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Theoretical Analysis of an Airborne Wind Energy Conversion System with a Ground Generator and Fast

Motion Transfer

Leo Goldstein, M.Sc., IEEE Member

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ABSTRACT

A novel airborne wind energy conversion concept is presented, in which the wind power, which is

harvested by the crosswind motion of a tethered wing, is transferred to a ground-based generator by a

belt with a high speed close to the speed of the wing. The belt trails behind the wing. The high speed of

the motion transferring belt results in a low belt tension, a high rotational speed and a low torque on

the shaft connected to the rotor. The theoretical analysis and numeric calculations, which consider the

drag of the tether and the weight of both the tether and the wing, demonstrate the practical feasibility

of the concept. Two practical constructions are described, one with a single wing and one with two

wings in counter phase. The economic analysis shows that the proposed system is 10 times less

expensive than a conventional wind turbine with a comparable average power output.

KEYWORDS

airborne wind energy; kite energy; kite power; altitude wind energy; wind energy; wind power

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Nomenclature

A wing surface area, m2

At,l, At,s sectional areas of the tether, m2

CL, CD coefficients of lift and drag, respectively

Ct tether form drag coefficient

cα approximate constant replacement for cos α

cp system efficiency coefficient

cs ratio of the tether length to the straight line length due to sag

Dk wing drag, N

Dt tether drag, N

Dtl total drag, N

Dw projection of weight on the drag axis, N

Dw,k, Dw,t drag equivalent of the weight of the wing and the tether, respectively, N

Dp projection of Fp on the drag axis, N

d width of the tether perpendicular to air flow, m

Fp force of the power transfer belt acting on the wing, N

Ft total tether force acting on the wing, N

Fw,k wing weight, N

Fw,t tether weight, N

f coefficient dependent on tether sectional form

g acceleration due to gravity, m/s2

K speed ratio, given by formulas (35 - 36)

L lift force, N

Mk, Mt, M, N dimensionless coefficients, given by formulas (28 - 31)

lD, lw length of tether for drag and mass calculation, respectively, m

mk, mt wing and tether mass, respectively, kg

P useful power, W

Paver average useful power, W

R radius of the sprocket, m

s safety margin

T usual tension force perpendicular to the wing motion, N

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U belt velocity, m/s

V wind velocity, m/s

Vϕ Vcos ϕ, m/s

Wg wing velocity relative to the ground, m/s

W relative air velocity, m/s

α angle between the ground and air velocities of the wing

β angle between the motion transfer belt and the drag axis

ϕ angle between the tension force and the horizon

σ tensile strength of the tether material, Pa

ρa air density at the altitude of the wing, kg/m3

ρt density of the tether material, kg/m3

ρS mass per surface of the wing, kg/m2

τ specific mass per surface of wing per square of the velocity, (kg s2)/m4

ω angular speed of the sprocket

A scalar value of a vector is shown using the same symbol in a non-bold font.

1. Introduction1

Wind energy is the most promising and widely used scalable renewable source of electrical energy, both

currently and for the foreseeable future. Examples of such prognoses can be found in [1] and [2].

Nevertheless, technological progress in the development of conventional wind turbines has slowed in

recent decades. The main changes have been an increase in the size of the turbines, the use of more

modern materials, and various optimizations. In 1980, Miles Loyd [3] introduced a breakthrough

concept for an airborne wind energy conversion system (AWECS) with a fast crosswind motion of the

wings. Ockels [4] invented the original Ladermill concept. Lansdorp and Ockels [5] developed the

concept into a pumping kite design, which was further developed by Williams et al. [6]. Canale, Fagiano,

Milanese, and Ippolito [7] and Canale, Fagiano, and Milanese [8], [9] have proposed a carousel concept,

which was developed and experimentally validated with control theory, for both the pumping kite and

1 Corresponding Author: Tel: +1 714 264 3640, Fax: +1 678 882 3421, email: leo.goldstein@awecs.org, L. Goldstein

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the carousel designs. Recently, theories of kite control or use have been developed, analyzed and

modeled by various researchers [10-22]. An up-to-date overview of airborne wind energy can be found

in [23].

AWECS have many advantages over conventional horizontal-axis wind turbines (HAWT). A tower is not

required in an AWECS. Winds at higher altitudes are stronger, more dependable, and less turbulent.

The wings of an AWECS are more efficient than HAWT blades because the air speed is constant along

the wingspan and because the aerodynamic forces are resisted more efficiently along the wing span or

in its center. Most AWECS designs with ground-based generators use flexible kite wings, the cost of

which are potentially negligible compared with the cost of HAWT blades. AWECS are equally effective

on land and offshore. In [3], Loyd described two methods for power removal from the wing: 1) tether

unwinding from a drum to rotate the rotor of a generator on the ground (lift power) and 2) turbine

generators installed on the wing (drag power). Unfortunately, both methods have serious practical

shortcomings. The airborne turbine generators used in the latter method are expensive and heavy, and

the transmission of generated electricity to the ground requires heavy cables or transformers to

increase voltage. The tether in the former method unwinds slowly, at less than one third of the wind

speed, and exerts a very large force. The angular speed of the revolving drum is very low, and the

torque is very high. Increasing the power delivered requires increasing the thickness of the tether,

which requires a proportional increase in the width of the drum, resulting in a system that is not

scalable. The rotation of the drum needs to gear up to 1,500–1,800 RPM to use typical generators, thus

necessitating a high-ratio gearbox. There are variations of the lift power approach that use secondary

devices to convert the slow extension of the tether into a rotation of the rotor of the generator, such as

carousels [9] or ships with underwater screws [24], but the secondary devices increase the cost of the

system. To date, no AWECS designs have been developed beyond the experimental phase.

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This paper proposes a new method for power removal that does not possess the shortcomings

described above.

2. AWECS design: a proposal

The proposed approach is to remove the power that is harvested by a tethered airborne wing using a

separate motion transfer cable or belt that trails behind the wing. This motion transfer belt rotates a

revolving element (a drum, a pulley, or a sprocket) on the ground, which in turn transfers the

mechanical power to the rotor of an electric generator, as is common in an AWECS with a ground-based

generator. A simplified scheme is shown in Fig. 1.

The wing is either a flexible airfoil with an airborne steering unit (a kite) or a rigid wing with ailerons and

an empennage with a vertical stabilizer, horizontal stabilizers, a rudder, elevators, and a control system

(a glider). The belt is pulled by the wing. The belt can rotate a drum by unwinding off of it. Better yet,

the belt can wrap around a pulley or a sprocket after unwinding from the drum and transfer the power

to the generator through this pulley or sprocket. The pulley or sprocket can have a smaller diameter

than the drum for higher RPM, and the drum will be relieved of most of the force that the belt would

exert on it if the drum serves as the revolving element.

The system works in cycles. Each cycle consists of two phases: the working phase, in which the wing

harvests wind energy and pulls the belt while the belt unwinds from the drum and transfers the

mechanical energy to the generator, and the returning phase, in which an electric motor on the ground

rotates the drum back, pulling the belt back, while the wing is controlled to fly in the opposite direction,

creating minimum drag. The returning phase starts with the wing doing a U-turn in the opposite

direction and ends with the wing doing another U-turn to arrive at the position at which the working

phase begins. The energy that is expended in the returning phase should be a small fraction of the

energy generated in the working phase.

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V

W Wg

L

T

Dk

Dp

tether

belt

generator

wing

attachment

Fig. 1

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I will use Fig. 1 for a simplified analysis of the working phase of the proposed method. In Fig. 1, the

tether is parallel to the wind vector V. Consequently, the wing velocity Wg relative to the ground is

perpendicular to the wind, and the relative air velocity is given by the following equation:

𝐖 = 𝐕 − 𝐖𝐠 (1)

The motion transfer belt is pulled directly behind the wing, perpendicular to the tether, and it unwinds

at the speed Wg. Here, let us not limit the angle of the belt toward the horizon but disregard the weight

of the belt and of the wing. Furthermore, let us assume that the lift of the wing is much higher than the

total drag of the wing (L>>Dtl). Assuming a constant speed of the wing, the force balance is written as

follows:

𝐋 + 𝐓 + 𝐃𝐤 + 𝐃𝐩 = 0 (2)

where L is the wing lift, T is the tether tension, Dk is the wing drag, and Dp is the drag component caused

by the power removal (i.e., “useful” drag). It is easy to see that this system is equivalent to Loyd’s drag

power system (in terms of the forces and the velocities), with the motion transfer belt used for power

removal instead of air turbines. Consequently, the same solution is obtained for the optimal power-

producing drag:

Dp = 1

2Dk =

1

3Dtl =

1

3 CD

CLT (3)

The maximum power is given by the following equation:

P = 2

27CL(

CL

CD)2ρaAV3 (4)

where CL and CD are the coefficients of lift and drag, respectively, ρa is the air density and A is the wing

surface. Dtl is the total drag. The wing speed, the radius of the receiving sprocket and the angular speed

are related as follows:

Wg = 2πRω (5)

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For example, to achieve 1,800 RPM without a gearbox, the system must fly the wing at 60 m/s and have

a sprocket with a diameter of 64 cm, which is quite easily accomplished, as will be shown in the next

section. The tension of the motion transfer belt is approximately equal to Dp, and (3) shows that it is

many times lower than the tension T of the tether. If it is desirable to take into account the tether drag

in (4), one can substitute the glide ratio Ge from ([16], equation 18) for CL/CD.

A simple device exemplifying this idea is shown in Fig. 2. A ground platform that houses the drum, the

sprocket and the generator is placed downwind of the attachment point. With this device, the wing is

tethered to a ground attachment point and flies in a vertical arc—upward in the working phase and

downward in the returning phase. The wing yaws in the plane perpendicular to the tether to perform

the U-turn. The wing speed is nearly constant in the working phase. The belt in this device exhibits very

little normal motion, and thus its form can be selected freely. For example, the belt can be very flat

(tape), or it can be perforated to engage the teeth of the sprocket. The details of the mechanical

construction (such as the material choice for the belt, the possible water cooling of the sprocket, and

active control to ensure desirable motion of the wing) are beyond the scope of this article. This device

functions efficiently even if the wind vector forms an angle of 30˚–45˚ with the vector attachment

point–platform. To accommodate larger changes in the wind, this vector should be changed by moving

either the attachment point or the ground platform. On land, it appears easier to move the effective

attachment point. Fig. 3 shows how to do so. The tether is not directly guyed to the ground but rather

attached by cables to two automatically controlled motorized pulleys. The effective attachment point

(EAP) of the tether is determined by the lengths of these cables. Thus, the control system changes the

EAP by extending and shortening these cables in response to changes in the direction of the wind.

Three motorized attachment points can ensure a 360˚ wind coverage. On water, it is easier to allow

circular motion of the platform. In our analysis, let us consider the vector attachment point–platform

aligned with the wind.

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Wg

V

W

U

L

T

Dk

Dp

Fw,t

Fw,k

Dt

β

α

ϕ

ϕ+ π/2

α

attachment

ground

platform

tether

belt

wing

Fig. 2

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3. Detailed analysis of the forces and the power formula

3.1. Derivation of formulas for the power and the forces

In this section, I present the derivation of the expression for the optimal power and other parameters of

the system in Fig. 2 when operating at the nominal wind speed. In this derivation, I consider the drag

and the weight of both the wing and the tether. I do not make the traditional assumption that the lift is

much higher than the total drag. The derivation is similar to that in [16] and [19] but uses a Cartesian

coordinate system. Assuming no tangential acceleration and neglecting radial acceleration, the

following vector equation can be written:

𝐋 + 𝐃𝐤 + 𝐅𝐰,𝐤 + 𝐅𝐭 + 𝐅𝐩 = 0 (6)

where L is the lift, Dk is the wing drag, Fw,k is the wing weight, Fp is the force of the power transfer belt

acting on the wing, and Ft is the tether force, which can be expressed as follows:

𝐅𝐭 = 𝐓 + 𝐅𝐰,𝐭 + 𝐃𝐭 (7)

where T is the tension, Fw,t is the tether weight and Dt is the tether drag. The relative air velocity is given

by (1). The forces in (6) can be decomposed into forces acting along the lift axis L and along the drag

axis 𝐃𝐤. The tension of the tether can be estimated as the value of the tension force T given by the

following expression:

T = L/ cos 𝛼 =1

2CLρaAW2/ cos 𝛼 (8)

The drag components of the forces can be determined from (6) and (7) as follows:

𝐃𝐭𝐥 = 𝐃𝐤 + 𝐃𝐭 + 𝐃𝐰 + 𝐃𝐩 (9)

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where the total drag Dtl is equal to the projection of T with the opposite sign, Dw is the sum of the

projections of the weights (the drag equivalent of weight) and Dp is the projection of Fp (the “useful”

drag). The effective drag is defined by the following expression:

𝐃𝐞 = 𝐃𝐤 + 𝐃𝐭 + 𝐃𝐰 (10)

The proposed device removes the useful power using drag. Loyd's formula ([3], equation 22) for the

maximum useful power in drag mode applies here. With the substitution of De for Dk, it is written as

Dp = 1

2De (11)

Combining equations (9), (10) and (11) results in the following expression:

Dtl = 3

2(Dk+Dt+Dw) (12)

The useful power is given by the following expression:

P = DpWg cos β (13)

To compute Dp and Wg in this equation, I will write expressions for the scalars of the forces in (10) and

simply substitute them.

Dtl = T sin 𝛼 = 1

2CLρaAW2 tg 𝛼 (14)

where CL is the lift coefficient, ρa is the air density at the altitude of the wing (which is also used for the

tether drag), and A is the wing area. The following can be obtained from the velocities triangle:

W

𝑉=

sin(𝜑+𝜋

2)

sinα=

cos 𝜑

sinα (15)

which gives us

𝛼 = arcsin(V cos 𝜑

W) (16)

The wing drag is expressed as usual:

Dk = 1

2CDρaAW2 (17)

where CD is the drag coefficient of the wing. The formula for tether drag was derived in [17] (equation

15). In our notation, it is expressed as

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Dt = 1

8CtρaAt,lW

2 (18)

where Ct is the drag coefficient of the tether and At, l is the longitudinal cross-sectional area of the tether.

Any variation of the air density with altitude is neglected. The perpendicular cross-sectional area is

given by the following expression:

At,s = sTmax/σ (19)

where Tmax is the maximum tension, s is the safety margin, and σ is the tensile strength of the tether

material. Because the computations are performed for the nominal conditions, Tmax=T. The

perpendicular cross-sectional area is expressed as a function of tether width d as follows:

At,s = fd2 (20)

where f is a coefficient that depends on the sectional form of the cable. For example, f = π/4 for round

cables, which makes it possible to compute At,l and substitute it into (18):

Dt = 1

8CtρalD√

CLρaAs

2fσcos 𝛼 W3 (21)

where lD is the tether length for computation of the tether drag, which can differ from the tether length

lW for the computation of the tether weight. The drag equivalent of weight is composed of the drag

equivalents of the wing weight and the tether weight:

Dw = Dw,k + Dw,t = (Fw,k + Fw,t) cos(𝜑 + 𝛼) (22)

which can be expressed as

Fw,k = mkg = ρSAg = τW2Ag (23)

and

Fw,t = mtg = ρtlwAt,sg = ρtlwsTg

σ= ρtlwsgCLρaA

2σ cos 𝛼W2 (24)

where mk and mt are the wing and tether weights, respectively, ρt is the density of the tether material,

ρS is the specific mass per surface of the wing and τ is the specific mass per surface of the wing per

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square of the velocity (as explained below in section 3.2). Substituting these expressions into (12) and

dividing both sides of the equation by ρaAW2/2cosα yields the following expression:

CL sin 𝛼 =3

2(CD cos 𝛼 +

1

4CtlD√

CLρas cos 𝛼

2fσA W + (

2τ

ρacos 𝛼 +

ρtlwsCL

σ) g cos(𝜑 + 𝛼)) (25)

An exact equation for W can be obtained by substituting α from (16). However, there is an easier way.

Traditionally, a simplifying assumption is made that L >> Dtl, which leads to cos α = 1. To preserve

accuracy, let us make a weaker assumption that cos α is constant and equals some value cα < 1.

Applying this assumption, designating V𝜑 = Vcos 𝜑, and decomposing cos (𝜑+α) = cos 𝜑 cos α - sin 𝜑 sin

α, this equation can be re-written as follows:

CLVφ

W=

3

2(CDcα +

1

4CtlD√

CLρascα

2fσA W + (

2τcα

ρa+

ρtlwsCL

σ) g (cα cos φ −

Vφ

Wsin φ)) (26)

The following inequality gives the upper limit of cα:

cα < √1 − (3CD

2CL)2 (27)

However, this approximation will not be used in the subsequent derivation. Multiplying by W and

designating constants related to the drag equivalents of the weights and the tether drag as follows:

Mk =2τcα

ρag (28)

Mt =ρtlwsCL

σg (29)

M = Mk + Mt (30)

N =1

4Ct

lD

√A√

CLρascα

2fσVφ (31)

Then, the following equation is derived:

2CLVφ = 3CDcαW + 3N

VφW2 + 3M(Wcα cos φ − Vφ sin φ) (32)

which is a quadratic equation with a canonical form:

N

VφW2 + cα(M cos φ + CD) W − (M sin φ +

2

3CL) Vφ = 0 (33)

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This equation yields the following meaningful solution:

W = KVφ (34)

where

K =−cα(M cos φ+CD)+ √cα

2 (M cos φ+CD)2+4N(M sin φ+2

3CL)

2N if N>0 (35)

or

K =3M sin φ+2CL

3cα(M cos φ+CD) if N=0 (36)

where K is the speed ratio (the analog of the tip speed ratio in conventional wind turbines). We are

interested in efficient systems. A system is efficient if the speed ratio is sufficiently high, for example,

K>3. M can be interpreted as the impact of the weights, and N can be interpreted as the impact of the

tether drag. The expressions for the useful drag and the total drag can be derived from (10), (11), (12),

(14) and (34):

Dp = CL

6cαρaAKVφ

2 (37)

the velocities triangle,

Wg =sin(π−(π/2+φ+α)

sin αV =

cos(φ+α)

sin αV = (

cα

sin α− tan φ) Vφ = (cαK − tan φ)Vφ (38)

Substituting this equation into (13), the converted power is expressed as

P = 1

6CLρaAKVφ

2(cαK − tan φ)Vφ cos 𝛽 (39)

or

P = 1

6CLρaAK(cαK − tan φ)V3 cos3 φ cos 𝛽 (40)

In the special case when there is no tether drag, no weights, φ = β = 0 and CL >> CD: M = N = 0, W>>V and

K =2

3

CL

CD (41)

P = 2

27CL(

CL

CD)2ρaAV3 (42)

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which is Loyd’s formula. For a better understanding of the system, let us derive the formulas for the

remaining drag components.

Mk =2τcα

ρag (43)

Mt =ρtlwsCL

σg (44)

Dw,k = τAgW2 cos(𝜑 + 𝛼) (45)

Dw,t = ρtlwgsCLρaA

2σ cos 𝛼W2 cos(𝜑 + 𝛼) (46)

Dt = KN

2cαρaAW2 (47)

Dw,k = Mk

2cαρaAW2 cos(𝜑 + 𝛼) (48)

Dw,t = Mt

2cαρaAW2 cos(𝜑 + 𝛼) (49)

where the cosine can be conveniently calculated as follows:

cos(𝜑 + 𝛼) = cα cos 𝜑 −sin 𝜙

K (50)

The power P in (42) is the power in the working phase, which is greater than the average power. To

compute the average power output, one needs to multiply the power in the working phase by a

coefficient while considering the proportion of the total cycle time that the system is in the working

phase (between 60% and 75%), the energy consumption in the returning phase and the losses

associated with conversion of mechanical energy to electrical energy:

Paver = cpP (51)

where cp is the system efficiency coefficient which is expected to be in the range of 0.5–0.7 for

production systems.

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3.2. Numerical examples and observations

The tether drag is expressed differently in the formulas in this article than the tether drag in previous

studies ([25] equation 18, [19] equations 55-56) because this article does not assume the thickness of

the tether to be constant but rather considers its dependence on the maximum tension. No matter how

the tether drag is expressed, it has a large impact and is a well-known issue in AWECS. Luckily, this issue

is already being addressed. [26] suggests a tether with a streamlined cross section for AWECS

applications. Such a tether has the drag coefficient of a 2D streamlined body, which can be 5–10 times

smaller than the drag coefficient of a cylinder. A streamlined tether can also be manufactured with a

more beneficial form factor f. For example, a tether with a load-bearing core in the form of a 3:1

rectangle has f=3, compared with f=π/4 for a round cable.

Wind

tether

motorized pulley 1

motorized pulley 2

cable 1

cable 2

wing

EAP

Fig. 3

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The weights of the tether and the wing cannot be disregarded in the device in Fig. 2 because they

decrease thrust rather than lift. Nevertheless, a closed analytical solution was derived while accounting

for these weights.

In the calculations, let us assume that lw is the distance from the attachment point to the wing and that

lD is the length of the tether and consider some sag:

lD = cslw (52)

where the coefficient cs is assumed to be a constant. The tether material is Dyneema. The safety

margin is assumed to be 1.5. It is important to note that the specific mass per surface of the wing

construction depends on the aerodynamic force, for which the wing is designed. This force can be

roughly estimated to be proportional to the square of the relative speed by assuming the use of the

same materials and construction techniques. This assumption yields the following formula:

τ =mk

AW2 (53)

τ is a non standard quantity. The value of τ varies widely, depending on the materials and the

construction techniques. It is estimated here for a kite wing composed of rip-stop nylon and for a rigid

wing composed of fiberglass. The estimates are made based on known wings in the relevant speed

range and attempt to consider design differences. The estimates of τ for the kite wing were made

conservatively based on [24] while taking into account the need for durability. The estimates of τ for the

rigid wing were made optimistically based on the specific densities of the fiberglass glider wings and

taking into account suspension at multiple points of the wing in the AWECS. τ is used only to calculate

the drag created by the wing weight, and thus the use of such rough estimates is justified.

Two types of wings can be used in the system: a rigid wing with an empennage (a glider) and a flexible

wing (a kite). One important difference between them is that the glider is aerodynamically stable, while

the kite is not. Attaching the tether in front of the aerodynamic center of the lifting wing and attaching

the motion transfer belt behind that center increases the longitudinal stability of the glider and does not

19

change its lateral stability. For kites, methods of dynamic stability control have been developed in the

studies cited in the Introduction. A continuous control input is applied to ensure the stability of the

whole system in both cases. The choice between kites and gliders is not obvious and depends on the

specific materials and the construction techniques used. Kites have greater aerodynamic drag but lower

specific weight than rigid wings. They are also potentially less expensive. A kite would do less damage

than a rigid wing if it hit something on the ground. However, a rigid wing is more durable than a kite,

and it is much more aerodynamically efficient. The rigid wing in this system can be more efficient than a

plane wing if suspension cables are employed to spread the tether tension over the whole wingspan. In

the sample computations, the rigid wing is assumed to be composed of fiberglass and is assumed to

produce a significant drag equivalent of weight.

Table 1 contains sample calculations for three hypothetical variants of the AWECS shown in Fig. 2 and

one for the AWECS that is described in the next section. Column one (Kite Wing RT) is an AWECS with a

kite wing and a round tether. Column two (Rigid Wing RT) is an AWECS with a rigid wing and a round

tether. Column three (Kite Wing ST) is an AWECS with a kite wing and a streamlined tether. These

calculations assume that the rigid wing has a significantly better aerodynamic quality than the kite wing

(CD=0.05 and CL=1.5 vs. CD=0.15 and CL=1.2). However, the rigid wing has a much higher mass per unit of

the area for the same speed (τ=0.002 vs. τ=0.0004). More advanced and complex variants (using a

streamlined cable or a double wing) are presumed to operate at a higher altitude than the simpler

variants (3,000 m vs. 1,000 m) with higher wind speed (15 m/s vs. 12 m/s). The results show that all of

these systems are feasible and efficient and have speed ratios between 4.25 and 7.28 and average

power outputs between 1.1 MW and 9.3 MW per device.

Table 2 contains additional calculations of the drag components and control values, including the

specific wing mass. The results are consistent with expectations.

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4. Possible enhancements to the basic design

One of the intermediate conclusions from the analysis and the numeric examples is that the drag and

weight of the tether have a large negative impact on the useful power that can be produced by an AWEC

device, as described above. One enhancement is shown in Fig. 4. In it, two wings are attached to a joint

tether by separate short tethers that join at point J. The wings move in counter phase—when the first

wing ascends, pulling the belt and generating power, the second wing descends. As a result, point J and

the tether below are relatively static. The motion of each wing is similar to the motion in the simple

device in Fig. 2, but the motion of the wing in the returning phase is also used to support the joint tether

(below point J). The working phase is shown as a dashed line on the trajectory of each wing. The first

part of the active phase is shown as a solid line. In this part of the trajectory, the lift of the wing

supports the joint tether. The second part is shown in dotted lines. In this part of the trajectory, the

wing simply moves into position for the beginning of the working phase. An additional advantage is that

a drum is not required for the belt, which is in the air all the time, as long as the wings are airborne. The

detailed computations for this case are beyond the scope of this article. The calculations in the fourth

column (Kite Wing RT Double) depend on the assumptions that two thirds of the distance from the

wings to the attachment point is covered by the joint tether, that the joint tether is fully supported by

the lift of the descending wing, and that this support allows for a slightly smaller average angle 𝜑. This

system operates continuously, and thus the system efficiency coefficient cp is taken to be 0.96. In

addition, it has lower values of lD and lw because the tether is partially supported and its lower part does

not move significantly. With these assumptions, the device produces an average of 20 MW.

21

Wind

sprocket

attachment

tether

wing 1

wing 2

belt

J

generator

Fig. 4

22

5. Economic effect of AWECS with fast motion transfer

The enormous potential of using AWECS with fast motion transfer is indicated in Table 3. Table 3 uses

data from [27], Table 9.1 on p. 155, and the proverbial estimate of the wind energy equipment cost as

$1/W ([28] etc.) and shows the costs of the components per kW of installed nominal power. The

capacity factors in Table 3 are based on [10], Table 6.1. The AWECS column contains zero for

components that are present in conventional wind turbines and are absent in the AWECS. These

“saved” components include the tower, the nacelle, the hub and the gearbox with the shaft. The low

cost of wings per kW is derived from the higher mechanical and aerodynamic efficiency and the simpler

construction of the AWECS wings compared with HAWT blades. In AWECS, there is constant air speed

along the wingspan (compared with the variable air speed over the HAWT blade), and the load can be

spread over the wing surface (compared with the huge bending moment at the root of HAWT blade).

The AWECS wing can be an inexpensive inflatable kite composed of nylon or a straight rigid wing

(compared with the difficult to manufacture curved blade of a HAWT). Table 1 shows that a wing

surface of between 0.27 m2 and 0.07 m2 is required per kW of power. Among other estimates, it is

assumed that the AWECS generator costs less because it is an off-the-shelf mass-produced generator

rather than a specialized wind turbine generator. The cost of the pitch system, the rotor brake, and the

coupling (rotor PBC) is replaced by the cost of the control surfaces of the wing. A generous allowance is

made for additional components of the AWECS that are not present in the conventional wind turbine,

such as the tether and the subsystem for launch and recovery. The total cost is $190 per kW for AWECS.

When comparing a conventional wind turbine with an AWECS, it is necessary to consider a capacity

factor. The winds near the land surface are highly intermittent, which is reflected in low capacity factors

of conventional wind turbines (HAWT), which stand at 25-35%. Above the ground, the winds are more

stable and dependable. Even at relatively low altitudes of 200-800 m, the capacity factor of an AWECS

can be twice the capacity factor of a HAWT, at 50-70% ([10], Table 6.1). After adjusting for a higher

23

capacity factor, the ratio of capital costs per kWh is $1,000/$190*2 = 10.53. In other words, the AWECS

proposed in this article is approximately 10 times less expensive than a conventional wind turbine of

comparable average power output. Another observation is that the AWECS proposed in this article can

be manufactured completely using existing and widely available materials, components and

technologies.

6. Conclusions

This paper presents a novel airborne wind energy conversion concept, in which the wind power, which is

harvested by crosswind wing motion, is transferred by a belt with a speed close to the speed of the

wing. Theoretical analyses and numeric calculations were performed in two different ways, and both

demonstrate the practical feasibility of the concept. A brief comparison of the costs shows that the

proposed system can be 10 times less expensive than a wind turbine of a comparable average power

output. The other advantages of the proposed system include the ready availability of all of the

required components and technologies and the suitability of the system for offshore deployment.

7. Disclosure statement

The author has pending patent applications related to the article content.

24

Tables

Table 1. Numerical examples

Kite Wing RT Rigid Wing RT Kite Wing ST

Kite Wing RT Double

V, m/s 12.0 12.0 15.0 15.0

ρa, kg/m3 1.1 1.1 0.8 0.8

CL 1.2 1.5 1.2 1.2

CD 0.15 0.05 0.15 0.15

φ, deg 30.0 30.0 30.0 24.0

β, deg 15.0 15.0 15.0 10.0

lD, m 2,000.0 2,000.0 6,000.0 2,000.0

σ, Pa 3.0E+09 3.0E+09 3.0E+09 3.0E+09

ρt, kg/m3 970.0 970.0 970.0 970.0

Ct 1.2 1.2 0.2 1.2

f 0.79 0.79 3.00 0.79

s 1.5 1.5 1.5 1.5

τ, kg*s2/m4 6.0E-04 2.0E-03 6.0E-04 6.0E-04

cs 1.1 1.1 1.1 1.0

g, m/s2 9.81 9.81 9.81 9.81

A, m2 500.0 500.0 3,000.0 3,000.0

cα 0.98 1.00 0.98 0.98

lw, m 2,200.00 2,200.00 6,600.00 2,000.00

Vφ, m/s 10.39 10.39 12.99 13.70

Mk 1.05E-02 3.56E-02 1.45E-02 1.45E-02

Mt 1.26E-02 1.57E-02 3.77E-02 1.14E-02

M 2.31E-02 5.13E-02 5.21E-02 2.59E-02

N 5.67E-03 6.39E-03 6.31E-04 2.60E-03

K 4.25 7.28 4.25 4.45

W, m/s 50.98 87.39 63.75 66.75

P/A, W/m2 3,642.97 14,537.35 5,179.45 7,084.01

Height, m 1,000 1,000 3,000 3,000

P, W 1.82E+06 7.27E+06 1.55E+07 2.13E+07

cp 0.60 0.60 0.60 0.96

Paver, W 1.09E+06 4.36E+06 9.32E+06 2.04E+07

25

Table 2. Specific drags and other control parameters

Kite Wing RT Rigid Wing RT Kite Wing ST

Kite Wing RT Double

T/A, N/m2 1746.13 6308.07 1985.94 2177.52

Dp/A, N/m2 137.01 288.38 155.76 163.10

Dk/A, N/m2 214.40 210.01 243.84 267.36

Dt/A, N/m2 35.02 195.59 4.44 21.00

Dw,k/A, N/m2 11.21 119.31 17.53 21.14

Dw,t/A, N/m2 13.40 52.58 45.71 16.70

Dtl/A, N/m2 411.03 865.86 467.28 489.30

At,s, m2 4.37E-04 1.58E-03 2.98E-03 3.27E-03

d, m 2.36E-02 4.48E-02 3.15E-02 6.45E-02

ρS, kg/m2 1.56 15.27 2.44 2.67

Table 3. Economic comparison

Component \ $/kW Conventional AWECS w/FMT

Blades / Wings $177 $20

Hub $77 $0

Gearbox $143 $0

Generator $76 $50

Yaw System $19 $10

Nacelle cover & structure $60 $0

Tower $219 $0

Variable Speed System $73 $0 Rotor PBC / wing control surfaces $52 $20

Shaft $41 $0

Other (incl. control system) $63 $90

Total $1,000 $190

Wind Energy Capacity Factor 35% 70%

Ratio, Adjusted by CF 1.000 0.095

26

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