Content uploaded by Roland Schmehl

Author content

All content in this area was uploaded by Roland Schmehl on Jan 08, 2019

Content may be subject to copyright.

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=180◦the 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=90◦−β,(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 =

cosβs−sinβs0

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 =

cosβscosα−sin 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

rA−rB=

lt,x

lt,y

lt,z

,(22.13)

the coordinates of this vector can be calculated as

rA−rB=

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=|rA−rB|=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 (rA−rB) =

−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=rA−rB

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,y−rB,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,z−rA,zlt,y)sinα+ (rA,xlt,y−rA,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=90◦−β,βs=0◦β=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 30◦and respectively 60◦indicate 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<60◦the

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<90◦the tensile force in the tether contributes a positive

moment, acting in the direction of the rotation, while for γ>90◦it contributes a

negative moment, acting against the direction of the rotation. At the limiting case

γ=90◦the 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

30◦results in a consistent and nearly uniform shift of the sine-type curve to lower

values. The steps from 30 to 60◦and further to 90◦follow 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=90◦directly 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 90◦results 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=0◦and 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=30◦the 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,i−rK)×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,x−minFk

a,x+maxFk

a,x+minFk

a,x

+maxFk

a,y−minFk

a,y+maxFk

a,y+minFk

a,y(22.36)

applying the min and max operators to to the complete interval 0◦≤ωt≤360◦.

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=30◦and δ=30◦. Initial values for the minimum search are α0=60◦,βs,0=0◦and 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=Ma−Mg,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=90◦−βand 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=180◦no 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=vw−vk,

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,o−R2

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=60◦and βs,0=0◦the 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,i⊥ek

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=cotβ≈1.73 is the reference for

the lower limit, for α=90◦−β

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

Rksinβ−Rk,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=90◦−β)

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=cotβ≈1.73 indicates how much the angle of attack αin steady-

state operation deviates from the value α=90◦−β=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=90◦−βthe

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,i⊥ek

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.

References

1. Ahrens, U.: Wind-operated power generator. US Patent 8,096,763, Jan 2012

2. Ahrens, U., Pieper, B., Töpfer, C.: Combining Kites and Rail Technology into a Traction-

Based Airborne Wind Energy Plant. In: Ahrens, U., Diehl, M., Schmehl, R. (eds.) Airborne

Wind Energy, Green Energy and Technology, Chap. 25, pp. 437–441. Springer, Berlin Hei-

delberg (2013). doi: 10.1007/978-3-642-39965-7_25

576 Pierre Benhaïem and Roland Schmehl

3. Archer, C. L., Caldeira, K.: Global Assessment of High-Altitude Wind Power. Energies 2(2),

307–319 (2009). doi: 10.3390/en20200307

4. Argatov, I., Silvennoinen, R.: Asymptotic modeling of unconstrained control of a tethered

power kite moving along a given closed-loop spherical trajectory. Journal of Engineering

Mathematics 72(1), 187–203 (2012). doi: 10.1007/s10665-011-9475-3

5. Argatov, I., Rautakorpi, P., Silvennoinen, R.: Estimation of the mechanical energy output of

the kite wind generator. Renewable Energy 34(6), 1525–1532 (2009). doi: 10.1016/j.renene.

2008.11.001

6. Argatov, I., Silvennoinen, R.: Energy conversion efﬁciency of the pumping kite wind genera-

tor. Renewable Energy 35(5), 1052–1060 (2010). doi: 10.1016/j.renene.2009.09.006

7. Beaujean, J. M. E.: 500MW Wind Turbines. Windtech International, 11 Nov 2011. https :

//www.windtech-international.com/content/500mw-wind-turbines Accessed 21 July 2016

8. Benhaïem, P.: Eolienne aéroportée rotative. French Patent 3034473, Oct 2016

9. Benhaïem, P.: Land and Space used. In: Lütsch, G. (ed.). Book of Abstracts of the International

Airborne Wind Energy Conference 2013, p. 59, Berlin, Germany, 10–11 Sept 2013. http:

//resolver.tudelft.nl/uuid:e3e8aaa4-8ae1-498a-82ce-fdc7a149963f

10. Benhaïem, P.: Rotating Reeling. In: Schmehl, R. (ed.). Book of Abstracts of the International

Airborne Wind Energy Conference 2015, p. 100, Delft, The Netherlands, 15–16 June 2015.

doi: 10. 4233/uuid :7df59b79-2c6b- 4e30-bd58- 8454f493bb09. Poster available from: http:

//www.awec2015.com/images/posters/AWEC25_Benhaiem-poster.pdf

11. Breuer, J. C. M., Luchsinger, R. H.: Inﬂatable kites using the concept of Tensairity. Aerospace

Science and Technology 14(8), 557–563 (2010). doi: 10.1016/j.ast.2010.04.009

12. Breukels, J., Schmehl, R., Ockels, W.: Aeroelastic Simulation of Flexible Membrane Wings

based on Multibody System Dynamics. In: Ahrens, U., Diehl, M., Schmehl, R. (eds.) Air-

borne Wind Energy, Green Energy and Technology, Chap. 16, pp. 287–305. Springer, Berlin

Heidelberg (2013). doi: 10.1007/978-3-642-39965-7_16

13. Burton, T., Jenkins, N., Sharpe, D., Bossanyi, E.: Wind Energy Handbook. 2nd ed. John Wiley

& Sons, Ltd, Chichester (2011). doi: 10.1002/9781119992714

14. Canale, M., Fagiano, L., Milanese, M.: Power kites for wind energy generation - fast predictive

control of tethered airfoils. IEEE Control Systems Magazine 27(6), 25–38 (2007). doi: 10.

1109/MCS.2007.909465

15. Diehl, M., Horn, G., Zanon, M.: Multiple Wing Systems – an Alternative to Upscaling? In:

Schmehl, R. (ed.). Book of Abstracts of the International Airborne Wind Energy Conference

2015, p. 96, Delft, The Netherlands, 15–16 June 2015. doi: 10. 4233/uuid :7df59b79-2c6b-

4e30-bd58-8454f493bb09. Presentation video recording available from: https://collegerama.

tudelft.nl/Mediasite/Play/1065c6e340d84dc491c15da533ee1a671d

16. Duquette, M. M., Visser, K. D.: Numerical Implications of Solidity and Blade Number on

Rotor Performance of Horizontal-Axis Wind Turbines. Journal of Solar Energy Engineering

125, 425–432 (2003). doi: 10.1115/1.1629751

17. Fletcher, C. A. J., Roberts, B. W.: Electricity generation from jet-stream winds. Journal of

Energy 3(4), 241–249 (1979). doi: 10.2514/3.48003

18. Hodges, T.: Centrifugally Stiffened Rotor. NIA Task Order Number 6528 Final Report, Na-

tional Institute of Aerospace, 1 June 2015, pp. 57–147. http://ntrs.nasa.gov/archive/nasa/casi.

ntrs.nasa.gov/20160001625.pdf

19. Ippolito, M.: Kite wind energy collector. Patent WO2014199407 A1, Dec 2014

20. Loyd, M. L.: Crosswind kite power. Journal of Energy 4(3), 106–111 (1980). doi: 10.2514/3.

48021

21. Michel, D., Koyama, K., Krebs, M., Johns, M.: Build and test a three kilowatt prototype of

a coaxial multi-rotor wind turbine. Independent Assessment Report CEC-500-2007-111, Dec

2007. http: //www.energy.ca.gov/2007publications/ CEC- 500- 2007-111/CEC - 500 - 2007 -

111.PDF

22. Moore, M. D.: Eternal Flight as the Solution for X. Presented at the NIAC 2014 Symposium,

Stanford University, Palo Alto, CA, USA, 4–6 Feb 2014. https://www.nasa.gov/sites/default/

ﬁles/ﬁles/Moore_EternalFlight.pdf

22 Airborne Wind Energy Conversion Using a Rotating Reel System 577

23. Rancourt, D., Bolduc-Teasdale, F., Demers Bouchard, E., Anderson, M. J., Mavris, D. N.:

Design space exploration of gyrocopter-type airborne wind turbines. Wind Energy 19, 895–

909 (2016). doi: 10.1002/we.1873

24. Read, R.: Opportunities and Progress in Open AWE Hardware. In: Schmehl, R. (ed.). Book

of Abstracts of the International Airborne Wind Energy Conference 2015, pp. 118–120,

Delft, The Netherlands, 15–16 June 2015. doi: 10. 4233 /uuid :7df59b79 - 2c6b - 4e30- bd58 -

8454f493bb09. Poster available from: http://www.awec2015.com/images/posters/AWEC23_

Read-poster.pdf

25. Roberts, B. W., Shepard, D. H., Caldeira, K., Cannon, M. E., Eccles, D. G., Grenier, A. J., Frei-

din, J. F.: Harnessing High-Altitude Wind Power. IEEE Transactions on Energy Conversion

22(1), 136–144 (2007). doi: 10.1109/TEC.2006.889603

26. Rye, D. C., Blacker, J., Roberts, B. W.: The Stability of a Tethered Gyromill. AIAA-Paper

81-2569. In: Proceedings of the AlAA 2nd Terrestrial Energy Systems Conference, Colorado

Springs, CO, USA, 1–3 Dec 1981. doi: 10.2514/6.1981-2569

27. Schmehl, R.: Large-scale power generation with kites. Journal of the Society of Aerospace

Engineering Students VSV Leonardo da Vinci March, 21–22 (2012). http://resolver.tudelft.nl/

uuid:84b37454-5790-4708-95ef-5bc2c60be790

28. Schmehl, R.: Parotor. https://github.com/rschmehl/parotor. Accessed 25 Oct 2016

29. Selfridge, J. M., Tao, G.: Centrifugally Stiffened Rotor: A Complete Derivation and Simu-

lation of the Inner Loop Controller. AIAA-Paper 2015-0073. In: Proceedings of the AIAA

Guidance, Navigation, and Control Conference (AIAA SciTech), Kissimmee, FL, USA, 5–

9 Jan 2015. doi: 10.2514/6.2015-0073

30. Snieckus, D.: Giant airborne ’power station’ could blow rivals out of the water. Recharge

News, 6 Mar 2012. http://www. rechargenews. com/news/technology / article1295509 . ece

Accessed 21 July 2016

31. Williams, P., Lansdorp, B., Ruiterkamp, R., Ockels, W.: Modeling, Simulation, and Testing

of Surf Kites for Power Generation. AIAA Paper 2008-6693. In: Proceedings of the AIAA

Modeling and Simulation Technologies Conference and Exhibit, Honolulu, HI, USA, 18–

21 Aug 2008. doi: 10.2514/6.2008-6693