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The study proposes a new airborne wind energy system based on the carousel concept. It comprises a rotary ring kite and a ground-based rotating reel conversion system. The moment generated by the ring kite is transferred by several peripheral tethers that connect to winch modules that are mounted on the ground rotor. A generator is coupled to this rotor for direct electricity generation. Because the ring kite is inclined with respect to the ground-rotor the length of the peripheral tethers has to be adjusted continuously during operation. The proposed system is designed to minimize the used land and space. This first study describes the fundamental working principles, results of a small-scale experimental test, a kinematic analysis of steady-state operation of the system and a power transmission analysis. Design choices for the ring kite are discussed, a strategy for launching and landing and methods for passive and active control are described.
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Chapter 22
Airborne Wind Energy Conversion Using a
Rotating Reel System
Pierre Benhaïem and Roland Schmehl
Abstract The study proposes a new airborne wind energy system based on the
carousel concept. It comprises a rotary ring kite and a ground-based rotating reel
conversion system. The moment generated by the ring kite is transferred by several
peripheral tethers that connect to winch modules that are mounted on the ground
rotor. A generator is coupled to this rotor for direct electricity generation. Because
the ring kite is inclined with respect to the ground-rotor the length of the peripheral
tethers has to be adjusted continuously during operation. The proposed system is
designed to minimize the used land and space. This first study describes the fun-
damental working principles, results of a small-scale experimental test, a kinematic
analysis of steady-state operation of the system and a power transmission analysis.
Design choices for the ring kite are discussed, a strategy for launching and landing
and methods for passive and active control are described.
22.1 Introduction
The potential of airborne wind energy conversion has been investigated by early
explorative research [17, 20, 26] and confirmed by a larger number of recent the-
oretical and experimental studies [5, 6, 25, 27, 31]. It is however also clear that
despite of the advantages of reduced material consumption, access to a larger wind
resource and higher yield per installed system, the system-inherent use of a flexi-
ble tether requires a comparatively large surface area [9]. This contrasts the general
Pierre Benhaïem (B)
7 Lotissement des Terres Blanches, 10160 Paisy-Cosdon, France
e-mail: pierre-benhaiem@orange.fr
Roland Schmehl
Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft,
The Netherlands
539
540 Pierre Benhaïem and Roland Schmehl
motivation for designing an economically competitive wind energy that sweeps the
whole frontal airspace, using less land and airspace.
Several concepts have been proposed to maximize the land use efficiency. For
single kite systems operating on single ground stations the surface density can be
increased by optimizing the spacial arrangement and operation of the systems while
accounting for sufficient safety margins to avoid hazardous mechanical or aerody-
namic interactions. The next conceptual improvement leads towards systems that
operate multiple wings on a single ground stations [15]. For such systems the useful
swept area can reach the occupied swept area, however, the technical complexity of
such systems also increases significantly. Alternatively, single kite systems operat-
ing on single ground stations can be upscaled to increase the land use efficiency [15].
Finally, the complexity of the ground conversion can be increased, for example, us-
ing a large rotating structure (carousel) driven by several kites [14] or, alternatively,
using carts that are pulled by kites on a round track [1, 2].
The present study proposes a new airborne wind energy system, the Rotating
Reel Parotor (RRP), which combines a rotary ring kite with a ground-based rotat-
ing reel conversion system [8]. The concept has also been presented at the Airborne
Wind Energy Conference 2015 [10]. Other airborne wind energy systems involving
rotary kites are the “Gyromill” [23, 25], presented also in Chap. 23 of this book,
which is based on onboard electricity generation, and the “Daisy Stack” [24], pre-
sented also in Chap. 21, which is transmitting shaft power to the ground, as the
present concept. A related technology in the field of aviation is the tethered gy-
rocopter. In Sect. 22.2 the components of the system and their functions are de-
scribed while Sect. 22.3 details the fundamental working principles. In Sect. 22.4 a
small-scale model is presented and experimental results are discussed. In Sects. 22.6
and 22.5 the kinematics of the system and the torque transmission characteristics
are investigated. Section 22.7 elaborates on ongoing and future investigations and
Sect. 22.8 presents the conclusions of this study.
22.2 System Design
A conceptual sketch of the ground-based part of the system is illustrated in Fig. 22.1.
Similar carousel-type configurations have been proposed for airborne wind energy
Fig. 22.1 The ground-based
horizontal ring and its vertical
axis of rotation. For direct
conversion of the rotational
motion a generator is coupled
to the ring. The winch mod-
ules for the traction tethers are
mounted on the ring and are
indicated by circles
22 Airborne Wind Energy Conversion Using a Rotating Reel System 541
conversion [1, 14]. To convert the rotational motion of the ring structure directly
into electricity it can be coupled to a generator using a gear mechanism. The periph-
eral traction tethers (not depicted) which drive the rotational motion of the ring are
deployed from winch modules that are mounted at equidistant intervals along the
ring. Each winch module comprises a cable drum with a connected generator that
can also be used in motor mode.
A conceptual sketch of the rotary ring kite, denoted as Parotor, is illustrated in
Fig. 22.2. The flying rotor is represented as an actuator ring which defines the swept
Fig. 22.2 The flying rotor is
represented as actuator ring
which is inclined to the flow
by an angle α, its axis of
rotation tilted downwind from
the vertical axis by the same
angle (for simplicity a sideslip
angle βsis not included here)
Wind
α
area of the physical rotor. A possible implementation of a small-scale model for test
purposes will be discussed in Sect. 22.4.1. The flying rotor has a size that is about
the size of the ground rotor and it is inclined with respect to the wind by an angle
α. This inclination angle, also denoted as angle of attack, is identical to the angle
between the axes of rotation of the ground and flying rotors.
Figure 22.3 shows how the flying rotor is connected to the ground rotor by pe-
ripheral tethers. Because the axes of rotation of the two rotors are not aligned the
geometric distance between the ground and flying rotor attachment points changes
continuously during rotation. As consequence the length of the connecting traction
tethers needs to be adjusted continuously. This is the function of the ring-mounted
Fig. 22.3 The assembled Ro-
tating Reel Parotor (RRP) in
flight, just before operation.
The tether attachment points
at the flying rotor are indi-
cated by circles. The radial
line from the center of the
ground rotor to one of the
tether attachment points is an
illustration element indicating
the phase lag δof the ground
rotor. Before transmitting a
torque the phase lag of the
ground rotor is zero. The axis
of rotation of the ground rotor
is always vertical
Wind
δ
542 Pierre Benhaïem and Roland Schmehl
Fig. 22.4 The RRP system
in operation with an angular
speed ωand a phase lag
angle δ=35. The arrows at
the winch modules indicate
whether the corresponding
tether is reeled out and energy
is generated (green) or reeled
in and energy is consumed
(red). This definition implies
that the reeling motion is
relative to the winch modules
which move on a circular
path around the center of the
ground rotor
Wind
ω
ω
δ
winch modules shown in Figs. 22.1 and 22.3. When the geometric distance between
two attachment points of a tether is increasing the corresponding winch module
functions as a generator. When the distance is decreasing in the second half of the
revolution, the winch is retracting the tether and is consuming energy. Figure 22.4
illustrates the Rotating Reel Parotor in operation. The flying rotor and the ground
rotor are co-rotating at identical angular speeds, however, the driven ground rotor
lags the flying rotor in phase.
A system of additional suspension lines can be added to support the flying ro-
tor from the center of the ground rotor. Three different options are illustrated in
Fig. 22.5, using lines or line segments of constant length. When in tension, all three
implementations enforce a constant distance between the centers of the two rotors.
(a) Full tilt support (b) Strong tilt support (c) No tilt support
β
Fig. 22.5 Implementation options for suspension lines (in red) to support the flying rotor
22 Airborne Wind Energy Conversion Using a Rotating Reel System 543
The variant sketched in Fig. 22.5(a) additionally enforces a kinematic coupling be-
tween the orientation of the flying rotor, quantified by its angle of attack αand
sideslip angle βs, and the position of the rotor, quantified by the ground elevation
angle βand azimuth angle φof the rotor center point. Although this constraint could
be a way to stabilize the operation of the system, the additional lines increase the
losses due to aerodynamic drag. The bridle-type variant sketched in Fig. 22.5(b)
reduces the drag losses and and allows for some tilt motion of the rotor while the
central line variant sketched in Fig. 22.5(c) has no additional drag losses and does
not impose any constraint on the tilt motion. It should be noted that the suspension
lines for the flying rotor can alternatively be attached to an additional lifting kite.
22.3 Working Principles
A general feature of airborne wind energy is the use of flying devices to extract
kinetic energy from the wind and to transfer it as either mechanical or electrical
energy to the ground, using flexible tethers. Because flexible tethers can only trans-
fer tensile forces an additional mechanism is required on the ground to convert the
traction power into shaft power, which can be converted by electrical generators.
22.3.1 Power Transfer and Power Takeoff
The proposed concept employs a set of peripheral tethers to transfer the rotational
motion of a flying rotor to a ground rotor. This tensile torque transmission system
makes use of the tangential components of the tether forces acting on the ground ro-
tor. The function of the normal force components is to keep the transmission system
in tension, which is an obvious prerequisite for the functioning of the system.
It is important to note that the transmission of torque implies torsion of the tether
system. As can be seen in Fig. 22.4 the angle of twist, which is identical to the phase
lag angle δof the ground rotor, determines how the tether force is decomposed into
tangential and normal components. At small to moderate values of the twist angle,
an increasing torsion reduces the angle at which the tethers attach to the ground
rotor. This geometric effect increases the tangential components and it allows the
tether system to adjust to variations of the torque which can occur, for example, as
a result of a fluctuating wind speed. At larger values of the twist angle, for δ>90,
the effect decreases because the tether system increasingly constricts in a point on
the axis of rotation. At δ=180the tether system reaches the singular condition
at which all tethers intersect in one point and no practically relevant torque can be
transmitted.
The transmission characteristics are also influenced by the distance between the
two rotors in relation to their diameter. The further the rotors are apart the smaller the
tangential components of the tether forces, the less effective the above mentioned
544 Pierre Benhaïem and Roland Schmehl
coupling effect between torsion and torque and the lower the torsion stiffness of the
tether system. If the rotors are many diameters apart the tether system can not be
used effectively for torque transmission.
It can be concluded that on the level of the individual tethers the torsion stiffness
of the system is caused by tensile forces, the rotational motion generated by circu-
lar traction of the ground rotor. Because the axis of rotation of the flying rotor is
tilted downwind the rotational motion requires that the tether lengths are adjusted
continuously to the varying geometric distances between the attachment points. As
described in Sect. 22.2 this is the function of the winch modules on the ground rotor
which compensate the distance variations by reeling the tethers in and out. The two
fundamental modes of energy generation are discussed in the following.
22.3.2 Direct Mode of Energy Generation
In this mode the rotational motion of the ground rotor is converted directly into
electricity, using one or more generators that are coupled to the rotor by a gear
mechanism, as illustrated schematically in Fig. 22.1. The winch modules manage
the kinematically induced length variation of the peripheral tethers, as shown in
Fig. 22.4. They are controlled in such a way that the tension in the tethers is equal
and constant during operation. The modules are electrically interconnected such
that the generated and consumed energy is balanced, avoiding the implementation of
expensive temporary energy storage. To account for losses in the electrical machines
a small amount of electricity is provided by the main generator which is driven
directly by the rotor.
By adding suspension lines, as shown in Fig. 22.5, the force level in the system
of peripheral tethers is lowered and, as consequence, also the generated and con-
sumed amounts of energy. Because of the reduced losses in the electrical machines
the total amount of electrical energy required for the actuation of the tether sys-
tem is decreased. However, with the addition of suspension lines the tensile torque
transmission system becomes more complex and in particular also statically indeter-
minate (hyperstatic). As consequence this poses additional challenges to the control
systems of the winch modules.
22.3.3 Secondary Mode of Energy Generation
In this mode the length variation of the peripheral tethers is converted into electric-
ity, using the winch modules on the ground rotor alternatingly as generators and mo-
tors. The suspension lines are essential and are used to selectively reduce the tether
tension during reel-in. As consequence, the winch modules consume less energy
during reel-in than they generate during reel-out, resulting in a positive net energy
of the phase-shifted interconnected modules. The proposed technique is illustrated
22 Airborne Wind Energy Conversion Using a Rotating Reel System 545
Fig. 22.6 The secondary
mode of energy generation
with two tensioned tethers
and two tensioned suspension
lines highlighted. Unloaded
tensile components are hinted.
The two winch modules
producing electricity are next
to the green arrows, pointing
away from the modules,
while the two winch modules
reeling the tethers in are next
to the red arrows, pointing
towards the modules. The
doted loop is the ground track
of the resultant tensile force in
the system assuming perfect
unloading during reel-in
Wind
ω
ω
δ
schematically in Fig. 22.6. The two winch modules in reel-out mode operate on ten-
sioned tethers while the two winch modules in reel-in mode operate on untensioned
tethers. The shift from tensioned reel-out to untensioned reel-in is managed by the
force control of the winch modules. When switching from reel-out to reel-in the
set value of the tether force is decreased from its nominal value to a low value. As
consequence, the tensile load shifts from the peripheral tether to the corresponding
suspension line which inevitably affects the static force balance and geometry of the
entire torque transmission system. Accordingly, the set value of the tether force is
increased back to the nominal value when switching to reel-out and the tensile load
shifts from the suspension line back to the peripheral tether.
Because of the induced rotational asymmetry of the force transmission the re-
sultant force acting on the ground rotor does not pass through a constant point on
the ground plane anymore, as it does for the direct mode of energy generation. The
resultant tensile force in the transmission system is essentially unsteady and tracks
a periodic loop on the ground plane which is shifted sideways towards the half of
the ground rotor that moves against the wind. This is indicated as dotted line in
Fig. 22.6. The rotational asymmetry affects also the flying rotor which inevitably
performs a tumbling motion. In particular the switching of the force transfer, which,
in the illustrated example affects two winch modules at the same time, introduces a
strong discontinuity in the transmission system. In practice, the switching needs to
be replaced by a sufficiently smooth process to avoid a periodic jolting of the entire
system.
546 Pierre Benhaïem and Roland Schmehl
22.3.4 Discussion
The direct and secondary modes of energy generation differ only in the force control
strategy implemented for winch modules. Because of this, the two modes can in
principle be blended by the control algorithm. However, because of its rotational
asymmetry and unsteadyness it is still an open question whether the secondary mode
has any practical relevance.
22.4 Experimental Tests of a Small-Scale Model
A physical model of the proposed RRP system has been designed and built at small
scale. Initial tests have been performed to demonstrate the fundamental working
principles and to provide an initial assessment of the transmitted torque.
22.4.1 Test Setup
The small-scale model is shown in operation in Fig. 22.7 and the parameters of the
test setup are summarized in Table 22.1. The geometric proportions and the eleva-
tion angle are roughly the same as for the intermediate-scale system described in
Sect. 22.6.5. In place of the winch modules that a larger production system would
Fig. 22.7 Small-scale system
built with two spars, a ring,
four retractable leashes, a
rotating tray, a parachute
kite and semi-rigid rotor
blades. The system uses four
peripheral tethers and several
suspension lines. The flying
rotor measures 1.3 m from tip
to tip
22 Airborne Wind Energy Conversion Using a Rotating Reel System 547
Table 22.1 Design and op-
erational parameters of the
small-scale system. Because
of the close proximity of the
flying rotor to the ground
(about 1 m) it was exposed to
significant turbulent fluctua-
tions of the wind velocity. The
setup uses suspension lines
Parameter name Symbol Value Unit
Average wind speed vw6.0 m/s
Ground rotor diameter dg0.8 m
Flying rotor inner diameter dk0.6 m
Flying rotor outer diameter dk,o1.3 m
Number of rotor blades b8
Blade span 0.35 m
Blade root chord 0.12 m
Blade tip chord 0.04 m
Flying rotor swept area S1.0 m2
Lifting kite area 2.0 m2
Number of peripheral tethers N4
Tether length, minimum lt,min 0.8 m
Tether length, maximum lt,max 1.4 m
Tether length lifting kite 10 m
Elevation angle kite center β40 deg
use, this technology demonstrator has off-the-shelf retractable leashes mounted on
the ground rotor. As they are equipped with a rotational spring mechanism, these
leashes do not produce a constant force but one that is linearly increasing with the
deployed tether length. This is an important aspect for the interpretation of the re-
sults and the comparison with the analytical calculations and numerical simulations
in the following sections. For standalone testing of the rotating reel conversion sys-
tem the ring kite is replaced by a top ring which is rotated by hand. To assess the
torque transmission characteristics the torque imposed on the top ring, τk, and the
torque arriving at the ground rotor, τg, are measured with two torque meters. These
tests showed that the torque transmission coefficient is about τg/τk=0.5.
The design challenge of this small-scale test setup was the matching of the
torques generated by the ring kite and converted by the described rotating reel con-
version system. The baseline design of the ring kite shown in Fig. 22.7 uses eight
semi-rigid rotor blades. To operate this kite at wind speeds between 5 to 6 m/s a sled
kite was added to provide additional lift. With active conversion system a rotational
speed of one revolution per second has been obtained for short times. This relatively
high value is due to the small dimensions of the technology demonstrator. The rotor
with 8 blades has a high solidity, so a low efficiency compared to the Betz limit [16].
However, the generated torque was appropriate for the tests. A rotor with 16 blades
has also been tested and, as expected, produced a higher torque, while achieving
lower angular speeds. More complete test data is provided in Sect. 22.4.2.
As concluded in Sect. 22.3.1 the rotating reel conversion system works only if
the tethers are not too long compared to the inner diameter of the ring kite. This
diameter is indeed approximately equal to the tip height of the system, as shown
in Sect. 22.6. Because the wind is generally stronger at higher altitudes [3] the
RRP system will have to be quite large. However, the implementation of a mo-
548 Pierre Benhaïem and Roland Schmehl
torized ground rotor could be studied for the purpose of increasing the transmitted
torque with longer tethers and for applying the second mode of energy generation,
as described in Sect. 22.3.3. Such a motorized ground rotor could also be used for
launching.
22.4.2 Experimental Results
The objective of the experimental tests has been to demonstrate the fundamental
working principles and to quantitatively assess the effectiveness of the energy con-
version mechanisms. As none of the elements was optimized the coefficient of the
transmitted power cannot be directly deduced. Because the test setup does not in-
clude a central generator the achievable direct power takeoff of the ground rotor is
assessed by the power that is required to overcome the internal friction torque of the
central swiveling tray. Because the test setup uses retractable leashes instead of con-
trolled winch modules, the energy budget related to the tether actuation is assessed
on the basis of the stored potential energy of the leashes. The test results for the
setup defined in Table 22.1 are summarized in Table 22.2. The limiting values ωmin
Table 22.2 Measured proper-
ties of the small-scale system
Parameter name Symbol Value Unit
Angular speed, minimum ωmin 2 rad/s
Angular speed, maximum ωmax 6 rad/s
Angular speed, average ω3 rad/s
Angular speed, freewheelaωτ=012 rad/s
Tip speed ratio, minimum λmin 0.216
Tip speed ratio, maximum λmax 0.648
Tip speed ratio, average λ0.324
Tip speed ratio, freewheelaλτ=01.3
Tether force, minimum Ft,min 0.88 N
Tether force, maximum Ft,max 1.76 N
Tether reeling power, average Preel 1.5 W
Friction torque central swivel τµ0.225 Nm
Friction power central swivel Pµ0.675 W
Flying rotor power, Betz limit P
max 35 W
aperipheral tethers detached
and ωmax describe the range of measured angular speeds of the system, ωa rep-
resentative average value. The value ωτ=0is achieved without conversion system,
using only suspension lines. Similarly the values λmin and λmax describe the range
of measured tip speed ratios, λa representative average and λτ=0the ratio without
conversion system. Ft,min and Ft,max describe the limiting values of the tether forces
that correspond with the tether lengths lt,min and lt,max.
22 Airborne Wind Energy Conversion Using a Rotating Reel System 549
Assuming linear elastic behavior, the potential energy stored in the spring mech-
anism of the leash can be calculated as
E=1
2(Ft,max +Ft,min)(lt,max lt,min).(22.1)
The tether extends from lt,min to lt,max during half a revolution of the rotor which is
associated with the time period
t=π
ω.(22.2)
Considering that two leashes of the system are continuously in reel-out mode we
can derive the average equivalent power for these two leashes as
Preel =2E
t= (Ft,max +Ft,min)(lt,max lt,min)ω
π.(22.3)
Based on the numerical values in Tables 22.1 and 22.2, and using the average value
of the angular speed, we can calculate the value of Preel specified in Table 22.2. The
friction torque τµof the central swivel was measured at the average angular speed
and using this value we can calculate the value of the friction power Pµlisted in
Table 22.2.
The power values Pµand Preel provide a first insight into the energy budget of the
proposed concept. Assuming that the friction in the swivel can be reduced substan-
tially, a power in the order of Pµwould be available for direct continuous conversion
into electricity. In contrast to this, the potential energy Equantified by Eq. (22.1) is
cyclically progressing through the spring mechanisms of the leashes but in balance
for the entire system. This potential is only accessible when using suspension lines
to selectively reduce the tether tension during reel-in, however, this was not possible
in this simple test setup. As a general conclusion it should be noted that an extrapo-
lation of these values to larger systems is critical if not questionable because of the
small scale and the significant measurement uncertainties in this setup.
The efficiency of the flying rotor was not measured, but as it uses numerous semi-
rigid blades forming a high-solidity rotor the efficiency is considered to be far below
the value of the Betz limit. Defining the wind power density as
P
w=1
2ρv3
w,(22.4)
this limiting power value can be computed as
P
max =P
wS16
27 cos3β,(22.5)
where the factor cos3βaccounts for the misalignment of the flying rotor with respect
to the wind [13, p. 98]. By inserting the applicable numerical values we can calculate
the value listed in Table 22.2.
The initial tests have shown the potential but also the challenges of the concept.
Indeed there have been jolts during rotation of the system and the tests indicated
550 Pierre Benhaïem and Roland Schmehl
that the turbulent fluctuations of the wind at close proximity to the ground was a
possible cause of these jolts. Another contribution is due to the use of retractable
leashes with spring mechanisms. The inevitable force variations during rotation in-
duce a tumbling motion of the flying rotor, which becomes stronger with decreasing
elevation angle.
Following the initial tests, the effect of parameter and design variations has been
studied. Firstly, leashes with lower tensile strength were used. While the baseline
design used leashes which generated a force of 1.91 N for 1.30 m of reeled out
tether, these generated the same force with 2.20 m of reeled out tether. Secondly,
the tensile strength was increased by pairing leashes such that each pair of leashes
generated a force if 1.91 N with 0.82 m of reeled out tether. These tests indicated
that the tensile strength must be sufficiently high to avoid excessive twist of the
tether system and eventually entangling of the tethers. On the other hand if the
tensile strength is to high the tether system can not transfer the torque required for a
continuous rotation. A larger Rotating Reeling Parotor system of about 5 m diameter
would allow harnessing better wind at a height of 5 m.
To address the problem of turbulent wind fluctuations and their effect on the
reproducibility of results a leaf blower was used to produce a constant airflow. The
center of the ring kite was suspended in space by means of a bar. The modified
design and test setup is summarized in Table 22.3. Parameters that are not listed
Table 22.3 Design and op-
erational parameters for the
modified design with 16 ro-
tor blades and an increased
flow velocity. To increase the
tensile strength leashes are
arranged in pairs. The setup
does not use suspension lines
Parameter name Symbol Value Unit
Number of rotor blades b16
Elevation angle kite center β65 deg
Number of peripheral tethers N4
Tether length, minimum lt,min 0.20 m
Tether length, maximum lt,max 0.62 m
Tether force, average Ft0.91 N
Angular speed ω5 rad/s
Angular speed, freewheelaωτ=09 rad/s
Tether reeling power, average Preel 1.16 W
aperipheral tethers detached and suspension lines added
have not been modified from the baseline design summarized in Table 22.1. The
average tether force is calculated as
Ft=1
2(Ft,max Ft,min)(22.6)
In these tests it was possible to operate the RRP system in a steady state rotation
without jolts and generating some power. It is envisioned that more thorough results
including the torque transmission efficiency as a function of the elevation angle can
be achieved using a wind tunnel.
22 Airborne Wind Energy Conversion Using a Rotating Reel System 551
22.5 Kinematics of Steady-State Operation
The revolving system of peripheral tethers has the double function of anchoring the
rotary ring kite to the ground and transferring the generated aerodynamic moment
to the ground-based conversion system. Uncommon for airborne wind energy sys-
tems, the combination of these two functions entails comparatively complex tether
kinematics which is governed by strong nonlinear coupling effects. In this section
a kinematic model for the steady-state operation of the tensile torque transmission
system is derived. This model is used to formulate analytical expressions for the
instantaneous tether length and rotor attachment angles which are the starting base
for the analysis of the power transmission characteristics in the following section.
22.5.1 Steady-State Operation as an Idealized Condition
The distinguishing feature of the ring kite is that it employs the effect of autorotation
to convert kinetic energy from the wind into aerodynamic lift and usable shaft power.
To analyze the steady-state flight of this kite the spinning rotor is represented as a
non-spinning planar actuator ring. This abstraction, which hides the implementation
details of the physical rotor, is shown in Fig. 22.8. The orientation of the actuator
ring with respect to the flow is described by the sideslip angle βsand the angle of
attack α. The actuator ring is regarded as a flying object with three translational
and two rotational degrees of freedom. The two rotational degrees of freedom of the
actuator ring, roll and pitch, tilt the spinning axis of the rotor. The aerodynamic lift
Fig. 22.8 The actuator ring
model of the rotary ring kite.
The inclination of the ring
with respect to the flow is
described by two successive
rotations. The sideslip an-
gle βsdescribes the rotation
around the vertical axis while
the angle of attack αde-
scribes the rotation of the ring
around its pitch axis. Roll and
pitch axes are attached to the
actuator ring and not to the
physical rotor. The angular
speed ωof the rotor is an
operational parameter which,
next to the flow angles βsand
α, affects the aerodynamic lift
and drag of the ring
vw
Pitch
Roll
ω
βs
α
552 Pierre Benhaïem and Roland Schmehl
Land drag Dof the actuator ring are functions of the sideslip angle βs, the angle
of attack α, the angular speed ω, the physical dimensions of the rotor and the wind
speed vw.
The objective of the study is to add a system of actuated peripheral tethers, as out-
lined in Sect. 22.2, to constrain the degrees of freedom of the ring kite to a steady
flight state at a constant position with a constant axis of rotation. However, although
the length of the tethers is adjusted continuously to the required geometrical dis-
tance, the tether attachment angles at the rotors vary periodically with the rotation
angle. Caused by the rotational asymmetry of the tilted tether system, the directional
variations of the tether forces lead to transverse resultant forces that induce periodic
compensating motions of the flying rotor.
For the purpose of the kinematic analysis these compensating motions are ne-
glected, assuming an idealized condition of steady-state operation in which the ring
kite has a constant position with a constant axis of rotation. By prescribing this con-
dition, the length of the individual tethers can be formulated as analytic functions
of time and other relevant problem parameters. For the purpose of the analysis it is
assumed that all tethers are inflexible and tensioned and can thus be represented as
straight lines.
Figure 22.9 shows the configuration of the RRP system with four tethers and
without any additional suspension lines. For simplicity we restrict the analysis to
the case of steady-state operation of the ring kite with its center point Kalways in
the xwzw-plane. In this particular case the azimuth angle φvanishes at all times.
When using additional suspension lines, as illustrated in Fig. 22.5, the distance lK
of the kite center point from the origin is constant and the axis of rotation of the ring
kite has to pass through the origin Owhich the following kinematic constraints
α=90β,(22.7)
βs=0.(22.8)
Aand Bdenote a pair of representative tether attachment points at the flying rotor
and the ground rotor, respectively. Because the angular speed ωof both rotors is
assumed to be constant the rotation angle is given by ωt, adding a constant phase
lag δfor the flying rotor. The tethers are attached on the ground rotor at a distance
Rgfrom the center O, on the flying rotor at a distance Rkfrom the center K. The tips
of the rotor blades are at a distance Rk,ofrom the center K. The distance lKbetween
the centers of the two rotors is regarded as a parameter that is prescribed either as
a distance constraint when using suspension lines, as shown in Fig. 22.5, or by the
controlled actuation of the tether system.
22.5.2 Dimensionless Problem Parameters and Reference Frames
From the illustration of the steady-state operation of the system in Fig. 22.9 we
can identify α,βs,β,δ,ωt,Rg,Rkand lKas the fundamental parameters of the kine-
22 Airborne Wind Energy Conversion Using a Rotating Reel System 553
yw
yb
xb
B
ωt
β
xw
O
zb=zw
lK
lt
ωt
δ
α
xk
xa
yk=ys
A
yaza=zk
βs
K
Rg
vw
Rk,o
Rk
α
βs
zs
xs
Fig. 22.9 Configuration of the RRP system with N=4 revolving tethers for steady-state operation
in the xwzw-plane (φ=0). The winch modules and the attachment points on the flying rotor are
indicated by circles, Aand Bdenote a representative pair and ltdenotes the length of the connecting
tether. The distance of the kite center point Kfrom the origin Ois denoted as lK. The ground rotor
lags the flying rotor in phase by and angle δ
matic problem of steady-state operation with the kite center restricted to the xwzw-
plane (φ=0). The corresponding set of dimensionless parameters are the angles
α,βs,β,δand ωttogether with the geometric ratios Rg/Rkand lK/Rk.
Included in Fig. 22.9 are the right-handed Cartesian reference frames which are
used to describe the relative positions on the two rotors. The wind reference frame
(xw,yw,zw)is considered to be an inertial frame with origin O, its xw-axis aligned
with the wind velocity vector vwand its zw-axis pointing towards zenith. The ref-
554 Pierre Benhaïem and Roland Schmehl
erence frame (xb,yb,zb)is attached to the ground rotor, with origin at O, its xb-axis
pointing towards the tether attachment point Band rotating with angular velocity ω
around the zw-axis.
The sideslip reference frame (xs,ys,zs)has its origin at the kite center point K
and is constructed from the wind reference frame by rotating the xw- and yw-axes by
the sideslip angle βsaround the vertical axis. The kite reference frame (xk,yk,zk)is
constructed from the sideslip reference frame by rotating the xs- and zs-axes by the
angle of attack αaround the ys-axis. Following a common aeronautical convention,
the xk- and yk-axes coincide with the roll- and pitch-axes of the actuator ring, re-
spectively. The reference frame (xa,ya,za)is attached to the flying rotor, with origin
at K, its xa-axis pointing towards the tether attachment point Aand rotating with
angular speed ωaround the zk-axis, leading the rotation of the ground rotor by an
angle δ.
22.5.3 Kinematic Properties
In the following the kinematic relations for the two rotors are derived formulating
the positions of points Aand Bas functions of the geometric and kinematic parame-
ters of the steady-state problem. Point Bis fixed to the ground rotor at radius Rgand
its coordinates in the wind reference frame can be written as
rB=
cos(ωt)
sin(ωt)
0
Rg.(22.9)
The coordinates of the kite center point Kare
rK=
cosβ
0
sinβ
lK.(22.10)
Point Ais fixed to the flying rotor at radius Rk. To determine its coordinates in the
wind reference frame we first define the transformation matrices Tws and Tsk which
describe the individual rotations by angles βsand α, respectively,
Tws =
cosβssinβs0
sinβscosβs0
0 0 1
,Tsk =
cosα0 sinα
0 1 0
sinα0 cosα
.
Combining these by multiplication we can derive the matrix Twk which describes
the coordinate transformation from the kite reference frame to the wind reference
frame by two successive rotations
22 Airborne Wind Energy Conversion Using a Rotating Reel System 555
Twk =TwsTsk =
cosβscosαsin βscos βssinα
sinβscosαcos βssin βssinα
sinα0 cosα
.(22.11)
Using this transformation matrix we can formulate the coordinates of point Ain the
wind reference frame as
rA=Twk
cos(ωt+δ)
sin(ωt+δ)
0
Rk+
cosβ
0
sinβ
lK.(22.12)
Defining the instantaneous distance vector pointing from point Bto point Aas
rArB=
lt,x
lt,y
lt,z
,(22.13)
the coordinates of this vector can be calculated as
rArB=
cosβscosαcos(ωt+δ)sin βssin(ωt+δ)
sinβscosαcos(ωt+δ) + cos βssin(ωt+δ)
sinαcos(ωt+δ)
Rk
+
cosβ
0
sinβ
lK
cos(ωt)
sin(ωt)
0
Rg,(22.14)
and used to determine the geometric distance as
lt=|rArB|=ql2
t,x+l2
t,y+l2
t,z.(22.15)
Following the convention used in Sect. 22.5.2 the dimensionless tether length is
defined as lt/Rk.
To derive the tether reeling velocity as the rate of change of tether length, vt=
dlt/dt, we apply the general differentiation rule
d
dt r·r=r
r·r·dr
dt ,(22.16)
to Eq. (22.15) to get
vt=1
ltlt,xdlt,x
dt +lt,ydlt,y
dt +lt,zdlt,z
dt .(22.17)
The individual coordinate derivatives included in the right hand side of this equation
are obtained by differentiating Eq. (22.14) as
556 Pierre Benhaïem and Roland Schmehl
d
dt (rArB) =
cosβscosαsin(ωt+δ)sin βscos(ωt+δ)
sinβscosαsin(ωt+δ) + cos βscos(ωt+δ)
sinαsin(ωt+δ)
Rkω
sin(ωt)
cos(ωt)
0
Rgω.(22.18)
The dimensionless tether reeling velocity is defined as vt/(ωRk).
Next to the tether length ltand its rate of change vta third important derived
kinematic property is the angle γat which the tethers attach to the rotor rings. This
angle controls the transfer of torque from the flying rotor to the tether system and
further to the ground rotor. Considering the attachment of the tether to the ground
rotor and defining the unit vectors pointing along the tether and from the origin to
point Bas
et=rArB
lt,(22.19)
eb
x=rB
Rg,(22.20)
the tether attachment angle γgcan be computed from the zw-component of the cross
product of both vectors as
cosγg=eb
y·et= (ez×eb
x)·et= (eb
x×et)·ez,(22.21)
=1
RgltrB,xlt,yrB,ylt,x.(22.22)
This derivation involves the unit vectors eb
x,eb
yand eb
z=ezof the rotating reference
frame (xb,yb,zb)and is illustrated in Fig. 22.10.
Fig. 22.10 Definition of the
tether attachment angle γgfor
the ground rotor. The cosine
of this angle is obtained as
orthogonal projection of the
tether unit vector etonto the
tangential unit vector eb
yeb
x
γg
et
O
B
eb
z=ez
eb
y
cosγg
ω
In a similar way, the tether attachment angle γkat the flying rotor can be com-
puted from the unit vectors ea
x,ea
yand ea
z=ek
zof the rotating reference frame
(xa,ya,za)and the tether unit vector etas
22 Airborne Wind Energy Conversion Using a Rotating Reel System 557
cosγk=ea
y·et= (ek
z×ea
x)·et= (ea
x×et)·ek
z,(22.23)
=1
Rklt(rA,ylt,zrA,zlt,y)sinα+ (rA,xlt,yrA,ylt,x)cosα.(22.24)
Physically, Eqs. (22.21) and (22.23) represent the contribution of the tether force to
the dimensionless torque in the system. This kinematic expression will be used as a
starting point for the analysis of the torque transfer in Sect. 22.6.
The derivations in this section are for a representative pair of tether attachment
points. For the other pairs similar relations can be formulated by applying additional
phase shifts to the phase angle ωt.
22.5.4 Parametric Case Study
The kinematics of the torque transmission system is fully described by the Ndis-
tance vectors which connect the flying rotor to the ground rotor and which are given
by Eq. (22.14) for a representative pair of tether attachment points. In the following
the effect of the angular parameters α,βs,β,δand ωton the geometry of a tether
system with representative proportions Rg/Rk=1 and lK/Rk=2 is analyzed.
The variation of the minimum and maximum tether lengths with the elevation
angle is quantified in Fig. 22.11(left). At the limiting case of a vertical tether system,
β=90, the axes of rotation of both rotors coincide and accordingly the tethers are
of constant length lt,min =lt,max. For vanishing phase lag angle, δ=0, the tether
0 15 30 45 60 75 90
Elevation angle β[]
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Tether length lt/Rk[]
0 15 30 45 60 75 90
Angle of attack α[]
0.5
1.0
1.5
2.0
2.5
3.0
3.5
03060 90
δ[]0
30
60
90
δ[]
lt,max/Rk
lt,min/Rk
lt,max/Rk
lt,min/Rk
α=90β,βs=0β=30,βs=0
Fig. 22.11 Minimum and maximum tether lengths, lt,min and lt,max, as functions of the elevation
angle β(left) and angle of attack α(right) for Rg/Rk=1 and lK/Rk=2. The left diagram illustrates
the special case of kinematically coupled angle of elevation and angle of attack, e.g. by means of
suspension lines, while the right diagram illustrates the study for a specific constant elevation angle.
The vertical lines at 30and respectively 60indicate identical conditions in both diagrams
558 Pierre Benhaïem and Roland Schmehl
length equals the distance between the two rotors, lt=lK, and for increasing phase
lag also the tether length increases continuously. For decreasing elevation angle the
variation of tether length increases. At practically relevant values 30<β<60the
dimensionless length difference lt/Rkis roughly between 1.5 and 1.0.
The variation of the minimum and maximum tether lengths with the angle of
attack of the flying rotor is quantified in Fig. 22.11(right) for a representative value
of the elevation angle, β=30, and a vanishing sideslip angle. At the limiting case
of a horizontal flying rotor and vanishing phase lag the tethers are aligned with the
axis of rotation and accordingly the tether length is constant. It should be noted that
this holds only for the special case of Rg/Rk=1 because for any other value the
tethers are generally not aligned with the axis of rotation.
The variation of the tether attachment angles during one full revolution of the
system is illustrated in Fig. 22.12. For the interpretation of the diagrams it is im-
0 90 180 270 360
Phase angle ωt[]
0
30
60
90
120
150
180
Tether attachment angle γ[]
0 90 180 270 360
Phase angle ωt[]
0
30
60
90
120
150
180
0
30
60
90
δ[]
moment
+moment
δ[]
0
90
60
30
Fig. 22.12 Tether attachment angle γat the ground rotor (left) and at the flying rotor (right) as
functions of the phase angle ωtfor β=30,α=60,βs=0,Rg/Rk=1,lK/Rk=2
portant to note that for γ<90the tensile force in the tether contributes a positive
moment, acting in the direction of the rotation, while for γ>90it contributes a
negative moment, acting against the direction of the rotation. At the limiting case
γ=90the moment contribution vanishes (see also Fig. 22.10).
Figure 22.12(left) shows the tether attachment angle γg, as defined by Eq. (22.21),
for different values of the phase lag angle. It can be seen that the step from δ=0 to
30results in a consistent and nearly uniform shift of the sine-type curve to lower
values. The steps from 30 to 60and further to 90follow this trend and increase the
asymmetry of the curves with respect to the limiting case γ=90, however, they are
also characterized increasingly by nonlinear kinematic effects. The asymmetry with
respect to γ=90directly affects the transfer of torque to the generator because it
quantifies the net moment contribution of the corresponding force per revolution of
22 Airborne Wind Energy Conversion Using a Rotating Reel System 559
the system. It can be concluded that for the analyzed case a phase lag angle between
60 and 90results in the best achievable moment contribution. The curve for δ=0
shows the expected change of sign of the moment contribution at ωt=180 and
360, however, the extreme values γmax =151.1 and γmin =28.9 do not occur at
ωt=90 and 270, as one might expect, but at ωt=81.6 and 278.4. This is a
consequence of the geometric asymmetry of the revolving tether system tilted in
downwind direction.
Figure 22.12(right) shows the tether attachment angle γk, as defined by Eq. (22.23),
for different values of the phase lag angle. Compared to the ground rotor attachment
angle the variation is substantially smaller, for this particular case almost one magni-
tude. Furthermore, the frequency of the variation is doubled, for example, the curve
for δ=0 changes the sign of the moment contribution at ω=90,180,270 and 360.
For practically required values of the phase lag angle, as can be seen for δ&30,
the moment contribution is shifted entirely to positive values.
This behavior can be explained by the fact that for the case of kinematically cou-
pled angle of elevation and angle of attack, for which the axis of rotation of the
flying rotor passes through the center of the ground rotor, the tether system attaches
orthogonally to the flying rotor, which minimizes the kinematically induced varia-
tion of the attachment angle of the individual tethers and allows a stable counterbal-
ancing of the aerodynamic moment. On the other hand the tether system attaches
to the ground rotor at the elevation angle which causes a fundamental asymmetry
of the moment transfer to the rotor and as consequence the tether attachment angle
and the moment contribution of the tether force alternate periodically, as illustrated
in Fig. 22.12. The torque transfer mechanism will be investigated in more detail in
Sect. 22.6.
22.5.5 Conclusions
The objective of this section was to derive a kinematic model for the steady-state
operation of the tensile torque transmission system. To achieve this, it was assumed
that the system configuration in steady-state operation is known and can be de-
scribed by the angle of attack αand sideslip angle βsof the flying rotor, the eleva-
tion angle βof the kite center point, the phase lag angle δof the ground rotor, the
distances Rgand Rkof the tether attachment points from the centers of the ground
and flying rotors, respectively, and the distance lKof the kite center point from the
origin. For such a prescribed operational state Eq. (22.14) describes the time evo-
lution of the vector connecting the ground and flying rotor attachment points of the
tether, Eq. (22.15) of the length of the tether, Eq. (22.17) of the reeling velocity of
the tether and Eq. (22.21) of the attachment angle of the tether at the ground rotor.
The noncoaxial arrangement of the rotors and the phase lag distort the geome-
try of the tether system to an asymmetric state and introduce nonlinear kinematic
effects. The parametric case study has shown how these effects intensify with in-
creasing distortion of the tether system. Furthermore, the tether attachment angle
560 Pierre Benhaïem and Roland Schmehl
was identified as an important kinematic property for the moment transfer. Because
the special case of kinematically coupled angle of elevation and angle of attack leads
to nearly constant tether attachment geometry at the flying rotor, which is optimal
for a stable torque transfer, we will only consider this configuration in the remainder
of the chapter.
22.6 Power Transmission in Steady-State Operation
The aerodynamic force and moment of the ring kite are transferred to the ground
conversion system by tensile forces only. The particular feature of the system is
the power takeoff by two different, intrinsically coupled energy conversion mecha-
nisms. The direct mechanism is based on the resultant moment that the tensile forces
exert on the ground rotor, whereas the secondary mechanism is based on the length
variation of the tethers. In this section a model for the power transmission charac-
teristics of the tether system is formulated for steady-state operation. This model is
used to assess the transmission efficiency as a function of the problem parameters,
as well as the relation between transmitted torque and aerodynamic force. The fo-
cus of the analysis is on the tether system and not on the ring kite itself. It should be
noted that the use of suspension lines is not considered in this analysis.
22.6.1 Energy Equation of the Single Tether
To assess the power transmission by the revolving tether system we first analyze
the energy balance of the single tether. For this purpose the tether is cut free at the
attachment points, as illustrated in Fig. 22.13. Neglecting the effects of aerodynamic
Fig. 22.13 Forces and veloc-
ities at the attachment points
of a representative tether. The
other tethers and their attach-
ment points are not depicted.
The attachment points Aand
Bmove with circumferen-
tial velocities vA=ωRkand
vB=ωRg. In the depicted
situation the tether length is
decreasing which requires the
winch module at attachment
point Bto reel the tether in
with a velocity vt
B
A
Ft
ω
ω
vA
vB
Rg
Rk
vt
Ft
γg
γk
22 Airborne Wind Energy Conversion Using a Rotating Reel System 561
drag and inertial forces and assuming that the tether is straight and inelastic, it can be
concluded that the tensile forces at the two attachment points are of equal magnitude
and pointing in opposite direction. In reference to Fig. 22.13 the energy equation can
be formulated as
Ftcos γkωRk=FtcosγgωRg+Ftvt.(22.25)
The left hand side represents the power transferred from the flying rotor to the tether
by the circular motion of the attachment point A, while the first term on the right
hand side represents the power transferred from the tether to the ground rotor by the
circular motion of the attachment point B. The third contribution is the mechanical
power that is transferred to the winch module that is attached to the rotor at point
B. If we define a characteristic power of the tensile torque transmission problem
as FtωRkand divide Eq. (22.25) by this expression we obtain the dimensionless
equation
cosγk=cosγgRg
Rk+vt
ωRk.(22.26)
This fundamental equation relates the two tether attachment angles and the dimen-
sionless tether reeling velocity introduced in the context of Eq. (22.18).
The variation of the three dimensionless power contributions is shown in Fig. 22.14.
The case of vanishing phase lag is depicted in Fig. 22.14(left) and, as expected, in-
0 90 180 270 360
Phase angle ωt[]
-1.0
-0.5
0.0
0.5
1.0
Dimensionless power []
0 90 180 270 360
Phase angle ωt[]
-1.0
-0.5
0.0
0.5
1.0
δ=0δ=30
cosγk
cosγgRg
Rk
vt
ωRk
vt
ωRk
cosγk
cosγgRg
Rk
Fig. 22.14 Kinematic modulation of the dimensionless power balance at the tether during one
revolution for Rg/Rk=1,lK/Rk=2,β=30,βs=0and α=60. The dashed line represents the
sum of all contributions
dicates that the net power that is transferred from the flying rotor to the tether during
one revolution is close to zero. As consequence, the other two power contributions,
the shaft power contribution to the ground rotor and the reeling power transferred to
the winch module have to cancel out each other. When applying a phase lag angle
of δ=30the net power transferred from the flying rotor to the tether is positive,
562 Pierre Benhaïem and Roland Schmehl
which is indicated by the upwards shift of the corresponding curve. It is obvious
from Fig. 22.14 that for this particular case, the input power is balanced by com-
paratively large variations of the output power contributions. In the real system, the
associated losses would be significant, which is a point of concern.
It is important to note that Eq. (22.25) does not provide any information about the
actual values of the tensile force and their power contributions but only the relative
distribution of these contributions depending on the instantaneous kinematics of the
system. To derive the actual values of the tensile forces the equations of motion
of the ground and flying rotors have to be considered, which is the topic of the
following section.
22.6.2 Quasi-Steady Motion of the Flying Rotor
Because of the relatively low mass of the flying rotor and the tethers the airborne
system adjusts rapidly to force imbalances. The resulting quasi-steady motion is
governed by the equilibrium of the aerodynamic force distribution, the tether forces
and gravitational forces. If we neglect, for simplicity, the effect of gravity, the equi-
librium of forces and moments acting on the flying rotor can be formulated as
Fa=
N
i=1
Ft,i,(22.27)
Ma=
N
i=1
(rA,irK)×Ft,i,(22.28)
which is illustrated in Fig. 22.15.
Fig. 22.15 Forces and mo-
ments acting on the ground
and flying rotors. The resul-
tant aerodynamic force and
moment are represented by
their components in the kite
reference frame. The reaction
force and moment acting in
the bearing mechanism of
the ground rotor are repre-
sented by their components
in the wind reference frame.
Mg,zdenotes the transmitted
moment that is available for
conversion into electricity
Mk
a,z
Mk
a,x
vw
O
Fk
a,z
Fk
a,y
Fk
a,x
Mk
a,y
Ft,i
Mg,x
Mg,y
Mg,z
Fg,xFg,z
Fg,y
22 Airborne Wind Energy Conversion Using a Rotating Reel System 563
The resultant aerodynamic force and moment vectors, Faand Ma, are represented
by their components in the kite reference frame. Fk
a,zis the main force component
acting along the rotor axis, while Fk
a,xand Fk
a,yare the two transverse components.
Accordingly, Mk
a,zis the main moment component acting around the rotor axis, while
Mk
a,yand Mk
a,xare the components around the pitch and roll axes of the kite. The
zk-components of the aerodynamic force and moment are the two key functional
elements of the RRP system, responsible for tensioning the tether system and for
generating torque that is transferred to the ground to be converted into electricity.
The aerodynamic loading of the flying rotor is balanced by the Ntether forces
Ft,i. The calculation of the individual moment contributions specified by Eq. (22.28)
differs from the calculation of the tether attachment angle γk, as specified by
Eq. (22.23), only by the additional multiplicative factors Ft,i, the magnitudes of the
tether forces.
The difficulty in solving the quasi-steady equilibrium equations for the unknown
tether forces Ft,icomes from the fact that except for the design parameters Rg,Rk
and Rk,o, the actuated tether lengths lt,iand the wind velocity vwall other problem
parameters, α,βs,β,φ,δ,ωand lKhave to be regarded as degrees of freedom, sub-
ject to additional kinematic coupling conditions. This differs from the starting point
of the kinematic analysis in Sect. 22.5 where we assumed steady-state operation of
the system with known values of these problem parameters.
22.6.3 Approximate Solution of Steady-State Operation
Instead of attempting to solve the problem of quasi-steady motion of the flying rotor
exactly, as described by Eqs. (22.27) and (22.28), we derive an approximate solution
of the idealized problem of steady-state operation. Following the approach described
in Sect. 22.5 we consider only the principal force axis of the system, which is the
axis of rotation of the flying rotor. To fulfill the force equilibrium in this axis we
assume that the components of the tether forces in this direction are all of equal
magnitude, which is formally expressed by the conditions
Ft,i·ek
z=Fk
a,z
N,i=1,...,N.(22.29)
Representing the force vectors as Ft,i=Ft,iet,i, where et,irepresents the unit vector
along tether i, the individual force magnitudes can be derived as
Ft,i=Fk
a,z
Net,i·ek
z
,i=1,...,N.(22.30)
The tether forces defined by these equations exactly balance the axial aerodynamic
force component Fk
a,z. Furthermore, the resultant roll and pitch moments of the tether
forces vanish because the geometric center of the tether attachment points coincides
564 Pierre Benhaïem and Roland Schmehl
with the kite center Kand the moment-contributing force components Ft,i·ek
zare all
equal. As consequence, the corresponding aerodynamic moment components Mk
a,x
and Mk
a,yvanish and
Ma=Mk
a,z.(22.31)
However, the tether forces defined by Eq. (22.30) induce transverse force compo-
nents which need to be balanced by the transverse aerodynamic force components
Fk
a,xand Fk
a,yand which lead to transverse compensating motions. We can derive the
following expressions for the ratios of the transverse aerodynamic force components
to the axial force component
Fk
a,x
Fk
a,z
=1
N
N
i=1
et,i·ek
x
et,i·ek
z
,(22.32)
Fk
a,y
Fk
a,z
=1
N
N
i=1
et,i·ek
y
et,i·ek
z
.(22.33)
The moment components acting around the rotational axes of the flying rotor and
the ground rotor can be evaluated as
Ma
RkFk
a,z
=1
N
N
i=1
(ea
x,i×et,i)·ek
z
et,i·ek
z
=1
N
N
i=1
cosγk,i
et,i·ek
z
,(22.34)
Mg,z
RkFk
a,z
=1
N
Rg
Rk
N
i=1
(eb
x,i×et,i)·ez
et,i·ek
z
=1
N
Rg
Rk
N
i=1
cosγg,i
et,i·ek
z
,(22.35)
using the product RkFk
a,zas a characteristic moment of the tensile torque transmis-
sion problem, for normalization of the moment components.
To compute an approximate solution of the steady-state operation of the flying
rotor we regard the transverse aerodynamic force components given by Eqs. (22.32)
and (22.33) as perturbations. Based on the formulation of an optimization problem
we minimize the perturbations to find the best solution. Starting point of the opti-
mization is a specific configuration defined by the dimensionless parameters β,δ
and lK/Rk. The orientation of the flying rotor with respect to the wind, defined by
the flow angles αand βs, is varied to minimize the perturbations. Because the trans-
verse forces oscillate periodically we use the following objective function
f(α,βs) = maxFk
a,xminFk
a,x+maxFk
a,x+minFk
a,x
+maxFk
a,yminFk
a,y+maxFk
a,y+minFk
a,y(22.36)
applying the min and max operators to to the complete interval 0ωt360.
The solution of the optimization problem is the combination of flow angles αand
βsthat minimizes Eq. (22.36). The solution is approximative because the residual
transverse forces are causing compensating motions which are not taken into ac-
22 Airborne Wind Energy Conversion Using a Rotating Reel System 565
0 90 180 270 360
Phase angle ωt[]
-0.010
-0.005
0.000
0.005
0.010
Transverse force []
Fk
a,x/Fk
a,z
Fk
a,y/Fk
a,z
0 90 180 270 360
Phase angle ωt[]
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
Moment around rotor axis []
Ma/(RkFk
a,z)
Mg,z/(RkFk
a,z)
M/(RkFk
a,z)
Fig. 22.16 Steady-state operation of the flying rotor with dimensionless transverse force compo-
nents (left) and moment components around the rotor axes (right) for N=4, Rg/Rk=1, lK/Rk=2,
β=30and δ=30. Initial values for the minimum search are α0=60,βs,0=0and the solution
values are α=62.36,βs=4.38
count in the analysis. However, the following results indicate that the effect of the
compensating motions is minor and can be neglected.
A representative result is illustrated in Fig. 22.16. The left diagram shows the
periodic variations of the transverse force components acting on the flying rotor
which are of the order of 1% of the axial force component. The mean values Fk
a,x
and Fk
a,yvanish. The right diagram shows the periodic variations of the generated
aerodynamic moment and the usable moment at the ground rotor, as well as the
difference of both curves. It should be noted that the product RkFais only a reference
moment used for normalization and does not have any other physical meaning than
providing a characteristic order of magnitude value. Compared to the single-tether
behavior, as shown in Figs. 22.12 and 22.14, the frequency of the oscillation is
increased by a factor of N=4, which is caused by the superposition of phase-shifted
data.
It can be recognized that the periodic variations of the moments Mk
a,zand Mg,z
are shifted in phase by the angle δ=30. The moment difference M=MaMg,z
is associated with the periodic variation of the net mechanical energy processed by
the winch modules. For a single tether this relationship is given by Eq. (22.26). For
the entire system the normalized moment difference is computed as
M
RkFk
a,z
=1
NωRk
N
i=1
vt,i
et,i·ek
z
.(22.37)
It can further be recognized that the mean value of the moment difference for a full
revolution of the tether system is zero, which means that the average moments are
identical,
566 Pierre Benhaïem and Roland Schmehl
Ma=Mg,z.(22.38)
This essentially means that the transmission efficiency for the ideal system in
steady-state operation is, as expected, 100%. For a real system the electrical in-
terconnection of the winch modules will cause conversion losses that will signifi-
cantly reduce the transmission efficiency. Based on the presented analytic modeling
framework these losses as well as all other types of losses (tether aerodynamic drag,
bearing friction losses, etc.) can be taken into account in a future study. It is also ob-
vious from the analysis that the number of peripheral tethers affects the frequency
of variation the instantaneous kinematic properties and the associated forces and
moments but has no effect on the mean values.
In Fig. 22.17 the representative example is expanded to the full range of values
of the phase lag angle δ. The left diagram shows the computed values of the flow
0 30 60 90 120 150 180
Phase lag angle δ[]
0
10
20
30
40
50
60
70
Flow angles []
α
βs
0 30 60 90 120 150 180
Phase lag angle δ[]
0.0
0.1
0.2
0.3
0.4
0.5
Transferred moment []
Ma/(RkFk
a,z)
45
β[]
60
30
30 45
60
β[]
Fig. 22.17 Flow angles αand βs(left) and dimensionless average moment Ma/(RkFk
a,z)(right)
as functions of the phase lag angle δ, for various values of the elevation angle βand for N=4,
Rg/Rk=1 and lK/Rk=2. Initial values for the minimum search are α0=90βand βs,0=0
angles αand βs, while the right diagram shows the average moment Manormalized
by the reference value RkFk
a,z. It can be recognized that for the limiting values δ=0
and δ=180no moment can be transmitted, while the maximum moment Ma,max
can be transmitted for δmax. For this particular example we have δmax .90. This
maximum moment increases with increasing elevation angle β.
22.6.4 Requirements for the rotor aerodynamic design
To this point the focus of the analysis has been the transmission of torque from
the flying rotor to the ground rotor. From Fig. 22.17(right), or similar diagrams for
22 Airborne Wind Energy Conversion Using a Rotating Reel System 567
other combinations of problem parameters, the possible range of the transmittable
aerodynamic moment Macan be determined as a function of the aerodynamic force
Fk
a,z. It can further be determined how within this range the moment varies with the
phase lag angle δ. From Fig. 22.17(left) we can determine the required orientation
of the flying rotor to transmit this moment to the ground while in a steady state of
operation. However, these parameters also have a major effect on the aerodynamics
of the flying rotor. In fact, the two key functional components of the RRP system,
the generation of the aerodynamic moment and the transmission of this moment
to the ground rotor, need to be matched properly to achieve steady-state operation.
It is the purpose of this section to derive the top-level requirements for the rotor
aerodynamic design. The specific implementation of the rotary ring kite is however
not within the scope of the present analysis.
To determine the aerodynamic characteristics of the ring kite it is useful to de-
compose the resultant aerodynamic force Fainto lift and drag components. By def-
inition the drag force Dis aligned with the apparent wind velocity va=vwvk,
while the lift force Lis perpendicular to the drag component. Assuming that the
velocity of the kite vk=drK/dt can be neglected during steady-state operation we
can use the components of Fain the wind reference frame to calculate
L=qF2
a,y+F2
a,z,(22.39)
D=Fa,x.(22.40)
Using the transformation matrix Twk defined by Eq. (22.11) the components of the
instantaneous aerodynamic force and its mean value can be calculated as
Fa=
Fa,x
Fa,y
Fa,z
=Twk
Fk
a,x
Fk
a,y
Fk
a,z
and Fa=
cosβssinα
sinβssinα
cosα
Fk
a,z,(22.41)
because Fk
a,x=Fk
a,y=0. Furthermore, the mean values of lift and drag can be cal-
culated as functions of the axial aerodynamic force component and the flow angles
L=Fk
a,zqsin2βssin2α+cos2α,(22.42)
D=Fk
a,zcosβssinα,(22.43)
which are related by
L
D=qsin2βssin2α+cos2α
cosβssinα.(22.44)
Equations (22.42), (22.43) and (22.44) define the required aerodynamic character-
istics of the airborne system as functions of the axial aerodynamic force Fk
a,z, the
angle of attack αand the sideslip angle βs.
The dimensional forces and the moment are generally expressed in terms of di-
mensionless aerodynamic coefficients
568 Pierre Benhaïem and Roland Schmehl
L=1
2ρCLv2
wS,with CL=CL(αeff,λ),(22.45)
D=1
2ρCDv2
wSwith CD=CD(αeff,λ),(22.46)
Ma=1
2ρCMv2
wRk,oSwith CM=CM(αeff,λ),(22.47)
where S=π(R2
k,oR2
k)is the swept rotor area, λis the tip speed ratio defined by
λ=ωRk,o
vw(22.48)
and αeff is the angle between wind velocity vector vwand the rotor disk, defined by
cosαeff =ek
x·ex,(22.49)
αeff =arccos(cosβscosα).(22.50)
The sideslip angle and the angle of attack contribute equally to αeff because of the
ring-shaped swept area of the rotor. For a static wing this is not the case and the
effects of sideslip angle and angle of attack have to be differentiated. It can be shown
that the axial moment coefficient CMis formally related to the more customary
power coefficient Cp[13, p. 45] by the relation
CM=Cp
λ.(22.51)
It should also be noted that the induced velocity is not taken into account in the
above simplified aerodynamic analysis. An excellent follow-up study in this direc-
tion is [13, p. 99–103] which assesses Glauert’s momentum theory for a gyrocopter
in autorotation.
Aside of the influence of the operational parameters αeff and λ, the aerodynamic
coefficients depend also on design parameters, for example, the solidity σof the
rotor. Because the rotor aerodynamic design is out of the scope of the present study
the analysis will not be continued at this point. It should be noted though that rotary
kites with flexible wings have not been studied scientifically so far.
It has to be assumed that the aerodynamic characteristics required for steady-state
operation of the tensile torque transmission system, namely Eqs. (22.42), (22.43)
and (22.44), can not necessarily be achieved by a specific design of the ring kite.
This problem can be overcome by first designing the ring kite for the required aero-
dynamic moment and then, in a second step, designing an additional lifting kite
which is tethered to the center of the ring kite and which supplements the aero-
dynamic characteristics of the ring kite to meet the overall requirements for the
combined system.
22 Airborne Wind Energy Conversion Using a Rotating Reel System 569
22.6.5 Conceptual Design Example
In this section we outline a conceptual design process based on the developed mod-
eling framework. Starting point is a tensile torque transmission system with a given
geometry. We chose the intermediate-scale system defined in Table 22.4. The value
Table 22.4 Geometric and
operational parameters of
an intermediate-scale tensile
torque transmission system.
This configuration is also
portrayed in Fig. 22.9
Parameter name Symbol Value Unit
Ground rotor diameter dg50 m
Flying rotor inner diameter dk40 m
Distance between rotors lK100 m
Elevation angle β30 deg
Phase lag ground rotor δ45 deg
Wind speed vw12 m/s
Angular speed ω2.05 rad/s
Nominal power P1.4 MW
of the phase lag angle is set well below the limiting value for maximum torque
transfer, δmax to ensure good control behavior. From Table 22.4 we get
Rg
Rk=1.25 (22.52)
lK
Rk=5.(22.53)
In a first step we calculate the aerodynamic moment that is required for transmit-
ting the nominal power Pat an angular speed ωof the rotor as
Ma=P
ω=683kNm.(22.54)
We then determine the orientation of the flying rotor, in terms of the flow angles α
and βs, which minimizes the transverse perturbation forces defined by Eqs. (22.32)
and (22.33). To compute this best approximation of steady-state operation we min-
imize the objective function defined by Eq. (22.36). Starting from the initial values
α0=60and βs,0=0the iterative optimization procedure leads to the values
α=60.08,(22.55)
βs=1.05,(22.56)
which reduce the oscillation amplitudes of Fk
a,x/Fk
a,zand Fk
a,y/Fk
a,zto below 0.05%.
From Eq. (22.34) we can then calculate
Ma
RkFk
a,z
=0.1365,(22.57)
570 Pierre Benhaïem and Roland Schmehl
which, using Eq. (22.54) and the value of Rkcan be solved for the axial aerodynamic
force
Fk
a,z=250kN.(22.58)
Using Eqs. (22.42), (22.43) and (22.44) we can now compute the lift and drag force
as
L=125kN,(22.59)
D=217kN,(22.60)
L/D=0.576 (22.61)
It is important to note that the numerical values given by Eqs. (22.58), (22.59) and
(22.60) are not the result of an aerodynamic analysis but instead are required to
transmit the aerodynamic moment specified by Eq. (22.54) to the ground rotor while
maintaining a steady state of operation of the revolving tether system.
As a next step we analyze the aerodynamic requirements of the airborne subsys-
tem. For conventional wind turbines the tip speed is generally limited by a noise
constraint. In [13, p. 339] this tip speed limit is given as 65 m/s. Considering the
value of ωlisted in Table 22.4 and using a tip speed limit of 70 m/s we can calcu-
late the outer diameter of the rotor, the swept area of the rotor and from Eq. (22.48)
the tip speed ratio as
dk,o=70m,(22.62)
S=2592m2,(22.63)
λ=5.98.(22.64)
Based on these values we can compute the aerodynamic coefficients from Eqs. (22.45),
(22.46), (22.47) and (22.51) as
CL=0.546,(22.65)
CD=0.948,(22.66)
CM=0.0854,(22.67)
Cp=0.51.(22.68)
The practical design of a ring kite would aim to achieve the required moment co-
efficient specified by Eq. (22.67) and then, in a second step, supplement its lift and
drag forces by tethering an additional lifting kite to the center of the ring kite, as
explained in Sect. 22.6.4.
22.6.6 Design Recommendations and Conclusions
The geometric proportions of the tensile torque transmission system have a decisive
role. It is evident that the longer the tether system and the smaller the ground ro-
22 Airborne Wind Energy Conversion Using a Rotating Reel System 571
12345
Relative distance between rotor centers lK/Rk[]
0
1
2
3
Rotor size ratio Rg/Rk[]
0.1
0.2
0.3
0.5
0.7
1.0
1.0
1.5
2.0
2.5
h<0
h<0
et,iek
z
R
g
Fig. 22.18 Transferable aerodynamic moment Ma/(RkFk
a,z)as function of the relative distance
lK/Rkbetween rotor centers and the rotor size ratio Rg/Rkfor β=30,δ=45. The colored
contour plot and the solid black isolines cover only valid regions with positive ground distance
of the tether attachments on the flying rotor (h>0). The dashed line R
gmarks the condition of
maximum transferable moment which is also a validity limit for the approximate solution of steady-
state operation. The dotted red isolines mark the condition of ground contact for different values of
the relative outer size Rk,o/Rkof the flying rotor. The limiting isoline (Rk,o/Rk)h=0=1 coincides
with the border of the contour plot. The dashed line at lK/Rk=cotβ1.73 is the reference for
the lower limit, for α=90β
tor the lower the transferable torque. The fundamental relationship is quantified by
Eq. (22.26) which describes the influence of the tether attachment angles and the
rotor size ratio. To support this recommendation quantitatively we have computed
the transferable aerodynamic moment as a function of the geometric proportions of
the tether system. The result of this analysis is illustrated in Fig. 22.18 for a system
with representative elevation angle and phase lag angle. The contour plot and the
solid isolines show that the transferable moment decreases for increasing distance
between the rotors and that it increases with increasing size of the ground rotor. The
diagram also includes the condition of ground contact of the flying rotor for differ-
ent values of its relative outer size Rk,o/Rk. As shown in Fig. 22.19 this condition
(Rk,o/Rk)h=0can be derived from the ground distance function
h
Rk=lK
RksinβRk,o
Rksinα,(22.69)
by setting h=0 and solving for Rk,o/Rk. For example, if we consider a system with
a relative outer size Rk,o/Rk=2 only the region to the right of the dotted isoline
labeled by the value (Rk,o/Rk)h=0=2 is physically feasible because of positive
ground distance (h>0). The data point at lK/Rk=5 and Rg/Rk=1.25 refers to the
specific calculation example in Sect. 22.6.5 which results in values Ma/(RkFk
a,z) =
572 Pierre Benhaïem and Roland Schmehl
Fig. 22.19 Calculation of
the distance hof the flying
rotor from the ground. The
specific illustrated geometric
case has been described in
Sect. 22.6.5. Because of the
relatively large value of lK/Rk
the sideslip angle is in this
case small (βs<1) and
the axis of the flying rotor
approximately points to the
origin (α=90β)
Rk,o
zw
α
βh
lK
xw
vw
OR
g
Rg
0.1365 and (Rk,o/Rk)h=0=2.88. A general conclusion from Fig. 22.18 is that an
increasing size of the flying rotor requires generally an increasing distance between
the rotors.
The deviation of the limiting isoline (Rk,o/Rk)h=0=1 from the dashed reference
line at lK/Rk=cotβ1.73 indicates how much the angle of attack αin steady-
state operation deviates from the value α=90β=60. For 1.2<Rg/Rk<1.8
the physically feasible region extends to values far below lK/Rk=1.73. This indi-
cates that for these geometric proportions the flying rotor has an increased ground
clearance as consequence of a relatively low angle of attack.
The dashed line in Fig. 22.18 marks the condition where for α=90βthe
flying rotor plane touches the ground rotor. Considering Fig. 22.19 where this point
is marked as R
gthe equation of the limiting line can be derived as
R
g
Rk=1
cosβ
lK
Rk=1.155 lK
Rk.(22.70)
Above this line the geometric proportions of the system are such that the revolving
tethers pass through constellations in which they are momentarily orthogonal to
the axis of the flying rotor. In this specific situation the fundamental assumption
on which the approximate solution of steady-state operation is based, Eq. (22.30),
becomes singular which introduces large artificial forces in the system. However,
this anomaly of the theoretical model occurs in a region of the design space that has
to be avoided for the sake of operational stability and for this reason the region is
excluded as an invalid region (et,iek
z).
It is obvious from Fig. 22.18 that the size of the flying rotor cannot be much
larger than the diameter of the ground rotor if a practically significant torque is to
be transferred. This has been confirmed also by the experimental tests. From a rotor
aerodynamics point of view, the rotational speed ω= 2.05 rad/s, implies a tip speed
ratio of around 6, which is a typical value for conventional wind turbines, and which
is achievable with rigid wings. Lower values of the tip speed ratio, for example 4,
are achievable with soft wings.
The Parotor should be restudied in all possible variants, including soft and rigid
rotors, parachutes with a large opening [24] (with a diameter of 2 to 3 times the wing
22 Airborne Wind Energy Conversion Using a Rotating Reel System 573
span), including also some adaptations of centrifugally stiffened rotors [18, 22, 29],
and above all C-shaped modular rigid structures with hinges [19] rotor components.
Wings or blades should sweep more area and travel faster, like kites making loops
[4], but within the rotating structure.
22.7 Current and Future Investigations
The focus of the present study has been the technical feasibility of the proposed
RRP system. We have used a small-scale test setup to demonstrate the fundamental
working principles and a theoretical model of the revolving tether system to show
that steady-state operation is in principle feasible for a specific combination of de-
sign and operational parameters. A next important development step will be the
design of a rotary ring kite and lifting kite combination with specific aerodynamic
characteristics. Of similar importance will be the design of a rotating reel system
with efficient energetic balancing of the interconnected winch modules. A possible
realization could be mechanical coupling of the winch modules using differential
reeling to avoid the additional losses of electrical conversion. With the worked out
conceptual and preliminary designs of these two key technology components the
assessment of the energy harvesting potential of the RRP system can be further re-
fined.
Next to the overall system design and the conversion performance we will also
investigate other important aspects of the technology. A key advantage is vertical
take off and landing (VTOL) of the flying rotor with the help of the ground rotor. For
this purpose the generator, which is connected to the ground rotor, acts as a motor
to power the rotation of the launching Parotor. A possible VTOL configuration of
the small-scale model described in Sect. 22.4.1 is shown in Fig. 22.20.
Fig. 22.20 Possible config-
uration of the small-scale
system shown in Fig. 22.7 be-
fore vertical launch maneuver
574 Pierre Benhaïem and Roland Schmehl
As shown in Fig. 22.9, and also in the conceptual design example discussed in
Sect. 22.6.5, the outer diameter of the flying rotor can exceed the diameter of the
ground rotor to some degree. It is not a problem in the case of the implementation
of a rigid or semi-rigid [11] flying rotor. But in the case of the implementation of
a flexible rotor, the diameter of the Parotor should not exceed the diameter of the
ground rotor.
If there is no or very low wind the generator of the ground rotor is operated as a
motor to keep the flying rotor airborne in a helicopter mode. The winches are also
suitable to assure a fast landing in hazardous whether conditions. The envisaged
emergency strategy for urgent depower uses a central depower line as illustrated in
Fig. 22.5(c). The peripheral tethers are detached from the Parotor which is only kept
by the central rope. Thus the Parotor turns around, losing its lift and drag, coming
down towards the central station. In case of implementation of the second mode of
generation, as described in Sect. 22.3.3, the suspension lines are also detached.
In case of failure of the electrical system and/or in case of rupturing of one or
more tethers, the Parotor can be held by the central rope. The Parotor can also be
held by the suspension lines (Figs. 22.6 and 22.5) if the second mode of generation
is implemented as described in Sect. 22.3.3.
The wind velocity can vary significantly over the swept area of a huge flying
rotor. A flexible rotor could employ active deformation of its blades to change their
aerodynamic characteristics [12] and to adjust to varying wind conditions.
The RRP system follows the topology model of a single large rotary kite in
steady-state rotation, anchored to the ground or sea surface by tethers [7, 30].
Thanks to its uniform motion a huge flying rotor is more easily recognized by other
users of the airspace than a farm of smaller units with wings moving in multiple
directions. Small wind turbines carrying lights are launched then move along the
peripheral tethers. Then they are fixed at a desired height. They provide needed
visibility markings.
An implementation of superimposed rotors is also studied. According to some
observations [21, 24] there are possible interesting aerodynamic features increasing
the efficiency of each rotor from a stack with regard to an identical but single rotor.
A phase lag angle of a rotor with the nearby rotor can increase the transmission with
relatively longer peripheral tethers. The rotors act then as “ring torque” [24].
22.8 Conclusions
In this chapter we have presented a rotary ring kite which uses a revolving tether
system to transfer the generated aerodynamic torque to a ground rotor which is con-
nected to a generator. To analyze this novel concept we have developed a kinematic
model of the tether system and a numerical procedure to determine an approximate
solution for steady-state rotation. This operational mode is characterized by minimal
periodic compensation motions of the flying rotor. To realize this mode the flying
rotor has to have specific aerodynamic characteristics and a specific inclination with
22 Airborne Wind Energy Conversion Using a Rotating Reel System 575
respect to the flow, also the length of the tethers has to be adjusted continuously
with the rotation of the system.
The analysis has further revealed that the power transmission is an interplay be-
tween three periodically varying terms of equal magnitude: the power generated by
the ring kite, the shaft power available at the ground and the net reeling power of the
interconnected winch modules. For an ideal lossless system the net reeling power
vanishes over an entire revolution and the transmission efficiency is 100%. In reality,
however, energy conversion losses in the winch modules will reduce the transmis-
sion efficiency significantly. A possible solution to reduce these losses would be a
mechanical interconnection, using electrical machines only to provide a differential
reeling power.
We have also analyzed a secondary mode of energy conversion which is based on
the selective unloading of the tethers during reel in. This is realized by periodically
shifting the tensile load to additional suspension lines, with the theoretical result of
a positive net reeling power of the interconnected winch modules. However, because
of the inevitable cyclical force imbalance the system will tumble and a steady-state
of operation can not be achieved.
Experimental tests with a small-scale model of the Rotating Reel Parotor system
have confirmed some of the theoretical findings. In place of electrical machines,
which would allow for precise actuation of the tethers, this first physical demonstra-
tor uses winch modules with rotational spring mechanisms. As consequence, the
results of this experiment can hardly be used to assess the original concept.
The present study serves as a starting point for future investigations. The planned
prototypes increase in logical scaling steps: 5 m rotor diameter and tip height, then
10 m as small-scale models; 25 m, 50 m and 100 m as intermediate-scale models
along with a critical assessment of the market opportunities in remote locations; 500
m, 1 km and more as large-scale models harnessing high-altitude winds at utility
scale. An essential part of this roadmap is the question about the scalability of the
Parotor towards very large dimensions.
The Python source code of the analysis tools developed in the frame of this chap-
ter is available from a public repository [28].
Acknowledgements The authors would like to thank Antonello Cherubini for his help with the
mechanical analysis; Antoine Delon, for the geometrical and mathematical representations of the
reference axis and kinematics; Ben Lerner for the reorganization of some elements; David Murray
for proofreading.
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... Rotating Reeling Parotor A more detailed description of the system can be found in [7]. The Parotor uses a single rotor and TRPT. ...
... It will therefore be very challenging to keep all rotors operating at an optimal tip speed ratio. It analysing the operation of a TRPT [7]. More research and analysis is required to identify an optimal TRPT conguration. ...
... Other than this work, the only mathematical representation of a rotary AWES, that incorporates TRPT, was undertaken by Benhaïem and Schmehl [7]. They analyse the steady state operation of the RRP system described in Section 2.2.4. ...
Thesis
Full-text available
Airborne wind energy is a novel form of wind power. Through the use of lightweight wings and tethers it aims to access locations out of reach to current wind harvesting devices, at a lower cost and with a lower impact on the environment. There are multiple airborne wind energy systems currently under development, one group of these, referred to as rotary systems, use multiple wings networked together to form rotors. This thesis presents an analysis on the design and operation of rotary systems, with a particular focus on the power transmission from the airborne components down to the ground. There are various power transmission methods used for rotary systems, among them tensile rotary power transmission uses multiple networked tethers held apart by a small number of rigid components to transfer torque from a flying rotor down to a ground station. The aim of this research is to improve the design and operation of rotary airborne wind energy systems that incorporate tensile rotary power transmission, and to assess system performance based on mathematical modelling and test data. It focuses on the Daisy Kite system design, a rotary system, being developed by Windswept and Interesting. Included in this thesis work is the development of three mathematical representations to support systematic analysis and design improvement. The first representation, a steady state model, is used to analyse rotary system design. The second and third models are dynamic representations of varying complexity. Also included is an experimental campaign conducted on the Daisy Kite in collaboration with Windswept and Interesting. Field tests are carried out on nine different Daisy Kite prototypes at their test site on the Isle of Lewis, Scotland. Measured data is collected for the various prototype designs under different operating conditions. The measured data is used to assess the reliability of the three mathematical representations. This allows the models to be validated and compared to one another in terms of their accuracy and computational efficiency. During the experimental campaign several design and operational improvements are made that increase the power output and lead to more reliable operation. The mathematical representations are used to identify key design factors and to optimise rotary system design. Improved understanding and design of the rotary airborne wind energy system has been achieved through this holistic investigation.
... Rotating reel A similar concept using a rotation reel is given in [27] hexmesh multi-mesh fractal: recursion rule Differential Circuses J.M.E Beaujean published an idea with two antagonistic circulararranged sail patters whose differential motion is used [28] ...
Preprint
Full-text available
Major hindrances in land-based wind-energy at Germany are the availability of locations, slow approval procedures, and the opposition of nearby residents. Pit mines, on the other hand, represent large open areas whose industrial use is permitted, and which are also a natural location for pumped storage hydro power. However, conventional wind turbines are not be suited to be placed inside the pit. AWE (airborne wind energy) provides a solution for the height. Currently available systems however have small single-unit power, and grouping them into a farm is not straightforward. The scaling of single airborne units is limited by increased area weight and large inertial forces limiting the turn rate of the airborne wing. A network approach solves the grouping problem and removes the need to scale the airborne units to extreme sizes. This approach however still needs a lot of research to be done. Having direct feedback between a running prototype and science would make the Saxony coalfield an ideal test-bed for this type of large-scale wind energy system. In summary, a research institution should be founded ("the NASA of Wind energy") comprising the research areas of • CFD Simulation (Aerodynamics with simplified models and arbitrary topology, Weather, Aerolastics) • Mechanical engineering, High-performance hydraulics • Textile engineering • computer vision and robotics for inspection and maintenance, optimal control • hydrology and spatial planning for global site selection • ecology studying on the one hand the impact of different solutions to wildlife and on the other hand possible solutions to revitalize the pit mines's landscape 2
... • Auto-gyro concepts (flying rotors) with tensile torque transfer to the ground and ground-based energy conversion [16,17,18]. ...
Article
Full-text available
Airborne wind energy systems convert wind energy into electricity using tethered flying devices, typically flexible kites or aircraft. Replacing the tower and foundation of conventional wind turbines can substantially reduce the material use and, consequently, the cost of energy, while providing access to wind at higher altitudes. Because the flight operation of tethered devices can be adjusted to a varying wind resource , the energy availability increases in comparison to conventional wind turbines. Ultimately, this represents a rich topic for the study of real-time optimal control strategies that must function robustly in a spatiotemporally varying environment. With all of the opportunities that airborne wind energy systems bring, however, there are also a host of challenges, particularly those relating to robustness in extreme operating conditions and launching/landing the system (especially in the absence of wind). Thus, airborne wind energy systems can be viewed as a control system designer's paradise or nightmare, depending on one's perspective. This survey article explores insights from the development and experimental deployment of control systems for airborne wind energy platforms over approximately the past two decades, highlighting both the optimal control approaches that have been used to extract the maximal amount of power from tethered systems and the robust modal control approaches that have been used to achieve reliable launch, landing, and extreme wind operation. This survey will detail several of the many prototypes that have been deployed over the last decade and will discuss future directions of airborne wind energy technology as well as its nascent adoption in other domains, such as ocean energy.
Article
Full-text available
Rotary airborne wind energy (AWE) systems are a family of AWE devices that utilise networked kites to form rotors. One such device is the Daisy Kite developed by Windswept and Interesting. The Daisy Kite uses a novel tensile rotary power transmission (TRPT) to transfer power generated at the flying rotor down to the ground. Two dynamic models have been developed and compared; one with simple spring-disc representation, and one with multi-spring representation that can take account of more degrees of freedom. Simulation results show that the angular velocity responses of the two TRPT models are more closely correlated in higher wind speeds when the system shows stiffer torsional behaviour. Another interesting point is the observation of two equilibrium states, when the spring-disc TRPT model is coupled with NREL's AeroDyn. Given the computational efficiency of the simpler model and the high correlation of the results between the two models, the simple model can be used for more demanding simulations.
Book
Full-text available
Airborne wind energy is an emerging field in the renewable energy technologies that aims to replace the use of fossil fuels for energy production on an economical basis. A characteristic feature of the various concepts that are currently pursued is the use of tethered flying devices to access wind energy at higher altitudes where the wind is more consistent. This booklet contains 70 abstracts that were presented at the Airborne Wind Energy Conference 2015 (AWEC 2015), which was held from 15-16 June 2915 at Delft University of Technology. Further included are 37 additional full page photos and illustrations, mainly of prototypes characterising the state of airborne wind energy technology in 2015.
Article
Full-text available
Wind at higher altitude is a major source of renewable energy. However, this potential is far beyond reach for conventional wind energy systems using rigid tower structures. One of the possible solutions to capture high altitude wind energy is the use of kite power systems, such as the one developed by the research group of Delft University of Technology. The innovative development is reviving a comprehensive scientific and engineering heritage.
Chapter
Full-text available
The chapter describes a simulation framework for flexible membrane wings based on multibody system dynamics. It is intended for applications employing kites, parachutes or parasails with an inflated tubular support structure. The tube structure is discretized by an assembly of rigid bodies connected by universal joints and torsion springs. The canopy of the wing is partitioned into spanwise sections, each represented by a central chordline which is discretized by hinged rigid line elements. The canopy is modeled by a crosswise arrangement of spring-damper elements connecting these joints. The distributed loading of the wing structure is defined in terms of discrete aerodynamic forces. Acting on the joints, these forces are formulated per wing section as functions of local angle of attack, airfoil thickness and camber. The presented load model is the result of a comprehensive computational fluid dynamic analysis, covering the complete operational spectrum of the wing. The approach captures the two-way coupling of structural dynamics and aerodynamics. It is implemented as a toolbox within the commercial software package MSC ADAMS. For validation, the model is compared to existing wind tunnel data of a similar sail wing.
Chapter
The AWE concept presented in this paper is put into practice by the NTS-GmbH in Berlin. An AWE plant based on this principle—an X-Wind plant—utilizes automatically steered kites at altitudes between 100 and 500 m to pull rolling carts continually along an oval railway track. Each cart is equipped with a generator to convert its kinetic energy into electricity. The mechanism applied is comparable to regenerative braking systems in modern trains and trams. Hence, the NTS concept merges well known technologies to a unique and flexible AWE plant: kites and rail technology. In this paper, a short introduction into the concept is given and the current status of the NTS-project is presented.
Article
IntroductionThe actuator disc conceptRotor disc theoryVortex cylinder model of the actuator discRotor blade theory (blade-element/momentum theory)Breakdown of the momentum theoryBlade geometryThe effects of a discrete number of bladesStall delayCalculated results for an actual turbineThe performance curvesConstant rotational speed operationPitch regulationComparison of measured with theoretical performanceVariable speed operationEstimation of energy captureWind turbine aerofoil designReferencesWebsitesFurther readingAppendix A3 lift and drag of aerofoilsDefinition of dragDrag coefficientThe boundary layerBoundary layer separationLaminar and turbulent boundary layersDefinition of lift and its relationship to circulationThe stalled aerofoilThe lift coefficientAerofoil drag characteristicsCambered aerofoils
Article
This paper presents a multidisciplinary framework for the design and analysis of gyrocopter-type airborne wind turbines. In this concept, four rotary wings provide lift to a flying vehicle, and excess power is extracted using gearboxes and generators before being transferred to the ground through electrical conductors embedded in a structural tether. A physical breakdown of the system was performed, and five models were constructed: wind model, rotor aerodynamics, structural mass, electrical system, and tether (structures and aerodynamics). A stochastic optimizer in the framework enforces interdisciplinary compatibility and maximizes electrical power transmitted to the ground under various operating conditions. The framework is then used to explore the design space of this advanced concept in numerous flight conditions. The effect of implementing new technologies was also studied in order to evaluate their effect on the overall performance of the system. It is shown through a 1.3MW design that a gyrocopter-type airborne generator could provide more power than a ground-based wind turbine for a given blade radius, although only a fraction of the available wind power can be harvested using off-the-shelf technologies and components. The work presented in this study demonstrates the challenges of designing a high altitude wind generator and shows that performance is affected by complex interactions between each subsystem. Copyright © 2015 John Wiley & Sons, Ltd.
Article
A numerical study was conducted to examine the impact of rotor solidity and blade number on the aerodynamic performance of small wind turbines. Blade element momentum theory and lifting line based wake theory were utilized to parametrically assess the effects of blade number and solidity on rotor performance. Increasing the solidity beyond what is traditionally used for electric generating wind turbines led to increased power coefficients at lower tip speed ratios, with an optimum between 3 and 4. An increase in the blade number at a given solidity also increased the maximum C-P for all cases examined. The possibility of a higher aerodynamic power extraction from solidity or blade number increases could lead to a higher overall system power production. Additional advantages over current 5% to 7% solidity, high speed designs would include lower noise, lower cut-in wind speed, and less blade erosion.