SANDIA REPORTSAND86-- 1085 Unlimited Release UC–60Printed September 1986

,

Developments in Blade ShapeDesign for a Darrieus VerticalAxis Wind Turbine

Thomas D. Ashwill, Timothy M. Leonard

Prepared by

Sandia National LaboratoriesAlbuquerque, New Mexico 87185 and Livermore, California 94550

for the United Statea Department of Energyunder Contract DE-AC04-76DPO0789

SF ?9[)O(jf,8 31I

,

Issued by Sandia National Laboratories, operated for the United StatesDepartment of Energy by Sandia Corporation.

NOTICE. This report was prepared as an account of work sponsored by anagency of tbe United States Government. Neither the United States Govern-ment nor any agency thereof, nor any of their employees, nor any of theircontractors, subcontractors, or their employees, makes any warranty, ex-press or implied, or assumes any legal liability or responsibility for theaccuracy, completeness, or usefulness of any information, apparatus, prod-uct, or process disclosed, or represents that its use would not infringeprivately owned rights. Reference herein to any specific commercial product,prucess, or service by trade name, trademark, manufacturer, or otherwise,does not necessarily constitute or imply its endorsement, recommendation,or favoring by the United States Government, any agency thereof or any oftheir contractors or subcontractors. The views and opinions expressed here-in do not necessarily state or reflect those of the United States Government,any agency thereof or any of their contractors or subcontractors.

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2

SAND86– 1085Unlimited Release

Printed September 1986

DistributionCategory UC –60

Developments in Blade Shape Design for aDarrieus Vertical Axis Wind Turbine

Thomas D. AshwillWind Energy Research Division

Timothy M. LeonardAdvanced Systems Development Division II

Sandia National LaboratoriesAlbuquerque, NM 87185

AbstractA new computer program package has been developed that determines the troposkein shapefor a Darrieus Vertical Axis Wind Turbine Blade with any geometrical configuration orrotation rate. This package allows users to interact and develop a “buildable” blade whoseshape closely approximates the troposkein. Use of this package can significantly reduceflatwise mean bending stresses in the blade and increase fatigue life.

3-4

———-——— .———.. — .——.-..—._. ——. ————

—

Developments in Blade Shape Design for aDarrieus Vertical Axis Wind Turbine

IntroductionAs the wind turbine industry enters an era with-

out government tax credits, it becomes increasinglyimportant that the cost per kilowatt hour of wind-produced power be substantially reduced. Wind tur-bines that are less expensive to manufacture but moredependable to operate are required in order to com-pete with other sources of energy. New turbine de-signs, therefore, must become less conservative andincorporate improved fatigue design and analysistechniclues for increased turbine longevity.

Vertical Axis Wind Turbine(VAWT) blades, be-cause of their large oscillatory loading conditions, arevery susceptible to fatigue failure. When combinedwith the oscillatory loading, the mean loading due tocentrifugal forces and gravity also contributes signifi-cantly to fatigue damage. One way of lowering meanstresses and extending the fatigue life is to design theblade such that its shape closely approximates anideal shape called the troposkien or “skipping-rope”shape. This reduces the flatwise bending stresses dueto centrifugal and gravitational forces as the bladetends to displace less from its original shape. Recentlya methodology for designing an improved blade shapeand thus lowering the mean stresses for VAWTS wasdeveloped at Sandia and is the subject of this report.

Development of DarrieusBlade Shape

It was realized early in the development ofDarrieus VAWTS that the shape of the blade wasimportant. G. J. M. Darrieus states in his 1931 U.S.patent (of a VAWT that each blade should “have astream-line outline curved in the form of a skippingrope.’” More recently, in the early 1970’s, the NationalResearch Council of Canada independently developedthe concept of a VAWT and noted that under theaction of centrifugal forces, a perfectly flexible bladeassumes the approximate shape of a catenary.* This isnot precise, however, as a catenary is the shape formedby a perfectly flexible cable of uniform density and

cross section hanging freely from two points. Once thecable is rotated about an axis through the end points,the shape deviates from the catenary and becomes a“troposkien.” Figure 1 shows a comparison of a sym-metric (gravity omitted) troposkien and a catenary fora VAWT blade of uniform density.

TOWER CENTERLINE ~1I

/

/

I

SYMMETRICTROPOSKIEN

- —- CATENARY

Figure 1. Symmetric Troposkein vs. Catenary Shape

5

In 1974, Blackwell and Reis, in their report, BladeShape for a Troposkien Type of Vertical-Axis WindTurbine,’ defined the term troposkien as “the shapeassumed by a perfectly flexible cable of uniform den-sity and cross section if its ends are attached to twopoints on a vertical axis and it is then spun at constantangular velocity about that vertical axis.” Since aVAWT blade is not perfectly flexible, it should bebent or formed as closely as possible into the shape itwould become during rotation if it were flexible, thusminimizing the flatwise bending stresses. Blackwelland Reis developed the equations that geometricallydescribe a troposkien shape for a blade of uniformdensity and used an iterative solution of these equa-tions in their computer program TROP. The equa-tions were developed for only half the blade, andgravity effects were neglected in the solution; thus, theresulting troposkiens were symmetric about the equa-tor. This was a good approximation for high-rotation-rate, small-diameter turbines like the Sandia 2-mturbine.z

In the late 1970’s the iterative technique em-ployed by Blackwell and Reis to define any uniform-density troposkien was extended by Sandia to includegravitational effects and blades of three differentcross sections. These modifications were implementedin the computer program BENDO.

Current Sandia blade-shape designs have beenbased in general on the computer programDMG,:’which formulates the blade shape as an ap-proximation to the symmetric troposkien (as deter-mined by BENDO). This approximation consists ofthree sections: a straight section at both the top andbottom portions of the blade and a circular arcthrough the equator that meets the straight sectionstangentially. The DMG user inputs the height anddiameter of the turbine rotor and the upper and lowerblade-to-tower angles. DMG then determines thestraight-circular arc-straight (S-C-S) geometry thatapproximates the symmetric troposkien for that par-ticular turbine. Figure 2 shows a comparison of asymmetric troposkien and its S-C-S approximationfor a VAWT blade of uniform density. The S-C-Sapproximation has an advantage over the catenaryapproximation in that the blade-to-tower angles canbe made to match those of the troposkien. This tendsto lower the flatwise bending stresses. When it wasrealized that gravity should be included in the tropos-kien formulation, the blade-shape design continued tobe S-C-S approximations to a symmetric troposkien,but the blade-to-tower angles were adjusted to ac-count for the blade sag.

In the remainder of this report the definition of atroposkien shall be expanded to become “the shape

TOWER CENTERLINE —

—–—SYMMETRICTROPOSKIEN \ \

SYMMETRICs-c-sAPPROXIMATION

\

\

\

Figure 2. Symmetric Troposkien VS,Approximation

Symmetric S-C-S

assumed by a flexible structure of uniform or nonuni-form density attached at its ends to a vertical axissuch that when it is spun at a constant angular veloc-ity about the vertical axis, no flatwise bending stressesoccur in the structure.” With the inclusion of nonuni-form densities, the definition becomes more generaland allows for design conditions where blades areconstructed in multiple sections with varying geomet-rical or material properties and heavy joint sections.This is the case for the design of the Sandia 34-m TestBed.* It should be noted that a troposkien shape for aparticular blade or flexible structure is different foreach rate of rotation when gravity is included. Whengravity is excluded, the troposkien shape is the samefor any rotation rate.

*The 34-m Test Bed is a prototype VAWT being designedand constructed by Sandia. It has a rotor diameter of 110 ft(34 m) and an H/D ratio of 1.25. Each blade has fivesections: a straight 48-in. chord section at each end of theblade, two 42-in. chord intermediate sections, and a 36-in.chord center section. The 48-in. chord has an NACA 0021

contour and the 36- and 42-in. chords have an SNLA 0018/50 contour.4

6

Development of NewTroposkien Program

A recently developed troposkien shape-determi-nation program called TROP-113 combines the previ-ous developments of the programs TROP andBENDO and includes additional features and im-provements. It employs the iterative technique devel-oped by Blackwell and Reis to determine the tropos-kien shape and includes gravity, nonuniform bladedensities, lumped masses, and the enforcement of aconstant blade length. It also allows for the offset dueto tower radius. These enhancements will enable thedesigner to produce blades that will more closelyapproximate exact troposkiens.

Figure 3 is a schematic that shows the loads on aperfectly flexible cable rotating at a constant angularvelocity about a vertical axis Z. The distance from theZ axis to a point on the cable is indicated by R. R~.X isthe maximum distance from the Z axis to a point onthe cable. This point is called the equator and alwaysoccurs where a tangent to the cable is in a verticalorientation. The loads acting along the length of cableare the centrifugal forces and the gravitational forces.

I

II(0

&

.

CENTRIFUGAL FORCES —

GRAVITATIONAL FORCESi

I

I

Figure 3. Loads on a Perfectly Flexible Cable RotatingAbout a Vertical Axis

Figure 4 is a free-body diagram that shows theloads on a section of the cable when it is rotating at aconstant angular velocity. TOis the tension in the cableat the equator and acts vertically downward. T is thetension at an arbitrary point P. Intermediate pointson the cable section are designated as Pl, Pz, and P~,and n is the number of cable segments between theequator E and the point P. Summing forces in thehorizontal direction for this cable section results in

T sin/3 = C (1)

where C, the centrifugal force, can be formulated as

fC= ‘au2Rds. (2)

,,

The quantity u is the mass of the cable per unit length,and S is the length of cable between point E, theequator, and point P in Figure 4.

z

A

u

T

6

/[

Pn

P33

c P22

PI1=1

E

I

I

\

GC = CENTRIFUGAL FORCES

G = GRAVITATIONAL FORCES

To

IFigure 4. Free-Body Diagram of Section of Rotating, Flexi-ble Cable

Summing forces in the vertical direction results in

TCOS6=TO+G (3)

where G, the gravitational force, can be written as

fG= ‘ugds (4)

!)

Here, g is the acceleration due to gravity.

Dividing Eq (1) by Eq (3) gives

tanf3 =c

(5)T,, +G”

Holding the mass per unit length constant (thus mak-ing the gravitational force per unit length constant)and substituting Eqs (2) and (4) into Eq (5), oneobtains

Jotantl =

TO + ags “(6)

This is the same as Eq (6) in Reference 1, where it issolved after neglecting ugs and gravity. For the moregeneral case of nonconstant mass per unit length (andthus nonconstant gravitational force per unit length)substitution of Eqs (2) and (4) into Eq (5) yields

\

s~? uRds

tan~ = “ s

/

(7)

To + g udso

This equation can be solved by breaking it up into aseries of integrals as follows:

‘ano=F2+[F0+gJ:”’ds)+F0+gr”2ds)+...+ro+gl:l,uds)]}]}

r ,s. r.s.. . . + /s uiRids] (8)

(Jo Js, JSn_, J

where Si is the length of cable from point E to point Pi.R, is the distance from the Z axis to the midpoint ofcable section i, and ai is the mass per unit length ofcable section i.

The solution to Eq (8) is accomplished with theuse of an iterative process. In this process the entireblade is broken into 40 segments. The blade length iscomputed using input parameters such as the rotordiameter and the H/D ratio. An initial value for TOandthe equator location are assumed and 0, is then deter-mined segment by segment from the equator to eachend of the blade. After the first iteration, the ends of

the blade end up at positions different from the blade-to-tower attachment points because TO and the equa-tor location were approximated. Depending on theposition of the blade ends, TOand the equator locationare adjusted on the next iteration. This iterative pro-cess is continued until the blade ends are at the properattachment points. Thus the troposkien is defined.During the iterative process the rotor diameter andblade length are held constant and slight changes inblade geometry are accommodated by modifying therotor height and thus the H/D ratio.

The troposkien shape for a cable or blade ofuniform density has a continuously changing radius ofcurvature. An example of this is shown in Figure 5,where the radius of curvature is plotted versus bladelength for a troposkien of 37.5 rpm. A 42-in. bladesection is used so that the troposkien roughly approxi-mates a blade of the 34-m Test Bed. The high radiusof curvature at the ends of the blade gradually dimin-ishes towards the equator. When blade joints areincluded, the extra masses associated with the jointscause sudden changes in the radii of curvature of thetroposkien at the joints. This is evidenced in Figure 6,which shows a plot of the radii of curvature along atroposkien at 37.5 rpm corresponding to the actual34-m Test Bed geometry (including joints). The loca-tion of the joints is obvious by the sudden changes inradii of curvature which are due to the tendency of theblades to bulge outward at these positions. The effectsof rotation rate on the troposkien shape when gravityis included are apparent in Figure 7. This figure showstroposkien shapes for different rates of rotation for auniform-density blade of the Low Cost turbine scale.5The troposkien shape droops significantly at 5 rpm.As the rpm is increased, the troposkien shape sags lessand less as centrifugal forces offset the gravitationalforces. The effects of gravity are also apparent inFigure 8. This plot, which is to scale, compares thesymmetric troposkien (gravity omitted) with theasymmetric troposkien (gravity included) at 37.5 rpmfor the multiple-density blade of the Test Bed. Theseemingly slight difference between the two shapes isimportant, as will be shown later. Designing a blade tothe asymmetric troposkien can reduce the flatwisemean bending stresses significantly.

U)7000 I I I I 1 1 I I 1 I

d 1 1 I I I I I I 1 1 1

0.10 0.20 0.300.40 0.50 0.60 0.70 0.80 0.90 1.00

RATIO OF DISTANCE FROM TOP OF BLADE TOTOTAL BLADE LENGTH

FigLlre5. Radius of Curvature forthe Troposkien of the34-m Test Bed with a Uniform-Density Blade

Figure 7. Effects of Rotation Rate on Troposkien Shape fora Uniform-Density Blade

t I I I I I I I I I

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.60 0.90 1.00

RATIO OF DISTANCE FROM TOP OF BLADE TOTOTAL BLADE LENGTH

Figure 6. Radius of Curvature for the Troposkien of the34-m Test Bed With Multiple-Sectioned Blade

—.—

TOWER CENTERLINE _

/

SYMMETRIC

ASYMMETRIC

Figure 8. Symmetric Troposkien vs. Asymmetric Tropo-skien for the 34-m Test Bed at 37.5 rpm

9

Design of Blade Shapes

Methods Used for Design ofExisting Blade Shapes

The computation of the troposkien, or ideal,shape of a VAWT blade for any configuration is thefirst step in the blade shape design process. Thesecond step is designing a buildable shape that fits thetroposkien as closely as possible. Constructing a bladebent exactly to a troposkien with its constantly chang-ing radius of curvature would be very expensive. Aspreviously noted, for either a symmetric or asymmet-ric troposkien a good approximation is an S-C-Sshape. The Sandia 17-m research machine,G which wasdesigned in 1976, has an S-C-S blade shape thatapproximates a symmetric troposkien. Figure 9 showsa plot of the flatwise mean stresses along the blade at50.5 rpm for this machine as predicted by Sandia’sforced response code FFEVD.T Because the blade isnot shaped exactly to a 50.5-rpm troposkien andgravitational effects were not included in designingthe blade shape, flatwise bending occurs. The peakflatwise mean stress of 9800 psi occurs at the lowerroot and is much higher than elsewhere along theblade. In the design of the DOE/ALCOA Low Costturbine around 1980,b it was determined that gravityeffects could easily be taken into account by rotatingthe S-C-S blade shape. This was done simply bymodifying the blade-to-tower angles. For a symmetrictroposkien approximation, the S-C-S shape attachesto the tower with identical angles, both top and bot-tom. In the case of the Low Cost turbine, the sag dueto gravity was taken into account by determining thebest fit S-C-S symmetric troposkien and then decreas-ing the angle at the top and increasing the angle at thebottom. These angle changes effectively “sagged” theblades and approximated gravity effects. The angleswere chosen in a trial-and-error manner by determin-ing the stresses for a series of blade configurationsthat differed only in the blade-to-tower angles. Theangles that resulted in the lowest mean bendingstresses were incorporated into the blade design.FFEVD predicts a flatwise mean stress distributionfor the Low Cost turbine at 48 rpm, as shown in Figure10. Bending stresses of up to 8000 psi occur, but thehigh stresses at the root are not evident.

8000

z& 6000”

i-

I I I I i I I I

~ OUTER FIBER~ INNER FIBER

~ -6000IL t Ii

-8000 b

I 1 I I I I I I I

0 100 200 300 400 500 600 700 8009001000

DISTANCE FROM TOP OF BLADE, INCHES

Figure 9. Flatwise Mean Stresses for Sandia 17-m Turbineat 50.5 rpm

I I I I I I I I I 1 I I I

ii

-6000— OUTER FIBER

~ INNER FIBER

I I I I I I I I I I I I

o 200 400 600 800 1000 1200

DISTANCE FROM TOP OF BLADE, INCHES

Figure 10. Flatwise Mean Stresses for the DOE/ALCOALow Cost Turbine at 48 rpm

10

Ne!w Blade-Shape DesignMethodology

A blade-shape design software package, TROP-FIT~ has been developed that incorporates the previ-ously discussed program TROP-11. This package al-lows the user to determine the troposkien shape for aparticular blade and then develop a buildable approx-imation to this shape. TROPFIT contains severaloptions that can be used in the troposkien approxima-tion. One can still use the S-C-S approximation orincorporate any or all of the following options.

I} Multiple radii of curvature along the blade“ Straight joint sections anywhere along the blade(t Slope discontinuities or “kinks” at the joints.

The motivation for including multiple radii ofcurvature and slope discontinuities in the designpackage resulted from the blade design of the 34-mTest Bed, where these approximating techniques wereused. Figure 11 is a plot of the blade shape geometryfor the Test Bed. Because the design called for fiveseparate blade sections, use of multiple radii of curva-ture could easily be implemented. As shown in Fig-ure 6,,joints, because of their extra mass, cause suddenchanges in the radius of curvature of the troposkien.These sudden changes can best be modeled by usingslope discontinuities in the blade shape at the jointsthemselves. The “kinks” improve the troposkien ap-proximation and substantially reduce the flatwisebending stresses when compared to an S-C-S approxi-mation,

A simplified flowchart for TROPFIT is shown inFigure 12. The troposkien is first calculated by sub-routine TROP-11 and stored as a series of coordinates.Subroutine MSCFIT then takes these coordinatesand, based on a three-point curve fit, computes theradius of curvature that best approximates each sec-tion of the troposkien. Straight sections are used forthe sections nearest the tower, both top and bottom.This causes slope discontinuities at the joints, andMSCFIT determines the kink angles required for thegeometry and stores this initial approximation. InTRAICKIT, the user interacts to adjust the radii ofcurvature, kink angles, or section lengths to obtain abuildable geometry. TRACKIT then determines thenew coordinates and stores these. Finally, the user-designed blade shape is used as a model in FFEVD,and a forced response calculation is carried out.The resulting centrifugal and gravitational bendingstresses are compared to other designs in order todetermine the “best” design.

13 6“

, 10wER CENTERLINE

?&55 “

(IACA)02 1-48

33.56 /11.64” ‘m”

SANDIA 00 i 8150-42

“7

= 239.7S7.52”

Y

30.00”1180.00”R

/

+

SANOIA 001 S150-36

I675.00” 58.65°

ARC LENGTH

/

\1 lS0.00”R

SAM)IA00181 S0-42

\57.000

IACA021-48

/

/

/>

36.56 “

Figure 11. Blade Shape Geometry for 34-m Test Bed

Figures 13 through 17 are plots from FFEVD ofpredicted flatwise mean stresses along the bladelengths for the 34-m Test Bed at 40 rpm. The meanstresses for the troposkien itself are shown in Fig-ure 13. Here, the inner and outer surfaces of the bladehave the same stress distribution, which indicatesthat the blade has no flatwise bending. These meanstresses are the lowest obtainable for this blade. Fig-ure 14 shows the flatwise mean stresses for the “best”S-C-S approximation. The top and bottom blade at-tachment angles were optimized to obtain 52° and54°, respectively, resulting in stresses of up to 8700psi, 7000 psi of which is due to bending as the bladeshape tries to form itself to the troposkien.

During the blade design process for the Test Bedthe radius of curvature and kink angles were modifiedwith the help. of TROPFIT to minimize the mean

——— ---

11

bending stresses. Figures 15 and 16 are the flatwisemean stress plots from intermediate blade shape de-signs for the 34-m Test Bed. In proceeding from the S-C-S approximation to the first intermediate design,multiple radii of curvature were incorporated. As seenin Figure 15, radii of curvature of 1100 in. for theintermediate sections of the blade and 660 in. for thecenter section were chosen. This design change re-duced the peak bending stress from 8700 psi to 6700psi.

For the second intermediate design, as shown inFigure 16, the peak mean bending stress was loweredto 5200 psi by using radii of curvature of 1300 and 660in. and adding kinks at the joints of 3° to 4°.

The final blade design resulted in the plot ofFigure 17. With radii of curvature of 1180 and 675 in.and kink angles of 6.5° to 7.5°, the peak mean bendingstress was further reduced to 4300 psi. Thus, themaximum stress at 40 rpm is down from a peak of 8700psi in the best S-C-S approximation (Figure 14) to43OO psi in the final blade design (Figure 17). Thesestresses of the final design represent a significantdecline in the typical flatwise mean bending stressesof Darrieus VAWTS and may increase the fatigue lifeof the blade by a factor of 2 to 4.

PROGRAM TROPFIT

+

BLADE DEFINITION-SECTION PROPERTIES AND SECTION LENGTHS

\

DETERMINETROPOSKIEN

DETERMINE USER INTERACTS TOSTORE CHOOSE “NICE” VALUE

COORDINATES TROPOSKIEN FOR RADIUS OF CURVATUREAND KINK ANGLES

STORECOORDINATES

DETERMINECLOSED FORM

GEOMETRY

.

dSTORECOORDINATES

Figure 12. Flowchart for TROPFIT

12

8000

6000

4000

2000

0

-2000

-4000

-6000

I I I I I I I I I 1 I

1A A A OUTER FIBER

— INNER FIBER 1

I I 1 1 1 I 1 I I I I

o 400 800 1200 1600 2000 2400

DISTANCE FROM TOP OF BLADE, INCHES

Figuro 13. Flatwise Mean Stresses for Troposkien BladeShape of 34-m Test Bed

8000

6000

U.1

4000

2000

0

-2000

I I I I I I I r 1 I I

~ OUTER FIBER~ INNER FIBER

g~ -4000

tROC INTERMEDIATE

SECTION =11 00 INCHES iz -6000

tROC CENTER SECTION= 660 INCHES

~ NO KINKS AT JOINTS -1L

1- ROC = RADIUS OF C1.RVAIWE-s000

IMIIIIU IIIo 400 600 1200 1600 2000 2400

DISTANCE FROM TOP OF BLADE, INCHES

Figure 15. Flatwise Mean Stresses for First IntermediateBlade Shape for 34-m Test Bed

u-1u.

I 1 I I I 1 1 I I I I I

8000

6000

4000

2000

0

-2000

-4000

-6000 I

t

~ OUTER FISER

-6000 ~ INNER FISERi

1 I I I I 1 I 1 I 1 1 t I

o 400 600 1200 1600 2000 2400

DISTANCE FROM TOP OF BLADE, INCHES

Figure 14. Flatwise Mean Stresses for S-C-S Blade ShaDe.–of 34-m Test Bed

Sooo

6000

4000

2000

0

-2000

-4000

-6000

I I I 1 I 1 I I 1 1 I 1

_ OUTER FISER~ INNER FIBER

1

ROC INTERMEDIATE SECTION= 1300 INCHESROC CENTER SECTION= 660 INCHES I

KINK ANGLES ==3“ -4°

1 1 I I 1 I 1 1 1 1 1 10 400 600 1200 1600 2000 2400

DISTANCE FROM TOP OF BLADE, INCHES

Figure 16. Flatwise Mean Stresses for Second IntermediateBlade Shape for 34-m Test Bed

13

.. . . .———.—

8000

za 6000

a-$ 4000

s(n

2000

z< 0

* -2000ulg

3-4000

1-a4

-6000

IA-8000

1 1 I I 1 1 ! I I I II

~ OUTER FIBER~ INNER FIBER i

1

ROC INTERMEDIATE SECTION = 11 BO INCHESROC CENTER SECTION = 675 INCHES

KINK ANGLES =6.5” -7.5”1

I I 1 I I I I I I I I I

o 400 800 1200 1600 2000 2400

DISTANCE FROM TOPOF BLADE, INCHES

Figure 17. Flatwise Mean Stresses for Final Blade Shape of34-m Test Bed

SummaryA program called TROP-II hasbeen developedto

determine the troposkien shape for a blade of anyconfiguration at any rotation rate. This program hasbeen incorporated into a blade-shape-design packagecalled TROPFIT, which allows user interaction todevelop a’’buildable” bladeshapethat closelyapprox-imates an established troposkien. With the use ofthese programs, one can significantly reduce meanbending stresses in the blade and thus increase fatiguelife. The practicality of the methodology was verifiedby applying it to the 34-m Test Bed.

References‘B. F. Blackwell and G. E. Reis, Blade Shape /or a

Troposkien Type of Vertical-Axis Wind Turbine, SLA-74-0154 (Albuquerque, NM: Sandia National Laboratories,April 1974).

‘B. F. Blackwell, R. E. Sheldahl, and L. V. Feltz, WindTunnel Performance for the Darrieus Wind Turbine withNACA 0012 Blades, SAND76-0130 (Albuquerque, NM:Sandia National Laboratories, March 1977).

3T. D. Ashwill and T. M. Leonard, “DMG-A DarrieusVAWT Finite Element Mesh Generator and Rotor DesignPackage; SAND86-1854 (Albuquerque, NM: Sandia Na-tional Laboratories, In Preparation).

‘D. E. Berg and T. D. Ashwill, “An Update on theStructural Design of the Sandia 34-m Vertical Axis WindTurbine,” Proceedings (SED-VO1. 2), Fifth ASME WindEnergy Symposium, February 1986.

5AICOA Laboratories, “Design and Fabrication of aLow-Cost Darrieus Vertical Axis Wind Turbine System,Phase I - Technical Report,” ALO-4272 (Albuquerque, NM:Sandia National Laboratories, March 1980).

‘M. H. Worstell, Aerodynamic Performance of the 17meter Diameter Darrieus Wind Turbine, SAND78-1737(Albuquerque, NM: Sandia National Laboratories, Septem-ber 1978).

7D. W. Lobitz, “Forced Vibration Analysis of RotatingStructures with Application to Vertical Axis Wind Tur-bines,” in Vol III of Proceedings of Fifth Biennial WindEnergy Conference and Workshop, October 1981,SERI/CP-635-1340 (Golden, CO: Solar Research Institute).

.

14

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DOE/ALOAttn: G. P. TennysonAlbuquerque, NM 87115

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DOE Headquarters (20)Wind/Oceans Technologies DivisionAttn: D. F. Ancona (5)

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FloWind Corporation (3)Attn: L. Schienbein

I. VasB. Im

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Indal Technologies, Inc. (2)Attn: D. Malcolm

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Iowa State UniversityAgricultural Engineering, Room 213Attn: L. H. SoderholmAmes, IA 50010

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DISI’RIBUTION (Continued):

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Kaiser Aluminum and Chemical Sales, Inc.Attn: D. D. Doerr6177 Sunol Blvd.PO BOX 877Pleasanton, CA 94566

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Kalman Nagy LehoczkyCort Adelers GT. 300s10 2NORWAY

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Robert LynetteR. Lynette & Assoc., Inc.15921 SE 46th WayBellevue, WA 98006

Massachusetts Institute of Technology (2)Attn: Professor N. D. Ham

W. L. Harris, Aero/Astro Dept.77 Massachusetts AvenueCambridge, MA 02139

H, S. MatsudaComposite Materials LaboratoryPioneering R&D LaboratoriesToray Industries, Inc.Sonoyama, Otsu, ShigaJAPAN 520

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,

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K. J. TouryanMariah Research6200 Plateau Dr.Englewood, CO 80111

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19

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