an acceptable aircraft; these results are obtained in relatively short time and with a
minimum engineering engagement.
The preliminary designing phase requires a massive use of statistical and semi-empirical
models.
These models summarize an important and expensive knowledge gained, rarely available
outside the factory and characterized by quickness in foreseeing and ability of managing a
higher and higher number of parameters in order to define the weight.
During the initial phases, in which geometry is only vaguely outlined, very simple models
with rough prediction will be used. These models are the result of procedures that manage
few parameters (called First class by some authors, like Roskam).
After this preliminary stage the aircraft configuration is improved, to check if the limits fixed
by the conceptual design are respected; more sophisticated predictive models ( of second
class) could be used. The main parameter to be determined is the take off weight, that is the
sum of all the weights of the elements of the aircraft, of the fuel and the paying load. The
empty weight and the fuel depend on the take off weight and,hence, more iterative
estimations are required to assess the final result.
During this phase the aspects concerning Aeroelasticity and fatigue are also taken into
account and care is taken in the manufactoring of some structural elements of
major
importance; the final result is the so called Preliminary Design. Different configurations can
be examined on the light of direct operative costs and fulfilment of the design requirements,
until a final solution is identified. During the third phase of designing, the Detail Phase, the
41
PrandtlPlane Conceptual Design
components that must be produced are elaborated: each particular is designed to be produced
according to the previous fixed constrains in terms of weight and global geometry.
Once completed the above phases, the activities concerning manufacturing, tests and initial
delivery, are developed.
The architecture of a today civil aircraft is practically defined following the experience
gained in the past on similar aircraft. In the case of the Prandt1Plane the conceptual design
can not make use of statistical data and tests in the same way of a conventional aircraft;
anyway, in order to give a preliminary definition of the aircraft, some tools are used even
though some modifications are applied when needed, as shown later on. The main goal of the
present chapter is to define a possible architecture of the fuselage, in order to obtain a first
prediction of the take off weight (in Chapter 5), starting from the following initial
requirements:
- 258 passengers in two classes (business and economy);
- medium-long range aircraft (typically 6000 n.m.);
- large cargo capacity;
- sea level airports;
- takeoff runway length: 3000 m;
- cruise altitude: 10500 m.
Other solution with more passenger have been also defined, with the same external shape of
the 258 passenger solution. This preliminary analysis is carried out in order to show that
PrandtlPlane aircraft is flexible in use.
42
PrandtlPlane Conceptual Design
3.2
Fuselage Design
3.2.1
Introduction
The fuselage is the shell which contains the paying load, to be transported to a certain
distance, at a certain speed and, with a given internal comfort and flight quality for
passengers .
In the Vision 2020 of the European Community, already mentioned, a requirement for future
aircraft is the presence of a larger air volume available per passenger. In this prelimimary
analysis of PrandtlPlane aircraft the fuselage has been concepited in such a way to allow
more space available for passengers and more good and laggage than in a conventional
aircraft. Another important goal of this proposal is to obtain a quick loading and unloading of
passengers, goods, laggage and refuelling. The solutions proposed are preliminar and
enclosed in the Vision 2020 context, as possibilities for future aviation. As a matter of fact, it
is well known that a typical design criterion is to use the minimum diameter, that is the
diameter strictly necessary for drag reduction. The present preliminarly proposal intends to
apply this criterion as a case study of the PrandtlPlane aircraft (as we will show later on) even
thought a smaller fuselage is possible in framework of the PrandtlPlane configuration.
Figure 1 shows the drag coefficient vs. λF=
LFus
φ Fus
ratio, where Lfus is fuselage’s length and
Φfus is fuselage’s diameter. It is useful to fix a general trend and aligned with what said
above; it definitely suggests a further observation: the current values of λF, 10-11, underline
the importance given , also and mostly, to other considerations.
A smaller fuselage confirms to the traditional deriving criterion, due to Prof. Torembeck:
“the fuselage should be designed from the inside outwards and the skin should envelop the
load in such a way that the wetted area is minimum, thus avoiding breack away of the
airflow as far as possible”.
38
PrandtlPlane Conceptual Design
CD0
Transiction at nose Re=107
λF=
1
LFus
φ Fus
CDfrontal
0.04
2
CDwet
0.02
2.5
4
λF
Figure 1. Drag coefficients of streamlines bodies of revolutions at low speed
at zero angle of attach neglecting the upsweep angle contribution
- CDfrontal is the drag parameter due to the frontal area of the fuselage that grows up for slim fuselages
- CDwet is the drag parameter due to the wetted surface of the entire fuselage that decreases for slim fuselages.
39
PrandtlPlane Conceptual Design
3.2.2
Internal layout according to AEA Regulations
Fuselage
The shape of the fuselage is related to mission requirements, to wing configuration adopted
and results as a compromise between requirements of aerodynamics, structures and
ergonomics (Figure 1).
Figure 1. A possibile fuselage for PrandtlPlane
The aerodynamical efficiency of the wing system depends on the non dimensional gap, that
is the ratio of the vertical distance between the wings and the wing span. Figures 1 and 2
shows two views of the aircraft in the case of two engines and in low noise position (engines
mounted over the front wing). This configuration allows one to obtain a high aerodynamical
efficiency together with the static stability of flight. This is obtained by positioning the rear
wing over the fuselage and connecting the same by two fins.
40
PrandtlPlane Conceptual Design
Figures 2-3. details of the position of wingback-fin joint
Both aerodynamical and structural considerations suggest that the distance between the fins
must be as large as possible. Consequently, the fuselage width is nearly constant along the
longitudinal axis up to the end. The result is a wedge-shaped tapering of the fuselage stern,
rather than conical as in conventional aircrafts (Figure 4).
41
PrandtlPlane Conceptual Design
Figure 4. Detail of the tail
Figures 5. Frontal view and dimensions
42
PrandtlPlane Conceptual Design
Figures 6. Lateral view and encumbrances
This section shape of the fuselage is optimum as far as load capability (passengers and cargo)
and the main dimensions (in Figure 5 and 6) are 46.5 m long and 7 m large.
With such a fuselage section, the structural design becomes non conventional and
experimental data are not available at the moment to optimize the structural weight. On view
of a structural optimization the presence of struts is foreseen both in cargo the vane and in
the passenger compartment (Figure.7).
Figure 7. Struts on symmetry plane
In the solution shown in Figure 6, a rear door is placed in the back fuselage.This door is very
large and, hence, it could be not convenient for the structural efficiencyans safety as far as
pressurizatio. Besides it could be difficoult to position the rear bulkhead.
43
PrandtlPlane Conceptual Design
Another possible configuration (Figure 8) would be obtained with a pressurization of both
decks. In such a case the bulkhead must embrace even cargo deck and the cargo doors in the
tail must be moved to the side of the fuselage. The containers are imbarked laterally, without
any disadvantage; a second cargo door is positioned in the front fuselage
Figure 8. Back cargo door on the side of the fuselage
Figure 9. Perspectic details of the bulkhead position
Passengers Deck
Two classes were located on the deck in the following way:
-
48 in business class, accommodated in the front part of the aircraft.
44
PrandtlPlane Conceptual Design
-
210 in economy class, accommodated in the rear part of the aircraft.
The layout of the interior was made following the A.E.A. (Association of European Airlines)
[5] regulations and is shown in the following figures. Two aisles have been adopted with a
larger width than present aircraft.
Figure 10. Plan view of passenger deck
Figure 11-12. Seat’s dimensions of business (left) and economy class
Platforms, provided with service stations, have been foreseen in front of them (Figure 10).
The sizes of the all doors are: height: 1.93 m and width: 1.07 m, so that they can be certified
as emergency exits of class A (Figure 13 and 14, [8]);.
The windows are rectangular shaped with rounded corners, 320 mm height and 300 width.
45
PrandtlPlane Conceptual Design
The window centres are positioned 1m above the deck level; the pitch between a window and
the next one is estabilished into 500 mm [5].
Figure 13-14. Classification of emergency exits and their dimensions
The present safety requirements are fully satisfied; in particular, the locations and dimensions
of the safety exits in order to permit an easy emergency evacuation a large space in front of
any emergency exit has been provided.
Along the cabin the following services are located:
-
toilette:
one for 30 passengers in business class;
2
one for 40 passengers in economy class. Area of every toilet ~1.2 m
2
-
galley:
0.05 m per passenger.
-
wardrobe:
0 ÷ 0.065 m per passenger.
2
These services are located in “islands” (as in the majority of the layouts currently adopted) as
shown in following figures.
46
PrandtlPlane Conceptual Design
GALLEY
TOILETTE
TOILETTE
Figure 15. First island, for the business class.
TOILETTES
Figure 16. Second island, for the economy class
47
PrandtlPlane Conceptual Design
TOILETTE
TOILETTE
Figure 17. Third island dimensions
GALLEY
GALLEY
Figure 18. Fourth island dimensions
The service area in the tail cone depends on the longitudinal position of the rear bulkhead,
which corresponds to the rear longheron of the fin (figure 19).
In the present proposal, the available service area is so large that a more advanced position of
the rear bulckhead is possible; even in this event the available space should be above the
minimum request.
48
PrandtlPlane Conceptual Design
TOILETTE
TOILETTE
~ 3 m2
~ 3 m2
GALLEY
GALLEY
Figure 19. Fifth island dimensions related to the position of bulkhead
Figure 20. Detail of liveability of business class
The front fuselage could be used in different ways. One is to provide a sitting room, equipped
with proper windows. In the present context we show a simple utilisation as a service area,
the passage to the pilot’s cockpit and the rest room (Figure 21.)
49
PrandtlPlane Conceptual Design
Figure 21. A possible solution for communicability between pilot’s room and passengers’ deck
The remaining space can be allocated for the board systems.
According to current regulations, the total number of crew members, pilots and flight
assistants, is of 9 units, consisting of:
-
2 pilots
-
7 flight assistants
A rest zone of about 19 m2, located behind the cockpit, is foreseen for the crew, as the main
carrier companies indicate as desirable.
50
PrandtlPlane Conceptual Design
Figure 22. Resting room
Figure 23. Definition of the pilot’s view according to [10].
51
PrandtlPlane Conceptual Design
Pilot’s cockpit
The cockpit was designed by taking into careful consideration the following aspects:
-
The innovative and peculiar shape of the fuselage imposes to set the cockpit in a far
advanced and, at the same time, lowered location, to comply with the requirements of
visibility envelop shown in Figure 23 and, in a cleaner form, in figure 24, 25, 26.
Figure 24. Horizontal angles of view envelopes
52
PrandtlPlane Conceptual Design
Figure 25. Frontal angles of view envelopes
Figure 26. Canopy generation
53
PrandtlPlane Conceptual Design
The location of the cockpit at the level of the passengers deck is not possible, because
it makes it very difficult to satisfy the requirements set by the view envelope .
-
Recent tragic terroristic events, have emphasized the importance of safety
considerations, with the need of isolating completely the cockpit from the rest of the
aircraft, for avoiding intrusions.
-
The particular case of the fuselage considered, with the cockpit located below the
passenger deck and accessible only to the crew, allows for a complete separation from
the passengers deck.
Cargo deck
The front wing, due to the reduced thickness (nearly the half of a conventional aircraft)
crosses the fuselage under the cargo deck; the fuselage is conveniently enlarged in this
reagion (and usable for locating systems). The main landing gear is located laterally of the
fuselage. Hence, the cargo compartment is as long as the complete aircraft, and the vertical
gap between the two wings is maximized. The internal volume of the cargo compartement is
406 m2, and allows to embark 38 LD1 or 34 LD 3 containers.
The access to the cargo deck is possible through two doors in the tail section and two more in
the front section as shown (Figures 27 and 28). The rear cargo doors, due to the before
mentioned reasons, can be conveniently located in lateral position, as in figure 29.
Figure 27. Cargo doors
Anyway, in a freighter aircraft, without cabin pressurization, the solution in figure 27 can be
applied as well.
54
PrandtlPlane Conceptual Design
Figure 28. Isometric view of cargo deck loaded with 32 LD3.
Figure 29. Cargo doors detail in case of cargo deck pressurized.
The position of the front cargo doors yields particularly critic the position of the leading edge
of the front wing during loading and unloading operations. A further optimization design
phase would lead to a new design of the rest room and to a different positions closely
correlated to a good solution of the cargo doors (Figure 30 ).
The advantages of these solutions will be shown in the following section 3.2.3.
Main landing gears
The position and size of the main landing ghear depend on the position of the centre of
gravity, on the aerodinamic performances of the aircraft at low speed, etc..
In the present activity, only preliminary assumptions are possible. The items of the main
landing gear design are the followings:
55
PrandtlPlane Conceptual Design
Figure 30. Lateral cargo operations
a)
the main landing gear is positionated at the fuselage sides in order to allows a
continuous cargo compartement.
b)
The solution adopted is modular, in the sense that it can be moved forward or backward
in the fuselage without any modification of the main landing gear.
c)
The main landing gear is positioned inside lateral sponsons to be optimized in the
aerodynamical context. The solution shown in this thesis is indicative.
56
PrandtlPlane Conceptual Design
3.2.3
Comparisons in term of ergonomic aspects
The phase of preliminary design of the fuselage includes ergonomic considerations, with
reference with two aircraft of the same design that is:
-
Boeing 767-300 ER
-
Airbus A330-200
The Boeing 767-300 ER is a twin engine aircraft (Figure 1) derived from the model 767-200,
which became operational in 1986. It hosts 269 passengers in two classes, 24 in business class
and 245 in economy class, housed on a surface of 184 m2 and in a volume of 484 m3. It can
also embark 30 containers of type LD2 or 15 LD1 containers; the maximum fuel volume is 93
m3 [3] .
Figure 1. Boeing 767-300 ER
The Airbus A330-200 (Figure 2) originated from a joint project of aircraft A330-A340, is the
first aircraft to be designed completely with the CAD technology. The A330-200 aircraft
originated from the A330-300, the basic design of the twin engine versions of the project. It
carries 253 passengers in three classes, 12 in first class, 36 in business class and 205 in
economy class, housed on a deck of 225.24 m2 and in a volume of 337 m3. It can load up to 26
LD3 containers and the maximum capacity of the fuel tanks is 140 m3 [3].
57
PrandtlPlane Conceptual Design
Figure 2. Airbus A330-200
Figure 3. Containers LD1
58
PrandtlPlane Conceptual Design
Figure 4. Containers LD2
Figure 5. Containers LD3
The following characteristics were taken into consideration for the comparison:
•
Comfort in the passengers deck;
•
Loading capabilities of the cargo deck;
•
Loading and unloading capabilities for passengers and cargo;
59
PrandtlPlane Conceptual Design
Passengers comfort
In order to quantify the comfort of the passengers and compare different aircraft, proper
indexes needs to be defined,in particular,two indexes were considered as comparison; the ratio
of the passengers number (PN) to the floor area (FA) and the ratio of the passengers deck
volume (PDV) to the passengers number.
•
Load index
FA
PN
=
Floor.area
Number.of . passengers
m2
•
Comfort index
PDV
=
PN
Passenger.deck.volume
Number.of . passengers
m3
Data relative to the three aircraft are reported in Table 1, with reference to layouts hosting two
passenger classes.
PP
A 330 200
B 767 300
Passengers Number
258
293
[Ref.3]
269
[Ref.3]
Floor Area
240
225
[computed]
184
[computed]
Passengers Deck Volume
500
337
[computed]
484
[Ref.3]
PDV 3
[m ]
PN
1.4/1.6
1.15
1.79
FA
[m2]
PN
0.93
0.76
0.68
Table 1. Data for comparisons
The area of the passenger deck for A330-200 was obtained with CATIA® ,even though the
available data are not complete (Figure 6).
60
PrandtlPlane Conceptual Design
225 m2
Figure 6. Determination of Floor Area of the A330 200
With reference to the parameter
FA
, the different capabilities of taking advantage of the
PN
potentialities offered by the surface of the passengers deck in the different cases, are
emphasized.
Consequently it turns out to be impossible to make a realistic size comparison.
It becomes therefore necessary to make homogeneous the parameters for the comparison.
Thus the number of passengers was computed, which would allow the PrandtlPlane to equal,
in both cases, the load index of the competitive aircrafts.
It appears that the passenger accomodations for B 767 and A 330 are fixed. In the case of
PrandtlPlane the low density configuration is one of the possible accomodations.In order to
obtain the same
FA
coefficients other high density passenger configuration could be design in
PN
particular:
•
312 passengers to have the same value of the A 330 200 (54 more than in the proposed
layout)
•
350 passengers for the B 767 300 ER (92 more than in the proposed layout)
61
PrandtlPlane Conceptual Design
1
2
3
4
Figure 6. Passengers’ deck of PrandtlPlane High Density (1), PrandtlPlane low density (2), B767 (3), A330 (4)
62
PrandtlPlane Conceptual Design
The new comfort indices becomes:
•
m3
 PDV 

 = 1.6
passenger
 PN  PP
m3
 PDV 
= 1.15


passenger
 PN  A330200
•
m3
 PDV 

 = 1.4
passenger
 PN  PP
m3
 PDV 
= 1.79


passenger
 PN  B 767300
The results obtained show a comfort index better than that of the A330 200 but lower than the
B767 300. This result displays once more the good ergonomic potentialities of the particular
shape of the fuselage.
The layout proposed has only an indicative value and it is far from an optimization of the
volume available, which would require more detailed knowledge, of important factors like
longitudinal position of bulkhead, position and volume of the cockpit for systems,etc.
The number of passengers can be increased in different ways as, for example:
-
by reducing the very large space in front of the central exits, thus dropping the four
emergency type A exits ;
-
by reducing ( 12 cm ) the width of each aisle in the economy class. In this way it would
be possible to set two additional seats in the central zone, provided one could reduce the
diameters of the central struts;
-
by reducing the width of each aisle in the business class. In this way it would be possible
to set an additional seat in the central zone, provided one could reduce the diameters of
the central.
-
by utilising the wide surfaces usable in the stern and front areas with a more rational
distribution of passengers and service platforms.
Considering the high flexibility of this project, two configurations has been provided:
Configuration 1
Changes done:
-
reduction of corridors width in Economy class from 674 mm to 420 mm
-
reduction of corridors width in Business class from 715 mm to 480 mm
-
introduction of a couple of seats near the simmetry plane in Economy class.
-
introduction of a line of seats in the central zone near the simmetry plane in Business
class.
-
Reduction from 4 emergency exits type A, to 2 type A and 2 type I, each side of airplane.
63
PrandtlPlane Conceptual Design
-
Higher passenger distribution in isles in front of emergency exits.
Results:
With those changes it is now possible to transport 318 passengers divided in 264 in economy
and 54 in business.
Remarks:
-
It should be possible to increase passengers in economy class just reducing the high
number of seats in business.
-
In this configuration, the area of the passengers deck located near the prow of the
aircraft, remains unusable becouse it is not enough high to locate seats; more
refinements are possible to improve the passenger capacity.
Figure 7. Plant view of configuration 1
Configuration 2
Operations done:
-
Fuselage has been stretched out 2 m near the sponson, where fuselage has constant
section. In this way an optimisation of passengers deck is obtained.
-
Area reduction of the little rest room just beside the pilot’s cabin.
-
Realisation of a zone located between the cargo vane and the pilot’s cabin, in wich
locate other passengers.
-
Reduction of corridors width in Economy class from 674 mm to 420 mm
-
Reduction of corridors width in Business class from 715 mm to 480 mm
-
introduction of a couple of seats in lines near the simmetry plane in Economy class.
-
introduction of a line of seats in the central zone near the simmetry plane in Business
class.
-
Reduction from 4 emergency exits type A, to 2 type A and 2 type I, each side of airplane.
-
Higher passenger distribution in isles sited in front of emergency exits.
64
PrandtlPlane Conceptual Design
Figure 8. Detail of configuration 2
Figure 9. Detail of configuration 2
Results:
With those changes it is now possible to transport 329 passengers, 270 in economy, 49 in
business and 16 in first class.
65
PrandtlPlane Conceptual Design
Remarks:
-
With a different layout,36 economy seats more, can be obtained and the total number
becomes 354 passengers.
Figure 10. Plant view of configuration 2
Loading capabilities of the cargo deck volume
Data related to the volumetric capacity of cargo bays for the three aircrafts under
consideration show the large conceptual differences of the respective designs .
The values obtained for the Volume Cargo Deck (VCD) are the following [3]:
PrandtlPlane
406 m3
Airbus 330 200
186 m3
Boeing 767 300
102 m3
The large differences of the data depend mainly on two reasons:
-
the shape of the front section;
-
the different wing configuration which, in case of the Prandtlplane, allows the central
section of the front wing to cross the fuselage below the loading deck; in this way it was
possible to avoid the interruption of the cargo deck, as in figure 7, obtaining the
maximum possible load capacity (Figure 8).
66
PrandtlPlane Conceptual Design
Figure 7. Conventional cargo deck diveded into two zones
Figure 8. PrandtlPlane cargo deck charged with 38 containers LD1
Boarding and unloading of passengers and cargo
The large continuous cargo deck allows to provide the fuselage of four accesses for loading
and unloading goods and laggage. This solution is very useful, infact in the case of a
conventional aircraft , the cargo load and offload operations are not critical, as shown in
table1; but it would be the most critical in the case of the cargo embarked in a PrandtlPlane.
67
PrandtlPlane Conceptual Design
Table 1. Tipical report of terminal operation time for a long range commercial aircraft
The result is a large time saving, even thought, at present, it cannot be estimated. Anyway it
can be easily realised that it is now possible to load and unload cargo at the same time by a
continuous flux of containers (they could be unloaded by rear doors and at the same time,
loaded by the front doors or reverse). In the figures below, the operations are carried out by
the means of ramps, to save time;
68
PrandtlPlane Conceptual Design
Figure 9. Loading operations from the four available cargo doors
Figure 10. Loading operations from the two rear cargo doors
69
PrandtlPlane Conceptual Design
Figure 11. Loading operations from the two forward cargo doors
Figure 12. Loading operations from the right forward cargo door
70
PrandtlPlane Conceptual Design
Figure 13. Loading operations from the left forward cargo door
Figure 14. Loading operations
71
PrandtlPlane Conceptual Design
Concerning the boarding of the passengers, two access doors in the front of the aircraft are
used, linked to the boarding halls of the airport by mean of passenger connections.
The operations involving passengers are separated from loading and unloading of container.
Passengers embarcation could be done using both the sides of the airplane as shown in the
sketch in Figure 14, because the aircraft fuselage is sufficently wide. It could be a way for
saving time.
72
PrandtlPlane Conceptual Design
3.2.4 Friction drag of the fuselage at low speed
Drag Forces
In the textbooks of aerodynamics the drag force is usually defined as the component of the
aerodynamic forces in the direction of the velocity vector. The drag is usually split into
components, according to their physical origins; one possible classification of the several
components is shown in Figure 1 [7] .
Skin friction drag
Profile drag
Total drag
Form drag
Viscous
Lift forces
Induced drag
Inviscid
Wave drag
Figure 1. Drag classification
The total drag can be split into a component normal to the surface, named as lift force, and a shear
drag. This depends on the viscosity of the fluid:
surface of the body, it results the so-called drag.
τ
=
 ∂ u
 ∂ y
µ 



and by integrating over the
y = 0
The form drag (or boundary layer pressure drag) results from the change in pressure distribution
due to modifications in the boundary layer. It is essentially due to the existence of viscosity,
because in an inviscid fluid, the resultant of drag forces in nil (D’Alembert Paradox).
The form drag depends therefore on the boundary layer which implies a distribution of stresses on
the body different from the distribution which would exist in case of inviscid potential flow. The
difference is small for bodies with aerodynamically optimized shape, in which the boundary layer
thickness is small, while it is large in case of bodies of blunt shape, in which a separation of the
boundary layer occurs.
73
PrandtlPlane Conceptual Design
For an aircraft in cruise flight, the skin friction drag accounts for about 50% of the total drag the
friction drag is computed by solving the boundary layer problem.
Today’s numerical methods based on finite element techniques, combined with the availability of
powerful computers, would make a solution of the boundary layer problem an attainable task.
According to NASA reports [13], however, the hardware capabilities are limited to a few
specialized research centres.
In the stage of preliminary design, the only possible approach consists in the application of a
computational technique based on the so called Flat Plate Analogy.
The conceptual design of the fuselage is founded on the basic considerations, that its shape
approximates as closely as possible a streamlined body. Using meridian lines with smooth
curvature variations, the designer tries to avoid an early flow separation. Hence, the most crucial
part of the fuselage design is the final part and, in particular, the rear fuselage angle, that must not
exceed 10-12 degrees. An upsweep of about 25 degrees can be tolerated in cargo aircraft. In these
aircraft the blunt shape of the tail produces a characteristic vortex configuration which minimizes
the drag increment due to the lack of streamlined geometry of the tail itself (Appendix B).
In the aerodynamic design of fuselages in take off and landing, the ground effect have to be taken
into account, as well. The contribution of the Upsweep angle to the total drag will be illustrated
later on.
Flat Plate Analogy
Assuming that the follows preliminary conditions are satisfied:
•
The fuselage have the characteristics of a streamlined body
•
surface protuberances are not present;
•
t
airfoil .thickness
=
< 0.25;
c mean.aerodynamic.chord
•
Φ fuselage.diameter
=
< 0.25, 0.35;
l
fuselafe.lenght
•
the cross section varies gradually;
•
small angles of attack;
•
cruise Mach number is assumed as the Drag rise (M = 0.85);
In the present aircraft, CD0 is given by the sum of two components:
74
PrandtlPlane Conceptual Design
CD0 transonic= CD0 subsonic+∆CD0 Drag Rise
(4.1)
The drag coefficient CD0
subsonic
is evaluated for the fuselage alone, independently of the other
components of the aircraft; this assumption is suggested by the fact that subsonic aerodynamics is
linear.
Other important remarks are the following:
1.
In a PrandtlPlane, the non-dimensional coefficients (e.g. CLα, Cmα ) are obtained by
assuming the total wing (front and rear ) surfaces; in a conventional aircraft, the tail
surface is not considered ( the equilibrium in pitch is not taken into account ). Hence, a
direct comparison of non dimensional coefficients, is not correct.
2.
The fuselage of a PrandtlPlane is totally different from a conventional one; the main
difference regard the fuselage shape and the effects introduced by the vortex generated by
the unconvenctional tail cone of the PrandtlPlane. The flat plane analogy has been
developed for fuselages with a double taper ratio (as the majority of the civil planes) and
a not single, as the present one. This peculiar configuration is much more similar to
military Cargo. More details are given in Appendix B.
Hence, the comparison of the three aircraft ( PP, A 330, B 767 ) needs to be assumed in an
homogeneus way, by considering the fuselage indipendently of the drag forces due to the lifting
system. Some more details are given in the following.
Evaluation of the parasitic drag coefficient
Within the frame of the flat plate analogy [1], the parasitic drag coefficient (CD0-subsonic) of
the aircraft is given by
C D 0 subsonic =
(4.2)
∑C
Fi
FFi Qi SWi
i
S
+ C Dmisc
C Fi is the Flat plate skin friction drag coefficient for the i-th component, computed with the
flat plate analogy at zero angle of attack. The expressions of CF are well known:
(4.3)
CF =
1.328
Re
[12]
( For laminar flow )
(4.4)
CF =
0.455
(log Re )2.58 (1 + 0.144M 2 )0.65
[12]
( For turbulent flow )
75
PrandtlPlane Conceptual Design
with:
M
Mach number
Re
Reynolds number for the i-th component Re =
ρVl
µ
If the surface of the i-th component is “rough”, the friction coefficient CF is bigger than above.
This fact can be accounted for by using the smaller of the two Reynolds numbers given by:
(4.5)
ρVl
Re =
µ
l
Re = 38.21 ⋅  
k
(4.6)
ρVl
Re =
µ
Re = 44.62 ⋅ M
1.053
(for subsonic regime)
1.053
1.16
l
⋅ 
k
(for supersonic or transonic regime)
where:
l
Reference length for the i-th component;
V
Velocity;
ρ, µ
Density and viscosity of air;
k
Roughness of the surface.
FFi is the form factor of the i-th component and evaluates the pressure drag due to the viscous
separation. It is computed from the following relations.
(4.7)


4

0.6  t 
t
0.28
0.18
 1 +
  + 100 ⋅    ⋅ 1.34 ⋅ M (cos Λ m )
  x   c 
c 
   c m



60
f 
FF 1 + 3 +

400 
f

 0.35 
1 +

f 



















For wings and vertical and
horizontal tails
For fuselage
For nacelles
Where:
 x
 
 c m
Position, along the chord, of the maximum thickness of the profile;
76
PrandtlPlane Conceptual Design
Λm
f =
Wing sweep angle of the line corresponding to the maximum thickness
l
=
d
l
4
π
Amax
Amax
Area of the cross section of the fuselage or of the engines nacelles.
Qi is the interference factor for the i-th component (component interference factor) which
evaluates the reciprocal interference between components. Its numerical value is given by:
1.5
for the nacelles or for any other load appended to the fuselage or to the wing
(1.3 if the nacelles or the loads are mounted at a distance less of one diameter;
1 if the nacelles or the loads are mounted at a distance larger than one diameter).
1
For an high wing, a medium size wing or a low but well connected wing.
1.4
If the low wing is not well connected to the fuselage.
1
For the fuselage.
C Dmisc is a term which collects several contributions:
D
C Dmisc =  
+ C D 0 protuberances
 q  upsweep
(4.8)
Several cargo aircraft have a rather blunt airfoil in the rear part of the fuselage. This shape
enhances the drag forces beyond the value estimated with the form factor FF. This additional drag
is a complex function of the variation of the cross section of the fuselage and of the angle of
attack of the aircraft. It can be estimated by applying the relationship:
D
= 3.83 ⋅ u 2.5 ⋅ Amax
 
q
  upsweep
(4.9)
where:
u
Up-sweep angle of the fuselage.
(angle between the fuselage axe and tail cone, Figure 1)
Amax
Maximum cross section area for the fuselage; all the values have been obtained as
a CATIA® output :
Boeing 767-300
21 m2
77
PrandtlPlane Conceptual Design
Airbus A 330-200
25 m2
PrandtPlane
35 m2
The increase of drag forces due to several protuberances of the aircraft, as for instance the
antennae, is taken into account by increasing the CD 0 subsonic by a 2%.
In this situatuation the interest is turned exclusively to the C D 0 of the fuselage, and one can
consequently write the following fundamental relation:
CD 0 subsonic =
(4.10)
∑C
Fi
FFi SWi
i
S
+ CDmisc
where
Qi
1 (for the fuselage)
S
Wing gross surface is the surface visible from above considering also the part
included inside the fuselage.
In this case, due to the particular size of the PrandtlPlane configuration, the wing gross
surface for the referenced aircraft, has been increased by the tail’s surface.
Boeing 767-300
283 m2 (wing gross)+ 59 m2 (tail surface) [3] = 342 m2
Airbus A 330-200
361 m2 (wing gross) [3]+ 60 m2 (tail surface)1 =421 m2
PrandtlPlane
356 m2 (wing gross) calculated as a CATIA output
Sw
Fuselage’s wetted areas obtained as a CATIA output; they are:
Boeing 767-300
796 m2
Airbus A 330-200
863 m2
PrandtlPlane
985 m2
The numeric output relevant to the upsweep angle drag according to [1]. It can be otherwise
useful to show how relevant is this particular contribution in the total drag increase).
(4.11)
1
 D
 
= 3.83 ⋅ u 2.5 ⋅ Amax
 q upsweep
Defined as a CATIA calculation based on a sketch.
78
PrandtlPlane Conceptual Design
Where:
u
Fuselage up-sweep angle:
Airbus A 330 200
6.9 degrees
Figure 5
Boeing 767 300
9 degrees
Figure 4
PrandtlPlane
10 degrees
(7 degrees)
Figure 2 (Figure 3)
Upsweep angle 10o
Tail cone angle
Figure22 . PrandtlPlane up-sweep angle
Upsweep angle 7o
Tail cone angle
Figure 32. PrandtlPlane up-sweep angle
2
Figures are not in scale.
79
PrandtlPlane Conceptual Design
Up-sweep angle 9o
Tail cone angle
Figure 42. 767 300 up-sweep angle
Up-sweep angle 6.9o
Tail cone angle
Figure52. A300 200 up-sweep angle
 D
 
 q upsweep
Contribution to CD0 due to the Upsweep angles
Airbus A 330 200
0.0024
80
PrandtlPlane Conceptual Design
Boeing 767 300
0.0011
PrandtlPlane
0.0048
(0.0020 )
It can be remarked that the contribution of the sweep angle is remarkable. By collecting together
all the contributions, we have:
CD 0 subsonic =
(4.12)
∑C
Fi
FFi SWi
i
S
D
+  
+ CD 0 protuberances
 q  upsweep
and for the three aircraft into examination:
Airbus A 330 200
0.0070
Boeing 767 300
0.0049
PrandtlPlane
0.0106
(0.0077 )
Now is possible to introduce some helpful parameters useful to compare different fuselages.
1)
C D0
VLP
VLP = Volume Limited Payload
2)
C D0
CMW
CMW = Cargo Max Weight
3)
C D0
FA
FA = passenger’s deck Floor Area
4)
C D0
VPD
VPD = Volume Passenger’s Deck
5)
CD0
VCD
VCD = Volume Cargo Deck
with:
(4.13)
VLP = Wpayload + WCargoCapacity
where Wpayload is the sum of passenger weights, and WCargoCapacity = W1 + W2
(4.14)
W1 = T ⋅ (ρ pb ⋅ N p ) ⋅ ρ c
81
PrandtlPlane Conceptual Design
with:
T
Is the total container’s volume, that rapresents the number of containers multiplyed by
it’s own capacity.
LD 1 capacity has been considered in 5 m3 3
LD 3 capacity has been considered in 4.3 m3
NP
Passenger’s number
ρc
Cargo density estimated by [6] in 176 Kg/m3
ρpb
Passenger’s baggage density estimated by [6] in 0.125 Kg/m3
W2 = Vbulk ⋅ ρ b
(4.15)
in wich:
Vbulk
Cargo deck’s volume usually located in the bulk
ρb
Baggage’s density estimated by [6] in 160 Kg/m3
In this case, to guarantee a cautelative solution, the W2 term has been neglected.
Values calculated following these relations for VLP are:
Airbus A 330 200
52475
Kg
Boeing 767 300
39061
Kg
Prandtl Plane
37589
Kg
CMW
Cargo max weight, is the maximum weight that we can put into containers
negleting the hand baggage weight and bulk contibution.It is represented by the
product of T and ρc. Values calculated are:
Airbus A 330 200
20086
Kg
[3]
Boeing 767 300
17414
Kg
[3]
Prandtl Plane
32924
Kg
VPD
Volume Passenger’s Deck ( serviceable part of the deck )
Airbus A 330 200
337
m3
[3]
Boeing 767 300
484
m3
[3]
Prandtl Plane
500
m3
82
PrandtlPlane Conceptual Design
VCD
Volume Cargo Deck ( volume of the deck calculated considering the zone
included by the the first and the last container )
Airbus A 330 200
186
m3
[3]
Boeing 767 300
102
m3
[3]
Prandtl Plane
406
m3
C D0
VLP
C D0
CMW
C D0
FA
CD0
VCD
C D0
VPD
A 330-200 B767-300
PP ( 100)
PP ( 70)
2.02*10-7
1.47*10-7
1.79*10-7
1.3*10-7
3.21*10-7
2.33*10-7
3.48*10-7
2.81*10-7
4.41*10-5
3.20*10-5
3.11*10-5
2.66*10-5
2.61*10-5
1.89*10-5
3.76*10-5
3.3*10-5
2.16*10-5
1.57*10-5
2.07*10-5
1.01*10-5
Table 1. Comparison between some useful parameters
It is easy to remark that the upsweep angle is significant as far as the aerodynamic drag is
increased.
The friction analysis includes a PrandtlPlane configuration with a large volume of the passenger
deck; this configuration is proposed in view of possible requirements of large volume for
passenger, but it is only indicative. The results obtained show that the more space available
requirement costs in terms of drag. The shape optimization of the PrandtlPlane fuselage is an open
question, to be faced separately. Many ideas exist and some research activity are in development
at the Department of Aerospace Engeneering of Pisa
83
PrandtlPlane Conceptual Design
References
[1]
Raymer D.P., Aircraft Design: a conceptual approach, AIAA Education Series
[2]
Torenbeek E., Synthesis of subsonic Airplane Design, Kluwer Boston Inc., Hingham,
Maine 1982
[3]
Jane’s , All the world’s aircraft 1999-2000
[4]
Airbus, Airbus A 330 Manual Maintenance Facility Planning, Jan 2003
[5]
Association of European Airlines, Long range aircraft AEA requirements, December
1989.
[6]
Roskam J., Airplane design, Roskam Aviation Corporation
[7]
Buresti.G., Aerodinamica, Aerospace Engeneereng Departement of University of Pisa
[8]
Niu Michael C.Y., Aircraft structural Design, CONMILIT PRESS LTD
[9]
L.Prandtl, Induced Drag of Multiplanes, NACA TN-182, 1924.
[10]
FAR, Part 25.777 proposal, Jan. 1971.
[11]
Simha S. Dodbele, Three Dimensional Aerodynamic Analysis of a High Lift Transport
Configuratio,
NASA Langley Research Center
AIAA Paper No. 93-3536; AIAA Applied Aerodynamics Conference, Monterey,
California, August 9-11, 1993 http://techreports.larc.nasa.gov/ltrs/PDF/NASA-aiaa-93-
3536.
[12]
E. Pistolesi, Lezioni di Aerodinamica, Vallerini, Pisa 1924
85
Preliminary Fluidodynamical Analisys
CHAPTER 4
Preliminary Fluidodynamical Analisys
4.1
Aerodynamic project
The aerodynamical design of a transonic aircraft requires, the both numerical computation and
as a final stage wind tunnel tests. The present activity can not include a complete aerodynamical
design with CFD methods; as it will be shown in the next chapter, it was only possible to define
preliminary aerodynamical layout.
The Computational Fluid Dynamic (CFD) code FLUENT®, available at the Department of Aerospatial Engineering of the Pisa University, was intensively used for the present design. The main
purpose of this activity was to show that the design process of the PrandtlPlane is working well
in view of future aerodynamical optimisation; only high speed configuration is examined.
The choice of the main geometrical parameters and their first optimization were object of
previous investigations and these preliminary studies will be summarized briefly in the
following.
4.1.1
Preliminary High speed aerodynamical design
The values of CLcruise and Mcruise are fixed. Mcruise is defined as MDD relevant to ∆CD = 0.002.
The design of both the wing and the fuselage influences MDD. As far as wings are concerned, an
increase of MDD is obtained by changing the non dimensional thickness (t/c) and the sweep
angle (Λ25%). In case of subsonic flow, the elementary theory of swept wings gives good results,
apart high angles of attack (Figure 1).
86
Preliminary Fluidodynamical Analisys
Figure 1. Comparison between results from the theory of swept wings and experimental results [1]
In transonic flows the three-dimensional effects are important expecially in the root and tip
regions, where the isobars tend to rotate and to align normally to the aero-dynamical streamlines
(Figure 2).
Figure 2. Root and tip pressure effect conditions [1]
87
Preliminary Fluidodynamical Analisys
Figure 3. Root and tip pressure effect conditions [1]
A good design of the wing airfoils in these regions can minimize the negative impact upon the
performance of the wing, as shown in Figure 3.
88
Preliminary Fluidodynamical Analisys
Figure 4. Changes on aerodynamic characteristics in swept wings due to a good design of airfoil and plant shape
The main steps performed in the high speed design are reported in the following:
89
Preliminary Fluidodynamical Analisys
•
The aero-dynamical project starts with the choice of the airfoil, designed for the cruising
conditions and referring to a portion of the wing, namely corresponding to 60-70% of the
half span.
•
At his stage the airfoil non dimensional thickness is determined by CL value and by the
design Mach number of the same airfoil.
•
The before mentioned values of CL and Mach number are bi-dimensional values, and can
be obtained from three-dimensional values is shown in Figure. 5.
Figure 5. Mach number and CL assesment [1]
•
Hence it is possible to establish simple relationships between Mach number and CL value
of the wing design, sweep angle and airfoil thicknesses at the root , at 40% of the half span
(kink) and at tip.
•
The moment coefficient Cm is important both for the behaviour at stall (pitch-up) and for
stability and equilibrium considerations, in particular at the root it is desirable to have a
slightly negative or even a positive value, in order to reduce the tail load necessary for
equilibrium.
•
The maximum local Mach number on the upper wing must not exceed 1.2, to avoid strong
shock waves and wave drag penalties. The isobars at the root tend to retrocede, so one
tries to load the profile near the leading edge. In so doing one obtains also a favourable
pitching moment.
90
Preliminary Fluidodynamical Analisys
•
In the kink zone it is possible to take a maximum advantage from the aerodynamical
characteristics of the transonic airfoil, which is characterized by a wide supersonic area on
the back of the upper surface and by a leading edge with reduced curvature.
•
Because at the extremities the isobars tend to concentrate near the leading edge it is
important to load the profile in the rear part. Besides, one prevents stalling conditions by
using a rounded attack border, intrinsically dangerous because they may yield pitch-up.
A synopsis of the items listed is reported in Figure 6
Figure 6. Fondamental points in transonic wings project [1]
The aforementioned remarks, which are valid for a conventional aircraft, do not fully apply to
the case of the PrandtlPlane. In this case, in fact, the flow behaviour close to the wing tips is
strongly influenced by the vertical bulks.
The wing of the Boeing 747, is an example of the strong variations of the airfoils along a
transonic-swept wing as shown in figure below.
91
Preliminary Fluidodynamical Analisys
Figure 7. Boeing 747 Aerodynamic wing charactesistics [1]
4.1.2
Choice of the airfoils
The airfoils are supercritical, for satisfying the constraint of both the cruise speed and the fuel
volume. The airfoils vary along the wing span in order to modify the distribution of the isobars,
and hence the global wing characteristics. The airfoils are NASA SCA(2) – 0714 , NASA SCA(2)
– 0412 and GRUMMAN K2 and are taken from the literature (hence it is supposed that they are
not optimised). The airfoil position along the wing span and their relative twists are reported in
Table 3. They are the result of the following considerations:
92
Preliminary Fluidodynamical Analisys
•
Airfoil SC 20714, with 2o twist angle, accords with the trend of the isobars, which moves
rearward close to the symmetry plane (this phenomenon could induce a significant negative
pitching moment).
•
The airfoil SC 20714 is adopted in the kink zone with 1.8o twist angle, in order to obtain the
maximum aerodynamical efficiency and a high value of CL which allows to take the
maximum advantage from the large supersonic zone on the upper surface.
•
The wing tip of the PrandtlPlane configuration is substantially different from that of a
traditional one, because of the presence of the vertical wings. Wide round joints between the
horizontal and vertical wings were designed in order to avoid
possible transonic
interference effects (shock waves). GRUMMAN K2 airfoils, with 1.4o and 0o twist angles,
respectively, give a good solution to the above problems.
Similar considerations have suggested the choice of the rear wing airfoils.
A similar increase of the MDD can be hardly obtained for the fuselage, because the need of
straightening the nose would yield ratios Lfus/Φmax. fus unacceptable for a traditionally rounded
prow. After a more accurate analysis, shown particularly by [1], one deduces that the the wing
contribution is usually dominant on the CD value, as shown in Figure 8. The nose zone of the
present aircraft was designed with a layout only a little different from that of a conventional
aircraft, with a MDD value, surely smaller than that of the wing, which, in first instance, were
considered to be little significant.
93
Preliminary Fluidodynamical Analisys
CD
Figure 8. Example of the comparison of the CD value of wing and fuselage (weighted with the respective reference
surfaces).
94
Preliminary Fluidodynamical Analisys
4.2 CATIA model optimised for the grid generator
All the models were obtained by using the CAD software CATIA®, available at the Department
of Aero-spatial Engineering of the Pisa University. As said before, this code allows for a
detailed parametric shape generation of the aircraft. The model is a half aircraft due to the
simmetry. A proper methodology was adopted to transfer files from CATIA® to the software
package GAMBIT®, a submodule of FLUENT® used for mesh generation. The control volumes
were generated directly inside CATIA®. The interface files, written in IGES format, is allowed to
overcome a set of problems which usually cause a loss of time.
Figure 1. Model ready to be set into the grid generator.
The mesh generation is obtained, starting from the simplest geometrical entities (vertices and
edges) and proceeding towards more complex entities (surfaces and volumes). An example is
shown in the following figures.
95
Preliminary Fluidodynamical Analisys
Figure 2. Stages of the process of linear mesh generation.
Figure 3. Stages of the process of surface mesh generation.
This sequence has finally conducted to the realization of mesh of the whole volume.
96
Preliminary Fluidodynamical Analisys
Figure 4. Final stage: volume mesh.
Figure 5. Mesh around strong aerodynamic gradients.
97
Preliminary Fluidodynamical Analisys
The gain and the skewness of the mesh can be choosen in any of the element part of the volume;
the values of the skewness and aspect can be taken under control. The mesh refinement has been
improved in the regions where the gradients of the aerodynamic field are high (e.g. wing
connections, wing leadin edges, bulk connections etc...);
Figure 6. Mesh around strong aerodynamic gradients.
Figure 7. Mesh quality.
98
Preliminary Fluidodynamical Analisys
4.3 Fluidodynamical analysis with the software FLUENT®
The CFD code FLUENT® 6.0, has been used for the numerical analysis. Different solutions of
the equations of motion are available, namely:
A
Euler model;
B
The following Navier-Stokes model:
C
1
Spalart-Allmaras (with only one equation for the turbulece transport);
2
Three k-epsilon models (with two equations for the turbulece transport);
3
Reynolds Stress Model (RSM, with seven equations for the turbulent transport);
Complete Navier-Stokes model (LES= Large Eddy Simulation).
These models are listed in the order of an increasing complexity, and have been used mostly in
industrial applications, with the exception of the LES model, which was included for the first
time into the version 5.0.2 of the FLUENT® code, but does not yet provide reliable results.
The governing equation can be solved sequentially or coupled ( in the latter case with explicit or
implicit schemes). In all the simulations carried out in the present thesis, coupled equations were
solved with an explicit scheme, optimized for compressible, high speed flows, with a large
number of grid volumes.
The flow is assumed as potential, so that the geometrical configuration will not calculate the
flow separation of the boundary layer. The model used is applicable to bodies with small
thikness wakes with respect to the dimension of the cross sections, but not to blunt bodies. In
these hypothesis, the code yields good estimations of the lift forces. In general, however, it is
not possible to obtain estimations of the drag forces with the same degree of accuracy.
4.3.1
The aerodynamical field
As soon as the meshing has been transfered into the FLUENT® code, the following steps are:
-
Choice of the models and of solution parameters ( e.g. type of equations, viscosity
(turbulence) models and convergence conditions);
-
Definition of boundary conditions of the fluid domain;
-
Definition of the reference quantities. The “reference surface” is the horizontal
projection of wings and as “reference length” the sum of the mean aerodynamical
chords.
99
Preliminary Fluidodynamical Analisys
4.3.2
Choice of the computational model
About the method of solution we need to remember that the computational power available
makes it impossible to apply viscous models [3] due to the complex configuration and also that
this is a preliminary analysis hence the Eulerian model does better fit the requirements, and even
thought viscous terms are neglected, rotational flows, like transonic flows with shock waves
generation are simulated. In particular results obtained with the Eulerian model fit very well
experimental results obtained at small angles of attack.
Boundary conditions for the fluid domain
All the analyse were made in cruise flight conditions and for two angles of attach, zero and two
degrees.
Reference conditions used for the calculations
Cruising height Hcr
10500 m
Pressure
26440 Pa
0.41 kg/m3
Density ρ
Temperature
223.25 °K
Mach number Mcr
0.85
Flight speed Vcr
254.54 m/s
Table 1. Cruise conditions used for calculations in FLUENT® 6.0.
4.3.3
Mesh validation
The first computational analysis were aimed at validating the meshing. The validations consist
in verifying that numerical results, in particular the CL values, are independent of both the
number of cells used and the dimensions of the computational domain.
100
Preliminary Fluidodynamical Analisys
Number of elements
CL Value
0.8⋅106
0.46092
1.7⋅106
0.46206
Percentage error
0.24
Table 2. Mesh validation
According to FLUENT® manual, the errors reported in the above table are negligible with
respect to the errors inherent in the mathematical model adopted, and then the assumptions
made are justified.
101
Preliminary Fluidodynamical Analisys
4.4
Solutions and postprocessing
Configurations
In this section, three different configurations af a 250 seat PrandtlPlane aircraft are examinated.
The aim of this analysis is simply to show that the procedure for developing the configuration is
valid, the optimum aircraft configuration can be obtained after a longer process, which is not
possible in this thesis. Starting from an initial configuration, the aerodynamical analysis is
camed out; then on the basis of the results obtained, the second and the third configurations are
studied. The initial wing layout is shown in Figure 1. and the data of aifoils, chord lenghts, and
twist angles are shown in table 3
Figure 1. Wing geometry.
102
Preliminary Fluidodynamical Analisys
PROFILE
TYPE
ROTATION X
(deg)
ROTATION Y
(deg)
ROTATION X
(deg)
CHORD
(m)
1
SC20714
0
+2
0
6
2
SC20714
0
+1.8
0
4
3
GRUMMAN K2
0
+4
0
2.7
4
GRUMMAN K2
0
0
0
2.3
5
GRUMMAN K2
0
+1.6
0
5
6
SC20412
0
+1.6
0
4.3
7
GRUMMAN K2
0
0
0
2.5
Table 3. Profiles distribution.
The outputs shown here are the Mach number behaviour; as an example, some streamlines have
been appended in the first configuration.
•
CONFIGURATION 1 : Wing span of 45 m, tip chord length of 1.5 m, main landing gear
sponson well rounded.
•
CONFIGURATION 2 : Wing span of 44 m, tip chord length at the of 2.3 m, same landing
gear sponson of configuration 1.
•
CONFIGURATION 3 : Wing span of 44 m, tapered landing gear sponson and wing airfoils
twist angle reduced by 1.5 degrees.
CONFIGURATION 1
0 degree angle of attack
The computational results obtained with FLUENT are illustrated by the following plots. Shock
waves are present on the rear wing the front wing and fuselage.
103
Preliminary Fluidodynamical Analisys
Figure. 2
Shock waves are indicated in the figures 2 and 3; the reagion of the main landing gear sponson
is in a low speed field, and then, the shape of them is not so important.
Figure. 3
104
Preliminary Fluidodynamical Analisys
2 degree angle of attack
Figure. 4
Figure. 5
At a higher angle of attack, the shock wave intensities are higher too; in particular, a leading
edge front wave grows, wave front are trimming on the rear wing and on the internal part of the
105
Preliminary Fluidodynamical Analisys
wing bulks. The following figures show the streamlines behaviour; it is influenced by the
hypothesis of potential flow ( vortex generation is not allawed ).
Figure 6. Visualization of streamlines .
Figure 7.
106
Preliminary Fluidodynamical Analisys
Figure 8.
Figure 9.
107
Preliminary Fluidodynamical Analisys
Figure 10.
CONFIGURATION 2
0 degree angle of attack
Structural considerations have suggested the first modification of the geometry which consisted
in reducing the wing span from 45 m to 44 m and in increasing the chord tip from 1.5 to 2.3 m.
Fluid dynamical investigations had the purpose to verify, in spite of all simplifications inherent
in the computational tools used, the amount of variation the aerodynamical forces. It is in fact
well known that, at these speeds, shock waves of moderate intensity and localized on some
areas of the aircraft can be accepted. A slight variation of some parameter, like angle of attack,
speed or some other geometrical change, can however have strong impact upon intensity and
location of the shock waves.
108
Preliminary Fluidodynamical Analisys
Figure 11.
Figure 12.
As it can be seen from the figures, the situation is practically unchanged with regard to the
magnitude of the velocity vectors and to the position of the shock waves. The only noticeable
109
Preliminary Fluidodynamical Analisys
change is in inner part of the wing bulk which now, contrary to the preceding configuration, is
free from perturbations.
2 degree angle of attack
Also in this case, as in the preceding one, the phenomenon is amplified.
Figure 13.
Figure 14.
110
Preliminary Fluidodynamical Analisys
As in the case of the same configuration with 0 degree incidence angle, the only change consists
in the absence of significant shock waves in the inner of the bulk.
CONFIGURATION 3
0 degree angle of attack
This configuration turned was the result of modifications derived from structural and
aerodynamical considerations.
•
The first modification regarding structures is a new bulk geometry and in particular the
radius of curvature at the attachment wing-bulk was considerably reduced and bulk was
made stright. This structural modification was conceived in order to increase the
stiffness of the wing box and to reduce global displacements.
•
The second structural modification concerns the shape of the landing gear sponsons.
This modification aimed at accessing that, the aerodynamical field of fuselage would not
perturbed too much. At the present stage of design, the position of the main landing gear
is not yet defined.
•
Aerodynamical modifications concern airfoil sweep angles along the span, in particular,
decrease of 1.5 degrees on the whole front wing. This modification aimed at reducing
the intensity of the shock waves on the front wing. Infact the original sweep angles,
proved to be too high, with a lift on the front wing higher than 50%. In particular the
actual angles af attack along the front wing are about 3.8 degrees when the angle of
attack is 2 degrees with respect to the fuselage axis. The consequences were intense
shock waves and low efficiency of the supercritical airfoil.
111
Preliminary Fluidodynamical Analisys
Figure 15.
Figure 16.
The effect of the modifications introduced proved to be positive, with a reduction of the
intensity of the shock waves on the front wing, combined with a movement towards the trailing
edge (a condition which maximizes the performance of the supercritical profiles). The shock
waves on the external bulk disappears and finally, the landing gear sponsons were free from
aerodynamic perturbations.
112
Preliminary Fluidodynamical Analisys
2 degree angle of attack
In this case, in spite of the increased angle of attack, a slight decrease of the shock wave
intensity is visible from the figures. The shock wave maximum value is now Mach 1.6, smaller
than previously obtained value of Mach 1.75.
Figure 17.
Figure 18.
113
Preliminary Fluidodynamical Analisys
Concluding remarks
The procedure adopted to develop the configuration has been proved to be reliable. Hence, after
that modifications are introduced into the architecture of the PrandtlPlane, the aerodynamical
optimization process can be applied. The previous example show that the Mach number
behaviour can be conveniently modified, but a second aspect, the stability of flight, was not
considered, so that the optimisation process of the aircraft is more complicated than shown
before.
Anyway, the philosophy of development of the aircraft configuration is clear and the tools are
proved to be perfectly able to allow this optimisation. During this research activity, MSD code
was developed and, now it can be used finally to modify the aircraft shape quickly. The next
shape optimisation will regard the fuselage ( to reduce CDo) and the wing system (to optimise
it).
114
Preliminary Fluidodynamical Analisys
References
[1]
E. Obert, The aerodynamic development of a modern civil transport aircraft, CIRA
Short Course in Aerodynamics, Capua, Febbraio 1997W.
[2]
E. Stoney, Collection of zero-lift drag data on bodies of revolution from free-flight
investigations., NACA TN 4201, 1958
[3]
Three Dimensional Aerodynamic Analysis of a High Lift Transport Configuration
Simha S. Dodbele
NASA Langley Research Center
AIAA Paper No. 93-3536; AIAA Applied Aerodynamics Conference, Monterey,
California, August 9-11, 1993 http://techreports.larc.nasa.gov/ltrs/PDF/NASA-aiaa-
93-3536.pdf
115
Maximum Take Off Weight Estimation
CHAPTER 5
Maximum Take Off Weight Estimation
For a non-conventional aircraft it is hard to find procedures for a weight estimation. Therefore, in
agreement with the specifications of [2], the weight estimation Wempty is obtained as a mean value
based on data existing for aircraft of comparable class. These aircraft of comparable class, chosen on
the basis of design requirements, payload, landing gears position on the fuselage, engines on wings:
they turned out to be the Boeing 767-300 ER, the Airbus 330-200 the Lockeed C-141B and C5. The
Boeing and Airbus aircraft have been selected as representative because the passengers are 250-290
for medium-long range destinations. The two military aircraft, Lockeed C-141B and C5, have been
selected, in spite of their larger sizes and payload capabilities, because of the design of the fuselage,
which is closely related to that of the PrandtlPlane, specifically they have a similar location of the
main landing gear. The comparison is non based on the weights of the components, but on the ratio
between the component weights and the weight at take-off of the whole aircraft; in this way the
emphasis is put on the main parameters characterizing the type of the aircraft itself. In the case of the
military freighters, the deck is reinforced to carry high specific loads; this aspect has to be taken into
account properly. A bibliographic research was made in the respect but no satisfactory conclusion
was possible. Hence it was decided to evaluate the partial weight of the components of existing
aircraft by applying statistical models relevant to the conceptual design. Some models can be found
in the literature which appear to be applicable in the present problem [1,3,4,5].
The weight of the aircraft can be split in the following parts:
(5.1)
Wtakeoff = Wcrew + Wpayload + Wfuel + Wempty
where:
- Wtakeoff is the maximum takeoff weight (MTOW),
- Wempty is the operational weight empty (OWE),
- Wfuel
is the fuel weight,
- Wpayload is the payload weight assuming a weight for passenger of 95 Kg [13] .
In terms of the ratios Wfuel/Wtakeoff and Wempty/Wtake off, the above relation can be written as:
Wcrew + Wpayload
(5.2)
Wtakeoff =
1- ( Wfuel ⁄ Wtakeoff ) - ( Wempty ⁄ Wtakeoff )
116
Maximum Take Off Weight Estimation
The weight fraction corresponding to the empty-operational weight is estimated analysing of the
weight of the single components of the aircraft.
A comparison of the predictive capabilities of the above mentioned models was made in a
graduating thesis in aerospace engeenering [6].
A careful research analysis of data relative to today commercial aircraft was made to check the
models which would minimize errors in the case of the following aircraft: Boeing 727-200, 737-200
and 747-100, Airbus 300B2 and Mc Donnel-Douglas DC10.
Kg
737-200
727-200
Nicolai %
NASA %
Torenbeek %
Wing
4814
3457
-28.2
2301
-52.2
4547
-5.5
4013
-16.6
Tail
1233
961
-22.1
640
-48.1
1223
-0.8
606
-50.9
Fuselage
5492
5629
2.5
5497
0.1
6080
10.7
5803
5.7
nacelles
631
1248
97.8
3295
422.2
808
28.1
709
12.4
Landing Gear
1975
1910
-3.3
1524
-22.8
2000
1.3
1517
-23.2
Structure
14145
13205
-6.6
13257
-6.3
14658
3.6
12648
-10.6
Fixed Equipment
6696
4389
-34.5
10244
53
8106
21.1
7872
17.6
Wing
8405
6313
-24.9
3793
-54.9
7979
-5.1
7083
-15.7
Tail
1879
1397
-25.6
1132
-39.7
2122
12.9
967
-48.5
Fuselage
10167
8713
-14.3
10327
1.6
9586
-5.7
10464
2.9
nacelles
1009
2129
111
4272
323.3
1532
51.8
1131
12.1
Landing Gear
3605
2747
-23.8
2161
-40.1
3188
-11.6
2241
-37.8
Structure
25065
21299
-15
21685
-13.5
24407
-2.6
21886
-12.7
Fixed Equipment 12551
5501
-56.2
13326
6.2
12343
-1.7
10918
-13
26698
23324
-12.6
15253
-42.9
24640
-7.7
22929
-14.1
Tail
6657
6558
-1.5
4274
-35.8
4433
-33.4
4183
-37.2
Fuselage
21442
19774
-7.8
26669
24.4
20978
-2.2
18999
-11.4
nacelles
4140
4767
15.1
5898
42.5
3447
-16.7
3482
-15.9
Landing Gear
10685
10694
-8.5
5698
-51.2
10772
-7.8
6727
-42.4
Structure
70622
65117
-7.8
57792
-18.2
64270
-9.0
56320
-20.3
Fixed Equipment 27180
10974
-59.6
26710
-1.7
26554
-2.3
23418
-13.8
Wing
39191
37181
-5.1
27321
-30.3
43633
11.3
37740
-3.7
Tail
5375
7258
35
4994
-7.1
5248
-2.4
5388
0.2
Fuselage
32588
30476
-6.5
42550
30.6
29449
-9.6
48454
48.7
nacelles
4550
6171
35.6
8174
79.6
3602
-20.8
4966
9.1
Landing Gear
14255
15913
11.6
7338
-48.5
14664
2.9
8985
-37
Structure
95960
96999
1.1
90377
-5.8
96596
0.7
105533
10
Fixed Equipment 28796
15797
-45.1
33708
17.1
36288
26
29866
3.7
20017
12729
-36.4
8103
-59.5
15501
-22.6
14493
-27.6
Tail
2695
2916
8.2
1815
-32.6
2817
4.5
2118
-21.4
Fuselage
16248
14398
-11.4
15361
-5.5
16596
2.1
20514
26.3
nacelles
3193
3268
2.4
4116
28.9
2354
-26.3
2788
-12.7
Landing Gear
6174
7068
14.5
3437
-44.3
5762
-6.7
3783
-38.7
DC10-30 Wing
747-100
Raymer %
A 300-B2 Wing
117
Maximum Take Off Weight Estimation
Structure
48327
40379
-16.4
32832
-32.1
43030
-11
43696
-9.6
Fixed Equipment 15569
8930
-42.6
20604
32.3
20555
32
15403
-1.1
Table 1. Percentage errors due to predictional models .
The results obtained with the implementation of the several models were systematically compared
and the best one, i.e.the one that minimises the mean error on the empty weight, is selected for the
prandtlPlane weight estimation.
Data reported in Table 1 suggest that the best model in predicting the total weight of the structure is
the report NASA CR151970, which gives a mean error of 6%.
The Torenbeeck’s model (error of 8%), as well as E. Nicolai’s, are not much worse. The latter ones
yield however predictions oscillating from good to other ones not really smart. The worse
predictions are those by Raymer which led to a rather high mean error (15%).
Some important remarks are necessary:
-
Previsions are strongly affected by the reliable data.
-
The design philosophy and the manufacturer’s experience may infirm the adaptability of a
predictive model.
-
The prediction error related to a single component has not the same weight for all
components. In fact, if all applied formulae would give zero variance, one would have
(5.3)
∑ Wi = Wtakeoff
where Wi are the weights of the single components. Each weight is estimated with an error ε, such
that:
(5.4)
Wi = Wi + ε Wi
hence
(5.5)
∑ (Wi + ε Wi) = Wtakeoff (1 + εaverage)
or:
(5.6)
∑ (Wi + ε Wi) = (1 + εaverage)
Wtakeoff
118
Maximum Take Off Weight Estimation
The requirement of a small mean error implies that:
(5.7)
∑ ε Wi
≤ εaverage
Wtakeoff
As a metter of fact, it is obvious that high errors (of even 50%) can be accepted for a small
component, but not for components like wings and fuselage.
The NASA model seems the most reliable from this point of view.
Using the NASA model, a comparison was made between the weights of the aircrafts selected to
relate with the PrandtlPlane. Data ara displayed, as shown in Table 2.
The wing weights of the conventional aircraft, obtained with the NASA procedure, were
incremented by 15% to take into account the leading and trailing edge high lift devices, the actuation
systems, etc…
The data relative to the PrandtlPlane wings are obtained by a procedure for preliminary design [7].
It is reasonable to assume that the weight of the tail unit of the Prandtl-plane, given by the sum of
the weights of the two fins, does not exceed the weight of the empennages of traditional
configurations, that is rudder and horizontal tail surfaces; an evaluation of this hipothesis will be
possible only ‘a posteriori’.
Some preliminary tests made by Airbus Industries indicate, an increase of the tail weight, because of
the highest robustness requested, when the vertical distance between front and rear wings increases.
Accordingly, a weight incremented by 2% with respect to the computed average, has been assumed
for the tail.
119
Maximum Take Off Weight Estimation
Airbus
/W0
Boeing Lockheed Lockheed
A330-200 767-300
C-141B
C-5A
Average
PP
0.15 [7]
Wings
0.148
0.106
0.112
0.130
0.124
Tail
0.018
0.014
0.019
0.016
0.0167
Fuselage
0.11
0.11
0.117
0.154
0.122
Powerplants
0.08
0.083
0.097
0.065
0.08
0.08
Landing Gear
0.032
0.04
0.035
0.050
0.039
0.039
Fixed equipment
0.094
0.134
0.068
0.057
0.08
0.08
Wempty/W0
0.482
0.487
0.449
0.472
0.472
0.494
0.017
(precauctionary)
0.134
(precauctionary)
Table 2.. Component’s weights fractions estimated with NASA predictive method.
Due to the presence of the landing gears, the fuselage of the PrandtlPlane has a relative weight
bigger than that of a conventional commercial aircraft, which have the landing gears inside the wing.
In a preliminary way, an increase of about 9% was assumed for the fuselage (from 0.122 to 0.134).
The fraction of the weight in empty operative conditions is:
(5.8)
Wempty / Wtakeoff = 0.494
The above mentioned weight fraction can be further reduced by an amount of about 5% taking the
weight reduction allowed by the adoption of new advanced composite material in wing structures
and in the coating of the fuselage into account. Such weight reduction was considered as essential by
designers of the Airbus Industries for the realization of the A380 model.
Finally, the fraction of the empty weight turns out to be
(5.9)
Wempty / Wtakeoff = 0.470
The fuel weight can be estimated only if the aerodynamic efficiency of the aircraft is known it
depends on several parameters, mainly on the aspect ratio of the wings (A) an the wing load in cruise
(W/S).
The maximum range wing load in cruise depends on the Oswald efficiency factor e and on the
friction coefficient at zero lift, CD0
120
Maximum Take Off Weight Estimation
The PrandtlPlane efficiency factor, epp, may be estimated with the relation
e pp =
(5.10)
em
κ
where
-
em is the Oswald factor for a monoplane (equal to 1 for an elliptic distribution of the lift forces);
κ is defined as [Ref.8]:
-
(5.11)
D PP
D monoplane
h
1 + 0.45
D bestwingsystem
b
≅
=
h
Dmonoplane
1.04 + 2.81
b
in wich the PrandtlPlane is assumed as equivalent to the Best Wing System.
In (5.11) Dmonoplane is the induced drag of the optimum monoplane (em=1) that is with an elliptical lift
distribution. As well known Dmonoplane=
L2
.
qπb 2
The Best Wing System is the optimum lifting system for a given lift and span; figure 1 shows the
efficiency of the B.W.S compared with a biplane.
Equation (5.11) arises from the comparison of the relations for the induced drag of the monoplane
2
2
with a distribution of the lift forces characterized by the Oswald factor em ( Dm = L qπb em ) and
the corresponding value of the PrandtlPlane ( DPP = L qπb ePP ) assuming the PrandtlPlane as
2
2
the Best Wing System, which implies DPP = κ ⋅ Dm .
In the present case h/b (ratio of gap and span) is close to
(5.12)
h/b = 0.20
and, from 5.11, is possible to get the efficiency corrective factor for a BWS:
K ≅ 0.679
121
Maximum Take Off Weight Estimation
----- Biplane
PP
Best Wing Systems
Figure 1. Biplane efficiency factor as a function of h/b.
In [10] it is shown that the Prandtl solution is approximated and the closed form solution shows that
the Prandtl solution is understimated by nearly 2% One should also notice that Prandtl’s work
underestimated, till the optimum value, the variation of the ratio Dm/DBAC, as function of the ratio
h/b, by a value of 2%.
So one optains K = 0.679 ⋅ 0.98 = 0.665 .
In orther to take into account that the PrandtlPlane is not exactly a Best Wing System a further
increment by 3% was cautiously introduced
So one obtains K = 0.685 wich is approximated to 0.69.
For a monoplane of advanced design, em = 0 and from Eq. (5.10) one obtains ePP = 1.377.
The zero lift drag coefficient, at the current stage of the project, can be cautiously considered larger
than that of a wide-body cargo aircraft (0.0190 – 0.020), hence CD0=0.022 has been assumed.
A calculation of the transonic CD0 coefficient of the present configuration was done a posteriori,
using the Flat Plate Analogy, by applying the Component Build-up Method and is reported in
Appendix B.
The wing load corresponding to the maximum range efficiency can therefore be computed by [1]:
122
Maximum Take Off Weight Estimation
πAe PP C D 0
W
=q
S
3
(5.13)
where:
-
q is the dynamic pressure at the flight altitude and cruising speed.
-
A is the wing aspect ratio of the PrandtlPlane.
The value of q can be computed with reference to the cruise height of about 10,500 m (34,800 ft)
and to a M=0.85 cruise speed.
The aspect ratio of the PrandtlPlane, defined as ratio of the square of the wing span to the total
reference surface, can be assumed to be 5,7, equivalent to a monoplane of the same surface with
A=11.4. Inserting numerical values, Eq. (5.13) yields:
(5.14)
Kg
W
= 526 2
S
m
For the efficiency in cruising conditions, one has, [1]:
(5.15)
1
L
=
 
;
 D  cruise qC Do + W S
W S qπAePP
Insering numerical values in Eq. (3.15) one obtains
(5.16)
L
= 14.49
 
 D  cruise
Therefore the maximum efficiency becomes
(5.17)
1
L
L
⋅
= 16.46
  = 
 D  Max  D  cruise 0.866
The specific fuel consumption depends, as well known, on the type of engine adopted and the
cruising conditions. For the present aircraft a turbofan with high by-pass ratio, (like the Rolls-Royce
RB211-524) has been selected with the following values for the specific fuel consumption according
to [1]:
123
Maximum Take Off Weight Estimation
-
c = 0.5 1/h in cruising conditions,
-
c = 0.4 1/h in loiter conditions.
The mission profile used for the calculations is shown in Figure 2
3
2
30 m in . loit er
4
TO
0
LDG
1
5
6
60007400
n.m.n m
Figure 2. Mission profile used for calculations.
The fuel weight fraction can therefore be computed as follows:
(5.18)

W fuel
W6
= 1.05 ⋅ 1 −
 W
Wtakeoff
takeoff





The value obtained has been incremented by 5% to account for the spare fuel and the not usable
fuel.
The ratio W6/Wtakeoff can be further split into several contributions, each one relative to a phase of
the mission.
Some of them can be estimated from historical data, other ones are computed from the performances
of the aircraft.
124
Maximum Take Off Weight Estimation
Phase
Weight fractions
W1
1) Taxing and Takeoff
W takeoff
= 0 . 97 (statistical [Ref.1])
W2
= 1.0065 − 0.0325 ⋅ M = 0.978
W1
2) Climb and acceleration:
M = 0.85
3) Cruising:
− Rc
R = 6000 nm = 11112000 m
c = 0.5 1/h = 1.389E-4 1/s
W3
= e V ( L D ) = 0.651
W2
V = 252 m/s ÆM = 0.85
(h=10500m)
L/D = 14.25
4) Loiter:
− Ec
E = 30 min. = 1800 s
c = 0.4 1/h = 1.111E-4 1/s
(h=10500m)
W4
= e ( L D ) = 0.987
W3
L/D = 16.46
5) Descending
W5
= 0.995 (statistical [Ref.1])
W4
6) Landing
W6
= 0 . 997 (statistical [Ref.1])
W5
W6
= 0 .606
W0
W fuel
Wtakeoff

W6
= 1.05 ⋅ 1 −
 W
takeoff


 = 0.413


Table 3. Weight fractions for the different phases of the mission
The Results are reported in Table 3, where it is assumed that the cruising mission was performed in
only one step.
From the knowledge of the ratios Wfuel/Wtakeoff e Wempty/Wtakeoff and by assuming.
Using:
-
Wcrew = 810 Kg1,
-
Wpayload = 24510 Kg2.
1
2 pilots and 7 flight assistant considering 9o Kg each according to [Ref.13]
125
Maximum Take Off Weight Estimation
the maximum load at take-off turns out to be, in first approximation
Wtakeoff = 208804 Kg,
the fuel weight necessary for the mission:
Wfuel = 85353 Kg
and the weight of the structures
Wempty = 98130Kg,
With these values, one derives the following weights
Component
First weight estimation (kg)
Wing
31321
Tail
2430
Fuselage
27980
Power Plant
16704
Landing Gear
8134
Fixed Equipment
16704
Total empty weight
103300
Empty weight calculated
98130
Table 4. First weight estimation of PrandtlPlane’s components
As suggested in Ref. 2, the weight estimation is improved by taking the round-off errors into
account and compensating for them by means of a corrective coefficient C.
Thus, for each component one can define this coefficient as
(5.19)
(
C = Wempty − W ∗ empty
)WW
componente
∗
empty
where Wempty* is the empty weight computed by summing up the weights of each component.
2
258 passengers considering 95 Kg each according to [Ref.13]
126
Maximum Take Off Weight Estimation
In Table 5 the correction coefficients C and the modified weight of each component are reported.
The results obtained in this section allow to evaluate some other important characteristics of the
aircraft as:
-
the thrust to weight ratio T/W
-
the wing load W/S.
Corrective factor
Right weights
[Kg]
C [Kg]
[Kg]
Wing
31321
-1566
29754
Tail
2430
-122
2320
Fuselage
27980
-1399
26580
PowerPlant
16704
-835
15869
Landing Gear
8134
-407
7736
Fixed Equipment
16704
-835
15869
103300
-5371
102060
Component
Firt estimation
W∗empty
Table 5. New estimation for components Weights.
Both the parameters vary during flight.
Thrust to weight ratio
The thrust to weight ratio, T/W, is a fundamental parameter because it affects the performances of
the aircraft concerning take-off, at the raising speed and maximum speed. Because the T/W ratio is
not constant during flight. A fixed point is considered in take-off conditions, maximum weight, zero
speed, standard atmosphere and maximum thrust.
T/W is obtained with reference to historical data referred to comparable aircrafts [Ref.1]:
(5.20)
T fixed . po int
Wtakeoff
= 0.267 M max
0.363
where Mmax is the Mach number corresponding to the maximum speed in horizontal flight.
Assuming Mmax = 0.88, one obtains :
127
Maximum Take Off Weight Estimation
T fixed . po int
(5.21)
Wtakeoff
= 0.254
A second way of estimation of T/W ratio is the cruise matching. In cruise conditions one has T=D
and L=W and furthermore the possibility of a rising trajectory with a gradient, of 300 ft/min at
maximum speed must be guaranteed; This implies
Tcruise = Dcruise +
(5.22)
dh Wcruise
⋅
dt Vmax
where:
-
Dcruise
=
total drag in cruise conditions;
-
dh
dt
=
rising gradient;
-
Vmax
=
maximum cruise speed;
-
Wcruise
= weight at the beginning of the cruise phase;
When the take-off weight is known, this value can be determined by means of Table 3.
Equation (5.22) can also be written in the form
Tcruise = Dcruise ⋅ (1 + δ )
(5.23)
For a modern commercial aircraft δ =5%.
Introducing the cruising efficiency one obtains:
Tcruise =
(5.24)
Wcruise
⋅ (1 + δ )
Ecruise
With the assumptions made one gets a value of the thrust in cruising condition equivalent to 6.8% of
the weight at take-off and a
Tcruise
ratio equal to 0.073.
Wcruise
The Tcruise ratio must be referred to the standard sea-level conditions and zero velocity, and therefore
Wcruise
modified as follows:
128
Maximum Take Off Weight Estimation
(5.25)
 T fixed . po int

 W
 takeoff
  Tcruise
=
 W
  cruise
  Wcruise
 ⋅ 

  Wtakeoff
  T fixed . po int
⋅
  T
  cruise




 T fixed . po int
Equation (5.25) can be applied by only if a statistical relation relative to 
 Tcruise

 for engines with


high dilution ratio exists. This relation is a function of the Mach number in cruising conditions and
of the flying height. The latter enters through the ratio, σ, between the air density at sea level and at
the flying altitude.
This statistical relation is
(5.26)
T
T fixed . po int
[
]
= 0.568 + 0.25 ⋅ (1.2 − M ) ⋅ σ 0.7
3
Inserting the numerical values in Eq. (5.25) one obtains the thrust to weight ratio at take-off,
satisfying the cruising constraint
(5.27)
T fixed . po int
Wtakeoff
= 0.241
The value obtained with Eq. (5.21) is the higher one. This value has therefore been accepted, as the
value of the ratio of thrust to weight at take-off [1].The wing load is the ratio between the weight of
the aircraft and the reference surface, generally different from the wing wetted surface. In general it
is referred to the take-off conditions.This item is of paramount importance for the determination of
the weight at take-off: if it is reduced below an optimum value, the surface of the wings increases;
the result would be a structure under-loaded but with excessive weight. Each phase of flight has been
analysed and the corresponding wing load has been calculated. The lower wing load is then selected
as design value:
Wing load in cruising conditions
One can prove that a jet plane yields the maximum autonomy (fuel range) when the wing load is
such that the parasite drag is three times the induced drag. Eq. (5.13) provides the relation necessary
for the calculation. This value must be referred to the conditions of maximum weight at take-off.
This is achieved by considering the ratio of the weight of the aircraft at mid-flight to the maximum
weight at take-off.
By using the Breguet’s formula, this ratio is found to be 0.766, hence one obtains
129
Maximum Take Off Weight Estimation
(5.28)
W Wcruise
1
Kg
=
⋅
= 675 2
S
S
0.766
m
Wing load at take-off
During run-up at take-off, as speed progressively increases, the space available to stop in case of
emergency, like engine failure, decreases. The speed at which the range necessary to stop is equal to
the range necessary to take off with the remaining engines is called decision speed.
The balanced field length (BFL) is defined as the run-off range necessary to take off in the worst
possible case, namely with a failure occuring when the decision speed has just been reached. This
definition is bound to the additional condition to fly over an obstacle of 35 ft with a speed equal to
1.1 times the stall speed.
Knowledge of the BFL depends on a preliminary determination of the thrust to weight ratio and of
the wing load. The latter however can be assumed as unknown, as soon as is known the runway
length, which can be cautiously identified with the full length of the runway asked for in the
customer requirements. Once the thrust to weight ratio is known, it holds
(5.29)
TOP =
Wtakeoff S
σC L Ttakeoff Wtakeoff
TO
where:
- σ is now the ratio between the air density at the altitude of the take-off airport and the density of
the air at sea level. It is normalized to 1 in case of a take-off track at sea level and in standard
atmosphere conditions.
- CLTO is the effective value of CL at take off. Because of the take-off speed is prescribed by the
regulations as 1.1 time the stall velocity, the value of CLTO is obtained from the maximum lift
coefficient divided by 1.21. Assuming that the maximum lift coefficient attainable at take-off is
equal to 2.5, one obtains CLTO = 1.82. It is necessary to recall that values of CLmax actually realized
with commercial aircraft, like the Boeing 747-100, are of the order of 2.2 [10]; in this particular
configuration the wing has a double edge equipped with high lift devices, assuming the same
reference surface, an increment of the performances at low speed may be expected.
-
Assuming a sea level airport with a run-off truck of 10,000 ft (about 3,000 m) on the obstacle (35
ft), using TOP (Take Off Parameter) data from Figure 3, taken from [1], where plots relative to
two engines were selected, one deduces a TOP value of 240 lb/ft2 and finally one obtains
130
Maximum Take Off Weight Estimation
W
Kg
= 617 2
S
m
(5.30)
Figure 3. Take Off Parameter estimation
Wing load in climb conditions
Regulations require that, following take-off, the aircraft can perform a rising trajectory with a
gradient of 2.4% in the second phase (that is the most demanding) of climbing, with one engine
failure. The rising speed must be at least 1.2 times the stall speed in the take-off configuration.
Letting G be the rising gradient, the wing load can be estimated with the following formula [1],
obtained by a simple balance of forces on the aircraft on the rising trajectory, inclined by an angle
γ = arcsin(G) with respect to the horizon:
(5.31)
W [(T W ) − G] +
=
S
[(T W ) − G]2 − (4CD0
πAePP )
2 qπAePP
In equation (5.31) a value equal to half of that obtained from Eq. (5.21) simulates the failure of one
propeller. The value of CD0 is incremented to 0.042 to take into account the additional drag due to
the high lift system not yet completely retracted, while the ePP is reduced by 5%. With a rising speed
of about 75 m/s one obtains a dynamic pressure q=351 Kg/m2. Inserting the numerical values, Eq.
(5.31) yields:
131
Maximum Take Off Weight Estimation
(5.32)
Kg
W
= 670 2
S
m
Wing load at landing
The stall speed of an aircraft is a function of the wing load and of the maximum lift coefficient. The
FAR 25 regulations [13] require that the approaching speed of a commercial aircraft must be at least
1.33 times the stall velocity. A plausible value of the approaching speed is of about 75 m/s, hence
Vsmin = 56.4
(5.33)
m
sec
In landing conditions one has therefore
(5.34)
W 1
= ρ V s2min C LMAX .
S
2
In Eq. (5.34) the value of CLMAX is the only unknown. In fact, at this stage of the conceptual design, it
is very difficult to evaluate it, especially for the PrandtlPlane’s configuration, due to lack of data.
Commercial aircraft currently in service have anyway values of CL
max
varying in the range 2.4
(minimum) to 2.5 (maximum).
According to what was explained for the take off conditions, it seems reasonable to set it to 2.7.
Inserting numerical values into Eq. (5.34) one obtains:
(5.35)
W
Kg
= 670 2
S
m
Comparing the values obtained from Eq.s (5.28), (5.30), (5.32) and (5.35) it results that the
minimum value of the wing load in take-off conditions is the one provided by Eq. (5.30).
This equation provides the conditions for the wing surface which turned out to be:
S = 338 m2
Having assumed initially a wing aspect ratio of 5.7, the wing span becomes:
132
Maximum Take Off Weight Estimation
b = 43.9 m
and, from Eq. (5.12):
h = 8.8 m
Finally it is necessary to verify that the estimated WFuel could be loaded into the available fuel tanks.
The following verification made on the final lay-out, led to compute an available volume of about
120152 litres or 94920 kg, considering a fuel density of 0.79 kg/m3.
In conventional configurations fuel tanks are located in wings till the 70% of wing span between
front and rear spar; this particular structure allows to reach the 100% due to bulks which preserve
from electrostatic problems.
Figure 4. Isometric view of the distribution of fuel tanks .
The fuel in rear wing, gives many advantages in balancing problems during flight, making it
possible a small variation of the centre of gravity. Putting fuel even into the tail cone and in fin
133
Maximum Take Off Weight Estimation
structures, the total volume is about 130600 l; this volume has been reduced of 8% due to structural
constrains and to fuel dilatation (Figure 4). As a result, an available fuel weight surplus of 5136 Kg
(with respect to the requirements), gives a good flexibility to the aircraft.
134
Maximum Take Off Weight Estimation
References
[1]
Raymer D.P., Aircraft Design: a conceptual approach, AIAA Education Series
[2]
Roskam J., Airplane design, Roskam Aviation Corporation
[3]
Torenbeek E., Synthesis of subsonic Airplane Design, Kluwer Boston Inc., Hingham,
Maine 1982
[4]
Nicolai L.M., Fundamentals of aircraft design, METS Inc.,6520 Kingsland Court,
CA 95120
[5]
Trapp D.L. Kimoto B.W. Marsh D.P. Beltramo M.N., Parametric study of aircraft
systems cost and weight, Report Number: NASA-CR-151970 April 01,1977
[6]
Paolo Bianconi, Sviluppo di metodologie e modelli per il progetto concettuale di velivoli da
trasporto, master degree thesis in aerospace engineering, Aerospace Engeneering
Department of Pisa 2001
[7]
G.Tropea, Analisi ed ottimizzazione della struttura alare per una configurazione di tipo biplana ad
ali contrapposte, master degree thesis in aeronautical engineering, University of Rome “La
Sapienza”, 1997.
[8]
L.Prandtl, Induced Drag of Multiplanes, NACA TN-182, 1924.
[9]
Pistolesi, E., Lezioni di Aeronautica, Vallerini, Pisa 1924.
[10]
G. Montanari, Problemi di minimo della resistenza indotta in sistemi portanti chiusi, master
degree thesis in Mathematics, University of Pisa 1998.
135
Maximum Take Off Weight Estimation
[11]
M.Cannizzo, S.C.Rodà, Indagine sperimentale in galleria aerodinamica su una
configurazione biplana, master degree thesis in aerospace engineering, Aerospace
Engeneering Department of Pisa 1997
[12]
A. Longhi, P. Vicchio, Studio preliminare di un velivolo biplano ad ali contrapposte di
grandi dimensioni, master degree thesis in aerospace engeenering, Aerospace
Engeneering Department of Pisa, 1994
[13]
FAR, Part 25 – Airworthiness Standards: Transport Category Airplanes
136
Longitudinal Flight Stability
CHAPTER 6
Longitudinal Flight Stability
6.1
Foreword
Under the classical hypothesis of the Flight Mechanics and for the symmetry with respect to the
longitudinal plane it is possible to decouple the behaviour of the aircraft in the longitudinal plane
from the behaviour in the lateral plane; in this chapter, only longitudinal stability is studied. More
numerical procedure for the analysis of the longitudinal stability of a PrandtlPlane using CFD data is
used.
Forces and moments acting in the longitudinal plane of an aircraft are schematically represented in
Figure 1.
Figure 1. Equilibrium in longitudinal plane
-
Vwb
Vtail
-
αwb
αtail
M0wb
M0tail
PNwb
PNtail
CG
lt
asymptotic speed
: asymptotic speed on the tail
:
: angle of attach, with respect to the zero-lift direction, of the wing-fuselage group
: angle of attach, with respect to the zero-lift direction, of the tail
: aerodynamic torque, at zero lift, of the wing-fuselage group
: angle of attach, with respect to the zero-lift direction, of the tail
: neutral point of the wing-fuselage group
: neutral point of the tail
: center of gravity of the aircraft
: distance between the PNwb and PNtail points
137
Longitudinal Flight Stability
-
lt
Zcgwb
Zcgtail
c
hnwb
: distance between the CG and PNtail points
: vertical gap between the CG and PNwb points
: vertical gap between the CG and PNtail points
: mean aero-dynamical chord
: non-dimensional distance, between leading edge and
PNwb as percentage of the mean
aerodynamical chord
-
h
-
εt
T
Lwb
Ltail
Dwb
Dtai
W
: non-dimensional distance, between the leading edge and CG as percentage of the mean
aerodynamical chord
: slope of thrust force with respect to the direction of zero lift
: thrust force
: lift of the wing-fuselage group
: lift of the tail
: drag of the wing-fuselage group
: drag of the tail
: weight of the aircraft
With respect to the general case the known simplifying assumptions [1] are adopted in Figure 2
Figure 2. Simplified equilibrium in the symmetry plane
Assuming the neutral point (Figure 3) as reference pole for the evaluation of forces and moments
one obtains:
(1.1)
M = M 0 + L (h − h n ) c
Under the classical hypothesis of the Flight Mechanics, and with reference to the schemes
represented in Figures 3, one gets the following conclusions for the longitudinal static stability:
138
Longitudinal Flight Stability
Figure 3. Equilibrium referred to neutral point:
-
PN: Neutral point of the whole aircraft
-
hn: distance between leading edge and PN, at the mean aero-dynamical chord;
in order to have a total torque acting against a variation of the incidence angle, i. e. a stable
configuration with positive stiffness, it must hold:
C mα < 0
where:
(1.2)
C mα = C Lα ⋅ (h − hn )
Equation (1.2) implies therefore that, being C Lα > 0 , the neutral point must be behind the centre of
mass of the aircraft (hn > h).
For the rotational equilibrium of the aircraft for all values of alpha in the range alpha-min to alphamax, it must hold:
C m0 > 0
In terms of coefficients, corresponding to the conditions of static equilibrium one may write:
(1.3)
 W
 S
= C Lα α trim
1
 ρV 2
2
0 = C + C α
m0
mα trim

139
Longitudinal Flight Stability
In conventional aircraft, to achieve equilibrium conditions, corresponding to different angles of
attach, the value of Cm0 is modified by varying the direction of zero lift of the tail planes (Figure 4) .
A variation of the direction of zero lift of the wing is made possible by the deflection of the elevator,
which introduces additional terms in Eq. (2.12), which becomes:
 W
 S
= C Lα α trim + C Lδe δ e
1
 ρV 2
2
0 = C + C α
m0
mα trim + C mδe δ e

(1.4)
where the terms C Lδe e C mδe represent the slope of the lift and moments plots as a function of the
deflection of the elevator.
Figure 4. Equilibrium for different weights and incidence angles
Given the weight, Eq.s (1.4) yield an unique couple of values α trim and δ etrim which guarantee
equilibrium at a given speed.
Some remarks:
-
The maximum allowable value of the margin of static stability (h – hn), (hence the most
advanced position of the centre of gravity), must guarantee a sufficient safety range, imposed
by the regulations, from the saturation of the equilibrator.
140
Longitudinal Flight Stability
-
The rearmost position of the centre of gravity must conform to a minimum requirement (510%) of positive stiffness in pitch, according to safety regulations.
-
The difference (h – hn) depends on the wing volume V h which controls the position of the
neutral point, but also affects the position of the centre of gravity of the aircraft.
141
Longitudinal Flight Stability
6.2 Longitudinal equilibrium and stability of the PrandtlPlane
_
d ⋅l
Figure 1. PrandtlPlane Longitudinal Equilibrium:
-
M0f
: aerodynamical moment, at zero lift, of the front wing;
-
M0b
: aerodynamical moment, at zero lift, of the rear wing
-
M0fus
: aerodynamical moment, at zero lift, of thefuselage
-
PNf
: Neutral point of the front wing: aerodynamical moment
-
PNb
: Neutral point of the rear wing;
-
PNfus
: Neutral point ofthe fuselage
-
l
: distance between points PNf and PNb
-
d
: distance between points PNf and PNfus, normalized to l
-
h
: distance between points PNf and CG, normalized to l
-
hn
: distance between points PNf and PN, normalized to l ;
-
Lf
: lift of wing forward
-
Lb
: lift of rear wing
-
Lfus
: lift of fuselage
The equilibrium of the biplane configuration is studied referring to Figure 1 in which, the distance l
between the aerodynamical centres of the two wings has been chosen as geometrical characteristic
length of the system, to normalize all other lengths.
The moments equation of equilibrium respect to CG can be written in the following form:
(2.1)
h ⋅ l ⋅ L f + M 0 f + (h − d ) ⋅ l ⋅ L fus + M 0 fus − (1 − h ) ⋅ l ⋅ Lb + M 0b = M
142
Longitudinal Flight Stability
Let ∆α f an angle of attack perturbation, the stability condition yields:
h ⋅ l ⋅ ∆L f + (h − d ) ⋅ l ⋅ ∆L fus − (1 − h ) ⋅ l ⋅ ∆Lb ≤ 0
(2.2)
In terms of non dimensional coefficients we can write:
S f ⋅ h ⋅ C Lαf ⋅ ∆α f + S fus ⋅ (h − d ) ⋅ C Lαfus ⋅ ∆α fus − S b ⋅ (1 − h ) ⋅ C Lαb ⋅ ∆α b ≤ 0
(2.3)
where:
-
C Lαf ,CLαfus , C Lαb are the slopes of the lift plots of the front wing, rear wing and fuselage,
respectively;
-
∆α f , ∆α b are the angle of attack variations of the front and rear wings, respectively
-
Sf. Sb are the the projections on the horizontal plane of the surfaces of the forward and rear
wings, respectively.
In analogy to the wing-tail configuration one has
(2.4)

∂ε
α b = α f 1 −
 ∂α f


∂ε
 + i tb − ε 0 ⇒ ∆α b = ∆α b ⋅ 1 −

 ∂α f



where ε is the medium down-wash angle.
Besides, it is assumed:
∆α fus = ∆α f
(2.5)
The variation of moment with the angle of attack vanishes at the point:
(2.6)
hn =
1+
1
S f ⋅ C Lαf

∂ε
d ⋅ S fus ⋅ C Lαfus + S b ⋅ C Lαb ⋅ 1 −
 ∂α
f





The study of the stability needs the knowledge of the relative positions of the neutral point and the
centre of gravity; the neutral point being defined by Eq. (2.6). At this stage of the project, the
calculation of hn is not possible without some aerodynamical and geometrical simplifications.
143
Longitudinal Flight Stability
In the transonic domain (for Mach numbers between 0.85 and 1.2) the following relationship is
assumed [3]
C Lα =
(2.7)
 Sexp osed 
⋅F



S
2
2 2


tg (Λ 25 )  
AR ⋅ β 
2+ 4+
1+


β2
η2


2πAR
where:
- β = 1 − M 2 , is the compressibility effects term;
2
 D
- F = 1.07 ⋅ 1 +  , is the fuselage (of diameter D)corrective term;
b

- Sexposed , is the wetted wing surface less the part inside the fuselage;
C lα
, is the 3D aerodynamic corrective term.
2π
β
The application of Eq.(2.7) requires:
- η=
-
the knowledge of the wing-fuselage interference factor F;
-
that a unique profile is considered along the full wing length, which is a disadvantage in
transonic regime, because of the different profiles of the isobars at the wing attachment (see
Chapter. 4);
-
that its validity is extended to the wings with negative sweep angle;
-
that the vertical bulk can be neglected;
-
knowledge of the derivative
∂ε
.
∂α f
This last derivative depends in turn on several factors as Figure 6:
Figure 4. Dimension for computation
144
Longitudinal Flight Stability
•
Aspect Ratio: AR
•
Sweep angle: Λ
•
Distance between the aerodynamical centres of the lifting surfaces l t
•
Vertical gap between the lifting surfaces Z t
Relations between these parameters are known from experimental plots [2], which are not
straightforwardly applicable to the configuration of the PrandtlPlane (Figure 3)
Figure 3. Curves for determination of interference factor in a conventional configuration
For this reason, a numerical approach to the stability problem is illustrate in the next section
145
Longitudinal Flight Stability
6.3
Numerical Study of the PrantlPlane stability
The difficulties for the weight estimation and the set of aerodynamical approximations necessary for
computing the stability margin by means of conventional models, induce to consider an alternative
procedure to evaluate the trim and the stability conditions for the PrandtlPlane configuration.
The procedure uses reference directly the CFD computation; as already explained FLUENT® CFD
code was used in this research. Aerodynamic computation at two different incidence angles αWB
(with respect to the symmetry axis of the fuselage), M=0.85, 10.500 m altitude were performed.
In trim conditions, the position of the centre of gravity is coincident with the centre of pressure(CP1)
of the whole aircraft.
A variation of angle of attach ∆ α produces a new distribution of the aerodynamical pitch moment;
as shown in Figure 1, the resulting pitch moment with respect to CP1 centre is not in general zero,
because CP1 is no longer the centre of pressure at the new trimmed configuration.
_
hn ⋅ l
PN
Figure 1. Conditions changes due to a little incidence angle variation.
If the difference
∆M indicates the variation of the aerodynamical moments, computed for the two
angles of attackα1and α2, with respect to the same pole CP1, and ∆L is the relative lift variation it
holds:
146
Longitudinal Flight Stability
_ M −M
AC
(h − hn )⋅ l = AC
α2
(3.1)
α1
Lα 2 − Lα 1
In the trimmed condition the direct calculation of Μα1, Μα2, Lα1, L α2 gives informations about
stability of the aircraft and the margin of stability, according to Eq. (3.1).
Figure 2. Stability chart of the first possible configuration.
The CFD pressures are integrated over the aerodynamical surfaces of the following components:
front wing, rear wing, fuselage and the centres of pressures are calculated as the point with respect to
the pitch moment is zero.
A typical chart of the results for a preliminary wing system configurationis shown in Figure 2. This
system is not in the Best Wing System condition because the lift on the wings is not the same.
147
Longitudinal Flight Stability
It contains information of the actual geometry, including twist angles and chords along the wing
span and the aerodynamical results, so that the styability characteristics in pitch are immediatly
assumed. In the next figures 3 and 4 are plotted the lift and the pithing moment for an approximately
210 tons aircraft (results relative to an half lifting system are plotted).
Half lifting system
Half lifting system
Figure 3. Lift due to the different components and Global Lift .
148
Longitudinal Flight Stability
Half lifting system
Half lifting system
Figure 4. Pitching Moment due to the different components and Global Pitching Moment .
It is easily to see that the trimmed configuration, without deflection of the control surfaces, appears
at α=2°
149
Longitudinal Flight Stability
References
[1]
B.W. McCormik, Aerodynamics Aeronautics And Flight Mechanics, John Wiley & Sons,
New York 1979.
[2]
F.G. Irving, An Introduction to the longitudinal static stability of low-speed aircraft,
Pergamo
[3]
D.P. Raymer, Aircraft design: a conceptual approach, AIAA Education Series, 1992.
150
Conclusions
CHAPTER 7
Conclusions
The aeronautical research hasdemonstrated economical limits connected to further
tecnological development of the traditional configurations.
It Becomes very important to pursue this improvement through the analysis of unconventional
configurations.
It was shown that the PrandtlPlane configuration can be competitive in comparison with
conventional one.
The most important advantages are summarized in the following categories:
-
aerodynamics,
-
aeromechanics,
-
strctural and aeroelastic
-
operational.
Aerodynamical advantages
-
lower induced drag due to the particolar wing configuration;
-
back wing lifting in every flight condition;
-
high values of Drag Divergence Mach number due to high wing sweep angles
reachable;
-
the connection between the fuselage and the lateral landing gear vane doesn’t seem to
be aerodynamically critical, due to its position behind the foward wing;
-
simple high lift device systems wich allow mantaining a good efficiency during take
off and landing;
Aeromechanical advantages:
-
small control surfaces, both in the longitudinal plane and in the lateral one;
-
the pitch control could be obtained by means of two elevators, one on the front and the
other one on the rear wing, moved in phase opposition; this control is a pure couple in
151
Conclusions
pitch. Another strategy of pitch control is that of using the elevators on the front wing
only; in this case, the behaviour of the aircraft is the same of a canard.
-
In general the PrandtlPlane is trimmed by means of small aerodynamic forces, because
the distance between aft and rear control surfaces is much larger than that of a
conventional aircraft.
-
The to-day available results show that the PrandtlPlane configuration is very stable
with respect to stall, because the stall angle of the rear wing is much higher than that
of front wing.
-
The lateral control is unconventional due to the double rudder and, also, to the
presence of the vertical tip wings.
-
The vertical wings give a positive contribution to the lateral static stability; they could
be also used for lateral control as well.
-
The number of vertical surfaces allows to realize a more safety kind of lateral control.
-
The ailerons could be positioned on the rear negative-swept wing or on the front wing.
They could be used as flaperons; in this case, the front and rear wings are fitted with
high lift devices along the whole span and the best wing system condition can be
obtained also in take off and landing.
-
Fuel can be contained into both the twowing boxes and it can be consumed in the same
amount; so, small variations of the centre of gravity occur during cruise, and one
single flight condition can be optimised with positive effects on the aircraft
performances.
Structural and Aeroelastic advantages:
-
The lifting system is over-constrained to fuselage and, even though the local stiffness
along the wing span is lower than conventional aircraft, the aeroelastic phenomena
appear as less dramatic (but more research is needed on this subject).
-
Type and position of the engines is to be defined and many solutions are possible; in
particular with four or two engines. In the case of two engines, they can be positioned
under the front wing or, in the case of low noise aircraft, over the same wing. Given
the lack of concentrated loads and the possibilities of tailoring the primary structures,
the lifting system could be manufactured in composites. This is an important subject of
the future research; the aim is to provide a potential reduction of weight and
production costs.
152
Conclusions
-
Fuselage is equivalent to a doubly supported beam, the supports being the front and
rear wing attachments; so, the fuselage bending moments are zero in the connections
between fuselage and wings, contrary to conventional aircraft and, during touch down,
the fuselage bending stresses relax the stresses in flight.
-
The lifting system provides an intrinsic structural safety as far as Damage Tolerance is
concerned. In fact, a wing can be damaged without producing a global failure, due to
the over-constrained solution adopted.
-
The horizontal bilobed fuselage seems to allow both the possibility of solving
pressurization with usual techniques and obtaining wetted surfaces comparable with
conventional aircraft.
Operational:
-
Small wing span allows a better airport management
-
The particular wing structure allows to house 38 containers type LDl in a big cargo
vane able, more it is possibile to load and unload at the same time. In practise, the
PrandtlPlane concept is a mixed passenger-cargo aircraft.
The present work has besides shown the huge flexibility of the PrandtlPlane due to the
particular shape of the fuselage.
Some possibile configurations were analyzed easily varing the internal layout; it was possible
to house up to 350 passengers with a fuselage’s lenght shorter than the conventional one.
The reduced wingspan in comparison with conventional configuration gives the possibility to
increase considerably the number of passengers respecting the 80*80 square limit for airport
operations.
The first purpose of this graduation thesis was to evaluate the potentials of the PrandtlPlane
model and to reach a first conceptual design for the 250 seat configuration. The results seem
to be promising and let imagine the possibility to extend to other kind of aircraft the
PrandtlPlane configuration:
Application as a freighter
The application of Twin-Fin PrandtlPlane configuration as a freighter aircraft is
straightforward, due to the fuselage shape. As already said, the main landing gear is made of
153
Conclusions
multiple legs with small wheels, in order to be contained inside the lateral fairings and obtain
a continuous cargo deck.
Besides, cargo doors can be positioned on the back of the fuselage, and, hence, the loading
and disembarkation of goods and luggage is simpler and quicker. The very high maximum
take off weight of this aircraft needs a very large wing surface. In this configuration it is
immediate to obtain a large wing surface without compromising the static stability of flight;
on the contrary, in a conventional aircraft, a very large wing surface must be accomplished by
a very large horizontal tail for flight stability. Hence, the very large freighter of the future can
not be conventional aircraft.
The development of the cargo PrandtlPlane configuration is a great challenge of the future
transport aviation.
Application as a cryogenic freighter
The PrandtlPlane configuration is very suitable for a cryogenic power plant application, in
which the hydrogen tanks are positioned under the lower cargo deck. A seaplane freighter is a
transportation aircraft from point to point all over the world, using sea ports instead than air
ports. Sea ports can be obtained using also lakes, rivers or proper water fields but, in order to
avoid fuel contamination, fuel must be hydrogen or methane. The large hydrogen tanks are
positioned under the cargo deck owing to the large width fuselage. This proposal aims at
flying 24 hours per day, using routes totally different from those for passenger aircraft.
Figure 1
154
Conclusions
Application to small aircraft
The small aircraft industry of Europe is important and, even more so, it will be in the next
future. European industry could obtain important benefits from PrandtlPlane configuration,
taking into account structural safety, high distance between engine and passengers, high
stability of flight, high efficiency, new appealing design. At the Technical University in Turin,
wind tunnel tests have been carried on a scaled model of a two seat aircraft, showing that the
aircraft has a small induced drag and a high degree of stability to the stall (Figure 2).
Figure 2
The present work gives the initial layout of the 250 seat configuration to other graduate thesis
started at the Aerospace Engeenering Department of the University of Pisa. The aim is to
completely define structural problems connected to the particular wing and the fuselage to
contribute to the final detail design of all the aircraft structure.
In the next future a great campaign of wind tunnel test is hoped to find a procedure of
optimizing wing design.
A particular attention must be direct to the “T “ connection between fin and back wing were
CFD analysis found intense shock wave.
As regards structures is now absolutely important to study (with experimental proofs) the
wing bulks and the “T” connection.
155
Appendix A
APPENDIX A
PrandtlPlane CD0 computation
The Component Buildup Method gives an assessment of the skin friction drag coefficient CD0
when the flat plane analogy can be used (as it is shown in Chapter 3):
C D 0 subsonico =
∑C
Fi
FFi Qi SWi
i
S
+ C Dmisc
The geometrical characteristics to use for calculation are reported in the following table:
GEOMETRY
0
COMPONENT N
SWETTED Characteristic
(m2)
Length (m)
Λmax
(deg)
fuselage
1
985
Length = 46.5
foreward wing
1
313
back wing
1
fin
-
(t/c)max (x/c)max
-
Sfrontal
(m2)
-
35
m.a.c. = 4.60 36.94 0.125
0.39
-
324
m.a.c. = 3.75 23.57 0.102
0.42
-
2
108
m.a.c. = 5.90 26.3
0.06
0.4
-
bulk
2
38
m.a.c. = 2.40 45.36 0.102
0.42
-
nacelle
2
25
-
-
Length = 3.70
φmax
= 2.33
-
-
Table A.1. geometrical characteristics for CD0 computation
The following hypothesis are made to reach the CD0 value:
•
completely turbolent motion;
•
the fuselage contribution to CD0 has been determined in Chapter 3;
156
Appendix A
•
for the interference factors (Qi), these values are considered according to [1]1:
Qfus
=1
Qf.w
=1
Qb.w
=1
Qfin
=1
Qbulk
=1.25 (is assumed for tip wing missiles or tank)
(wing well connected to the fuselage)
Qnacelle = 1 (wing mounted nacelle at a distance greater than max fuselage diameter)
•
10500 m, cruise altitude.
The final result is reported in Table A.2.
COMPONENT CD0 transonic
fuselage
foreward wing
back wing
fins
bulks
nacelles
0.0106
0.0031
0.0033
0.0009
0.0004
0.0002
TOTAL
0.0225
Table A.2. Contributes to CD0 calculated for every aircraft component
1
Raymer D.P., Aircraft Design: a conceptual approach, AIAA Education Series
157
Appendix B
APPENDIX B
Up-sweep angle’s effect of a cambered fuselage tail
The rear part of the fuselage is often slightly upswept in order to obtain the required rotation angle
during take-off or landing.
The drag resulting from this slight camber is negligible.
However, on freight aircraft with a rear loading door the fuselage must be swept up over a
considerable angle, especially on small freighters like the old De Aavilland Caribou and Buffalo.
Adverse interference may occur in the flow fields induced by the wing (downwash), the weel
fairings and the rear fuselage.
The formation of vortices below the rear part of the fuselage is shown in figure1:
Figure 1. Formation of vortices below the rear part of the fuselage
These vortices are unstable and can cause lateral oscillation, especially at low speeds, high power,
and high flap deflection angles.
A considerable drag penalty in cruising flight is also caused by a large fuselage camber (Figure 2).
158
Appendix B
Figure 2. Drag increment vs upsweep angle
Sharp corners on the lower part of the fuselage may relieve the problem by generating stable
vortices, inducing up-wash below the fuselage and thereby creating attached
flow.Measurements have shown that the penalty can be limited to reasonable values (Figure 3).
Figure 3. Effect of cross-sectional shape on drag
159