Chapter 13Airborne Wind Energy Conversion Systems withUltra High Speed Mechanical Power Transfer

Leo Goldstein

Abstract A novel Airborne Wind Energy Conversion System with a ground-basedelectric generator is proposed. The construction uses two interacting tethered wingswith a single motion transfer cable, separate from the tethers. The speed of tangen-tial motion of the cable exceeds the speed of the wings, flying cross wind, and isfurther increased by a block and tackle mechanism, thus ensuring high rotationalspeed and low torque on the receiving shaft of the ground-based drivetrain. Thedrivetrain does not require a gearbox. This device is estimated to be more than 10times less expensive than a conventional wind turbine with the same average poweroutput.

13.1 Introduction

Fundamental theoretical research and mechanical inventions in the field of Air-borne Wind Energy Conversion Systems (AWECS) date back several decades. MilesLoyd proposed AWECS with crosswind wing motion and developed the theoreticalfoundation for it [21]. Wubbo Ockels invented the original Ladermill concept [22]and, together with Bas Lansdorp, developed a pumping kite design [20]. Other re-searchers proposed a carousel [5] and ground rail concepts [1] and developed andexperimentally validated control theory for both the pumping kite and the carouseldesigns. Moritz Diehl proposed the concept of two ”dancing kites” on one tether[6]. A more detailed review and analysis can be found in [23]. Control theory forAWECS and its experimental verification has been reported by [2–4, 7–12, 16–18,24]. An early version of fast motion transfer was proposed in [13].

AWECS can be broadly divided into two categories: those with airborne electricgenerators and those with ground-based electric generators. This chapter is con-cerned with the latter category. The most recent AWECS with ground-based gener-

Leo Goldstein (B)5280 Colodny Dr. 8, Agoura Hills, CA 91301, USA, e-mail: leo.goldstein@awecs.org

235

236 Leo Goldstein

ators employ one or more wings flying crosswind and transfer mechanical energyfrom the wings to the ground generator through a tether.

While a kite wing, flying crosswind, is extremely efficient, the tether moves inthe tangential direction slowly. According to Loyd [21], the maximum power outputis provided at the tether extension speed, equal to one third of the wind speed, ifthe tether is collinear with the wind (i.e., the speed is further reduced by the anglewith the horizon). The low speed of the tether extension requires high tether forcesto transmit the same amount of power. In a conventional design with the tetherunrolling from a drum, the drum has low RPM, a high-ratio gearbox is required toincrease the angular speed to 1,500–1,800 RPM, as required by conventional electricgenerators. Thus a large part of the advantage that an AWECS has compared witha conventional wind turbine is offset by the higher cost of the drive train. The drivetrain constitutes 40% of the cost of the conventional wind turbine, according to [19,p. 178].

This chapter proposes a solution: an AWECS construction that transfers thepower of the wing motion directly to the revolving element on the ground with aspeed exceeding the speed of the wing.

13.2 Proposed Construction

In this construction, a generator, a belt drum and a drivetrain are installed on arotating platform on the ground. Two wings are flying in the air, as shown in Fig.13.1.

The wings are attached to the platform by tethers. Each wing carries a fork pulleythat is suspended under the wing with suspension cables. A belt unwinds from adrum on the platform. The top end of the belt is attached to a motion transfer cablethat wraps around fork pulley 3. After fork pulley 3, the cable wraps around forkpulley 1, then around fork pulley 2, and then, its end is attached to fork pulley 3.After unwinding from the drum, the belt engages a pulley or (if the belt is perforated)a sprocket on the platform. The motion transfer cable pulls the belt, and the beltrotates the sprocket. The tethers are inclined at some angle (such as 35◦) to thehorizontal plane. The system operates in cycles, each cycle consisting of a workingphase and a returning phase.

In the beginning of the working phase, the wings are at points A1 and A2, andthey begin to move away from one another. The wings move in the same plane withthe tethers, the motion plane. Fig. 13.2 shows the motion plane.

The solid lines in Fig. 13.2 illustrate the beginning of the working phase, andthe dashed lines show the end of the working phase. Under wind power, the wingsmove away from one another, from point A1 and A2 toward points B1 and B2. Asthe wings move away from one another, the belt unwinds from the drum and rotatesthe sprocket. The rotation of the sprocket is transferred to the rotor of the generator.Thus, the belt transfers mechanical power from the wings to the rotor of the electricgenerator, which converts the mechanical power into electric power.

13 AWECS with Ultra High Speed Mechanical Power Transfer 237

wind wing1

wing2

A1

A2

B1

B2

pulley2

pulley1

generator

pulley3

sprocket

drum

tether2

belt

tether1cable

C

Fig. 13.1 Proposed construction

When the wings arrive at the ends of the arcs (points B1 and B2), the workingphase ends and the returning phase begins: the wings yaw (move in an arc in aplane perpendicular to the tether) 180◦ and fly back. The fork pulleys are attachedon bearings that do not prevent this U-turn. In the returning phase, the generator,acting as an electric motor, rotates the drum in the opposite direction, and the drumwinds the belt back with a small expenditure of energy. The wings are controlledto minimize drag. When the wings approach each other, near points A1 and A2,they make another U-turn and come into the position for the beginning of the nextworking phase.

In the beginning of the working phase, most of the belt is wound around thedrum, both wings are close to each other, and fork pulley 3 is close to them. In theend of the working phase, the belt nearly meets fork pulley 3.

The system is omnidirectional because of the rotating platform. The altitude ofthe wings’ motion can be anywhere between 100 m and 12 km, and it can be ad-justed dynamically according to the current wind conditions. The wings can movemuch faster in the returning phase than in the working phase, because they do nothave to perform work pulling the cable and can even receive some power from thepull of the cable. U-turns have to be short, compared with the working phase. Theworking phase constitutes one half to three quarters of the cycle time and a produc-

238 Leo Goldstein

wind

D

B1

A1

A2

B2

Fig. 13.2 Plane of motion

tion deployment of this system would utilize multiple devices with time overlap.During the working phase, the angle of attack of each wing can be controlled toensure a constant speed of the belt, despite changes in the angle of the wings’ mo-tion with respect to the wind and each other, wind variation and other factors. Thelightweight wings in this system are considerably more responsive than the heavyblades used in conventional wind turbines. A group of a few such devices can gen-erate grid-quality AC current. Collisions between the tethers and the motion transfercable or belt are prevented by letting the cable and the belt sag more than the tetherand controlling the rate of the cable tension change in the phase transitions.

13.3 Analysis

13.3.1 Derivation of Power, Forces and Velocities

Fig. 13.3a shows the velocity triangle for one wing. Fig. 13.3b shows forces in themotion plane acting on the wing. Fig. 13.3c is a side view of the system, showing theangle of the tether with respect to the horizon. Using Fig. 13.3, we will analyze thesystem in its working phase by assuming uniform motion of the wings. In this case,point C (pulley 3) moves uniformly as well. Thus, the forces acting on it from thethree segments of the motion transfer cable total zero. Because all of the segments

13 AWECS with Ultra High Speed Mechanical Power Transfer 239

vk

va

vφ

α

β +90◦

a)

βDt

T

C

Fc2Fc1 Dk

α

L

b)

c)φ

C

Fig. 13.3 Derivation of theory

belong to the same cable, all the forces have the same scalar value. Thus, there isan angle of 120◦ between each pair of cables. The triangle pulley 1–pulley 2–pulley3 is symmetrical by design (maintained by control inputs); consequently, its anglesare 120◦, 30◦ and 30◦.

Referring to Fig. 13.2, if the end of the motion transfer cable reaches the groundplatform when the wings are next to each other (at the meeting point), and touchespoint C (pulley 3) when the wings are at points B1 and B2, then the cable’s lengthequals the radius R of the circle in which the wings move and equals the perimeterof the triangle CB1B2. Thus maximum half angle between the tethers is β max≈13◦.

Similarly, we can calculate the relationship between the tangential speed of themotion transfer cable and the speed with which the wing moves away from themiddle point between the wings:

240 Leo Goldstein

u =dlcdt

=2dxdt

(1+

1cos30◦

)− dx

dttan30◦ =

(2+√

3)

V ≈ 3.73V (13.1)

where dx and V are the displacement and speed, respectively, of one wing relativeto the midpoint between the wings. The speed v is close to the speed vk of thewing. Thus, the construction achieves its main purpose—the tangential speed of themotion transfer cable is greater than the speed of the wing.

For power computations, we shall consider the system operating at the nominalwind speed (i.e., the minimum wind speed at which the system yields nominal poweroutput). We shall disregard the weights of the wings, the tethers, the cable and thebelt. Consequently, we can disregard the sag of the cables and tethers and assumethat all motion happens and all forces act in the plane containing the tethers, whichwe will call the motion plane. The derivation is similar to that in [17] and [2], butuses a Cartesian coordinate system. Referring to Fig. 13.3b, assuming the motion ofthe wings without tangential acceleration and disregarding radial acceleration, wecan write the following vector equation:

L+T+Dk +Dt +Fc1 +Fc2 = 0 (13.2)

where L is the lift, T is the normal component of the tension (approximately equalto the tether tension), Dk is the wing drag, Dt is the tether drag, and Fc1 and Fc2are the forces exerted by the motion transfer cable. Dt is assumed for simplicity tobe collinear with Dk. As Fig. 13.3 shows, the relative air velocity va is given by thefollowing equation:

va = vϕ −vk (13.3)

where vϕ is the projection of the wind velocity on the motion plane and vk is thewing velocity relative to the ground.

The forces in Eq. 13.2 can be decomposed into their components along the liftaxis L and the drag axis Dk. By design, Fc1 = Fc2 >> L. Disregarding projection ofFc1 on the L axes, the tension of the tether can be written as follows:

T = L/cosα =12

CLρAv2a/cosα (13.4)

The projection of Eq. 13.2 onto the drag axis yields the following equation:

Dtl = Dk +Dt +Dp (13.5)

where the total drag Dtl is equal to the projection of T with the opposite sign andthe power generation drag Dp is given by the following equation:

Dp = Dp1 +Dp2 (13.6)

where Dp1 and Dp2 are projections of Fc1 and Fc2, respectively. Following the ex-ample of [17], we define the effective drag as follows:

13 AWECS with Ultra High Speed Mechanical Power Transfer 241

De = Dk +Dt (13.7)

The proposed construction removes the useful power using drag. Loyd’s formula[21, Eq. 22] for the maximum useful power in the drag mode applies here, withsubstitution of De for Dk:

Dp =12

De (13.8)

To compute Fc, Dp and va, we will describe the forces along the axis of drag:

Dtl = T sinα =12

CLρAv2atgα (13.9)

From the triangle of the velocities in Fig. 3a:

sinα =vϕ

vacosβ (13.10)

The wing drag is expressed as usual:

Dk =12

CDρAv2a (13.11)

According to Houska and Diehl [17]:

Dt =18

CtρAt,lv2a (13.12)

The perpendicular cross-sectional area is given by the following equation:

At,s = sTmax/σ (13.13)

Because we perform computations for the nominal conditions and disregardingtether drag’s contribution, Tmax = T . The perpendicular cross-sectional area is pro-portional to the square of the tether width, as shown below:

At,s = f d2 (13.14)

where f is a coefficient that depends on the sectional form of the tether. For example,f = π/4 for the usual round form. Assuming that L >> Dtl , we notice that cosα≈1.Let us introduce a non-dimensional quantity related to the tether drag:

N =14

CtlD√

A

√CLρs2 f σ

vϕ (13.15)

Solving scalar equivalent of Eq. 13.5 with substitutions given by Eqns. 13.7-13.15, we get:

va =−CD +

√C2

D + 83 NCL

2Nvϕ (13.16)

242 Leo Goldstein

We will define the ratio:

K =−CD +

√C2

D + 83 NCL

2N(13.17)

as an effective glide ratio. The expression for K is not similar to the expressionsfor the effective glide ratio in [17, p. 18] and [2, pp. 55–56] because we take intoaccount the dependence of the required tether thickness on the maximum tension.We are interested in efficient systems that have reasonably high glide ratios (K >4), corresponding to α < 15◦,vk≈va. The useful power is given by the followingexpression:

P = Dpvk cosα cosβ (13.18)

Substituting Dp and vk, we obtain the following:

P =16

CLρAK2v3w cosϕ3 (13.19)

Notice that this is the power for one wing. The power of the whole system inits working phase is twice that amount. To compute the average power output, weneed to multiply this by the efficiency coefficient η , taking into account what pro-portion of the total cycle time that the system is in the working phase (between60% to 75%), the energy consumption in the returning phase and the mechanical toelectrical energy conversion losses:

Paver = 2ηP (13.20)

where η is expected to be in the range 0.5–0.7 for the production systems. From Eq.13.1, the speed of motion transfer cable is given by the following equation:

u =(

2+√

3)

vk cosβ =(

2+√

3)

cos(α +β )va (13.21)

andFc =

Pu≈ L

3(2+√

3)

K< 0.03L (13.22)

An engineer constructing the system might want to keep the cable speed u con-stant over the working cycle.

13.3.2 Sample Computations and Remarks

Table 13.1 shows the numerical results for three hypothetical system variants. Thefirst system (column KiteWing,RT ) has two kite wings with an effective area of 500m2 each and a modest L/D=8 and is designed for a nominal wind speed of 12 m/sat a flight altitude of 1,150 m. The effective glide ratio is only 4.49. The computed

13 AWECS with Ultra High Speed Mechanical Power Transfer 243

average power output is 2.5 MW, which is comparable to the 5 MW output of aconventional wind turbine because of the higher capacity factor.

Table 13.1 Numerical Samples

Kite Wing, RT Rigid Wing, RT Rigid Wing, STvw, m/s 12.0 15.0 15.0ρa,kg/m3 1.1 0.8 0.8CL 1.2 1.2 1.2CD 0.15 0.04 0.04ϕ , deg 35.0 35.0 35.0lD, m 2,000.0 4,000.0 4,000.0σ , Pa 3.0E+09 3.0E+09 3.0E+09Ct 1.2 1.2 0.2f 0.79 0.79 3.00s 2.0 2.0 2.0A, m2 500.0 500.0 500.0η 0.60 0.50 0.50vϕ , m/s 9.83 12.29 12.29K 4.49 6.39 14.24Height, m 1,147 2,294 2,294wa, m/s 44.2 78.6 175.0P/A, W/m2 4,218 12,136 60,215u, m/s 145.5 258.9 576.7Paver, MW 2.53 6.076 30.1

The second system (column RigidWing,RT ) has two rigid wings with an effec-tive area of 500 m2 each and an L/D=30 and is designed for a nominal wind speedof 15 m/s at a flight altitude of 2,300 m. A higher L/D is an advantage of a rigidwing, but the system has an obvious deficiency: its tether drag is more than twice itswing drag. The tether drag is a well known AWECS problem. Luckily, this issue isalready being addressed. Griffith [14] has suggested the use of a self-aligning tetherwith a streamlined cross section for AWECS applications. Such a tether has the dragcoefficient of a 2D streamlined body, which can be 5–10 times smaller than the dragcoefficient of a cylinder. A streamlined tether can also be manufactured with a morebeneficial form factor f. For example, a tether with a load-bearing core in the formof a 3:1 rectangle has f=3, compared with f=π/4 for a round cable. The computedaverage power output is 6 MW, which is comparable to a 12 MW conventional windturbine.

The third system (column RigidWing,ST ) is the same as the second one, exceptthat it uses a tether with a streamlined profile. The computed power output is 30MW, which is comparable to the 15–20 conventional wind turbines of 5 MW each.The result is hypothetical, though. This variant involves the belt moving at a speed

244 Leo Goldstein

of 600 m/s. The engineering issues of interaction between the belt and its drum andthe sprocket at such speeds can be difficult to solve.

One can design an asymmetrical system with only a single pulley under one ofthe wings and fixed cable attachment to another wing, having lower belt speed.

13.4 Additional Considerations

Two types of wings have been mentioned as candidates for use in the system: arigid wing with an empennage (a glider) and a flexible wing (a kite). One importantdifference between them is that the glider is aerodynamically stable, while the kiteis not. For the glider, it is easy to see that attaching the tether in front of the aero-dynamic center of the lifting wing and attaching the pulley for the motion transfercable behind that center increases the longitudinal stability of the glider and doesnot change its lateral stability. For the kite, methods of dynamic stability control ofthe kites have been developed in the previously cited research. Thus, either of thesewing types can be used in the system. Continuous control input is required to ensuredynamic stability of the whole system in both cases.

The choice between kites and gliders is not obvious. Kites are potentially lessexpensive. Because of their low weight, they can stay in the air even in very lowwinds. Their low L/D and relatively low speed are not necessarily a shortcoming inthis construction because the mechanical disadvantage of the multi-pulley systemincreases the speed of the motion transfer cable and the belt. Additionally, the tetherdrag decreases the L/D advantage of the rigid wing. Finally, kites would do lessdamage, if they hit something on the ground. On the other hand, the rigid wingis more durable. It is more efficient than a wind turbine wing and can be moreefficient than a plane wing if suspension cables are employed to spread the tethertension over the whole wing span. The L/D advantage over the flexible wing can bemaintained if an aerodynamically streamlined tether is used. On the other side, thevery high speed of the belt resulting from the high speed of a rigid wing with a highL/D may be excessive. Various options for implementation of a revolving element,involving converting the linear motion of the belt into rotational motion of the rotor,are beyond the scope of this paper.

Aspects that have not been covered here and are subject for the future work in-clude: wing steering and optimizing the angle of attack; specific algorithms for sys-tem stability control; wings launch and landing.

Fig. 13.4 is the artist’s impression of the system.

13.5 Conclusions

The construction described in this paper can be used in the marine environment aswell as on land. Other advantages of AWECS are preserved. The proposed AWEC

13 AWECS with Ultra High Speed Mechanical Power Transfer 245

Fig. 13.4 Artist’s impression of the system

device does not require a gear box, a tower, a nacelle, or a converter. Only an electricgenerator is required, and its cost is only 4% of the cost of a traditional wind turbine.Heavy and complex turbine blades are replaced by cheap kites or straight fiberglasswings. Thus, the proposed AWECS construction can save 90–95% of wind turbinecosts, based on data by both Hau [15, pp. 725–763] and Jamieson [19, pp. 153–170].The capacity factors of 60–70% of the proposed systems, compared to 30–35% forconventional wind turbines, further increase the advantage. The device uses onlywell-known and mass-produced parts and techniques (excluding the streamlinedtether, which is an option, not a requirement). This makes it possible to decreasethe capital costs of wind energy by a factor of 10 or more. Because the electric gen-erator is the main cost component, this construction can generate energy below thecost of fossil fuel power plants supplied with free fuel.

Acknowledgements The author thanks Dr. Gabriel Hugh Elkaim (University of California, SantaCruz), Dave Lang (NASA) and Dave Culp (Kiteship) for productive discussion.

Nomenclature

α angle in Fig. 3a [◦]β angle in Fig. 3b [◦]

246 Leo Goldstein

ϕ elevation angle [◦]σ tensile strength of tether material [N/m2]ρt density of tether material [kg/m3]At,l , At,s sectional areas of tether [m2]Ct tether form drag coefficient [-]Dk wing drag [N]Dt tether drag [N]Dtl total drag [N]Dp power generation drag [N]d tether width [m]Fc1,Fc2,Fc tension of motion transfer cable [N]lD length of tether [m]Paver average electric power, generated by the system [W]s tether safety margin [-]u belt speed [m/s]vϕ projection of the wind velocity on the motion plane [m/s]

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