Control, Propulsion and Energy Assessment of a Spherical UAS for Low Speed Operations

Conference Paper (PDF Available) · September 2017with 547 Reads
DOI: 10.4271/2017-01-2065
Conference: AeroTech Congress & Exhibition 2017, Volume: SAE Technical Paper 2017-01-2065
Cite this publication
This paper presents a comparison between different hypotheses of propulsion of a spherical UAS. Different architectures have been analyzed assessing their specific aerodynamic, energetic, and flight mechanics features. The comparison has been performed assuming the robustness of flight control in different wind conditions, defining for each the specific operative ranges, mission profiles, and energy assessment. An effective energy assessment and comparison against a commercial UAS has been produced. Even if the paper considers a preliminary simplified configuration, it demonstrates clearly to be competitive against traditional quadcopters in a predefined reference mission.
This paper presents a comparison between dierent hypotheses of
propulsion of a spherical UAS. Dierent architectures have been
analyzed assessing their specic aerodynamic, energetic, and ight
mechanics features. The comparison has been performed assuming
the robustness of ight control in dierent wind conditions,
dening for each the specic operative ranges, mission proles,
and energy assessment. An eective energy assessment and
comparison against a commercial UAS has been produced. Even if
the paper considers a preliminary simplied conguration, it
demonstrates clearly to be competitive against traditional
quadcopters in a predened reference mission.
This paper presents a new UAS concept. It is new design spherical
drone taking advantage of a series of innovation with respect to any
possible competitor. The specic aircraft has a new propulsion
system that s based on Coanda eect and take advantage of the
induced supercirculation. The propulsion is ensured my mean of a
series of air jets on the surface explicating a former concept that was
dened by Coanda in one of his patents.
Figure 1. Preliminary concept drawing
The above preliminary concept has been directly exploited from a
former patent by Henri Coanda [1].
Figure 2. Henry Coanda lifting device patent [1]
Control, Propulsion and Energy Assessment of a Spherical
UAS for Low Speed Operations
Published 09/19/2017
Sebastian Bandycki
Independent researcher
Michele Trancossi
Sheeld Hallam Univ.
Jose Pascoa
Universidade Da Beira Interior
CITATION: Bandycki, S., Trancossi, M., and Pascoa, J., "Control, Propulsion and Energy Assessment of a Spherical UAS for Low
Speed Operations," SAE Technical Paper 2017-01-2065, 2017, doi:10.4271/2017-01-2065.
Copyright © 2017 SAE International
Downloaded from SAE International by Michele Trancossi, Monday, September 25, 2017
The idea is to produce a spherical drone that can safely ight safely
over people and in aggressive environment, such as the presence of
high temperatures, pollutants, electromagnetic radiation, minimizing
the risk for men in environments, which cannot be explored by
ground based robots because of their nature, and present problems for
the activities of traditional drones.
It is well known that a sphere is not optimized for ight, but, as
research on ying saucers unconventional air vehicles demonstrates,
can produce generate interesting vehicle concepts.
A later patent by Coanda [2] presents a control system and method
for unconventional ying saucers that is based on the compositions of
the thrust produced by means of a number of jet propellers placed on
the external section of the ying saucer.
Figure 3. Coanda device for the simultaneous control of lifting and
directional elements [2].
Figure 4. A preliminary model derived from Coanda patent [2]
This patent allows assimilating the ight motion rules for a ying
saucer to the ones that applies to a helicopter (Figure 3 images Fig. 9
and Fig. 10). A sketch that explains the hypothesis by Coanda by
evidencing the dierent forces is provided in gure 4.
The equation of ight on a vertical plane of the object can be derived
by the ones of a helicopter by considering the schema in gure 4.
Assuming a symmetric shape aerodynamic lift is neglected.
If we consider the helicopter energy model dened by Wood [3] and
Zuang [4], the energy state of a helicopter during ight is given by
equation (1):
By taking the partial derivative with respect to time of equation 1, the
energy rate is expressed as:
In which it can be assumed that the angular acceleration is negligible
against other terms. Equation (3) reduces to the following:
Other Flying Saucer Concepts
Probably the rst related concept has been the aeronautical machine
by Robinson [5].
Figure 5. Aeronautical Machine by Robinson [5]
Sharpe [6] proposes and evolution of the Coanda’s lifting device [1]
Crabtree [7] has developed a wingless heavier than air aircraft, in
which the fuselage is generally at, and is annular in conguration.
This aircraft could travel vertically as well as laterally, and which is
provided with means for controlling the tilt thereof.
Downloaded from SAE International by Michele Trancossi, Monday, September 25, 2017
Figure 6. Fluid sustained and pan annular shaped bodyaving annular shaped
body [6]
One interesting ying saucer concept has been patented by Mulgrave
and Ringlieb [8]. This invention relates to a ying sauced shaped
compact integral structure with an interior uid impelling apparatus
that derives sucient lift to provide vertical takeo and landing.
Figure 7. The discord airfield vehicle concept [8]
Lent [8] has elaborated a circular wing aircraft elaborating the
originals Coanda [1] and Robinson’s [5] concepts. In particular, it
presents an interesting nearly spherical architecture (Fig. 15) the
reference directly the actual vehicle concept that is the argument of
this aircraft.
Figure 8. Mulgrave and Ringlieb flying saucer
Mulgrave and Ringlieb [9] present a concept based on a vertical
axis rotor and embedded jets to allow the ight of a new concept
of ying saucers.
Louvel [10] has designed an electrical remote-control and remote-
power ying saucer (gure 8).
Figure 9. Multicopter based flying electrical flying saucer. [10]
Figure 10. Davis directionally controllable propelled circular vehicle.
Davis [11] has developed the concept of a directionally controllable
ying vehicle and a propeller mechanism for accomplishing the
same." U.S. Patent 8,272,917, issued September 25, 2012.
Downloaded from SAE International by Michele Trancossi, Monday, September 25, 2017
Figure 11. VTOL aircraft by Beck
Beck has patented a VTOL aircraft concept that improves the idea of
Mulgrave and Ringlieb by introducing lateral apping winglets.
Figure 12. Fixed circular wing aircraft [13]
Bose [13] has patented an interesting xed wing aircraft, but still with
some limits in manoeuvrability.
Figure 13. Aerodynamic lift apparatus [14].
Chen [14] has patented a very interesting lifting concept based on
Coanda eect uid stream over the top surfaces of the vehicle. It
produces the lift by mean of using the method of blowing air over the
upper surface of the vehicle to generate lift by virtue of the balance of
outside pressures against the body of the vehicle.
Even if not directly related to the aeronautic sector, the Dyson bladeless
ventilator regards the arguments of the present study. It presents a fan
assembly for creating an air current by a bladeless fan assembly,
including a nozzle and a device for creating an air ow through the
nozzle. The nozzle includes an interior passage and a mouth receiving
the air ow from the interior passage. A Coanda surface located
adjacent the mouth and over which the mouth is arranged to direct the
air ow. The fan provides an arrangement producing an air current and
a ow of cooling air created without requiring a bladed fan, that is, the
air ow is created by a bladeless fan.
Figure 14. Dyson Bladeless fan [15]
Figure 15. Compressor of the Dyson bladeless ventilator [15]
An interesting attempt of assessing the propulsion for an almost
spherical vehicle has been dened by Hatton [16].
There have been past proposals for air vehicles employing the
Coanda eect. A jet of uid, usually air, has blown in radial direction
outwardly over a dome-shaped canopy to create lift. A cross-section
through the canopy is curved to follow a segment of a circle or it may
have a radius of curvature that increases in the direction of ow. The
radius (r) of the canopy curve decreases towards the downstream
direction (x) in a way that is related to the decrease in the width of
the jet as it ows over the surface. This means that the radius of
curvature decreases (instead of increasing) towards the downstream
direction with the rate of decrease being progressively less rapid
towards the downstream direction. This kind of shape allows a better
aerodynamic adherence of the uid to the canopy and increases
consequently Coanda eect.
Downloaded from SAE International by Michele Trancossi, Monday, September 25, 2017
Figure 16. The two configurations of Hatton Patent. [15]
Definition of the Propulsion System for a
Spherical Object
The above analysis of some of the most relevant congurations,
which have been dened, constitutes a good basis for the study of the
specic problem of the propulsion of a spherical air vehicle.
The design method is derived from the optimization of the equations
of motions such as in Trancossi et al. [18]. This method is an
improvement of second principle analysis [19] according to the
EMIPS method [20] as adapted by Trancossi [21, 22]. It is then a
method dened on the ight mechanics equations and energy
equations of the system, to dene a preliminary optimal conguration
that can be then designed and tested.
Considering the equation of motion it is evident that a vehicle with
almost zero aerodynamic speeds, such as a ying sphere is, a
certain amount of power must be used for keeping the aircraft in
ight conditions.
Figure 17. Preliminary 3D rendering of the spherical drone.
Figure 18. Preliminary system cad drawing.
Figure 19. Principle of operations: schema of fluid flows; schema of applied
The choice of a ducted fan system has been originated by two
dierent reasons:
1. The duct provides vectored thrust, which increases propulsive
eciencies while adding to lateral and longitudinal stability [32].
2. The duct surrounds the prop, which reduces the noise caused by
tip eects.
The system is subject to a 3D system of parallel forces. In the case of
motion on a at plane, and assuming that T0 has a null moment with
respect to the centre of gravity G, the resultant force is the sum of the
forces T1, T2, and 2T0. Its line of action can be determined by the
equilibrium of momentums or by the graphical equilibrium of T1 and
T2. The resultant will lie at a distance δ from the centre of the sphere
on the side of the largest force.
Flight Model
Such as a helicopter the system will be obliged to assume a negative
angle of attack α, such as in a helicopter that allows having a resultant
force, which equals the drag and the weight components. It must
ensure the equilibrium of the forces against rotation that depends on
the intensity of T1 and T2. In particular, the weight force will be
moved against the vertical of a distance ε, which is a function of both
RG and α. Assuming
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1. T1 + T2 = 2T0
3. T = T1 + T2 + 2T0 = 4T0
4. ε = RG · sin α
A specic ight model can be possible assessed by adopting the
equations of the dynamic of the system according to Newton’s second
law on a 2D plane that reduces to:
The net thrust of a ducted fan unit can then be expressed as:
Consequently, the power imparted to the uid is:
Considering the propeller it can be possible to write the thrust as:
and the torque applied to the propeller as
It can be then possible to express the power input as
in which
Consequently, it can be possible to consider the total propulsive
eciency as:
Equation of motion in horizontal motion reduces to:
in vertical motion to
And in case of stabilization
In addition, an accurate 3D model can be produced, but those
equations are sucient to produce an energy ight model for the
specied system.
Energy Model
A measure of the energy state of a helicopter [9] is given by equation
(2) at any altitude and airspeed-RPM combination, and by (3) and
(3’) in term of power.
Power can be expressed by the simplied equations by McCormick
[8] for horizontal ight.
and for vertical ight
Total power is consequently
The total power required is obtained by rotor power and overall
eciency factor η is
Optimization of Helicopter Equations
By equations (4) and equations (8) and (9), it is possible to produce a
preliminary abstract optimization of a theoretical system that can act
as according to those equations and then performing the same
operations that a helicopter does. Starting from the optimization of
the system of forces that may be produced by a hypothetical ying
vehicle that can act as a helicopter it is immediate to observe that the
best conditions are the ones that allow minimizing thrust or moment
in any direction.
Analysis of Forces and Moments
Equation of rotation around a vertical axis shows clearly that
avoidance of the propulsion system with a vertical axis of rotation
allows making null the rear rotor moment. Equation of rotation
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around z-axis shows that it can minimize thrust by an aerodynamic
system that can grant an adequate momentum by mean of
aerodynamic lift by wings or ailerons. A similar conclusion is
obtained by the equation of vertical motion. The vertical thrust Ty = T
cosϕ lowers by both increasing the vertical lift by aerodynamic
surfaces and lowering the vertical drag. The equation of horizontal
motion shows that the minimization of horizontal thrust requires the
minimization of horizontal drag.
Energetic Model
Further analysis will relate to the energy analysis of the system. The
power equation found in traditional bibliography, which have been
cited in the preceding paragraph, can be improved by a more accurate
analysis according to Trancossi [4, 9, and 10].
Figure 20. Energy dissipations in a multicopter
Figure 20 shows energy losses for the moving vehicle. A schema of
the powertrain indicating the dierent losses is provided in Figure 2.
Losses depend on the ight condition in which the helicopter operates.
For simplicity, the model will be developed neglecting minor energy
components and assuming that vertical lift force is mostly produced by
propulsion and not by aerodynamic appendices. Applying this model, it
is evident that the energy components that have to be considered are
more complex with respect to other transport modes. They are:
The evaluation of exergy needs for moving can be performed by
equation (12)
Equation (12) can be divided into two equations, one related to the
vehicle and one to the payload:
It can be also possible to write express energy losses of the engine
and power train:
Equations (12), (13) and (14) allow analysing the performances in
service conditions during operations of the vehicle. In particular, the
equations (13) and (14) allow expressing the energy consumption
required for moving the vehicle and the payload.
Energy Optimization
The above model allows an eective energy optimization of a vehicle
that virtually can operate according to the same physical laws that
applies to a helicopter. By the preliminary evaluations made on forces
and moments it can be possible to perform a preliminary
minimization of the terms that appear in the energy balance:
It simplies during horizontal ight:
Equation (16) can describe the system behaviour of a vehicle during
horizontal ight and lift operations. It could not describe the energy
equilibrium during vertical lift and during hovering. Those operations
can be described by the equation (17)
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It is necessary to consider the component that relates to horizontal
drag, because it is not frequent to be in the condition of ideal calm air.
However, this component can be neglected with very low airspeeds
around the vehicle
Preliminary Benchmark Case
A sphere with a diameter of 500 mm made by a 1 mm rotation
moulding PET bodies has been assumed. Installed fans are RC
Lander 70mm 3200kv 4S Lipo EDF with a 2839L 3200KV Brushless
Outrunner motor.
The comparison will be conducted against one of the more successful
drones ever built for professional use with interesting results.
The comparison has been produced according to equation (10) that
present the formulation of exergy dissipations according EMIPS
model [19] and revised by Trancossi [20, 21].
This comparison has just the meaning of a comparison in terms of
performances, but do not consider the fact that the two vehicles have
very dierent missions and objectives.
Table 1. Sphere vs. DIJ inspire quadcopter technical data
Figure 21. The CD coefficient as a function of roughness for different spherical
objects [25].
For the needs of this preliminary analysis, it has been assumed a CD
of the Spherical object as obtained by preliminary CFD analysis
equal to 0.36 which is in line with the actual CD of a sphere [24]
(about 0.5 for Re > 5 103). By considering Monson [25] it can
decrease with the surface roughness (Figure 21). The claimed value
in then in line with the values of roughness for a supercial
roughness ε/D = 1.25 x 10-2.
According to Johnson and Turbe [23], it is possible to assess the
power need of the vehicle by modelling the electric ducted fan units.
By the preliminary dened method, it is possible to assess an
eective comparison on a dened mission for both vehicles they have
been assessed according to the cited method and compared against
Dietrich [26] and Shi [27]. The mission has been dened in indoor
conditions. Vertical speed has been dened in 1 m/s. Average ight
speed has been assumed equal to 5 m/s. Values for the Results have
been evaluated conservatively and have been reassumed in Table 2.
They clearly show that the system can be competitive against
traditional drones in terms of energy consumption, notwithstanding
the conguration is still far from an optimal one.
Figure 22. Mission Profile
They clearly demonstrate that a spherical drone, even in a not
optimized architecture can ensure energetic performances, which are
inline with a traditional multicopter.
If the results are compared with the battery capacity it can be clearly
demonstrated that the actual spherical drone conguration have a
potential time of ight in the range of 15/20 min, which is analogous
to the one of the reference multicopter.
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Table 2. Comparison of ideal calculated performances of multicopter against spherical drone.
This paper has considered a very basic preliminary version of the
required drone. A more accurate aerodynamic denition both in terms
of propulsion (improving it by mean of Coanda eect) or in terms of
a better denition of the surfaces could generate future signicant
improvements, which are expected to be in line or improve the
theoretical model of the multicopter.
This paper, after a large bibliography and patenting reference
analysis, produces a preliminary energy assessment of an initial even
if not optimized architecture of a possible spherical UAS that can be
used for dierent possible future uses in the area of safety, security,
vigilance and monitoring.
This vehicle concept presents a major benet with respect to any
traditional multicopter because of an eective inoensive design that
can allow operating also over the people. Further uses can deal with
an eective use in hostile environments such as in the presence of
atmospheric chemical pollution.
The energy assessment made against a market leader commercial UAS
with the same expected weight demonstrates the system feasibility of
the proposed drone demonstrating that their energy consumptions are
fundamentally similar on the same reference mission.
These preliminary results can be easily extended also to future more
evolved vehicle concepts, which can be derived from further
improvements of the performances. Future and more evolved
versions are expected to improve their performances by a better
positioning of the propeller and a better shaping of the vehicle.
1. Coanda, H., "Propelling device." U.S. Patent 2,108,652, issued
February 15, 1938.
2. Coanda, H. "Device for the simultaneous control of lifting and
directional elements." U.S. Patent 2,939,654, issued June 7, 1960.
3. Wood T L, Livingston C L, An energy method for prediction of
helicopter maneuverability AD Report, ADA021266, 1971.
4. Zhuang N, Xiang, J. et al., "Calculation of helicopter
maneuverability in forward flight based on energy method",
Computer Modelling & New Technologies, 18(5) 50-54, 2014.
5. Robertson, P.J., "Construction of aeronautical machines." U.S.
Patent 1,123,589, 1915.
6. Sharpe, C. D., "Aerodynamic impelling device." U.S. Patent
2,468,787, 1949.
7. Crabtree, E.L., "Fluid sustained and propelled aircraft having
annular shaped body." U.S. Patent 2,718,364, 1955.
8. Lent, C. P., "Aircraft with discoid sustaining airfoil." U.S. Patent
3,034,747, 1962.
9. Mulgrave, T. P., and Ringleb, F.O., "Gyro stabilized vertical
rising vehicle." U.S. Patent 2,997,254, 1961.
10. Louvel, P., "Electrical remote-control and remote-power flying
saucer." U.S. Patent Application 10/048,091, filed April 5, 2001.
11. Davis, S., "Directionally controllable flying vehicle and a
propeller mechanism for accomplishing the same." U.S. Patent
8,272,917, 2012.
12. Beck, A.H. Jr, “VTOL aircraft.” U.S. Patent 5,170,963, 1992.
13. Bose, P. R., "Fixed circular wing aircraft." U.S. Patent
5,046,685, 1991.
14. Chen, C., "Aerodynamic lift apparatus." U.S. Patent 6,073,881,
15. Dyson, J., et al. "Fan." U.S. Patent D602,144, 2009.
16. Dyson, J., et al. "A Fan." U.S. Patent D602,144, 2010.
17. Hatton, G., "Thrust generating apparatus." U.S. Patent
7,857,256, issued December 28, 2010.
18. Trancossi, M., Stewart, J. and Pascoa, J.C., 2016, November.
A New Propelled Wing Aircraft Configuration. In ASME
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V001T03A048. doi:10.1115/IMECE2016-65373
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Part 2: Indicators and methods”, Exergy, An International
Journal, Volume 1, Issue 4, 2001, P. 217-233.
20. Dewulf J, and Van Langenhove H., “Exergetic material input
per unit of service (EMIPS) for the assessment of resource
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Transport Research Review 7, no. 1 (2015): 1-14. doi:10.1007/
22. Trancossi, M., "What price of speed? A critical revision through
constructal optimization of transport modes." International
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pp.425-448. doi:10.1007/s40095-015-0160-6
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23. Johnson, E.N. and Turbe, M.A., “Modeling, control, and flight
testing of a small-ducted fan aircraft.” Journal of guidance,
control, and dynamics, 29(4), 2006. pp.769-779.
24. Çengel, Y. A. and Cimbala, J. M., “Fluid Mechanics -
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Contact Information
Sebastian Bandycki
phone: (+353) 866019005
Michele Trancossi
Sheeld Hallam University
CD - Drag Coecient (-)
CL - Lift Coecient (-)
kt - Thrust coecient
kp - Power coecient,
kQ - Torque coecient
δ - Distance between vertical thrust and centre of gravity (m)
ε - distance between the point of application
α - Pitch angle (rad)
Ω - Angular velocity of helicopter propeller (rad/s)
ρ - Density (kg/m3)
A - Area (m2)
D - Drag force (N)
E - Energy (J)
Ex - Exergy (J)
I - Moment of Inertia (kg m2)
Ip - moment of inertia of main propeller (kg m2)
L - Lift Force (N)
P - Power (W)
R - Rotor Radius (m)
T - Thrust (N)
V - Air speed (m/s)
a - Acceleration (m/s2)
g - Gravity (9.81 m/s)
h - Height (m)
m - mass (kg).
t - Time (s)
v - Velocity (m/s)
EMIPS - Exergetic Material Input per Unit of Service (J)
D - drag (related to energy and power)
K - kinetic (related to energy and power)
R - rotor (related to energy and power)
T - Thrust (related to energy and power)
req - required
rot - rotor
x - horizontal
y - vertical
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requires a minimum of three (3) reviews by industry experts.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or
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Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE International. The author is solely responsible for the content of the paper.
ISSN 0148-7191
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This research hasn't been cited in any other publications.
  • Device for the simultaneous control of lifting and directional elements
    • H Coanda
    Coanda, H. "Device for the simultaneous control of lifting and directional elements." U.S. Patent 2,939,654, issued June 7, 1960.
  • An energy method for prediction of helicopter maneuverability AD Report, ADA021266
    • T L Wood
    • C Livingston
    Wood T L, Livingston C L, An energy method for prediction of helicopter maneuverability AD Report, ADA021266, 1971.
  • Calculation of helicopter maneuverability in forward flight based on energy method
    • N Zhuang
    • J Xiang
    Zhuang N, Xiang, J. et al., "Calculation of helicopter maneuverability in forward flight based on energy method", Computer Modelling & New Technologies, 18(5) 50-54, 2014.
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    A method is described for producing uniform droplets of a liquid comprising: supplying a stream of gas to a concentric tube, the stream of gas flowing through the concentric tube; supplying the liquid to a first end of a capillary tube positioned in the concentric tube; accelerating the stream of gas toward the first end of the capillary tube; and decelerating the stream of gas after the steam of gas passes the first end of the capillary tube; wherein the accelerating stream of gas detaches uniform droplets of diameter less than 450 micrometers of the liquid from the first end of the capillary tube as the accelerating stream of gas flows past the first end of the capillary tube, the detached droplets being spaced apart by a distance in the range of 100-600 droplet diameters.
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    • Jo Dewulf
      Jo Dewulf
    • Herman Van Langenhove
      Herman Van Langenhove
    This paper focuses on the assessment of the sustainability of transport technologies in terms of resource productivity. It proposes a concept that presents a firm base for quantification of material input on the one hand and generated transport service on the other hand. The concept of material input per unit of service (MIPS) is quantified in terms of the second law of thermodynamics, allowing the calculation of both resource input and service output in exergy terms. This exergetic material input per unit of service (EMIPS) has been elaborated for transport technology. The service not only takes into account the total mass to be transported and the total distance, but also the mass per single transport and the delivery time. The applicability of the EMIPS methodology has been illustrated by a case study comparing railway, truck and passenger car transport. # 2002 Elsevier Science B.V. All rights reserved.
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    • Mei Gong
      Mei Gong
    • Göran Wall
      Göran Wall
    This second part is the continuation of Wall and Gong [Exergy Internat. J. 1 (3) (2001), in press]. This part is an overview of a number of different methods based on concepts presented in the first part and applies these to real systems. A number of ecological indicators will be presented and the concept of sustainable development will be further clarified. The method of Life Cycle Exergy Analysis will be presented. Exergy will be applied to emissions into the environment by case studies in order to describe and evaluate its values and limitation as an ecological indicator. Exergy is concluded to be a suitable ecological indicator and future research in this area is strongly recommended.
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    Full-text available
    • Eric N. Johnson
      Eric N. Johnson
    • Michael A. Turbe
    Small ducted fan autonomous vehicles have potential for several applications, especially for missions in urban environments. This paper discusses the use of dynamic inversion with neural network adaptation to provide an adaptive controller for the GTSpy, a small ducted fan autonomous vehicle based on the Micro Autonomous Systems' Helispy. This approach allows utilization of the entire low speed flight envelope with a relatively poorly understood vehicle. A simulator model is constructed from a force and moment analysis of the vehicle, allowing for a validation of the controller in preparation for flight testing. Data from flight testing of the system is provided. Published in Journal of Guidance Control and Dynamics, 29(4):769-779, July, 2006.