National Renewable Energy Laboratory 

Innovation for Our Energy Future 

A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 

Subcontract Report 

NREL/SR-500-12087 

June 2006 

Determination of Elastic Twist in 

Horizontal Axis Wind Turbines 

(HAWTs) 

Final Report: August 1989 

F. Stoddard, V. Nelson, K. Starcher, B. Andrews 

Alternative Energy Institute – West Texas State University 

Canyon, Texas 
National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393 

303-275-3000 • www.nrel.gov 

Operated for the U.S. Department of Energy 

Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337

Subcontract Report 

NREL/SR-500-12087 

June 2006 

Determination of Elastic Twist in 

Horizontal Axis Wind Turbines 

(HAWTs) 

Final Report: August 1989 

F. Stoddard, V. Nelson, K. Starcher, B. Andrews 

Alternative Energy Institute – West Texas State University 

Canyon, Texas 

NREL Technical Monitor: 

Prepared under Subcontract No RL-6-06013 
This publication was reproduced from the best available copy 

Submitted by the subcontractor and received no editorial review at NREL

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SUMMARY 

This report presents the results of a project at the Alternative Energy Institute (AEI) which 

measured and calculated the elastic twist of three representative composite horizontal-axis blades: Carter 

300, Gougeon ESI 54, and UTRC 8 kW. The report covers the experimental method used to inspect and test 

the blades, the theory and computer programs used to develop semi-empirical analytical blade models, 

calculation of the steady elastic twist of the three blades in simulated operation, and comparison with actual 

field performance of the wind turbines. 

The experimental method employed is suitable for normal engineering blade testing, including 

quality control, verification of theoretical results, and iteration of design parameters. The computer codes 

developed under this project are suitable for engineering design of composite wind turbine blades. Suitable 

instructions for use of the programs are given. 

Theory developed under this project can calculate a practical aeroelastic model of geometrically and 

structurally complex composite wind turbine blades. Such blades show great promise for reducing the 

weight and cost of future wind turbines; however, they are usually highly twisted and tapered, have 

variation in mass and stiffness properties in both spanwise and chordwise directions, and employ various 

forms and orientations of reinforcement, all of which present significant uncertainties in determining the 

engineering stiffness constants. The method developed here allows straightforward derivation of the blade 

section properties (without resorting to difficult-to-implement and error-sensitive finite element 

computer codes) bv combinino classical beam analvsis with laboratorv test results in a semi-empirical 

process here termed "mass-elastic trianaulation." The aeroelastic blade model thus achieved has the same 

static deflection and the same fundamental frequencies of vibration, in flapping, lead-lag, and torsion, as 

the actual blade, and can thus be used in aeroelastic calculations. 

Linear beam theory with a simple unidirectional stress state is assumed. The analysis calculates 

area-weighted flexural and torsional moduli for the elastic beam, determines the beam properties relative 

to the principal axes, and then performs coordinate transformations to develop blade axis sectional 

properties. Deflections are calculated by referring the applied blade section loading and moments to the 

aerodynamic center (quarterchord), the mass center, the bending centroid (weighted area centroid), or the 

shear center (elastic axis) and transforming the deflections by superposition. Section geometry and 

moduli are verified by a series of laboratory bench tests including straightforward static load 

measurements on the actual blade, close blade inspection, and optional blade sectioning and coupon testing, 

which are also covered in this report. The section moduli and mass moments were verified by measuring 

experimental fundamental frequencies and modes of vibration. 

Elastic twist results are presented for the three test blades: Carter 300 glass-epoxy, Gougeon ESI 

54 wood-epoxy, and UTRC 8 kW pultrusion, illustrating the wide variation in the section properties 

predicted by (1) composite analysis alone, (2) static deflection empirical tests alone, (3) natural 

frequency tests alone, and (4) the present method, which combines all three. 

Elastic twist of the UTRC blade varied from 3.3 degrees nose down at 4.5 m/s (10 mph, 0 kW) to 

0.25 degrees nose up at 13.4 m/s (30 mph, 13 kW); the section torsion was dominated by the lift offset 

from the shear center and most of the twist occurred in the flexbeam. This was seen to greatly affect the 

performance and helped explain the actual vs. calculated UTRC 8 kW power curve. 

The ESI blade, for both the 77 and 90 rpm production versions, would have had less than 0.1 degree 

of elastic twist for all conditions if no tip flaps were present, due to its very high torsional stiffness. 

However, the elastic twist increased to about 0.33 degrees nose up for the standard flat plate tip, and 0.41 

degrees nose down for the larger "whisper tip." Still, the effects of this live twist on the ESI performance 

were negligible. 

The Carter blade has substantial blade leading edge ballast weight, which was seen to dominate the 

section torsion, resulting in over two degrees nose down live twist at high wind speeds. The ballast 

produced a very beneficial reduction of blade tip deflection, and also counteracted the large nose up elastic 

moment due to aerodynamic lift offset. Neither the ESI nor the Carter power curve test vs. theory 

discrepancies could be explained by elastic twist effects. The most significant factors affecting elastic twist 

were found to be shear center location, flap bending deflection, and added ballast weight. 
TABLE OF CONTENTS 

1 . 0 Introduction 

Background ............................................................................................................... 1 

Composite Blade Sources of Uncertainty .................................................................. .. 2 

Sources of Elastic Twtstlng Moments ....................................................................... 4 

2.0 Project Scope and Methodology 

Goal of the Project .................................................................................................... 5 

Semi-Empirical Approach ....................................................................................... 5 

Blades Chosen for this Project ................................................................................. 6 

3.0 Experimental Method 

Genera! .................................................................................................................... 7 

Initial Blade Inspection ............................................................................................ 7 

Blade Control Axis Location and Twist ..................................................................... 7 

Blade Template Construction .................................................................................... 7 

Blade Sectioning ..................................................................................................... 11 

Blade Mass Distribution ........................................................................................ 15 

Section Aerodynamic Corrections- ...................................................................... 16 

Blade Laminate Coupons ......................................................................................... 17 

Static Deflection Testing ........................................................................................ 18 

9.1 Setup and Method ........................................................................................ 18 

. 9.2 Load Cases ................................................................................................... 21 

. 9 -3 Deflection Measurement Method ................................................................ 22 

. 9.4 Deflection Corrections to Quarterchord ..... ............................... ............... 23 

. 9.5 Deflection Results ...................................................................................... 24 

. 1 0 Blade Vibration Modal Survey ............................................................................... 24 

4.0 Theoretical Method 

General- ................................................................................................................. 32 

Composite Blade Section Properties Calculation ................................................... 32 

2.1 Section Description .................................................................................... 32 

. 2.2 Section Area and Stiffness Properties .......................*............................... 33 

-2 -3 Section Torsional Rigidity .......................................................................... 36 

. 2 -4 Section Masses and Inertias. ...................................................................... 37 

Blade Static Deflection CalcuIation ........................................................................ 38 

Blade Natural Bending Frequencies and Modes ...................................................... 41 

Blade Torsional Frequencies and Modes ................................................................. 45 

5.0 Development of Blade Mass/Elastic Models 

Triangulation of MassIElastic Properties ............................................................ 47 

Uniform FRP Blade Example: UTRC Blade ............................................................. 47 

. 2.1 Method ........................................................................................................ 47 

. 2.2 Prediction of Engineering Moduli and Densities* ....................................... 47 

. 2.3 Prediction of Spar Properties ................................................................... . . 50 

. 2.4 ln~t~al Predicted Results ............................................................................ 50 

2.5 Specification Verification by Blade Sectioning.. ........................................ 50 

. 2.6 Verification by Deflection Tests ................................................................. 51 

. 2.7 Verification by Frequency Tests ................................................................ 53 

.2.8 Final Aeroelastic Model .............................................................................. 55 
Wood-Epoxy Blade Example: Gougeon ESI 54 Blade ............................................. 5 6 

.3.1 ESI Blade Description ................................................................................ 56 

. 3.2 Derive Initial Section Properties .............................................................. 57 

. 3.3 Verification by Flexural Tests .................................... .... .........*............. 61 

. 3.4 Verification of Static Twist ........................................................................ 61 

.3.5 Verification by Frequency Test.. ................................................. 6 4 

3 6 Final Aeroelastic Model .............................................................................. 66 

. 3.7 ESI Tip Flaps ........................................ .,, ................................................... 66 

Complex Composite FRP Example: Carter 300 Blade ........................................... 68 

CNm Blade Description ........................................................................... 69 

Ascertain Blade Geometry ........................................................................... 70 

Ascertain Ballast and Weight Distribution ................................................ 73 

Derive Carter Design Composite Values ..................................................... 75 

Derive Contribution of I-Beam .................................................................. 79 

AEI Measurements for Composite section Properties ............................... 80 ... Verlflcatlon by Flexural Test .................................................................... ... 81 

Verlflcatlon of Static Twist ........................................................................ 83 

Comparisons of Running Mass Distributions ............................................ 84 

Verification by Frequency of Vibration Tests ........................................... 86 

in 01 ........................................................................... 7 

6.0 Elastic Twist Calculation 

Genera! ................................................................................................................... 88 

Calculation of Blade Centrifugal Tension and Moments ......................................... . . 88 

Derlvatlon of Section Torsion ................................................................................ 90 

Aerodynamic Loads ................................................................................................. 92 

General Discussion: Operating Blade Elastic Deflections ................................... 93 

UTRC Bhde Deflections .......................................................................................... 95 

ESI Blade Deflections ............................................................................................. 97 

Carter Blade Deflections ........................................................................................ 98 

7.0 Performance Calculations and Results 

Aerodynamic Calculations .................................................................................... 106 

Operational Cases Considered .............................................................................. 110 

Turbine Power Curve Performance Results ....................................................... 110 

. 3.1 UTRC 8 kW Blade ..........................................................*.......................... 112 

. 3.2 ESI 545 Blade .......................................................................................... 112 

.3.3 Carter 300 Blade ..................................................................................... 112 

Discussion ............................................................................................................ 112 

8.0 Conclusions 

Comparison of Predicted and Experimental Results ........................................... 114 

use of Method for Analysis of Composite Blades .................................................. 114 

use of Method for Blade Quality Control for Manufacturers ............................... 114 

Design Implications of Results ............................................................................ 114 

Recommendations for Further Work and HAWT Improvemen? .......................... 115 

9.0 References 
10.0 Appendices 

-1 Computer Code: Determination of Composite Blade Section Properties .............. 118 

. . 1 1 Brief Discussion ...................................................................................... 118 

. 1 . 2 Program Listing, STRESSM ..................................................................... 118 

. 1 -3 Sample Run, Carter Blade ....................................................................... 126 

. 1 4 . Sample Run, ESI Blade . No Tips or Ballast .............................................. 130 

. 2 Computer Code: Blade Deflections and Stresses Under Loading ........................... 134 

. 2.1 Be Discussion ...................................................................................... 134 

2.2 Program Listing, STRESSDATA ............................................. .................., 134 

. 2.3 Sample Run, Carter Blade ........................................................................ 136 

. 2.4 Sample Run, ESI Blade, With Tip Weigh! ............................................... 138 

-3 Computer Code: Composite Blade Bending Frequencies of Vibration ................... 139 

-3.1 Brief Discussion ...................................................................................... . . 139 

.3.2 Program Listing, VIBRATE ...................................................................... 140 

3.3 Sample Run, UTRC Blade, Static and 108 rpm ........................................ 141 

.3.4 Program Listing, VIBETIP, (Tip Weight Version) .................................. 143 

-4 Computer Code: Composite Blade Torsional Frequencies of Vibration. ............... 143 

. 4.1 Summary ................................................................................................. 

. . 143 

. 4.2 Program L~st~ng, TORSVl B ...................................................................... 143 

. 4.3 Sample Run, ESI Blade ............................................................................. 145 

.4.4 Program Listing, TVIBTIP, (ESI Blade With Tip Inertia) ...................... 145 

. 4.5 Sample Run, ES1 Blade with Tip Inertia .................................................. 146 

. 5 Computer Code: Steady Elastic Twist Calculation ................................................ 146 

. 5.1 Program Listing, STRESsElJsw .......................................................... 146 

. 5.2 Sample Run, UTRC Blade ......................................................................... , 156 

. 6 Calculation of Drag Polars for Eight Wind Turbine Blade Sections .................... 158 

. 6.1 Procedure and Analysis ............................................................................ 158 

.6.2 Planform Data Files and Drag Polars ...................................................... 158 

-7 Checklist Sent to Blade Manufacturers ............................................................... 159 
LIST OF FIGURES 

Carter 300 Blade ................................................................................................................. I 

ESI 54 Blade ......................................................................................................................... 2 

UTRC 8 kW Blade ............................................................................................................... 2 

Composite Blade Sources of Uncertainty.. ........................................................................... 3 

Triangulation of MassIElastic Properties ........................................................................... 5 

Test Stand Fixture ................................................................................................................ 8 

Blade axis 1 station lines ....... ............................................................................................. 9 

Template construction ....................................................................................................... 10 

Twist Measurement by Mechanical Clinometer. ................................................................ 11 

Carter Blade interior Arrangement .................................................................................. 14 

Lift- Drag Polars Compared (Specified vs . Measured I EPPLER Code)- ........................... 18 

Laser Base Plane Alignmen! .............................................................................................. 19 

Carter Blade: Deflection and Creep ................................................................................... 20 

Clinometer Error Idiosyncrasy ......................................................................................... 21 

bad Cases ........................................................................................................................... 22 

Test Table ........................................................................................................................... 23 

Deflection Results, Carter (uncorrected).. ....................................................................... 25 

Deflection Results, ESI (uncorrected) ............................................................................. 26 

Deflection Results, UTRC (uncorrected) ........................................................................... 27 

Frequency of Vibration: Carter blade ................................................................................ 29 . . Frequency of Vlbratlon: ESI blade ...................................................................................... 30 

Frequency of Vibration: UTRC blade .................................................................................. 31 

General Spar-Shell Crosssection ...................................................................................... 32 

Actual vs . Equivalent Laminate .......................................................................................... 33 

Mohr's Circle for Principal Axes ...................................................................................... 35 

Section Torsional Moments ................................................................................................ 39 

General Deflected Blade: HolzerIMyklestad ....................................................................... 42 

Free Body Diagram: Holzer Table ....................................................................................... 42 

Unit toad and Moment Diagrams ........................................................................................ 43 

free Body Diagram for Torsional Vibration ...................................................................... 46

UTRC Cross section ............................................................................................................ 48 

Rule of Thumb, FRP Directional Properties ..................................................................... 49 

UTRC Flap Deflection, Test vs . Calculation vs Specifications . ..~..........................*... 51 

UTRC Vibration Modes, Test (modal survey) .................................................................... 53 

UTRC Flapwise Vibration Modes, Predicted vs . Test .......................................................... 54 

ESI Section EA: AEI Calculation vs . GBI Specification ........................................................ 57 

ESI Section Elnap: AEI Calculation vs . GBI Specification ................................................... 58 

ESI Section Ellag: AEI Calculation vs . GBI Specification .................................................... 5 8 

ESI Blade Running Mass: AEI Calculation vs . GBI Specification ........................................ 59 

ESI Section Shear Center: AEI Calculation vs . GBI Specification ....................................... 59 

ESI Section GJ: AEI Calculation vs . GBI Specification ........................................................ 60 

ESI Blade Deflection: Predictions vs . Test .................................. ..... ............................... 61 

ESI Blade Static Twist ....................................................................................................... 62 

ESI Blade Static Twist: (50 Ib torsion load case) ............................................................. 62 
ESI Blade Static Twist: Predictions vs . Test ..................................................................... 63 

ESI Blade Twist: Predictions vs . Test (flexure load case) ................................................. 63 

ESI Blade Frequency Modes- ............................................................................................... 6 4 

ESI Blade Final GJ Values ................................................................................................... 6 6 

ESI Tip Flaps ...................................................................................................................... 6 7 

Carter Blade Internal Structure .......................... .... ......................................................... 6 9 

Carter Blade Free Body Diagram ..........~.~......~.....................~~................~........~.~................ 6 9 

Carter Dead Load Twist ...................................................................................................... 7 I 

Carter Blade Twist from Measurement ............................................................................. 7 I 

Carter Blade Error Scatter Plot, Twist Data ..................................................................... 7 2 

Carter Blade Ballast Summary .......................................................................................... 7 4 

Carter Blade Laminate Schedule ......................................................................................... 77 

Carter Spanwise Weight Density (Spar Portion) ............................................................. 7 8 

Carter Static Deflection: Three Load Cases (Corrected) .................................................... 8 2 

Carter Static Deflection: AEI Calculation vs . Measured (Corrected) ................................ 8 2 

Carter Measured Twist: (225 Ib test) Predicted vs . AEI Calculation 

vs- Specification.. ............................................................................................................... 8 3 

Carter Measured Twist: 325 Ib test .................................................................................. 8 4 

Carter Measured Twist: Torsion Load Case ........................................................................ 8 4 

Carter Blade Running Mass Comparisons .......................................................................... 8 5 

Discrete Lumped Mass Case ............................................................................................... 8 8 

Blade Section Free Body Diagram ....................................................................................... 9 0 

Code Output: UTRC Blade, 30 mph Case ............................................................................. 9 3 

UTRC Flap Deflection (1 0-70 mph) ................................................................................. 9 6 

UTRC Elastic Twist (1 0-70 mph) .................................................................................... 9 6 

ESI Elastic Twist Distribution ........................................................................................... 99 

Cam Elastic Twist (10 and 30 mph Cases) ................................................................. 101 

Carter Pitching Moment Distribution (1 0 and 30 mph Cases) ..................................... 102 

Carter Section Free Body Diagrams ................................................................................ 103 

Carter Elastic Twist and Section Moment, No Ballast (30 mph) ................................... 104 

2-D Section Data Comparison: Standard vs . Viterna vs . Tangler ~...~~.~.....~.~~...~..~~~~~~1 0 7 

UTRC: Comparison of Post-stall Routines ....................................................................... 108 

ESI : Comparison of Post-stall Routines .......................................................................... 108 

Carter: Comparison of Post-stall Routines ..................................................................... 109 

UTRC Power Output: Comparison of Test, Predictions, and Elastic Twist ...................... 11 0 

ESI 54 Power Output: Comparison of Data, Predictions, and Elastic Twist. .................. 110 

Carter 300 Power Output: Comparison of Data, Predictions, and Elastic Twist... ......... 110 
LIST OF TABLES 

Internal Structural Measurements: Carter blade ............................................................. 12 

Internat Structural Measurements: ESI blade ................................................................... 13 

Internal Structural Measurements: UTRC blade ................................................................ 13 

Sectioned cg and Mass Data: Carter blade ........................................................................... 15 

Sectioned cg and Mass Data: ESI blade.. .............................................................................. 16 

Sectioned cg and Mass Data: UTRC blade ............................................................................. 16 

Frequency of Vibration Results fmm test (HZ) ................................................................ 2 8 

UTRC blade Section Properties Compared to Manufacturers' 

Specifications and Sectioned Values ................................................................................... 5 0 

UTRC Frequency of Vibration Results ................................................................................ 5 4 

UTRC Final Blade Model Analysis ....................................................................................... 5 6 

ESI Blade Frequency of Vibration: Predictions vs . Test .................................................... 6 5 

ESI m& Final Aeroektic Mode!.... ................................................................................. 6 6 

ESI Vibration Frequencies with Tips .................................................................................. 6 8 

Carter Blade Blade Geometry, Measured vs . Carter Specifications .................................. 73 

Carter Blade Weights Summary ........................................................................................ 7 4 

Carter Reinforcements, As-Built Summary ..................................................................... 76 

Carter Bkde Laminate Design ............................................................................................ 7 8 

Carter I-Beam Section Data ............................................................................................... 7 9 

Carter r-Beam Moments of Inertia .................................................................................... 8 o 

Carter Blade Section Measurements vs . Carter Specifications ......................................... 8 0 

Carter Blade Running Mass Comparison ............................................................................ 8 5 

Carter Blade Flapwise Frequency Comparison .................................................................. 8 6 

Carter Blade Final Masses and Section cg's ....................................................................... 8 7 

Carter Blade Final Aeroelastic Blade Mode!- ..................................................................... 8 7 

UTRC Flap Defiection ......................................................................................................... 9 5 

UTRC Elastic Twist ............................................................................................................. 9 5 

ESI Tip Flap Deflection ...................................................................................................... 9 8 

ESI Tip Elastic Twist .......................................................................................................... 9 8 

carter Flap Deflection ..................................................................................................... 100 

Carter Lead-Lag Deflection ............................................................................................. 100 

Carter Elastic Twist ........................................................................................................ 100 

Carter Blade Section Torsion Components ....................................................................... 1 0 1 

Airfoil Lift and Drag Data Input to PROPPC .................................................................... 1 0 6 

vii 
1 .O INTRODUCTION 

BACKGROUND 

High performance wind turbine rotors in the future may have light, flexible blades to increase cost 

competitiveness. Blades which are elastic in torsion will experience small pitch changes during operation 

which will cause large changes in aerodynamic loading leading to errors in wind turbine performance, 

especially near rated power conditions where blade loading and thrust are high. New airfoils for wind 

turbines have been and are being developed in order to attenuate the real-world detrimental effects of 

surface degradation, manufacturing tolerance, and unsteady aerodynamics in turbulent winds (Ref. 1). 

Certain wind turbine rotors now in use have demonstrated aeroelastic instabilities and blade 

flexibility problems in operation (Ref. 2). Invariably the primary cause of flutter and divergence is blade 

torsional flexibility. In stall-regulated (fixed pitch) rotor systems an added potential flexibility problem 

is stall flutter. In pitch-regulated (controlled pitch) rotor systems, blade elastic twist in operation can 

lead to major increases in pitching moment and the attendant pitching system power required. Elastic blade 

twist near rated conditions, if nose-down or towards reducina anale of attack, causes delay of stall and 

negates the desired load alleviation, thereby causing potential rotor overloading. Elastic blade twist if 

nose-u. or toward increasina anale of attack. causes premature blade stall. the potential for stall flutter, 

and loss of power. The same arguments, though less significant, apply at operating conditions below rated 

or stalled conditions. 

Up to now, the problem of calculating the blade elastic twist in operation has not been addressed 

except as qualitative or grossly estimated minor effects. Certainly that approach is defensible for heavy, 

massive blades which have little bending deflection and virtually no torsional deflection. For wind turbines 

to be cost-competitive in the future, however, the blade and rotor weights must be low, leading to 

unavoidably increased blade flexibility which must be accurately estimated. This project analyzed in a 

quantitative, practical, and reproducible way the amount of elastic twist for three representative wind 

turbines (Carter 300, ESI 54, and UTRC, Figs. 1.1 - 1.3), the origins of the elastic twist, and the likely 

changes in the wind turbine field performance. 

STATION 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.97 1 .o 

CONTROL AXIS 1 ,r-----. c-E9 - - - c I - I 

BLADE AXIS< -7 

unlwisted view 

I 

I -?-I-- &.+ I - -+-4--+-/--1-i,-- STAT lC - 15.0' 

OEFLECTlON 

CURVE 36 6' 

-1-J 1 

FIG 1.1 CARTER 300 BLADE 
STATION 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .O 

RADIUS 0 32 41 64.81 97.22 129.62 162.03 194.44 Z6.W 25825 291.65 324.06 

CHORD 16.80 20.85 24.20 22.72 19.13 19.09 17.20 15.43 13.66 1165 

FIG. 1.2 ESI 54 BLADE 

STATION 

RADIUS 

CHORD 

9-- - 

-.. - -. FlXTUnE CHORD 

5 7.0'- A, 

FIG. 1.3 UTRC 8 kW BLADE 

COMPOSITE BLADE SOURCES OF UNCERTAINTY 

The combined bending and torsion of composite structures, especially high aspect ratio (span-towidth) HAWT blades, is difficult to analyze, characterize, and predict (Ref. 3). The degree of structural 

anisotropy of a composite laminate in general extends to a stiffness matrix of 64 possible engineering 

constants. The methodology of isotropic strength of materials does not work since the molecular and 

physical structures of composites are radically different from metallic crystal structures (Ref. 4, 5, 6). 

Therefore, simplifying assumptions were made. For the unidirectional bending plus torsion indicative of 

wind turbine (and helicopter) blades a simple stress state was assumed, and the laminates were considered 

@ be bidirectional. needina onlv four el~ticitv constants for enaineerina analvsis: primary and transverse 

tensile and shear moduli. It was originally thought that these four could be verified in coupon tests, but 

that was found to be too difficult for the scope of this project. 

In addition to the modulus uncertainties referred to above, manufactured composite blades, 

particularly those which are molded by hand (Carter, ESI) have significant geometric and internal 

structural sources of uncertainty (Fig. 1.4). These generally boil down to geometric errors (twist, taper, 

location of control axis), mass location errors (structural weight distribution, ballast weights), and the 

unavoidable nonuniformities in the individual laminates or plies (section errors). 

SOURCES OF ELASTIC TWISTING MOMENTS 

The elastic twist of interest is the steady state twist due to ~teadv forces and pitchina moments on the blade. 

These produce the torsion on the blade which is resisted by the elastic blade structural sections. Additional 

elastic twist is due to structural coupling between bending and torsion. There are two major sources of the 

torsional moments: aerodynamic and inertial: that is, the moments due to aerodynamic pressure 

distributions and the moments due to centrifugal forces. The analysis of these moments is complicated by 

the difficult blade aerodynamics, which depends on historical 2-D data which does not model the true post 

stall and unsteady aerodynamic behavior in wind turbulence. and is further aggravated by manufacturing 

errors in blade airfoil post stall and section geometry. The analysis is also complicated by the typical 

composite wind turbine blade structure, which has complex geometry and is composed of fiber-reinforced 

resin, both of which introduce nonuniformities and structural coupling. A further complication is the 

blade-hub attachment. Soft attachments, such as the Carter "snubber," can cause large elastic pitch errors 

at the hub, which then add to the elastic twist, as verified during this testing program. Elastic twist 

introduced by the flexbeam and the pendulum weights for the UTRC was tma ed as a n assumed r' 

moment. 
2.0 PROJECT SCOPE AND METHODOLOGY 

GOAL OF THE PROJECT 

The major goal of this study was to ascertain the elastic blade twist due to wind turbine operation 

which leads to errors in the prediction of loads and performance for three promising and representative 

wind turbine rotors. A secondary goal was to develop, verify, and present a practical engineering 

methodology for the estimation of this elastic twist on other wind turbine rotors. 

SEMI-EMPIRICAL APPROACH 

This program was divided into two parts of equal importance, experimental and theoretical. There 

were not enough resources in the program to permit a sophisticated engineering analysis in either area, so 

a practical engineering approach was taken (Fig. 24, and has proved efficient and effective. This allowed 

the derivation of semi-empirical blade aeroelastic models with which to calculate the steady elastic twist. 

Computer Codes: l BLADE SECTION PROPERTIES 

l STATIC DEFLECTION & STRESSES 

l BLADE VIBRATION MODES 

Laboratory Tests: l EXTERNAL INSPECTION 

l SIMPLE FREQUENCY OF VIBRATION 

STATIC DEF ECTION UNDER LOAD 

BLADE SECTIONING & CLOSE INSPECTION 

.MODALSURVEY 

FIG. 2.1 TRIANGULATION OF MASS / ELASTIC PROPERTIES 

The structural analysis programs employ practical and verified engineering techniques for the 

analysis of complex composite structure beams (Ref. 3). The wind turbine performance programs were 

developed by Solar Energy Research Institute (SERI), and are the standard aerodynamic codes in use in the 

industry (Ref. 7). The blade tests were performed at the Agricultural Research Service, US. Department 

of Agriculture (USDA) facility in Bushland, TX, under the cooperative agreement with AEI. The test 

equipment and testing techniques employed are standard laboratory items and methods generally available, 

with the exception of the Fast Fourier Transform (FFT) modal survey equipment provided by SERI, which 

was more sophisticated (Ref. 8). 

The experimental testing program consisted of inspection, static loading, and frequency of vibration 

tests. Practical engineering laboratory techniques were used, which required only modest testing 

equipment (e-g., strip chart recorder, laboratory optical laser, laboratory strain gages), and permitted 

full-scale bending and torsion tests of the blades cantilevered from floor weldments. Simple mechanical 

measurement techniques were used at the cost of great accuracy (e-g., section twist measurements were to 

+I0 minutes of arc), but provided a simpler physical feel for the experiments. 

The theoretical program used a mainframe computer (PRIME) for the calculation of blade 

structural parameters, blade aero- and inertial elastic torsion and loading, blade bending and twist, and 

frequencies of vibration. The mainframe computer was also used for the calculation of aerodynamic loading 

and wind turbine rotor performance. However, all the programs could be compiled and run on personal 

computers. Again as in the testing program, a practical engineering approach was taken for the analysis of 

the blade structure, insofar that a beam analysis program was used that does not calculate the complex 

shear stress and shear flow, but instead assumes a principal stress state, unidirectional component 
laminates which are representable by only four (empirical) engineering constants, and linear beam theory 

(plane sections remain plane). Again, the practical approach allowed many more calculations and 

iterations to be made, and permitted a better and more transferable physical feel for the structural effects. 

2.3: BLADES CHOSEN FOR THIS PROJECT 

The blades selected for this project (Carter 300, Gougeon ESI 54, and UTRC 8 kW) represent a 

wide variety of promising blade characteristics: hub retention, airfoils, rotor diameters, aerodynamic 

geometries, and structural arrangements. The choice was limited somewhat by these major constraints 

(1) available field test data, (2) verified manufacturing quality control of mechanical .properties, (3) 

enough flexibility for potential aero- and inertial elastic effects to be seen, and (4) cost and time 

constraints. These blades were also chosen to represent a range of composite construction and 

manufacturing techniques which are all potential weight- and cost-savers for future wind turbines. 
3.0 EXPERIMENTAL METHOD 

3.1 : GENERAL 

The Carter and Gougeon blades (two blades of each) was procured directly from the manufacturer. 

One was returned for credit after static testing and the second was kept for sectioning. The UTRC blades 

were already the property of AEI. Additionally, a Carter hub was acquired for mounting its blade and 

ascertaining root compliance. ESI tip flaps were also acquired to determine their weights and predict their 

moments of inertia. The UTRC blade overspeed mechanism, the flexbeamlpendulum, was not studied in 

detail, only the outboard pultrusion. 

In addition to the blades and rotor hardware, manufacturers were asked to provide specific data for 

the rotors (Appendix 10.7). The Gougeon blade was the only well-documented blade in manufacturer's 

correspondence and in the open literature. The Carter blade required considerable effort to ascertain 

internal structure, arrangement, and geometry. 

INITIAL BLADE INSPECTION 

The first requirement was to determine the actual blade external geometry and airfoil shape 

(measured at .75 and .95 span). These were used as the basis for the aerodynamic loading on the blade. 

The internal structure including laminate thickness and geometry, and their spanwise distributions also 

had to be found at each tenth station (STA) for input to the structural model. Blade manufacturers had been 

asked to provide the specification for blade external geometry and structural geometry, and the mechanical 

properties of the individual laminates used, but this job ultimately rested on the test/inspection program. 

The hub attachment had to be measured in the same way for its input to the structural model. 

The blade geometric parameters, structural details, and airfoil were determined first. A test stand 

fixture was constructed for each blade (Fig. 3.1) which allowed the individual blades to be cantilevered 

above the laboratory floor. Each blade was either bolt-on or clamped mounted, or in the case of the Carter, 

mounted in its own rotor hub. 

BLADE CONTROL AXIS LOCATION AND TWIST 

A blade "control axis" is defined as the pitch axis for a pitching blade, hence "feathering axis" (e.g. 

as in the case of the Carter blade), or as the centroid of the root fixation for a rigid blade (ESI). Linear 

spanwise and chordwise measurements were taken to determine the blade taper and radius. Blade control, 

or feathering axis, was determined and then inscribed on the blades along with 0.1 radius section lines 

(Fig. 3.2). Control axis was assumed to be the root centroid axis for the ESI blade; it was the quarterchord 

axis for the other two. The blade control axis was used as the primary blade reference axis. Twist was 

first measured on the cantilevered blades by using a laboratory laser, optical bench, and mirrors mounted 

on the templates. This laserlmirror method was discarded since on the cantilevered blades a precise 

clinometer gave the same accuracy and was much easier to use. Blade static gravity deflection was zeroed 

by taking twist measurements for 0" and 180" pitch orientation. Root pitch alignment was also measured 

for the bladelhub attachment. There were minor discrepancies between the measured values and the 

manufacturers' specifications (see Section 5.0). 

BLADE TEMPLATE CONSTRUCTION 

Template construction was done by two methods: the first was nondestructive, the second was from the 

sectioned blade. The former method consisted of pine blanks (Fig. 3.3), which were rough cut on the 

inside, leaving a small gap between template and blade, to fit both the upper and lower surfaces of the test 

airfoils at each 0.1 radii (tenth station). The surface of the blade was coated with a thin layer of floor wax 

and then auto body filler was used to bridge the gap between template and blade surface, with care taken to 
FIG. 3.1 TEST STAND FIXTURE 

8 
FIG. 3.2 BLADE AXIS / STATION LINES 

preserve the chordline at the separation line between upper and lower template halves. Holes were drilled 

in the leading and trailing edges of the upper and lower parts of each stations' template and then dowel rods 

were inserted. Rubber bands and strapping tape were used to secure the templates together for inspection 

and installation on the blades. The clinometer was placed on top of the templates above the control line for 

measuring twist angles (Fig. 3.4). The template surfaces that butted together were located at the relative 

chordiine for the section at that radius. The floor wax allowed easy removal of the hardened templates after 

the tests were completed. The squared outer edges of the templates were used as the reference lines for 

determining the relative twist at each radii using the clinometer. The problems with this method were 

establishing an accurate chordline and achieving accurate airfoil shape. 

FIG. 3.4 TWIST MEASUREMENT BY MECHANICAL CLINOMETER 

The latter method was much easier but depended on the sectioned (cut up) blade portions. The 

sections were traced onto craft paper and the chordlines marked on the tracing using a projection technique 

(Fig 3.3). The paper tracings were hung on a wall and transparencies of the members of the airfoil family 

were projected onto the tracing and judgment used in the location of the chordline. The chordline was then 

marked on the tracing. The various airfoils were also marked on the tracing for qualitative analysis of the 

cut sections, which included sending the tracings for EPPLER Code analysis (Sec. 3.7 below). 

To construct the templates, the sections were placed on the above tracings with the chordline 

marked. The section then was placed on the two pine blanks with the chord line split between upper and 

lower surface. The section was then traced onto the wood for the construction of female templates for each 

station. The wood was finally cut and filed to closely approximate airfoil shape. Additional female 

templates were made at stations .75 and .95 for the aerodynamic evaluation. 

BLADE SECTIONING 

The internal structural geometry could only be accurately determined by cutting a blade into 

sections. A blade from each set was cut into sections corresponding to its 10 spanwise stations. For each 

station internal structural measurements were taken to verify the manufacturer's specification (Tables 

3.1, 3.2, and 3.3). This allowed internal arrangement verification of ballast and inserts; this was 

especially important for the Carter blade (Fig. 3.5). Another reason for sectioning the blade was to 

determine the chordwise center of gravity (cg) position (Sec. 3.6). 

An accurate mass axis was drawn from the spanwise cg positions; this turned out to be a very 

sensitive indicator of actual laminate thickness, reinforcement/resin ratio, and weighted area centroid. 

The lumped mass model of the blade, which was used in the frequency of vibration program, was readily 

determined from sectioned data. 

The actual airfoil section geometry was determined accurately from the sectioned blade. In the 

Carter blade, it was thought that shear relief could modify the airfoil shape when the section was cut, so the 

.75 and -95 airfoils were determined both before and after sectioning (Sec. 3.7). 
TABLE 3.1 : INTERNAL STRUCTURAL MEASUREMENTS: CARTER BLADE (in cm) 

4 

t arh 

STA 5-10 

STA 1-4 

STATION 1 2 3 4 5 6 7 8 9 9.5 
TABLE 3.2: INTERNAL STRUCTURAL MEASUREMENTS: ESI BLADE (in cm) 

C m 

STATION 

1 2 3 4 5 6 7 8 9 

TABLE 3.3: INTERNAL STRUCTURAL MEASUREMENTS: UTRC BLADE (in cm) 

STAION (Flexbeam) 4 5 6 7 8 9 10 
FIG 3.5 CARTER BLADE INTERIOR ARRANGEMENT 
3.6: BLADE MASS DISTRIBUTION 

The actual mass distribution of the individual blades was determined by measuring the mass of the 

individual sections on a balance scale and locating the local cg of each section using an edge balancing beam. 

The individual sections were placed on a sharp edge (angle iron) and the balance point was determined and 

the line marked on the section; this was done spanwise, chordwise and at a diagonal. The intersection of 

these lines was taken as the point mass location and was converted to X,Y,Z coordinates using the local 

quarterchord point as a 0,O point (X,Y origin), and the center of rotation as the Z origin. These points and 

masses are summarized in Tables 3.4, 3.5, and 3.6, and were included as input data points for the 

computer models. 

TABLE 3.4: SECTIONED cg AND MASS DATA: CARTER BLADE 

I cg POSITION (cm) I I MASS (kg) STA PANEL I I-BEAM 1 BLADE SHELL 1 I-BEAM SHELL 

1 SPAN W CHORDW I SPAN W CHORDW I 

0-1 1 I - I 

1-2 2 1 45.2 19.0 1 47.8 

2-3 3 1 50.8 16.5 1 48.8 

3-4 4 I 1 47.0 

4-5 5 I 1 49.2 

5-6 6 I (see note 4) 1 48.3 

6-7 7 I 1 52.2 

7-8 8 I 1 45.7 

8-9 9 I 1 55.4 

9-10 10 1 1 44.3 

NOTES: 

(1) BLADE WAS SECTIONED ON THE TENTH STATION LINES. 

(2) PANEL NUMBER REFERS TO SPANWISE SEQUENCE. 

(3) PANELS 4-6 CONTAIN SOME EMBEDDED I-BEAM AND POlTlNG RESIN. 

(4) ROOT RIB AND SNUBBER MECHANISMS ARE IN PANEL 1 PORTION. 

(5) PANEL 10 (BMDE TIP) CONTAINS BALANCE WEIGHT. 

(6) PANELS 9 81 0 FROM CARTER BLADE #29B, OTHER PANELS FROM CARTER #47A. 
TABLE 3.5: SECTIONED cg AND MASS DATA: ESI BLADE 

I cg POSITION (cm) I MASS (kg) STATION PANEL 1 SPANWISE CHORDWJSE 1 

NOTES: 

(1) PANEL 1 INCLUDED THE BLADE ROOT BUT NO STEEL STUDS. 

(2) NO TIP WEIGHT OR MECHANISMS INSTALLED. 

TABLE 3.6: SECTIONED cg AND MASS DATA: UTRC BLADE 

I cg POSITION (cm) I MASS (kg) STATION PANEL 1 SPANWISE CHORDWISE 1 

NOTES: 

(1) STATIONS 0 - 3 COMPRISED THE FLEXBEAM/PENDULUM. 

(2) STATIONS 4 -10 COMPRISED THE PULTRUSION. 

(3) PANEL 3 CONTAINED THE ATTACHMENT HARDWARE TO THE FLEXBEAM. 

SECTION AERODYNAMIC CORRECTIONS 

The airfoil shape manufacturing errors (for STA 0.75 and 0.95) were characterized in two 

methods (Appendix 10.6). The first method was to trace the airfoil shape from the cut edge of the sectioned 

blade. The second method used the undisturbed airfoil and auto body putty; a fine layer of wax was applied 

and the putty was placed around the entire airfoil at the desired station. The putty was allowed to harden 

and then was removed with breaks at the leading and trailing edges. The putty was reassembled and then 

finished so that one side was flat, then a Xerox copy was made to show the airfoil shape. The shapes were 

then digitized and smoothed by Prof. Stan Miley, Texas A&M University, who was the aerodynamics 

consultant for the project. EPPLER code calculation determined a CL at various angles of attack up to stall 
(Appendix 10.6). The zero lift angle and the lift at 90 degrees were also computed. The differences 

between the blade specifications and the computer liftldrag polar were compared (Fig. 3.6). 

3.8: BLADE LAMINATE COUPONS 

It was originally thought that the blade material engineering constants could be determined from 

laboratory bench tests on coupons obtained from samples cut from the discarded blade sections, for each 

laminate (Ref. 9, 10). The four modulus values needed were tensile (longitudinal and transverse) and 

shear (longitudinal and transverse). Samples measuring roughly 1 in. by 14 in. and .25 in. thick can be 

readily used with standard tensile testing equipment to give bulk modulus results. These results are 

accurate to about 5% with fiberglass, provided that the sample is truly planar and without residual strain. 

This turned out to be impossible with coupons from these blades, although the methodology could still work 

under properly controlled conditions. If time and resources permit, at least three representative samples 

should be tested for each laminate. Four graph points with test weights or torsion springs would allow 

adequate accuracy. It is helpful to verify the actual composite engineering constants since the static 

deflections and frequencies of vibration are very sensitive to them; however, a design range of values can 

be adopted and used, as was done in this case. 

STATIC DEFLECTION TESTING 

3.9.1 : SETUP AND METHOD 

The building at USDA, Bushland, TX, was large enough to allow all three blades to be separately 

tested from the same platform. The test stand was constructed from the leftover base of a 100 kW vertical 

axis wind turbine. This stand was bolted to the concrete floor and braced with two 8-inch 1-beams. The 

mounting connection for the Carter 300 blade was the spare hub borrowed from Carter Wind Systems. 

Mounts for the ESI and UTRC blades were manufactured in house. The most important part of the test rig 

was the establishing of a baseline using a laser. The line was defined by mounting the laser under the test 

stand and shining the light through a small peep hole and aligning the laser dot on the far wall (Fig. 3.7). 

The light line was leveled using a transit and placing a mark on the wall. 

When there was no load, the Carter blade had a large deflection just due to its weight. Therefore it 

was supported at the tip between tests. The template halves were secured together on the blade with 

strapping tape and rubber bands. When the blade deflected, the cross sectional area (blade shape) changed 

at stations 2-4. At station 3 the template came apart with a gap of 1 cm the first time the blade was loaded 

and then template 3 was loose and had to be repositioned several times during the different load cases. 
NACAA 231 12 +, Eppler Code (Miley) x 

(Eppler separate until stall, then copies NACA 231 12) 

FIG. 3.6 LIFT-DRAG POLARS COMPARED (SPECIFIED VS. MEASURED / EPPLER CODE) 

The static deflection tests were performed by using the setup shown in Figure 3.7. Lead-weighted 

bags were suspended from taped hooks located at the control axis of the blade sections. Lead shot was used 

for accuracy and tape was used to simulate suction (Sec. 3.9.2 below and Fig. 3.1 1). Experience with this 

type of test has shown that temporary creep is a problem with composites (Fig. 3.8 illustrates the Carter 

blade); therefore, the linear measurements were made relative to a relaxed datum, and averages of several 

trials were made. The elastic twist was measured in two ways: first, by optical laser and template 

mirrors providing accuracy to +I0 minutes of arc and second by the clinometer. The Fowler clinometer 

was acquired to take ideal local inclination measurements to within 1 minute accuracy. The base of the unit 

is beveled so that it can sit on a rounded edge and still give an accurate reading of inclination. The unit was 

able to read degrees of deviation from 0" (horizontal) to +180°. The major problem with this unit was in 

reading minor angles in the (-) direction. The unit has a manual dial calipered gauge and the negative 

readings must be read as subtraction's from the displayed degrees. That is, a reading of 45 minutes was 45 

minutes when the angle was positive (nose up) but that it was meant to be read as 15 minutes subtracted 

from the next higher degree reading if the angle was negative. This stet idiosyncrasy of the unit resulted in 

operator misreading data when very close to 0" and negative angle. The graph presented Figure 3.9 shows 

this in the Carter 300 data twist under load vs. station in stations 4 - 7. 


TWIST 

DIFFERENCE 

(DEGREES) 

' .I ). * w S w 

1 5 10 

STATION NUMBER 

FIG. 3.9 CLINOMETER ERROR IDIOSYNCRASY 

3.9.2: LOAD CASES 

Load cases used for all blades were (1) no load (right side up and up side down), (2) 25 Ib hung 

from the quarterchord line at each mid station (225 Ib total], (3) 50 Ib producing torsion at 0.70 span on 

the Carter blade and 0.90 span on the other two blades (with a zero torsion control case), and (4) 50 Ib at 

each station as possible [up to 375 Ib total]. Other load cases were tried as well with the Carter blade, 

totaling 19 different case loads (Fig. 3.10). These cases were chosen not to proof test the actual loads 

experienced in operation (which would have been greater and much more difficult to reproduce in the lab, 

e.g., including tension) but to establish the elastic properties of the blades. Hence, it was decided to opt far 

small linear deflections and the greater measurement accuracy thus required in testing. 

The Carter blade was the first blade tested and the initial trial and error learning was done with 

this blade. The placement of the test weights was attempted in three methods: (1) placement on the blade 

surface at the quarterchord line, (2) hung from eyebolts attached to a wooden bar attached to the blade, and 

(3) using wire rods formed into eyelets taped to the blade with an S-hook to support the bags of lead shot. 

The latter was determined to be the best method and was used on the rest of the blades. Concentrated loads 

were adequately supported by using the ropeleyelet method, and furthermore allowed placement of the bags 

directly on the quarterchord lines. The UTRC blade was not able to support a high load since the root began 

to delaminate at the 25 Ib per station load. 
STATION 

I I I I I I I I I I I 

CASE: 

1 t DEAD LOAD 

2 8 I - 1 I 1 225# DIST 

I I-I-C' 1. I 

25 25 25 25 25 25 25 25 25 

3 1 A + 450# DIST 

1 

50 50 50 50 50 50 50 50 50 

4, 1 ~~~~I

4 - 1-1- I 225# D+ 50#T 

25 25 25 25 25 25 25 25 11, T50 1 5 1 1 I 

t 50# TORSION 

t 

T50 

6 1 I I I 50# CONTROL 

NOTES: 1. 

2. 

3. 

4. 

fi + 

25 25 

All weights were lead shot in bags hung from s-hooks taped to blade at control axis 

Measurements were made on templates at each station 

Torsion weights (cases 4 and 5) were hung on templates 

Carter 325 Ib. case same as case 3 with 25 Ib. from STA .55 to tip 

FIG. 3.1 0 LOAD CASES 

3.9.3 : DEFLECTION MEASUREMENT METHOD 

The blades were loaded and the data collected for each station in turn for a known set of loads. The 

test table (base plane register) was moved from station to station and the loads repeated. The first station 

was routinely remeasured at the end of the test run to check for creep in the blade or a shifting of the blade 

mount. The portable base plane was constructed from an oak door and three pipe legs, one threaded (Fig. 

3.1 1). The pipe mounts were placed so that two were in line with the established laser line, and the third 

centered between these and placed at the opposite end of the table. The laser line ran over a massive 20- 

foot I-beam trough that was relatively flat. This trough held two legs of the table. Level adjustment was 

made by moving a nut up and down the all-thread rod on the third leg. Two pin holes were mounted on an 

optical bench on the table and placed outside of and in line with the two legs in the trough. The base plane 

could be raised and lowered by adjusting the nuts until the laser light could pass through both holes of the 

leveled optical bench. A large bubble level at right angles to the laser line edge and the third leg of the table 

was used to level the plane of the table relative to the laser line. Droop data then could be recorded from 

the tip side of each template relative to a registration point on the template (nail). A monofilament line 

with a construction plumb bob was used to find the relative X,Y position of the nail projected onto the laser 

base plane. A tape measure was then hung from the nail and the total droop distance from the nail to the 
laser plane was taken. In this way (X,Y,Z ) measurements could all be taken to an accuracy of 3.1 in. 

(2.5 mm). 

FIG. 3.1 1 TEST TABLE 

3.9.4: DEFLECTION CORRECTIONS TO QUARTERCHORD 

The procedure for the correction of the droop deflection measurements to the quarterchord point is 

described here. First, the original data (i.e., template nail to base plane) were summarized in a computer 

data file for each load case. These data consisted of the station position (station number), load case number, 

X direction deflection (relative to laser baseline), Y deflection (relative to a moving origin based on the 

laser table), Z droop measured relative to the laser plane, angular displacement of the chord in degrees and 

minutes, and the flapwise root fixture bending in degrees and minutes. During the collection of these data a 

clinometer convention was adopted: positive was defined as airfoil nose down (i.e., tendency for the nose of 

the airfoil to go into the wind). 

The method to calculate the coordinate shifts is described here. In the opening lines of each program 

were the measured data of the plumb bob support arm (nail) positions by station relative to the 

quarterchord point. These values were determined from the templates. The nails were already as close as 

possible to the quarterchord position. Both upper and lower (low and high pressure) sides of the templates 

were equipped with registration nails. These nail positions were related to the actual quarterchord by 

their angular deflection and offset (0 and L). V, the vertical offset, was measured as depicted in the sketch 

below: 
The following sketches show the four cases of nail position that were accommodated: the nail ahead and 

behind the quarterchord point, and with positive and negative local pitch. 

The input data and the constants (0 and L) were used to compute three new values: T, which is the 

radian equivalent of the degree measurements; P, the radians of the angle 8; and the calculated Z droop 

deflection based on measured local station twist and relative nail position: 

V = L { sin [( P SGN(P) ) + (T C)] ) 

V = vertical correction to droop 

L = distance from nail to quarterchord 

P = radian angle measure from nail to quarterchord 

SGN = sign function [returns the sign of the variable where -1 is 

returned for negative numbers and 1 is returned for positive 

numbers (0 is considered positive)] 

T = radian measure of local station twist 

C = correction sign based on if the nail position is ahead (noseward) or 

behind the quarterchord point. 

3.9.5: DEFLECTION RESULTS 

The deflection results under load and no-load conditions are best seen in the graphs of deflection 

versus station number (Figs. 3.12 to 3.14) for various load cases (Fig 3.10). These curves are very 

smooth even with varying loading methods. Of course, this is to be expected since the blades were 

purposely kept inside their linear limits of elasticity. 

3.1 0: BLADE VIBRATION MODAL SURVEY 

The laboratory frequency-of-vibration tests were performed in the same test fixtures. It was 

originally thought that the fundamental frequencies of vibration could be obtained simply with an 

accelerometer and strip chart recorder with a frequency response higher than the expected frequency. It 

was expected that the required frequency response would be about 100 Hz. However, it became clear that 

particularly for the Carter blade, no simple fundamental bending modes could be easily identified. Also, the 

torsional frequencies turned out to be higher than expected for the ESI (40.5 Hz) and UTRC (29 Hz) blades. 

Therefore, SERl was asked to perfom a more rigorous modal survey on the blades. The method and results 

are fully presented in Reference 8, and summarized here. 


STATION NUMBER 

180 

z 

DEFLECTION 

(CM) 

150 -. 

. 

120t 

LOAD KEY: (1 ) Dead Load, (2) Torsion, (3) 175 ib 

t 

* 

0 . * 

b 0 

0 

c 0 

a 

b * 1 

C * 

* 2 

. 

,3 

FIG. 3.14 DEFLECTION RESULTS, UTRC (UNCORRECTED) 

1 5 to 

Modal data collection primarily consists of the judicious application of a known input force and then 

measurement of the structure's response. In general, the dynamic response to an external excitation is a 

superposition of all the normal vibration modes of the structure. This collection of large amounts of data 

and the extensive harmonic analysis can be done with available electronic equipment and desktop 

computers, as in this project. The modal survey equipment sent by SERl included a Hewlett Packard HP 

5420A two-channel spectrum analyzer and an HP 9825 desktop calculator, calibrated impact hammer 

with charge amplifier, and pietoresistive accelerometers and bridge amplifiers. The outputs from the 

hammer (forcing function) and the amplified accelerometer signal (response function) were the inputs to 

the spectrum analyzer (S.A.). The S.A. computed frequency response functions from the impact testing 

which were then stored for later analysis on the desktop calculator. The comprehensive software for modal 

survey (Fast Fourier Transform) and the particular hardware system had been used by SERl on previous 

projects. The impulse method was used since the shakers available from SERl did not have sufficient 

masslamplitude for large blades. The shake test method would have given better mode resolution and would 

have been easier to install in addition to enabling the discovery of hidden modes with less effort. The zerocrossing (peak-picking) method was used to determine mode frequencies. 

Frequencies and mode shapes (Table 3.7 and Figs. 3.15 - 3.17) were determined. The Carter 300 

was the most complicated blade; it had a dashpot snubber in the root that had to be replaced with a rigid 

member to eliminate the interference of the snubber (pitching) action. The first flap bending mode turned 

out to be 0.59 Hz and the first torsion 13.25 Hz. Above the second flap bending the modes were more 

complex due to the complicated internal structure and ballast weights. Near 40 Hz, the modal frequencies 
were very highly coupled. The ESI was much stiffer and had a simpler internal structure. The vibration 

modes were well separated and classic in shape. First flap bending was at 3.5 Hz and first torsion at 40.5 

Hz. The UTRC blade was the simplest: constant chord and no twist. The first flap bending was 2.1 Hz and 

the first torsion 29 Hz. The modal survey results compare favorably with the results from the theory of 

elasticity (see Ref. 1 1, for example). 

TABLE 3.7: FREQUENCY OF VIBRATION RESULTS FROM TEST (HZ) 

MODE UTFC ESI CAFmR 

1ST FLAP 

2ND FLAP 

3RD FLAP 

1 ST LAG 

2ND LAG 

3RD LAG 

1 ST TORSION 

2ND TORSION 

NOTES 

(1) ALL BLADES TESTED IN FLYING CONDITION EXCEPT: CARTER SNUBBER LOCKED, NO ESI TIPS. 

(2) ROOT FIXITY IDENTICAL TO STATIC TESTS. 

(3) ESI 2ND TORSION IS COUPLED WITH 5TH FLAP. 

(4) CARTER 1 ST TORSION IS I-BEAM ROOT FLEXURE ONLY. 

(5) CARTER 2ND TORSION IS OUTBOARD TORSION ONLY. 



4.0 THEORETICAL METHOD 

An arbitrary cross-section, 3-dimensional beam subject to arbitrary distributed loading in 

bending and torsion is a formidable mathematical problem. It is usually accomplished in the aerospace 

industry by employing expensive finite-element structural programs (e.g. NASTRAN). This study did not 

have sufficient resources to employ such a state-of-the-art model, nor was it warranted, since the static 

bending and frequency of vibration results are very sensitive to the material mechanical properties, which 

were composite laminates for this effort. In using such computer programs a lot of effort can be wasted 

needlessly if these engineering constants are not known to a high degree of accuracy. 

In view of this, this project used a simpler elastic beam approach which modeled the composite 

blade sections by calculating area-weighted flexural and torsional moduli, calculated the beam properties 

relative to the principal axes, and then performed coordinate transformation to develop blade axis sectional 

properties. Arbitrary cross section including blade skin, spar, shear webs, and afterbodies are all handled 

in the above approach. The deflections were found, in a likewise manner, by referring the applied loading 

and moments to the aerodynamic center (quarterchord), the mass center (blade section cg), the bending 

centroid (weighted area centroid), and the shear center (elastic axis), and transforming the deflections by 

superposition. The deflections, when compared to the test results, then provide a reiteration error of the 

oriainal assumed laminate constants, hence the term "masslelastic trianw." 

COMPOSITE BLADE SECTION PROPERTIES CALCULATION 

4.2.1: SECTIONDESCRIPTION 

This section describes the beam section properties calculations (Ref. 3). The Bernoulli-Euler 

theory of bending ("engineers' theory of bending") calculation can be followed in any thorough strength of 

materials text (e.g., Ref. 12, 13). The key assumptions are 1) deflections are small and linear and 2) 

plane sections remain plane and normal to the beam axis. These assumptions make it possible to determine 

the deflections of any point on the beam in terms of points on the axis of the beam. Figure 4.1 shows a 

general blade cross section for a spar-shell composite blade. 

Y 

FIG. 4.1 GENERAL SPAR-SHELL CROSS SECTION 

The spar is shown as a constant thickness D-spar and a web at Xt in the nose, and the skin is shown 

also as constant thickness. Section axes have origin at the nose and abscissa along the airfoil chordline. In 

general the spar and skin will have entirely different constituents (laminate schedules). The spar is 

usually the principal bending structure, and the skin the torsion structure, also providing a shear load 

path for aerodynamic pressure forces into the spar. More complicated versions will have more webs and 

variation in the iaminate within the skin or the spar. For now we assume the skin and spar to be uniform. 

In general, the spar and skin constituents have directional properties; that is, the elastic constants 

vary depending on the orientation (0 degrees reference is spanwise and 90 degrees is chordwise). For 
simple bending only the longitudinal (UO) values are used. This gives four engineering constants which 

describe the longitudinal and shear (torsion) behavior of the section: h&APar and GsDara 

elastic and shear moduli of elasticitv. These engineering moduli can be calculated for a given laminate by 

the area-weighting method. For instance, suppose a laminate is composed of various layers as shown in 

Figure 4.2. 

t 1 

t 1 

FIG. 4.2 ACTUAL VS. EQUIVALENT LAMINATE 

Then the equivalent laminate has the same actual thickness as the aggregate (t = 211 + t2), and an 

elastic modulus based on area ratios is 

Clearly the complicated laminate on the left can only be approximately represented by the bulk laminate on 

the right; internal shear stresses (interlaminar shear), for instance, could be calculated also for each 

layer interface. This detail can be left for the end of the engineering process, after the overall beam 

deflection and bending stresses have been calculated. Then these residual internai stresses can be checked. 

In this application the actual thicknesses of the layers are maintained since these will also be used to 

calculate weights and moments of inertia, and will also be checked with measurements. Alternative 

approaches may use modulus-weighted thicknesses to simplify calculations. 

4.2.2: SECTION AREA AND STIFFNESS PROPERTIES 

Section area properties are found by simple integration. The airfoil shape (X,Y) is first calculated 

based on a specific table of offsets and a chordline, and using a simple second-order curve-fit subroutine 

through each series of three points. The contribution of each differential skin and spar segment is 

calculated and summed around the airfoil, starting at the nose and also ending there. These integrals are 

simply 

At = Total area = I dA 

Mx = 1st moment of the area about the X axis = y dA 

MY = 1st moment of the area about the Y axis = x dA 

I x = Moment of inertia about the X axis = y* dA 

I Y = Moment of inertia about the Y axis = x* dA 

IxY = Product of inertia = xy dA 
- 

X, = Bending centroid, 

- 

YC = Bending centroid, 

chordwise position = MY 

At 

Mx 

flapwise position = 

At 

The program corrects for shell thickness by using the skin (or spar) segment centers to define the moment 

arm. 

Section stiffness properties are found by the area-weighting method, combining the contributions 

from the skin and spar, and adding the spar web as a separate item for simplicity. This approach allows the 

addition of other shear webs or structural elements in the total composite section values. The spar web and 

further elements are simply described by their area properties: 

Aw = Spar web area 

rxw = Spar web moments of inertia 

Iyw = Spar web moments of inertia 

I, yw = Spar web product of inertia 

(X,Y), = Centroid 

Bending values relative to the (X,Y) axis system origin are 

EA = Eskin Askin + Espar Aspar + Eweb Aweb 

Bending centroids for total section are 

XT = - Eskin My skin + Espar My spar + Eweb My web 1 

B4 

- 1 

YT = - I Eskin Mx skin + Espar Mx spar + Eweb Mx web 1 

€4 

Now the bending stiffness for the section is found, but is referenced to the centroid of the composite 

section. This makes the calculation simpler, and correctly assesses the stiffness contribution of each 

element by superposition. The parallel axis theorem is used to move each (X,Y) moment of inertia value to 

the section centroid (XT, YT); an intermediate step moves the point to its own centroid. For example, for 

the skin only, the X-moment of inertia about the total composite section centroid is 

Therefore, the section stiffnesses 

Elx total structure = C Elx 

= Eskin { [ Ix skin 

+ Espar { [ Ix spar 

+ Eweb (Ix web + 

are simply the sums of the contributions : 

(where I, is referred to the bending centroid in each case.) 

- - - 

%kin y2skinl + Askin [ Yskin - YT I* - - - 

- Aspar y2spar I + Aspar I Yspar - YT l2 1 - - 

Aweb Yweb - YTI~ 1 
The last step is the calculation of the section principal axis values, which are used later to calculate 

blade deflections. The principal axes of inertia are found in the program from a Mohr's circle 

representation depicted here in Figure 4.3: 

El xy 

where 0 = principal axis angle 

EI[xpj,EI[yp] = sectional stiffnesses in the principal axes 

FIG. 4.3 MOHR'S CIRCLE FOR PRINCIPAL AXES 

These principal moments of inertia (stiffnesses) are the maximum and minimum values for this 

section. For the usual airfoil shapes, these are close to the original (X,Y) directions: chordwise and 

flapwise. This step simplifies the bending deflection calculation by eliminating the products of inertia. 
4.2.3: SECTION TORSIONAL RIGIDITY 

To calculate section torsional rigidity also requires care in referencing the contributions to the 

total torsional centroid (shear center), which in general is different from the bending centroid since the 

(EIG) ratio of the components are not the same. 

GA = Gskin Askin + Gspar Aspar + Gweb Aweb 

The torsional centroid (shear center) is then 

- 

YTT = [ 1 1 GA 1 I Gskin Mx skin + Gspar Mx spar + Gweb Mx web) 

- 

XTT = [ 1 1 GA] { Gskin My skin + Gspar My spar + Gweb My web 1 

And the torsional rigidity about the shear center is found by using the parallel axis theorem in sequence as 

before for the bending stiffness: 

- - 

+ Gspar I [ Ix spar - Aspar y2spar I + Aspar [ Yspar - YTT 12 1 

- - - 

+ Gspar { I Iy spar - Aspar x2spar I + Aspar [ &par - XTT 12 1 - - 

+ Gweb Iy web + Aweb [ Xweb - XTT l2 1 

Having derived the above expression we now reluctantly relate that this value of GJ is not usually 

practical for thin shells, since skin warping greatly reduces the stiffness. For example, in a usual thinskin airfoil with a D-spar, the above calculation is approximately four times the actual values of GJ from 

experiment. Therefore, the AEI program uses a shear flow approach in calculating GJ: 

where: A = cross-sectional area 

t = skin thickness 

cis = differential skin length 

In the above calculation the thicknesses (hence areas) are modulus-weighted to the skin value of 

shear modulus and the contribution of the spar web is ignored. The GJ calculated from the above expression 

has proven to be accurate enough for practical purposes. Further refinement of this calculation could be 

done for more complex section geometries. [Note: From later calculations, the major error introduced by 

dropping the web contribution is to incorrectly locate the shear center. For the ESI blade, which has a 

thick skin and substantial web, this error amounted to 4O0I0 chord (calculated) vs. 25% chord (test)]. 
4.2.4: SECTION MASSES AND INERTIAS 

At this point the required stiffness properties in bending and torsion have been calculated for each 

section of the composite beam. It remains to calculate the masses and inertias. As for the elasticity 

constants, the blade skin and spar will have different mass densities based on the percentage of 

reinforcement to resin volume. For the simplest unidirectional laminate with glass fiber reinforcement, 

the relationship between density and modulus is straightforward (Table 4.1). 

TABLE 4.1 : FRP UNIDIRECTIONAL WEIGHTS AND MODULI 

% Resin Volume % Fiber Volume % Resin Weight Density (Ib/cu in.) E(ksi) 

where resin = .0434 Ib/cu in. and glass = .09838 Ib/cu in. 

Practical laminates lie between these extremes in modulus and weight. 

The section mass integrals are formed in the same manner as the stiffness integrals above, by 

summing the individual components using the parallel axis theorem: 

= Wskin Askin + Wspar Aspar + Wweb Aweb = total running weight 

= Section cg = C WnXn l WA 

= Section CCJ = C WnYn / WA 

= X - component mass moment of inertia about origin X,Y = 0.0 

= Wskin 1x0 skin + Wspar 1x0 spar + Wweb [Ixweb + Aw (y)2 

= Y - component mass moment of inertia about origin X,Y = 0,O 

- 

= &kin Iyo skin + Wspar Iyo spar + Wweb [Iyweb + Aw ()02 1 = Mass Moments of inertia referenced to the section cg = Ixo - WA yg2 

= Now referenced to the elastic axis (shear center) 

= Iyg + WA [XT - xg]2 

Finally the section mass moment of inertia is the sum of both the X- and Y- components, for both the 

section cg and the shear center: 

IT = IXT + ~YT and I9 = 1x9 + Iyg 

The mass moment of inertia about the cg, Ig, is the minimum value for the section. 
Lastly, the program adds any ballast weight contribution to the mass integrals. In some blades, lead 

ballast is added to move the basic section cg position; in others the "ballast" contribution might refer to 

nonstandard elements embedded in the blade which change the masses but not the stiffness (e.g. tip control 

mechanism). These ballast contributions are again added by using the parallel axis theorem, as above. 

4.3: BLADE STATIC DEFLECTION CALCULATIONS 

The Bernoulli-Euler theory of bending of slender beams ("engineer's theory of bending") is used. 

The key assumptions are flexural deflections are small and linear, and plane sections remain plane and 

normal to the beam (centroidal) axis as the blade deforms. Stresses in the transverse direction are als~ 

nealected. This gives a uniaxial stress-strain relationship and satisfies the equilibrium condition since the 

stress resultants are in equilibrium with the applied forces. These assumptions also make it possible to 

determine the deflection of any point on the blade in terms of the deflections of the points on the centroidal 

axis of the blade since strain distribution is linear across the cross section. 

The cross products of inertia are dropped out by the adoption of the principal axes: 

Mj Y 

&i = - (simple flexure formula) 

E Ii 

and the total strain (or stress) can be found by superposition : 

where yp and zp are now the principal axes of the beam sections, and x is the axis down the spar of the 

blade. The 3-0 coordinate system is now 

X-axis: lies along the (undeflected) axis of the blade, with the origin at the blade root. 

Y-axis: lies in the lagging direction (i.e., toward the trailing edge of the airfoil). 

Z-axis: lies in the flapwise direction (i.e., in the direction of the free stream wind). 

The construction of the 3-D blade model now includes the manufactured blade twist angle at each 

station. Clearly this affects the principal axes for highly twisted sections, and has the effect of "softening" 

the blade in the lag direction. As seen below in Figure 4.4, the elastic twist must also be added to the twist 

before the final equilibrium principal axes and the final equilibrium blade deflections can be found. 

The applied loads, Ly and L, are assumed to be applied at the airfoil quarterchord (aerodynamic 

center) as would be true for airloading. For a bench test the applied loading would have to be carefully 

placed at the quarterchord to satisfy this requirement. Alternatively, the (arbitrary) applied load can be 

established as a load at the quarterchord plus a moment (couple) about the quarterchord. This way a 

twisting moment can be applied in the bench test and accurately reflected in the beam calculations. For 

example, a concentrated weight at .75 span, located on a jig forward of the blade leading edge, produces a 

load and a substantial moment about the .75 station quarterchord. This was the method used to produce 

primary blade torsion in the tests. 

The total quarterchord moment (M,) and loading (Ly,LZ) are calculated by the program. Then the 

twisting moment is calculated; this is the section moment about the shear center, which is the center of 

twisting. Then, using the blade torsional rigidity (GJ) values calculated above via the shear flow method, 

the blade twist is found. This must be first integrated from the blade tip inward, and then summed from the 

root to the tip, to accumulate all the differential twist of the blade. Finally the program finds the "elastic 

twist," which is simply the differential section twist at each station. This will usually be a maximum at 

the tip, for all practical cases. The blade twist calculation is simpler than the flexural calculation since 
principal axes are not needed. However, the twist must be solved first since it affects the actual resulting 

principal axes location for each station. The moment about the shear center is simply 

Qc = [ Ly cos 0 + LZ sin 0 ] ZT + [ Ly sin 0 - LZ cos 0 ] [ YT - .25 C] + Mx 

where: 

C = blade chord 

0 = principal axis angle + twist angle + elastic twist 

Lz = applied flapping load (quarterchord) 

Ly = applied lag load (quarterchord) 

Mx = applied pitching moment (nose down) 

(Y,Z) = shear center 

FIG. 4.4 SECTION TORSIONAL MOMENTS 

With the applied loading in the Y and Z directions (Ly,LZ) given, as for a static bench test, the blade 

shears and moments, in the lag and flap directions, and then in the principal axes directions, can be 

calculated. When the moments in the principal axes have been calculated, the blade strains can be found 

directly from the simple flexure formula above for each section of the blade. 

tip 

VY = inplane shear = I Ly d x 

root 

tip 

V, = flapping shear = J Lz dx 

root 
ti 

Mz = inplane moment (moment about the Z axis) = /'VY dx 

root 

ti 

My = flapping moment (moment about the Y axis) = LZ dX 

root 

The root shears are important because they combine with other blade root shears to yield hub 

shears. Likewise, the inplane moment combines with the other blade moments also to form the rotor 

torque. 

Applied moments in the principal axes are 

Myp = My cos 0 - MZ sin 0 

MZp = MZ cos 0 + My sin 0 

where 0 is the principal axis angle. 

Therefore, the bending strains at any given point on the airfoil are given simply by the (y,~)~ 

contributions 

MzP Ypi M~~ z~i 

& (x,y)i = - - 

Izp E IYP 

In the program the selected points on the airfoil ("stress offsets") are calculated first, and appear 

above as (y,z)Pi. Also, provision for blade tension (spanwise axial) loading is included, as would occur 

with centrifugal tension for a rotating blade. 

The linear flexural deflections of the blade are found simply by integrating the moments, now 

expressed in the true flap and lag (y,z) directions: 

M M M -=- coso + - sin 0 

IY IYP Izp 

The z and y deflection curves are simply the flap and lag deflections of the blade axis. 

In this calculation, a cantilevered blade has been assumed, as would be true for a rigid hub, or for a 

cantilevered blade bench test. Computationally, this is expressed as boundary conditions of the slope and 

deflection at the root (x = 0) being zero: 

Q, dy 0 

zo = yo = 0 and - - - = 0 

dx dx 
Analytically from St. Venant torsion theory, statically (Ref. 11): 

where: 

z( x ) = applied torque ( at the elastic axis) 

G J (x) = distribution of torsional rigidity 

de(x) = angle of twist 

dx 

The general torsional equation of motion is 

where I, = torsional mass moment of inertia (polar moment of inertia) per unit length. 

4.4: BLADE NATURAL BENDING FREQUENCIES AND MODES 

The static analysis so far has produced a beam model that has distributed elasticity (section 

properties) and masses (section masses) from a complex geometry composite blade. Bench tests can be 

expected to verify (and refine) the elastic constants, and blade sectioning will verify the masses. It 

remains to verify the dynamics of the blade model, which can only be done by calculating the natural 

frequencies of vibration (and mode shapes) in flexure and torsion, and checking these also with tests. The 

static deflection is most sensitive to the stiffness properties, but the frequencies of vibration are most 

sensitive to the masses. 

In the spirit of practical engineering calculation, the flexural frequencies and modes are considered 

to be uncoupled, flapwise from chordwise. This assumption is less valid for very highly twisted blades, but 

still accurate enough for present purposes. 

The method for solution was suggested by Holzer (Ref. 14) for the purpose of finding natural 

torsional frequencies of crankshafts, and was then modified by Myklestad (Ref. 15) for the bending 

vibrations of nonlinear beams. Later work for propellers included the centrifugal effect of rotation (Refs. 

16, 17). The continuous blade (beam) is represented by a number of discrete segments; analytically 

speaking, the partial differential equation for bending is thus replaced by a set of ordinary differential 

equations, one for each segment. The free body diagrams for each segment are easy to analyze, and lead to a 

direct physical knowledge of the vibrating beam; 10 segments are used here. The deflected blade is shown 

in Figure 4.5. The blade is segmented into ten equal lengths and the mass of each length is equally divided 

into lumped masses at either end. The elastic properties (EI and GJ) are assumed to be constant over the 

beam element. 
MOMENT 

SHEAR 

CENlRIFUGAL 

MASS ELEMENT 

- DEFLECTION 

FIG. 4.5 GENERAL 

BLADE RADIUS 

DEFLECTED BLADE: 

- ... I

HOLZER / MYKLESTAD 

The free body diagram for the nth element is shown in Figure 4.6. 

FIG. 4.6 FREE BODY DIAGRAM: HOLZER TABLE 

where: 

mn = nth lumped mass 

an = nth slope 

an = nth tension (centrifugal force) 

Mn = nth bending moment 

L, = nth segment length 

S, = nth shear 

Zn = nth bending deflection 

The partial differential equation of bending of the beam is fourth order; therefore, four coefficients 

are needed to express unit load effects due to an applied moment and an applied force. The unit load and 

moment coefficients are derived from a simple cantilever with a unit end load, F, or a unit moment, M 

(Figure 4.7). 
& 

;* LUnit Load Diagram 

Unit floment Diagram 

FIG. 4.7 UNIT LOAD AND MOMENT DIAGRAMS 

The resulting coefficients are 

UFn = deflection due to unit force = L~~ / 3(EI), 

VFn = slope due to unit force = L~~ / 2(EI)n 

UMn = deflection due to unit moment = L~~ / 2(EI)n 

VMn = slope due to unit moment = Ln / (EI), 

Note: the above coefficients are sometimes written in non-unit form as 

UFn = UF = F L3 / (6 EI) 

VFn = 8~ = F L2 / (2 El) 

UMn = UM = M L2 / (2 EI) 

VMn = 8~ = M L / (EI) 

Also, the Maxwell Reciprocal Relationship "the u due to the M = 0 due to the F" is easily seen above. Now 

the segmented blade, rotating at frequency Q, is assumed to vibrate at frequency o. An additional inertial 

force (Mn+l o2~,+~) is added to the free body diagram above. Force and moment equilibrium then yield 

The tension at the nth segment can be rewritten as a sum of tensions: 

n 

an= C mi Q2 ri 

i=l 

And the deflection can be substituted into the moment expression to give 

These recurrence formulas could be solved by successive substitution, working from the tip of the 

blade to the root. Shear, moment, slope, and deflection would be calculated for each segment, and resultant 

distributions would be known. The slope is assumed to be an arbitrary angle, 8, and the deflection a unit 

quantity. Then, trial values for frequency (or 02) are introduced. For the trial o to be the correct 

frequency, the slope at the root and the deflection must correspond to the appropriate root boundary 

condition; viz: 
Cantilevered: 

Slope at root = deflection at root = 0 

Hinged: 

Moment at root = deflection at root = 0 

Myklestad applied this to systematic computation by making judicious new definitions and 

substitutions, as follows. The load and moment coefficients and centrifugal forces can be combined via the 

"Myklestad definitions," which simplify the above expressions: 

Then, a set of assumed linear functions is substituted in the set of four recurrence formulas for 

shear, moment, slope, and deflection. The assumed slope at the tip, cp, is carried as the independent 

variable; the assumed Myklestad amplitude coefficients are 

Shear: Sn = - Gqnq + Gn 

Moment: Mn = hpn9 - Hn 

Slope: an = hqnq - hn 

Deflection: zn = - gQncp + gn 

Substituting these linear functions into the four original recurrence formulas and equating 

coefficients yields simple recurrence formulas for the amplitude coefficients now suitable for systematic 

computation. [Note: The classical Myklestad derivation is used here to avoid the ambiguity, which is seen 

in sign definitions in later works.] 

For the free tip case, the initial values are at the tip: 

This yields the initial values of the amplitude coefficients: 
Then the root, which is cantilevered, gives the condition (from deflection = 0) 

The remainder in the program is the root deflection, which is the trial value; e.g., when the remainder is 

zero, the trial value of w2 was correct and a solution has been found: 

Zroot = remainder = - gqroot c~ + Sroot = 0 (for a root of the equations) 

In general, this iterative method will give as many roots (frequencies) as there are lumped masses. 

The corresponding shear, moment, and deflection mode shapes are found for each root by simple 

substitution in the recurrence formulas. For most wind turbine blade dynamics, the lowest or fundamental 

frequency and mode shape are most important since they dominate the dynamic response (flap and leadlag) - 

The computer program uses for input data the running mass of the blade and the section stiffness 

(for either flap or lead-lag) at the operating rpm. Another version of the program also allows the addition 

of a concentrated tip mass to assess the effect of a tip weight or mechanism (Appendix 10.3, 10.4). 

BLADE TORSIONAL FREQUENCIES AND MODES 

The blade torsional frequencies are also calculated using the Holzer table approach. The model 

assumed a shaft fixed at the root, with flywheels (Ii) at each station representing the lumped masses, and 

torsional stiffness (ki) derived from the GJs: 

k = torsional stiffness = GJ / L = GJ / Ar 

where Ar is the segment length 

I = mass moment of inertia = I I r2 dm = J (p dx) r2 dA 

where: r = chordwise coordinate 

x = spanwise coordinate 

p = mass density 

[Note: the polar moment of inertia of a section is the ( r2 dA) portion.] 

The p r2 dA integration must be performed in the section properties calculations since the density 

varies along the composite beam. Also, ballast weight must be assessed since it changes the section mass 

moment. 

The question arises as to which value of section inertia to use, the minimum value (which occurs 

about the section cg), the value referenced to the shear center (about which section twisting occurs), or 

the value referred to the blade geometric axis (blade axis). In this treatment the elastic axis (shear 

center) is used as reference as explained here: 

For a uniform blade with a symmetrical cross section and uniform properties spanwise, the 

geometric, elastic, and mass axes coincide. Therefore, twisting in this case will occur in pure 

shear (twist) with the geometric center as its "axis of twisting." 

If the geometric axis is offset (chordwise) from the support at the root, the blade torsional motion 

still occurs on the rnass/elastic axis of the blade. The offset support has just added another 

resultant degree of freedom: that of rigid body flexure and twisting about the support. [Note: this 

can be easily visualized by making a sketch.] 

Next for an unsymmetrical weight on the shaft (ballast), the new twisting motion will occur about 

the (old) elastic axis as before, even though it is not the geometric (from above) or mass a& 

anymore. Finally, for a complex geometry, the action of pure twisting is as close as possible to the 

elastic axis of the blade, even though this may not be a straight line. [Comment: This line of 
reasoning, admittedly qualitative, was empirically verified in the modal analysis testing of the 

UTRC blade. The FFT software allowed computer graphics animation of the fundamental torsional 

motion, which clearly showed the twisting occurring about the elastic axis and not the mass axis.] 

If the blade contains nonstructural or ballast weights, the mass centers are relocated off the elastic 

axis. This adds 

1) torsional coupling to the bending modes (flutter), 

2) bending to the torsional modes, 

3) increasing mass moment of inertia to the section; thus lowering the natural torsional 

frequencies. 

The solution is found using the same approach as before. The free body diagram is shown in Figure 

Q = torque 

I = mass moment of inertia 

k = torsional stiffness 

9 = section twist 

FIG. 4.8 FREE BODY DIAGRAM FOR TORSIONAL VIBRATION 

The governing equations (recurrence formulas) are much simpler than before: 

The boundary condition at the tip (n = 1) is 8 = 1; the remainder is the twist (8) at the root which 

must equal zero for a solution. Actually this is precisely the method used by Holzer to calculate crankshaft 

frequencies by hand. 

Again, there is provision in one version of this program to assess tip weights (inertias) on 

torsional frequency (Appendix 10.4). 
5.0 DEVELOPMENT OF BLADE MASSIELASTIC MODELS 

5.1 : TRIANGULATION OF MASSIELASTIC PROPERTIES 

The primary need in this phase was to verify the accuracy of the engineering constants used in the 

beam analysis. This involved comparing the static bending and frequency of vibration results from the 

experiments with the predictions based on assumed engineering constants. The static bending and frequency 

tests "bracket" the error bounds on uncertainty of the engineering constants and masses, since the static 

deflection results are more sensitive to the moduli, and the frequency results to the masses. Discrepancies 

must be evaluated and solutions iterated until a satisfactory semi-empirical set of engineering constants 

exists for each blade that satisfies both the theory and the tests (static and vibration). Additionally, the 

blade root attachments were evaluated to obtain the bending and torsional compliance of the attachments, 

primarily by referencing the root restraint view in the modal survey and by baseline spanwise 

inclinometer readings in the static tests. At the end of this phase a practical, accurate, and workable 

mathematical model existed for each bladelhub combination of the study. 

5.2: UNIFORM FRP BLADE EXAMPLE: UTRC BLADE 

The UTRC blade was the simplest structurally since it was a uniform pultrusion. The 

flexbeam/pendulum mechanism was not tested since the twisting kinematics were considered to be beyond 

the scope of this work. Clearly, the majority of the elastic twist of the flexbeam rotor is occurring in that 

portion of the blade that could be easily modeled elastically, which is proved in the results. This blade was 

a good choice for this study since: 

a. Blade is uniform pultrusion construction, which is representative of many rotor designs, 

and offers good cost reduction potential. 

b. Blade section properties are uniform and straightforward. 

c. Rotor has shown performance and flutter problems in the past due to blade flexibility (these 

were likely due to the flexbeam, however). 

d. Rotor performance was documented by AEI and SERI. 

The UTRC blade is shown in Figure 1.3, at its full radius of 192 in., and with the root flexbeam 

portion comprising the inner 0.3 of the radius. The pultrusion was manufactured by Morrison Molded, and 

the flexbeam by UTRC. The pendulum weight and flexstrap pitching mechanism is not shown. The blade 

tested in this report was the outboard pultrusion, which has a cross-section as shown in Figure 5.1, from 

Ref. 18. This is a simple blade section, formed of a uniform laminate (constant thickness) skin with the 

airfoil shape and a solid spar in the leading edge, and a foam-filled aft section. The flexbeam portion was 

not tested but was actually very easily modeled since it was a simple rectangular cross section. This part 

of the report describes the development of a suitable aeroelastic model for this blade. 

5.2.1: METHOD 

To illustrate the derivation of purely theoretical section properties for a design, this discussion 

will begin by not including the test data, just the geometries and constituents. The airfoil shape NACA 

23112 is determined by a table of offsets. The standard for the AEI program is 33 pairs of points (X,Y) 

beginning at the nose, proceeding around the upper surface to the tail, and returning to the nose on the 

lower surface. This is the data set format used in the program. 

5.2.2: PREDICTION OF ENGINEERING MODULI AND DENSITIES 

The skin laminate was comprised of four layers of reinforcement of two types: unidirectional (0") 

and balanced (&4S0), with two layers of each type. In this case we are not told the reinforcement cloth 

makeup; instead we have the thicknesses, which are 

.040" per layer for k45" and 

.025" per layer for 0" 

This gives a total (specified) skin thickness of .I30 in. (Ref. 1). It remains to reduce this skin laminate to 

a single thickness with the proper overall density rskin, longitudinal modulus Eskin, and shear modulus 

Gskin. The same must be done for the spar later. 

4 7 
NACA 231 12 AIRFOIL 

t skin 

FIG. 5.1 UTRC CROSS SECTION 

To calculate these values for the skin, first look at this unidirectional layer: 

Y (go0) 

The properties of a unidirectional laminate are shown in Table 4.1, for glass reinforcement and 

epoxy or polyester resin matrix. If 50°/0 volume is glass, the E-modulus is 5'10~ psi and the density 

.0678 1blin3, from first principles (see Table 4.1). For the transverse E-modulus, zero is normally 

assumed, as it is only the resin matrix. Practically speaking the G-modulus is also zero. We will estimate 

50% fiber volume as representative of this pultrusion process, as it is for hand lay-up. This fiber ratio 

(or reinforcement to resin ratio) is very important in composites, as can be seen in this simple example. 

Fortunately, this ratio is easily found in an ASTM "burn-off" test, which simply burns off the resin under 

controlled conditions in a crucible to get an actual weight and thus a volume percentage. 
For the +4S0 layer we assume half the fibers run at O0 and the other half at 90". This changes the 

above modulus value by cutting it in half, since half are now at 90". This gives the 0°/ 90" properties, 

again based on a 50% volume, as 

E (0°/900) = 2.5'106 psi 

P = .0678 ~b/in.~ 

Since this layer is not oriented at 0° (but +4S0), we must decrease the longitudinal E-values by 50% 

(because the fibers are not aligned with the E-direction), and also increase the G-value by 50% (because 

at 4S0, the fibers are now along the principal transverse shear or twisting direction). This is shown in 

the "rule of thumb" directional properties engineering guide of Figure 5.2. 

CORRECTION 

FACTOR 

0 15 30 45 

9 0 75 6 0 4 5 

LOAD TO WARP ANGLE 

G - MODULUS 

E - MODULUS 

FIG. 5.2 RULE OF THUMB, FRP DIRECTIONAL PROPERTIES 

Now we can calculate the total skin values of E and G by using the rule of mixtures. Analytically: 

El tl + E2t2 + E3t3 +... 

Elaminate = 

ttotal 

This gives for the trial values: 

5'1 o6 '-050 + 1 .25'l o6 '.080 

Eskin = = 2.69 ' lo6 psi 

.I30 

0.050 + 1 .80'lo6 +.080 

Gskin = = 1.10 lo6 psi 

.I30 

Going on, the spar is a unidirectional bundle of rovings (fibers) in a compact resin matrix. We can expect 

a higher fiber volume (say 60%) and thus higher values than the less compact skin above: 
ESPar = 6 lo6 psi 

pspar = .0727 ~b/in.~ 

Gspar = 1.1 0 + 106 psi (for simplicity) 

5.2.3: PREDICTION OF SPAR PROPERTIES 

The skin contribution will be based on the composite values of E, G, and p determined above, 

integrated around the airfoil shape as input via the offsets. Also the spar values of E, G, and p have been 

estimated, but not the geometry. The program has the capability of assessing a D-spar in the leading edge 

and further spars or webs. Here we do not have a D-shape, so that calculation is eliminated. We treat this 

"spar" as a "web," so must describe it as a collection of moments of inertia and weights at its centroid. The 

program then adds its contribution simply by using the parallel-axis theorem. A graphic calculation of the 

spar yields 

As par = 2.7076 in.2 

I x = 0.3831 in.4 

IY = 0.9887 in.4 

IX Y r o 

(~,~)~~~t~~id = (1.4796, 0.1 843) in. 

The contribution of the foam is ignored. 

5.2.4: INITIAL PREDICTED RESULTS 

The above predictions yield section properties which we can only expect to be in "the ballpark." 

These are listed in Table 5.1 which also shows the 1) manufacturer's specifications (which have been used 

up to now), 2) the values from the blade sectioning, and 3) the final semi-empirical values after they 

have been verified by both testing and predictions. Obviously it is wise in most cases to perform the tests, 

including blade sectioning, because the blade model is much more accurate, as can be seen in the table. 

TABLE 5.1 : UTRC BLADE SECTION PROPERTIES COMPARED TO MANUFACTURERS' 

SPECIFICATIONS AND SECTIONAL VALUES 

Geometry (in.) Mass and Stiffness 

c ~AF tskin dspar Im (Iblin.) EIflap Ellag GJ ycg(%c) EA(%c) I 

Mfr's Spec 15 1.8 .I30 2.5 ( .352 4.15 292 3.75 26.0 37 6.14 

Init. Pred. (1 5) 1.8 (.130) 2.5 1 .431 6.57 377 7.43 31.8 33 8.59 

Measured 14.9 1.95 .1 18 2.56 1 .422 --- --- - - - 31.6 --- - - - 

FinalModel 15 1.95 .I18 2.56 1 .422 5.87 32.4 5.58 31.3 46.2 8.38 

5.2.5: SPECIFICATION VERIFICATION BY BLADE SECTIONING 

By close blade inspection, and specifically by cutting a blade into sections, some of the predictions 

of the above approach can be much more accurate. Referring to Table 5.1, the specified skin thickness of 

0.130 in. turned out to be 0.118 in. and the running mass went from 0.352 Iblin. to 0.422 Iblin. Clearly 

the manufacturer's specifications were wrong; thus the initial predictions above gave section properties 

that were also wrong; (see Table 5.1). At this stage, though, no direct measurement of EI and GJ can be 

made, nor have the mass and section inertia values been verified. 

What can be concluded is that blade inspection is important to verify a manufacturer's claims. Here 

all the structural and mass properties are different. The aerodynamic properties as well are different; 

with an actual section thickness of 13% (1.95/15), this airfoil will behave differently than the specified 

12% (NACA 23112). 
5.2.6: VERIFICATION BY DEFLECTION TESTS 

The key load case was 175 Ib total load, evenly distributed along the span applied to the quarter 

chord. Figure 5.3 shows the predicted flapwise deflection of the UTRC blade for the El's from both the 

initial calculation (above) and for the corrected semi-empirical values of El. The test data are also shown. 

When the correct values (e.g., of skin thickness, airfoil thickness), have been determined from sectioning, 

the E-modulus in this case is simply varied until the static deflection matches the theoretical prediction 

for test, as shown. 

There is more to this part, however. A test load case will generally produce flapwise, chordwise, 

& torsional deflections, and they all must be correctly predicted by the theoretical model. Therefore, it 

is not enough to match just the flapwise deflection; the chordwise deflection and twist must also match. In 

the AEI approach the loading is applied at the blade quarterchord. If the principal axes of the section are 

not exactly horizontal in the laboratory, some chordwise deflection will also occur. Also, if the section 

shear center (elastic axis) is off the quarterchord, twist will occur. For this load case (175 Ib) 10.47 in. 

flapwise and 0.08 in. chordwise deflection, and roughly 0.1" (nose up) twist were measured. (&&: the 

blade was mounted lifting surface down to mimic airload.) 

ncp tzm-nnu 1:-t UL UU IIUI'I (Ill) 

FIG. 5.3 UTRC FLAP DEFLECTION, TEST VS. CALCULATION VS. SPECIFICATIONS 

Looking at the section properties, the principal axes o.f the blade are 0.42" (nose up). This is the 

effect which causes the inplane deflection. When this value of 0.42" is used as a simple pitch input in the 

calculation, the flap and lead-lag deflections are reproduced accurately. The resulting values of modulus 

are 

initial values 

Eskin = 2.05 ' lo6 psi (2.67 lo6) 

ESpar = 5.70 ' lo6 psi (6.0 ' 106) 

Gskin =1.34*106psi (1.1 lo6) 

GSpar = 0.50 ' 1 o6 psi (I .I ' 106) 
The initial guesses are also shown. So far the values of EI (flap and lag) have been verified, but the value of 

GJ has not, since there was so little elastic twist in this 175 Ib load case. Also, the masses and moments of 

inertia have not been verified; these remain for the frequency tests. Using the torsional test case (23 ftIb @ STA 0.9) the predicted twist is 0.24" (at the tip) compared to the test value of 0.37". Either the GJ 

is too high or the elastic axis is slightly off. Rather than modify the G's to achieve congruence at this point, 

which could be done easily by reducing Gskin and Gspar equally until 0.37" is reached, we will depend on 

the frequency test still to come. 

&&: A blade analysis could stop at this point, depending on the static weights for mass distribution and the 

information gained so far for section cg and section inertia. However, these parameters are crucial to the 

elastic twist on a "flying" blade, which has far more centrifugal force than the loads that can be 

conveniently applied in the lab, so further verification is warranted. 

MODE 1 

Calculated = - 

Test values = * test: 2.1 0 Hz 

calc: 2.06Hz 

MODE 2 

test: 13.0 Hz 

calc: 13.0 Hz 

MODE 3 0 

test: 35.0 Hz 

cak: 37.6 Hz 

ROOT 7- . -- 

FIG. 5.5 UTRC FLAPWISE VIBRATION MODES, PREDICTED VS. TEST 

The frequency program results are shown in Table 5.2 below: 

TABLE 5.2: UTRC FREQUENCY OF VIBRATION RESULTS: TEST VS. PREDICTION 

&& I&! Prediction 

1 st flap 2.1 Hz 2.06 Hz 

2nd flap 13.0 Hz 12.99 Hz 

3rd flap 35.0 Hz 37.60 Hz 

1 st lag 13.0 Hz 15.22 Hz 

2nd lag 78.0 Hz 96.0 Hz 

The principal axis stiffnesses were used since they are the decoupled modes on a uniform blade. It 

can be seen that the flapwise values are in excellent agreement, verifying the EIflap and masses. The lag 

frequencies are different from the test presumably because lh Js r fixi 

drivina the laa freauencies down. In a sense the lag value is inconsequential anyway, because it is much 

higher than the first flap frequency. 

The torsional values are shown below. Clearly the test data have confirmed the blade values of GJ 

and I; final GJ is 6.2'1 o6 psi with Gspar = 0.1'106 and ~~~a~ 0.9'10~. 

Mode Test Prediction 

1st Torsion 29.0 Hz 28.39 Hz 

2nd Torsion 84.0 Hz 84.71 Hz 

In the torsional frequency calculation the blade is assumed to oscillate about its elastic axis (see 4.5 under 

Theoretical Method), which has a larger mass moment of inertia than about the section cg (10.51 vs. 

8.38). 
Going back to the flexure tests will "close the loop" on the GJ. The G's have been matched by the 

frequency tests, and the predicted static torsion of the load test above (23 ft-lb @ STA .9) now matches the 

test value of 0.37". This is a good indication that the blade masses and stiffness are correct since they 

match static and dynamic test values simultaneously. 

5.2.8: FINAL AEROELASTIC MODEL 

At this stage the pultruded UTRC blade has been successfully modeled; the following conditions have 

been met by the predictions matching the tests: 

1) total blade weight 

2) blade flexural deflection, flap and lag 

3) blade static torsional deflection 

4) blade flapwise frequencies and modes 

5) blade lag frequencies and modes 

6) blade torsional frequencies and modes 

It remains to construct the total aeroelastic model by adding the flexbeam portion and creating the 

appropriate blade properties file for the elastic twist calculations. 

The flexbeam is attached at STA 0.3 and has the rectangular geometry shown below from inspection: 

The input data for the flexbeam are derived from the manufacturer's specifications and the 

inspection values (the stiffnesses were not tested): 

also 

AI- beam = 4.4032 in.* 

Ix = 24.04 in.4 

IY = 0.2404 in.4 

1, Y z 0.0 

(X?Y)C = (5.5, 0.0) 
The final values for the UTRC aeroelastic blade model are shown in Table 5.3. 

TABLE 5.3: FINAL UTRC BLADE MODEL ANALYSIS 

Root 11 0 0 

10 .1 19.2 

9 .2 38.4 

8 .3 57.6 

7 -4 76.8 

6 .5 96.0 

5 .6 115.2 

4 .7 134.4 

3 .8 153.6 

2 .9 172.8 

Tip 1 1 .O 192.0 

5.3: WOOD-EPOXY BLADE EXAMPLE: GOUGEON ESI 54 BLADE 

The ESIIGougeon blade was chosen for this study for the following reasons: 

a. The blade is of composite wood construction, with good material and arrangement quality 

control and very good documentation by the manufacturer. 

b. The airfoil is NACA 230XX series, used for helicopter rotors and other wind turbines, and 

has substantial available test data. 

c. Field test data were available and accurate. 

d. Compared to other composite wood blades, this blade has relatively high torsional stiffness 

but still measurable elastic twist. 

e. The root attachment is indicative of a standard teetering approach with high stiffness and 

potential for pitchlflap coupling. 

f. The blade radius is midway between the 10- and 20-meter diameters of the other blades in 

the test program. 

9- The blade planform represents a "tip speed ratio tolerant" design, with slight taper and 

twist, indicative of most constant RPM wind turbines. 

h. Tip brakelweight complicates the loads analysis for both structural and aerodynamic loads 

and was thought to be responsible for possible elastic twist observed in the field. 

i. Because this blade uses a low pitching moment airfoil, inertial elastic twist (especially 

from the tip brake) is likely to dominate the results. 

u: this prediction turned out to be true. 

5.3.1 : ESI BLADE DESCRIPTION 

The ESI 54 blade, which is manufactured by Gougeon Brothers Inc. (Bay City, Mich.) is shown in 

Fig 1.2. It is of a wood-epoxy construction, and uses a web-reinforced shell with constant skin thickness 

at each span station and no D-spar. Also, it is not highly twisted and has no ballast weights or mechanisms. 

And probably most important, it has no structural discontinuities as do both the UTRC and Carter 300 

blades. The root fixture is an oval bolted-stud pattern of relatively large dimension, so the root fixity in 

the test rig was relatively rigid. The blade was much stiffer then the Carter, and there was consequently 

much less static gravity deflection, on the order of a few inches only, which simplified the testing. The 

blade was tested and analyzed bare without the tip flaps which were used in the ESI 54 turbine. The elastic 

Jwist due to the tip mechanisms. as seen later. dominates this blade's elastic twist. 

The manufacturer, GBI, was very cooperative, and provided a complete engineering description of 

this blade, along with drawings, section coordinates, section properties, and analyses (Ref. 21). These data 

are held proprietary to GBI, but the comparisons of the section properties are presented since they are 
important. Clearly this test program verified both AEl's and GBl's section analysis programs, with the 

exception of the shear center calculation(see below). 

5.3.2: DERIVE INITIAL SECTION PROPERTIES 

The section property code input file for this blade is much easier than for a glass-reinforced 

composite blade. Geometrically, the only values needed for each station are the offsets (airfoil shape), skin 

thickness, and web values. This blade uses a modified NACA 230XX airfoil, so the standard profiles could 

not be used. Instead the GBI specifications were verified by sectioning, and these actual values were used. 

The engineering moduli for Douglas fir vary over a rather wide range; however, the constituents 

and methods used by GBI are reliable and repeatable. Therefore, we had high confidence in the initial design 

spec: 

Egrain = 1.57 1 o6 psi 

G = 0.15 106 psi 

P = 0.025 ~b/in.~ 

It remains to find the skin thickness and web location for each blade station, either from the specs 

or from the tests, and then to calculate the section properties. The much more effective engineering 

approach factors in the test results from the very beginning, as illustrated here. 

The blade inspection (sectioning) yielded measured values of running mass, section Cg location, 

shear web location, and skin thickness. These values plus the estimated moduli and density (above) 

provided a set of section properties calculated by AEI (Figs. 5.6 to 5.11). As can be seen, the two 

predictions (AEI and GBI) are in close agreement, with the notable exceptions of the shear center and GJ 

(which are discussed further below). Clearly the GBI program has included the contribution of the 

plywood web differently (and as shown below, more accurately) than the AEI program. It remains to 

validate all the section data by comparison with flexural and dynamic test data. 

STATlON 

FIG. 5.6 ESI SECTION EA: AEI CALCULATION VS. GBI SPECIFICATION 



5.3.3: VERIFICATION BY FLEXURAL TESTS 

The ESI blade flexural data (e.g., deflections vs. load) were different than for the UTRC blade. First, 

the ESI blade was so stiff in torsion, owing to the large wall thickness for the wood epoxy blade, that 

practically no measurable (k6' arc) elastic twist resulted from the bending, even for 450 Ib. of 

distributed load (tip deflection of 5 in.). Second, the flap deflection values had to be corrected for the root 

elasticity; that is, when the blade was loaded, the steel root studs stretched allowing the blade root slope to 

change. This slope change amounted to 7 minutes of arc at 225 Ib load and 16 minutes of arc at 450 Ib. 

(Note: this introduced substantial tip errors of 0.66 in. and 1.51 in. in the raw distributions.) 

The corrected (and uncorrected) blade deflection is compared to both the AEI and GBI section 

predictions in Figure 5.12. The agreement is very good especially at the tip where it is most important. 

Therefore, the original input values were considered to be correct for this blade in flexure. 

hdm (in) STATION 

0 1 2 3 4 5 8 7 8 9 10 

f 1 

250 LB. LOAD CASE 

- 

450 LB. LOAD CASE 

2 - 

0 AEI CALCULATION 

A GBI SPEC 

- - TEST DATA 

FIG. 5.12 ESI BIADE DEFLECTION: PREDICTIONS VS. TEST 

5.3.4: VERIFICATION OF STATIC TWIST 

The static twist of the distributed load cases (225 Ib, 450 Ib) was too small to be useful (see Fig 

5.13). The torsion load case applied 50 Ib. concentrated load at STA 0.9 of the test blade, offset 12.4" 

forward of the blade quarterchord. The test result is shown in Figure 5.14; it is a small but very 

believable distribution with an accuracy at least as good as 0.1 deg (6' of arc). Therefore, there was good 

confidence in both test results, even though the amplitudes were very low. 
STATION 

FIG. 5.13 ESI BLADE STATIC TWIST 

0.1 I --- - 

TEMPLATE ERROR 

DUETO WEIGHT -\ 

0 

FIG. 5.1 4 ESI BLADE STATIC TWIST (50 Ib TORSION LOAD CASE) 

The original distributions are shown in the GJ calculation in Figure 5.11; the AEI prediction used G = 0.15. 

Lowering G to 0.10 gives the final GJ, which agrees well with the GBI specification. However, when these 

two distributions are used to predict the static torsion above, it can be seen in Figure 5.15 that the tip 

twist varies by about 1576, even though both distributions are close to the test values. The blade GJ can not 

6 2 
be considered to be verified yet though, since the load case was only a single static moment applied to the 

quarterchord. [As seen before for the UTRC blade, the torsional frequency is a much more accurate . 

determinant of GJ]. 

OD 1 

A AEI CALC (G = 0.10) 

0 GBI SPEC 

--- TEST 

FIG. 5.15 ESI BLADE STATIC TWIST: PREDICTIONS VS. TEST 

I 0 TEST, 225 LB 

A TEST. 450LB Y 

I - AEICALC I 

FIG. 5.1 6 ESI BLADE TWIST: PREDICTIONS VS. TEST (FLEXURE LOAD CASES) 
A further check on twist can be made, to compare the twist of the dead load cases and "bracket" the 

solution. These are shown overlaid with the test results in Figure 5.1 6; clearly, they do not match the test 

data. Since there is high confidence in the above range (0.1 - 0.15) of GJ, the error must be in the 

predictions of shear center (both AEI and GBI). These predictions are for an aft shear center (see Fig 

5.10) which produces a section moment when loaded at the quarterchord. The error in the predicted twist 

in Figure 5.16 is attributable to the difference in shear center prediction in Figure 5.10, as described 

here: 

The test data clearly show no effective elastic twist of the ESI blade when loaded at the quarterchord 

(See Fig 5.1 6). This is the requirement for the definition of shear center. Therefore, it must be concluded 

that the actual shear center of the blade is the quarterchord and both predictions are in slight error. Thus 

for the blade aeroelastic model, an empirical value for shear center must be used: when this value is input 

for the two high load cases the resulting twist is zero, as in the test data. This illustrates the necessity of 

doing both static tests; flexural and torsional, otherwise this important result would have been overlooked. 

5.3.5: VERIFICATION BY FREQUENCY TEST 

The total blade weight was measured and predicted to be 260 Ib., which lends credence to the 

calculated mass distributions. The first three flap bending modes and the first torsion mode are shown in 

Figure 5.17. The frequency results are shown in Table 5.4 for the test, the GBI specifications, and the AEI 

calculation. 

3rd FtAP 25.0 HZ 

1 st TORSION 40.5 Hz 

FIG. 5.1 7 ESI BLADE FREQUENCY MODES 

6 4 
TABLE 5.4 ESI BLADE FREQUENCIES OF VIBRATION: PREDICTION VS. TEST 

Test AEl GBI 

frequency Predict ion Prediction 

1 st flap 

2nd flap 

3rd flap 

1 st lag 

2nd lag 

3rd lag 

1 st torsion 

2nd torsion 

NOTES: (1) The range of the AEi predictions indicates the limits from the true flap and lag directions to the 

principal axis direction. 

(2) Torsional frequencies in parentheses indicate G modification (0.1 00 to 0.1 33 '1 06). 

The range in the AEI predictions derives from taking the EI values in the true lag and flap directions 

or in the principal axis direction which yield a softer "flapwise" frequency. The blade is not highly twisted 

(8 deg) so the principal axes are definable in blade terms. Also from Table 5.4, since the flap test 

frequencies are higher than the GB1 frequencies, it can be concluded that the GBI values are conservative. 

For lead-lag the same is probably true since non-ideal root fixity usually depresses the lag frequency test 

data. This effect is clear with the AEI predictions, but not the GBI values. This also illustrates how 

sensitive the frequencies are to EI values; Figure 5.7 would not lead one to suspect such a large variation in 

frequency. 

The torsion values clearly show the predicted GJ's to be too low. Recall that these GJ's were based 

on the static twist results (G = 0.10) and very low values of twist (48 minutes of arc). To bring the 

calculated frequencies up to the test values (shown in parentheses), the value of G was increased from 

0.1 00 to 0.1 33. This is understandable since the original prediction was 0.150. The resulting final GJ is 

shown in Figure 5.18. This value of GJ matches the static data less well (but still within the experimental 

accuracy of kO.lO), but the dynamic data are matched exactly; this is more believable since fixity 

problems are eliminated. 
GJ 

XI0 

PSI 

0-25 0-50 0-75 1-00 

STATION (rlR) 

FIG. 5.1 8 ESI BLADE: FINAL GJ VALUES 

5.3.6: FINALAEROELASTICMODEL 

The final values of the ESI aeroelastic blade model are shown in Table 5.5. The blade twist was 

determined by geometric calculation and verified by measurement. 

TABLE 5.5: ESI BLADE: FINAL AEROELASTIC MODEL 

(in .) (deg) (slugslin.) 1 06psi 1 06psi 106psi (in.) (in .) 

STArIR r po mo EI flap Ulag y~ yw b 

Root 1 1 0 0 0 

10 .1 32.4 2.13 

9 .2 64.8 2.13 

8 .3 97.2 2.13 

7 .4 129.6 2.45 

6 .5 162.0 2.87 

5 .6 194.4 3.38 

4 -7 226.8 4.04 

3 .8 259.2 4.94 

2 .9 291.7 6.12 

Tip 1 1.0 324.1 8.18 

5.3.7: ESI TIP FLAPS 

The operational ESI blade had tip flaps that were attached to a mount (see Fig. 5.19) and had the 

function of centrifugal overspeed brake. There were two versions of the tips: the "regular tip" and the 

"whisper tip," the latter incorporating a fiberglass-foam aerodynamic fairing. From tests and inspections 

of the two tips, the weights and Cg's of the assemblies (e.g., brackets, bolts, swing arms, springs, and bash 
plates) were analyzed to correctly account for the added weight and inertia. Given here are free-body 

diagrams and the resulting values of the equipollent system, which gives the correct mass locations. 

REGULAR TIP 

FIG. 5.19 ESI TIP FLAPS 
Reaular Tip; 

Whisper Tip: 

ACTUAL TlPS 

12-25 Ib 

EQUIPOLLENT SYSTEM 

17.438 Ib 

I 

These are treated as tip ballast in the calculations of section properties in the elastic twist 

computer runs. These values were verified with some (unpublished) test data taken by ESI on the blades in 

the field and made available for this report (Ref. 26); Table 5.6 shows how the added tip weight decreases 

the flap frequency, and the added tip inertia greatly decreases the torsional frequency. 

TABLE 5.6: ESI VIBRATION FREQUENCIES WITH TlPS (HZ) 

Mode No Tip Regular Tip Whisper Tip 

(Prediction) (Prediction) Prediction Test 

1 st flap 3.5 2.69 2.41 2.40 

1 st torsion 40.5 23.60 12.51 12.50 

5.4: COMPLEX COMPOSITE FRP EXAMPLE: CARTER 300 BLADE 

The tometer FRP Carter blade was a good candidate for this study for the following reasons: 

a The relatively high tip speed, blade radius, and chord give high Reynolds number and power 

output. 

b. The good quality control of the laminate molding and arrangement by the manufacturer 

yielded consistent material properties. 

c. The relatively low bending stiffness led to measurable structural twist coupling (due to 

elastic axis offset from loading axis). 

d. The large ballast mass added to the outboard blade caused substantial elastic twist. 

e. The highly twisted, tapered planform is indicative of high-performance wind turbine 

rotors. 

f. The LS(1) series airfoil was used; it is indicative of new wind turbine airfoil families, and 

possesses large aerodynamic pitching moment. 

g. The root attachment is indicative of underslung, non-pitchtflap coupled teetering hub. 
5.4.1: CARTERBLADEDESCRIPTION 

The Carter blade was manufactured by Carter Wind Systems (Burkburnett, Tex.); it has a ' 

composite shell with a reinforced leading edge (D-spar) plus webs (see Figs. 1 .I and 5.20). It has a 

radius of over 10 m (33.6 ft) and in a teetering rotor (2-bladed) configuration powers the Carter 300 

kW wind turbine. 

If the entire blade had a structure as in Figure 5.20 the structural analysis would proceed in the 

usual manner as for the above blades. However, the Carter blade incorporates an innovative internal 

pitching mechanism ("pitch-up snubber") which provides overspeed protection for the wind turbine by 

causing a pitch change (of roughly 14 deg nose up) past airfoil stall, by the action of an electrically 

released toggle (see Figs. 3.5 and 5.21). The release of the toggle allows a preloaded overcenter spring in 

the root to produce a large mechanical control moment between the (moving) blade shell and the 

(stationary) root I-beam. The I-beam is a high quality (high glasslresin ratio) unidirectional beam 

comprising the principal loading path in the inner 35% of the blade as shown. By its I-beam section, it has 

relatively stiff bending properties and relatively soft torsional rigidity; thus it acts as a torsional spring 

against the control actuator. In operation, once the blade is pitched up, it is gradually returned to the 

running pitch position by a springldamper actuator. This mechanism, unmodified, looks like a one-way 

spring damper to torsional motion of the blade, thereby drastically altering the fundamental torsional 

frequency of the blade and the torsional static deflections (via the relatively soft springldamper). 

Consequently, for the testing this control arrangement was replaced by a rigid turnbuckle, so the blade 

could be set at the correct (run) pitch angle and the true blade structural statics and dynamics could be 

measured. 

WEBS 45' SMN LAMINATE a 

UNlDlRECTlONAL 

REINFORCEMENT 

FIG. 5.20 CARTER BLADE INTERNAL STRUCTURE 

FIG. 5.21 CARTER BLADE FREE BODY DIAGRAM 
The free body diagram in torsion of this blade is also shown in Figure 5.21. The block/spring was 

replaced by the turnbuckle during testing. The inboard blade consists of a shell or "torque-tube" fixed 

around the I-beam, which is attached to the hub and a midrib at STA 0.37 radius, and "potted there in an 

epoxy resin compound. When the blade is pitched, the twist occurs primarily in the (torsionally soft) Ibeam and very little in the torque tube. It was the goal of this project to establish the torsional and 

flexural properties of both working in concert. This mechanical arrangement, of course. greatly 

complicated the testing and analysis, but could be adequately handled in the computer programs as seen 

below. 

The blade was further complicated by the addition of 138.8 Ib of lead weight ballast to the leading 

edge for mass balancing on the outboard third of the blade. This added weight (the basic unballasted blade 

with mechanisms was only 700 lb) caused a large static gravity deflection of about 30" when cantilevered, 

and also created a large section mass moment of inertia outboard. The latter doesn't affect the static elastic 

twist but does drastically modify the torsional frequencies and modes, as well as the flexural frequencies. 

Further structural coupling occurs due to the geometry of the blade. Figure 1.4 illustrates in three 

views the control and blade axes. The blade shell is geometrically constructed (e.g., twisted and tapered) 

about the blade axis which is at about 40% chord; but the blade is fixed (root) and acts about the control 

axis which is at the quarterchord, since the I-beam is placed there. The mass axis (not shown) is also 

roughly at or ahead of the quarterchord, and is definitely not a straight line. The intermodal coupling is 

best illustrated in the frequency mode shapes in the modal survey testing part (Sec 5.4.1 0). 

5.4.2: ASCERTAIN BLADE GEOMETRY 

The blade data furnished by Carter Wind Systems were meager in comparison to that furnished by 

GBi, in view of the information needed for this complex blade. The first task was to ascertain the actual 

blade twist, taper, and arrangement geometry. 

The blade radius and chord lengths were found accurately by inspection, as was the thickness 

distribution. Finding the twist was complicated by the gravity component due to the ballast weight. This 

effect was eliminated by measuring the dead load twist for the blade in normal position and inverted 

position. The six individual dead load cases are given in Figure 5.22, and the resulting twist distribution 

in Figure 5.23; the Carter specification is also shown. Clearly the STA 0.8 template was about lo off 

(which could have been the operator error referred to in 3.9.1); but otherwise the twist measurements 

were very repeatable. Figure 5.24 is an error scatter plot and shows the variation in cases to be subject 

to only 0.1% experimental error. 

The final blade geometry is given in Table 5.7 compared to the specifications. The actual blade 

length was only 0.75" longer than the spec. (376.25 vs. 375.50 in.). As can be seen, the values agree 

extremely well, verifying the tooling and assembly method of the Carter 300 blade. [Note: blade sectioning 

is not actually required for this task, but is a great help; it h required for later verifications.] 


TABLE 5.7: CARTER BLADE GEOMETRY, MEASURED VS. CARTER SPECIFICATIONS 

STA r/R r (in.) 1 chord (in.) I thickness (in.) I twist (O) I 

I meas. spec. I meas. spec. I meas. spec. I 

root 11 0 0 

10 .1 40.28 

9 .2 80.55 

8 .3 120.83 

7 .4 161.10 

6 .5 201.38 

5 .6 241.65 

4 .7 281.93 

3 -8 322.20 

2 .9 362.48 

tip 1 1 .O 402.75 

5.4.3: ASCERTAIN BALLAST AND WEIGHT DISTRIBUTION 

Ballast weight distribution information was furnished by Carter, as requested (see App. 10). Still. 

all the weights and ballast locations had to be accurately measured and verified, since mass distribution in 

the blade is crucial to its properties. 

The AEI sectioned blade actually consisted of portions of two separate blades (Carter #29B and 

#47A), identical in makeup except for the amount and locations of the lead ballast. There were two types 

of CARTER 300 blade: "mass-balanced" and "non-mass-balanced." The AEI flexural test blade (Carter 

#5l B), was "mass-balanced," and represented the majority of blades in service, so that configuration was 

chosen for the analysis. The ballast weights consist of molded lead inserts for the leading edge, with mass of 

0.8636 Ib/in. and of various lengths. The nondestructive test necessary for finding the ballast locations in 

the test blade successfully used a standard metal detector. Results are given in Figure 5.25. The "massbalanced" blade is very close to the Carter specification, but the "non mass-balanced" series does not match 

the specification, and has further additional weight at the tip. The chordwise ballast cg location was 

determined by measurement. The weight distribution summary is given in Table 5.8 for the Carter "mass 

balanced" 300 kW blade. 
, AEI TEST: # 298 12 22 6.7 J - 

AE1 TEST: MA - I 

AEI TEST: US1 B b-- 

NOTES: (1) Ballast weight is 0.836 Iblin, (2) ballast length indicated in inches. 

FIG. 5.25 CARTER BLADE BALLAST SUMMARY 

TABLE 5.8: CARTER BLADE WEIGHTS SUMMARY 

I (Ib) I (in.) ( I b ) baliast position 

STA Panel I Spar Skin Total 1 % ~allast3 % y~ 

835.454 138.8 

NOTES: 

1. includes root rib and mechanisms 

(27.5 * 5.98) + (22.27 1.75) 

2. adjusted to "mass balanced blade": = 4.09 in. 

47.77 

3. the ballast is centered at the station (i.e., 112 contribution for each adjacent panel) and 

slightly adjusted spanwise for convenience. 

4. Carter Wind Systems estimate 700 Ib. 
5.4 -4: DERIVE CARTER DESIGNED COMPOSITE VALUES 

Carter Wind Systems did not perform a stiffness analysis for this blade design; they relied on , 

allowable ultimate strength values for a specified laminate and load, and performed spot checks on the 

blade, using prescribed loads (unknown cases) and the trapezoidal approximation to section moment of 

inertia, (Ref. 27). The AEI study required a stiffness analysis and section properties; therefore, a blade 

section analysis had to be done based on the manufacturer's specified laminate design. This section covers 

the derivation of the code input. 

The Carter laminate, even though the blade is quite complex, consists of only four types of glass 

reinforcement; derivations of their expected as-built properties follows. 

1) Stvle 60140. 7.5 oz.lvd2 cloth: 

This woven cloth reinforcement has 4Ooh of the glass fibers on the 0° direction (y) and 60% in the 

90°(x). Assuming a layer (ply) thickness of 0.015" (CARTER estimate), a 1-yard square has a volume of 

(36)'(36)'(.015) = 19.44 in.3. The glass in the X-direction amounts to 60% of 7.5 oz. = 4.5 oz. 

Taking the density of E-glass of 0.09838 1b1in.~ (or 1.57408 oz~in.~) and the modulus of 10'10~psi 

gives 2.8588 in.3 of E-glass in the X-direction (90" orientation) for our "standard" square yard. The Emodulus of the laminate is easily found by the volume percentage of glass in that direction: 

aaSS J2U2Ud2 E-modulus 

90" or x direction: 4.5 oz = 2.8588 in.3 El = 10'10~ [2.8588/19.44] = 1 .47*106 

0° or y direction: 3.0 oz = 1.9059 in.3 Ep = 10'10~ [I .9059/19.44] = 0.98'10~ 

The glass content of this ply is: 

4.7647 in.3 (glass) 

glass content by volume = = .2451 */o 

19.49 in.3 (total) 

From the chart (Table 4.1) this gives a ply weight density of 0.05715 lb~in.~. Lastly the Gmodulus is estimated from the engineering chart (Fig. 5.2) and rules of thumb: 

G c 1 .47*106 0.6 (conversion factor for orientation) = 0.882 lo6 psi 

2) Stvle + 45". 10 oz. cloth: 

This bonded ply fiber reinforcement ("KnytexM)has balanced orthogonal properties oriented M5O. Carter 

assumed a layer thickness of 0.020" for this reinforcement. The calculation proceeds as before, except the 

orientation factor decreases the E-modulus by 50% and increases the G-modulus by 2: 
Volume = (36)(36)(.020) = 25.92 in.3 

alass EXrard2 E-modulus 

3.1 765 

90" or x direction: 5 oz. = 3.1765 in.3 E1,2 = (1 0*1 06)(.5)= 0.613*106 

25.92 

3.1 765 

0" or y direction: 5 oz. = 3.1 765 in.3 h,2 = (1 0'1 06)(.5)= 0.613'10~ 

25.92 

where .5 is the orientation correction factor (+45 deg) 

6.353 

glass content by volume = = .2451% 

25.92 

weight density (from chart) = .05715 lb I in.3 

G45O E (0.613 * 106)(110.5)(0.6) = 0.7356 * 106 psi 

GO0 z (.7356 * l0~)(1/0.5) = 1 1 o6 psi 

where 0.6 and 0.5 are the G-correction factor and the orientation factor (Fig. 5.2), respectively. 

3) Unidirectional Ta~e. 13 oz. (Knvtex A-130): 

This ply is the principal spanwise reinforcement in the blade; this is a convenient way to mold 

unidirectional properties in the hand lay-up process. This reinforcement weighs 1 3 oz./square yard, and 

Carter assumed a ply thickness of 0.015 in. The properties are calculated easily in the above manner. 

4) Style woven rovinn.240~: 

Woven roving consists of E-glass rovings (yarns) in an open weave pattern, with balanced orthogonal 

fibers, e.g., 50150. Carter estimated a ply thickness of 0.026 in. for this reinforcement. 

The summary predicted properties for the as-built plies are given in Table 5.9. 

TABLE 5.9: CARTER REINFORCEMENTS, AS-BUILT SUMMARY 

(in.) ('1 o6 psi) ('1 o6 psi) (tb/ina3) 

SrYLE t €0 G P glass % 
-45 

UNI 

* 45 

UNI 

60140 

NOSE LAMINATE L 45 BALANCED BIAS (10 02.) 

UNI UNIDIIREGTIONAL (1 9 OL) 

60140 W40 DIRECTIOW (7.5 oz) M WOVENROVLNO (24a) 

I[ 

I 1 . r I I 

ROOT TIP 

FIG. 526 CARTER BLADE LAMINATE SCHEDULE 

Now given the laminate schedule for the Carter blade (Fig. 5.26), an estimate can be made for the 

properties, thicknesses, and other inputs to the section calculation code. For this blade the PVC foam 

coring (in the aft upper and lower skin panels and the spar web) was ignored, and the laminates at each 

section were assembled ply by ply and then reduced to skin, D-spar, and web contributions. 

Clearly, as the laminate makeup changes, so also do the aggregate properties E, G and p. Therefore, 

an average value for the section properties code had to be chosen. One refinement to the section properties 

code would allow separate engineering values for each station. An example of this variation is shown in 

Figure 5.27 which plots the weight density distribution for the spar portion. Table 5.10 gives the skin and 

spar input values for the Carter design schedule. 
AVERAGE 0.643 -- 

0 2 4 8 8 10 

STATlON 

FIG. 5.27 CARTER SPANWISE WEIGHT DENSITY (SPAR PORTION) 

The unidirectional reinforcement in the skin and the nose webs were included separately. These 

values for each station were estimated as tilted rectangles (I = bh3/12) and summed using the parallel 

axis theorem. This resulted in the web input given in Table 5.10. Another refinement to the code would 

integrate these multi-"webs" as it does for the skin and spar rather than assume rectangles. 

TABLE 5.1 0: CARTER BLADE LAMINATE DESIGN SUMMARY 

=A r/R I SKIN I SPAR I WEBS 

I t (in.) I t (in.) p E G I AT Xg Yg hy lyg 

Root 11 0 1 .070 1 - - - - - - --- --- 1 --- --- --- ..-* --- 

lo .1 1 .070 1 .I42 .0632 1.986 1 .2O3 I 3.916 31.41 2.721 62 1255 

9 .2 1 .070 1 .208.0627 1.756 1.274 15.31228.19 2.04151 869 

8 .3 1 .070 1 .238 .0632 2.071 1.164 1 4.237 23.22 1.54 69.8 421.6 

7 .4 1 .070 1 .I88 .0663 3.039 0.911 f 3.346 19.40 1.01 24.8 202.1 

6 .5 1 .070 1 .I92 ,0646 2.899 .846 1 3.986 16.98 .70 15.51 53.6 

5 -6 1 -070 1 .I66 .0641 3.000 .766 1 3.510 15.07 .58 9.59 104.1 

4 -7 1 .070 1 .I16 .0646 3.086 .739 1 1.277 12.72 .57 2.68 33.9 

3 .8 1 .070 I .060 .0620 2.860 .641 1 .213 6.00 .73 .I25 0 

2 .9 1 ,070 1 .030 .0668 4.250 .400 1 .210 5.38 .71 .I20 0 

Tip 1 1.0 1 .070 f .030 .0668 4.250 .400 1 .202 5.00 .68 .I08 0 

SKIN SPAR WEBS 

~e (~b/in.~) -0572 .0644 ,065 

- 

E ('106 psi) .980 3.0000 3.500 

- 

G (*I06 psi) 1.219 0.8000 -500 
5.4.5: DERIVE CONTRIBUTION OF I-BEAM 

Lastly, the I-beam must be accounted for in the section properties code. The Carter I-beam cross ' 

section is shown below in Table 5.1 1; the beam portion is highly compacted filament-wound rovings, so it 

should have a very high glass ratio (in fact, the highest readily achievable in any glass-resin laminate) of 

90%. The test data and geometric data must be used to find the area, weight, and moments of inertia for the 

I- beam. 

TABLE 5.1 1 : CARTER I-BEAM SECTION DATA FROM TEST 

j (1/4 chord) 1 (in .) 

STA (r/R) 1 % Yg 1 h b w 

1 .I I 16.69 0 I (data lost) 1.562 

2 -2 1 13.20 0 113.88 10.56 2.38 1 .562 

3 .3 1 10.63 0 111.76 8.63 2.38 1.562 

4 -4 1 8.64 0 1 9.76 6.63 1.97 1.562 

From Carter data, the reinforcement of the unidirectional beams consists of 135 wraps of 40- 

strand rovings of E-glass. Therefore, the total number of ends are 135*40 = 5400; so in each beam there 

are 5400 rovings. The measured beam area is 1.562'2.380 = 3.778 in.? Taking the standard weight of 

roving as 450 yardsllb allows a calculation of glass percentage, 

For 450 yardsllb roving the yarn size is = 0.62765'10~ in.21roving (from PE-glass = 0.09838 lb/in.3) 

then: A (5400 ends) = (5400) (.62765'103) = 3.389 in.* 

so: 

This verifies the original assumption 

are, then, from Figure 4.1: 

Euni = 9.115' lo6psi 

Guni = 0.200' 106psi 

puni = 0.09351 Win? 

glass content = 3.38913.71 8 = 91 .I 5OA 

of 90% glass in the I-beam. The engineering values for this laminate 

Adding the small shear web contribution, consisting of mainly +45O plies, changes the aggregate values of 

the 1-beam to 

ELbeam = 9.0 lo6 psi 

%beam = 0.420 lo6 psi 

PI-beam = 0.0935 1b1in.~ 

At this point it is a good idea to make a quick check on this value from a weight comparison. 

&beam length = 194 in. 

weight of uni spars = 2 * 194 ' .09351 - 135 Ib. 

weight of k45O web = 194 * 6 .260 ' .05715 = 17.3 Ib. 

total weight 152.3 Ib. 

This compares favorably with the measured value of 165 Ib, allowing for gussets and fill at the root end. 

7 9 
Next the moments of inertia must be found, since the I-beam principal axis is not placed on the chord 

line because the blade's twisted. The chordline values of I are simply determined from the principal axis 

values of Imax and Imin, using a standard Mohr's circle solution (Ref. 12). This gives the moments of 

inertia (Table 5.12) of the I-beam at each station, in the section (X-Y or airfoil) coordinate system. 

TABLE 5.12: CARTER I-BEAM MOMENTS OF INERTIA 

5.4.6: AEI MEASUREMENTS FOR COMPOSITE SECTION PROPERTIES 

Along with the theoretical design input files developed above from composite engineering analysis, 

an additional input file was constructed on the basis of the blade sectioning measurements. Practically 

speaking, the sectioning allows an independent check of the above predictions (for example, cg, laminate 

thickness, weights) but also will quickly indicate where the actual blade differed from the design (e.g., 

more plies than specified, presence of defects). The section inspection values are listed in Table 5.13 along 

with the specified design values. 

TABLE 5.13: CARTER BLADE: SECTION MEASUREMENTS VS. CARTER SPECIFICATIONS 

(INCHES) 

I h, (airfoil 1 dw(nose I tie I tweb I tskin 

1 thickness) 1 to web) I I I 

r/ R 1 meas. spec. I meas. spec. I meas. spec. [ meas. spec. I meas. spec. 

Note: Blanks are missing data or missing component (e.g., web r 0.1 ) 

Conclusions that can be drawn from Table 5.13 are 

Difference in dw is evident since Carter assumed a distance from junction of the nose to the 

skin, and the actual web distance is inset somewhat. 

Difference in leading edge thickness is because actual blade has a much higher resin content 

than predicted, since it was formed in a deep concave mold with no vacuum-bagging or other 

compacting. 

The actual spar web is twice as thick (less PVC core) since the number of M5" plies was 

apparently doubled over the design vatue. 

The airfoil thickness is very close to the prediction, indicating good tooling and assembly. 

The skin thickness is very close to the prediction, since it was vacuum-bagged (pressure 

formed). 
This information now allows the blade section input values to be ascertained from the test values: 

(1) The new thicknesses and centroid locations (web) are the test values. 

(2) The new E- and G- modulus will be volume weighted to the new thickness since the 

reinforcement hasn't changed but the resin has. 

(3) The resin weight densities are volume-weighted to the measured values of glass content. 

In conclusion, the specified laminate schedule is probably close to the actual blade laminate, but 

there is no way to tell for sure until both AEI and Carter section properties are calculated and the 

deflections compared with the test values. The I-beam contribution is the same, since measured and 

predicted values agreed (see above). 

The initial (trial) values for the AEI blade model are 

Eskin = 4.0*106 psi ESpar = 4.0~10~ psi 

GSkin = 0.5~ o6 psi Gspar = 0.75'1 o6 psi 

Pskin = 0.05 lblin.3 spar = 0.05 lb~in.~ 

The initial values for the inboard I-beam portion are 

Sill UXP) WYP) P 

0.0 37.53 " 106 2817 ' 106 25" 

0.1 37.53 281 7 25" 

0.2 37.53 1980 14" 

0.3 31.59 1755 7.5" 

where: 

(1) El-beam = 9 * lo6 psi 

(2) The skin is assumed to contribute no bending stiffness from the root to 0.35 STA, by Carter 

design intent. 

(3) The I-beam values are carried to the origin. 

(4) The twist angle will affect the values in the true chordwise X-Y system, but the flexural tests 

are really in the principle axes of the I-beam. 

5.4.7: VERIFICATION BY FLEXURAL TEST 

The three bending tests used represent two distributed load cases (total load = 225 Ib and 325 Ib), 

and one torsional load case (50 lb @ STA 0.9 in torsion). This section discusses the bending tests only. 

Again, the test loads were placed on the blade quarterchord. The major deflection was in the flapping 

direction. As seen in Appendix 6, the inplane (chordwise) deflections were very small, indicating very 

little principal axis coupling. However, elastic twists were substantial, indicating the elastic axis was not 

on the quarterchord. 

Two corrections had to be made in the (flapwise) data: 

1) the dead load droop had to be eliminated, and 

2) the root compliance (teeter angle) had to be considered. 

The dead load droop was easily found from (averaged) dead load cases. The root angle was measured 

with the clinometer, with a repeatability better then three minutes of arc. The three flapwise 

distributions and the corresponding elastic teeter values are shown in Figure 5.28. 
FIG. 5.28 CARTER STATIC DEFLECTION: 3 LOAD CASES (CORRECTED) 

As stated above , the flexural stiffness inboard was initially assumed to be provided only by the Ibeam, as conceived by the Carter Wind Systems design. This resulted in predicted blade deflections that 

were much too large. However, by increasing the inboard section modulus in the flapwise direction by a 

"fudge-factor" of 2.67, all three bending cases matched the test data, as can be clearly seen in Figure 5.29. 

2OfF (in) 

I - TEST DATA I 

I V CWSSPEC 

I 

FIG. 5.29 CARTER STATIC DEFLECTION: AEI CALCULATlON VS. MEASURED (CORRECTED) 

8 2 
This is a very interesting result, and indicates that the blade shell js contributing after all to the 

flexural stiffness inboard, actually more than doubling the stiffness of the I-beam alone. This is evidently . 

caused by some transfer of bending moment through the root rib I-beam attachment, allowing some of the 

moment to be carried in the skin. For point of reference, if the root rib were riaidlv attached to the skin 

and the bbeam, the flexural stiffness would have been on the order of 50 times the I-beam stiffness, rather 

than only 2.67. In any case, the root rib joint has to be designed with this additional load in mind. 

Another conclusion from Figure 5.29 is that the Carter design laminate and AH observed laminate 

curves are very close, verifying the overall Carter laminate specification. 

5.4.8: VERIFICATION OF STATIC TWIST 

The corresponding static twist associated with the two bending cases (225 Ib and 325 Ib) above are 

shown in Figures 5.30 and 5.31, along with the Carter and AEI laminate predictions. Note the increased 

scatter of the test data inboard, where the skin profiles were being warped by shear lag, causing the 

templates to drift. However, the match is still very good, verifying the AEI and Carter laminate models. 

A further static torsion test case was also used. The results are shown in Figure 5.32. In this test 

load a point load at 0.70 STA was used, offset from the quarterchord to produce a point moment. This figure 

shows the marked difference in the AEI and Carter design laminate, whereas the distributed load cases above 

really did not. Clearly the AEI laminate values are more accurate than the Carter specs. Note the 

divergence of the test point right on the loaded template, presumably due to local warping amounting to six 

minutes of arc. 

0 

&war-) 

0.2 

0 

FIG. 5.30 

-.-.- TEST 

0 AEI CAtC 

A CWs SPEC 

STATION 

- 

L 

CARTER MEASURED TWIST: (225 POUND TEST) PREDICTED VS. AEI CALCULATION VS. 

SPECIFICATION 
0 

&w-) 0.6 r 

-.-.- TEST 

0.4 0 AEI CALC 

CWS SPEC 

0 

a 1 . 1 I 

FIG. 5.31 CARTER MEASURED TWIST: 325 POUND TEST 

I STATION 

t 

FIG. 5.32 CARTER MEASURED TWIST: TORSION LOAD CASE 

5.4.9: COMPARISONS OF RUNNING MASS DISTRIBUTIONS 

With the estimated weight densities above, the blade running mass distributions for the Carter 

design laminate and AEI measured laminate are compared with the actual running masses from the 

sectioning tests (Table 5.14 and Figure 5.33). 
TABLE 5.14: CARTER BLADE RUNNING MASS COMPARISON (LB) 

STA AFI Calculation CARTFR desian laminate Afl Test 

0.0 2.1 1 1.74 0.838' 

0.1 2.1 1 I .74 6.983' 

0.2 I .69 1.72 2.278' 

0.3 1.42 1.50 1.868' 

0.4 1 .I4 1 .I6 1.868' 

0.5 1.27 1.19 1.657 

0.6 1.07 1.08 1.384 

0.7 0.93 0.86 I .266 

0.8 1.30 1 .I9 1.1 27 

0.9 1.42 1 .I6 1.236 

1 .O 0.61 0.35 1.063 

Total 559.9 Ib 512.7 Ib 835.4 Ib 

NOTES: 

1 ) The total blade weight of 835.4 lb is from test; the (*) items contain mechanisms, 

counterweights, root rib, mid-rib, an amount of potting resin to attach the I-beam. and an 

unknown amount of undocumented extra laminate, all adding up to over 200 Ib of weight. 

2 ) The two calculations contain the outboard ballast weights, but not the inboard ballast 

weights, which were unknown and impossible to determine nondestructively. 

3 ) The two calculations have weights from STA 0.0 to 0.4 which are artificially low since no 

weight density correction was used for the (much denser) I-beam portion. 

-.- TEST 

0 AEIWC 

v CWSWK: 

I I 1 I t 1 1 1 I 1 

SlAllUN 4 I u n 

FIG. 5.33 CARTER BLADE RUNNING MASS COMPARISONS 

However, the only accurate method for determining mass accuracy is in the frequency test comparisons 

below. 
5.4.1 0: VERIFICATION BY FREQUENCY OF VIBRATION TESTS 

The frequency of vibration tests resulted in the first three fundamental modes in flap and lead-lag, ' 

well-separated; two fundamental torsional modes were also produced: one called "root torsion" in which the 

blade performs as a rigid body about the I-beam root segment at the root rib, and the next called "outboard 

torsion" in which the outboard blade oscillates about the midblade, under the major influence of the 

outboard ballast weights (See Figure 3.15). 

The frequency comparisons are given in Table 5.15 for 

1 ) The Carter design laminate and weights. 

2 ) The AEI calculated value. 

3 ) The AEI calculated value with no ballast. 

4 ) The AEI calculated laminate and measured weights. 

5 ) The test results. 

As can be seen, the following conclusions can be made about the flap values: 

1 ) All the calculated values had lower masses than the actual blade and thus had higher 

frequencies of vibration. 

2 ) The calculated value with ballast weight omitted ("AEI-No ballast") had the highest 

frequencies of all, as expected; this illustrates the degradation of blade natural frequency by 

adding ballast weights. 

3 ) With the correct (measured) mass distribution, which includes over-specified resin, 

mechanisms, and so on the flap frequencies are correctly predicted. 

TABLE 5.1 5: CARTER BLADE FLAPWISE FREQUENCY COMPARISON 

Mode Test CARTER AEl AEI AEI 

design cafc no ballast test weights 

1st flap 

2nd flap 

3rd flap 

1 st lag 3 .OO 3.08 3.1 6 3.03 

2nd lag 16.0 12.63 19.79 17.56 

3rd lag 40 -4 33.01 51.78 43.74 

root torsion only 13.25 

I st outboard torsion 1 9.74 19.76 15.3 14.89 

The conclusions about the lead-lag values are similar; the test weights correctly predict the frequencies. 

For the torsional frequencies, these conclusions can be drawn: 

1 ) The root torsion (rigid body mode) was not predicted since root torsional rigidity GJ was not 

reduced to the I-beam value in the code. This was not considered realistic for the blade study since 

this motion is really a change in root pitch and not an elastic twist. However, this frequency 

(degree of freedom) with the Carter dashpot snubber in place will cause the root pitch to change 

slightly when the blade is in operation. Actually this vibration mode directly affects the root pitch 

setting and the operation of the pitch-up snubber mechanism in the field, and is bound to be 

troublesome to the tutbine on both counts. 

2 ) The torsional frequency is correctly predicted by the Carter design specification, but not by the 

actual blade weights. The error is in the actual placement of the "extra mass" seen in the section 

test weights. They were assumed to be added to the section cg, but in actuality were close to the 

elastic axis, thus decreasing section mass moment of inertia. This is not considered to be a large 

mismatch or error since all the other torsional values do check with the data. A refinement in the 

Carter 300 model would iterate with the "extra masses" to find a new cg (and section mass moment 

of inertia) to raise the torsional frequency slightly. 
The final blade weights (cumutative), section running mass, and section cg's are given in Table 

5.1 6. 

TABLE 5.16: CARTER BLADE: FINAL MASSES AND SECTION CG'S 

r/R STA I Cumulative Weight I Running Mass I Section cg 

I AEI model Test I AEl model Test I AEI model Test 

root 0.0 11 I 

0.1 I0 I 

0.2 9 I 

0.3 8 I 

0.4 7 

0.5 6 

I 

0.6 5 

I 

I 

0.7 4 I 

0.8 3 I 

0.9 2 I 

tip 1.0 1 I 

5.4.11: FINALAEROELASTICMODEL 

The final values of the Carter 300 aeroelastic blade model are shown in Table 5.17. 

TABLE 5.1 7: CARTER BLADE: FINAL AEROELASTIC BLADE MODEL 

STA r P mo Elf lap Q3 ycg yea 

(in.) (deg) (sluglin.) (1 psi) (1 06 psi) (1 06 psi) 

b3 

root 1 1 0 

10 40.3 26.1 

9 80.6 15.5 

8 120.8 9.4 

7 161.1 4.5 

6 201.4 2.3 

5 241.7 2.0 

4 281.9 2.0 

3 322.2 2.0 

2 362.5 2.2 

tip 1402.8 2.6 
6.0 ELASTIC TWIST CALCULATION 

6.1 : GENERAL 

After the blade structural models were developed, the next step was to calculate the expected elastic 

twist under normal operating wind turbine conditions. This was assumed to be steady-state (e-g., gravity 

and cyclic loads were not considered). This task consisted of calculating the blade section pitching moments 

and forces, and then calculating the elastic twist due to those applied loads. These bads are both inertial 

and aerodynamic. This was the primary theoretical goal of the project and had to be theoretical since no 

flight testing was done. Briefly, the inertial and aerodynamic loads were used with the structural 

deflection program described above to obtain the elastic twist due to each component of loading in order to 

ascertain design significance; that is, to point out where most of the elastic twist in fliaht originates. 

6.2: CALCULATION OF BLADE CENTRIFUGAL TENSION AND MOMENTS 

The inertial loads on the blade sections are caused by centrifugal forces (and moments) acting on the 

mass elements. This section derives the centrifugal loads on a flying blade (see also Ref. 28, for example). 

Up to now the analysis has been static, with beam mass and stiffness properties expressed, calculated and 

verified. Now the mass properties are combined with the operating condition to give the inertial blade 

loads. 

Consider the discrete lumped mass blade shown in Figure 6.1, which is the easiest way to express 

centrifugal forces. The figure shows an undeflected lumped mass blade at precone angle Ppc, rotating at 

angular speed 112 about the z-axis. The root reactions are F, and M,, or centrifugal force (tension) and 

moment. Mass elements at radius r, and flap deflection z, have an inertial centrifugal force of mnr,-&22, as 

shown. 

FIG. 6.1 DISCRETE LUMPED MASS CASE 
Basic static theory states 

and the centrifugal moment at any mass element n is 

n-1 n-1 

= Fcent i zi - C Fcent i zn 

i=l i=l 

These expressions can be generalized to a continuum form, just by imagining many lumped masses, (which 

in the limit are differential elements) and by starting the integration at the blade tip rather than the root. 

Note: here x = R - r and is zero at the tip.) 

Blade Tension at x = J rn r Q2 dx 

Blade Moment at x = J m r R* z dx - z(x) ' [Blade Tension] 

The above expressions can be easily checked by hand with a simple blade, such as the uniform UTRC blade. 

Referring to Figure 6.1, it can be seen that the calculation algorithm does not change if the blade 

shape is curved, as it will be when under the combined action of section forces and moments. The 

calculation program starts with an undeflected (straight) blade and then allows it to deflect in flap, lag, and 

twist until a loop convergence is reached (Appendix 10.5). 
6.3: DERIVATION OF SECTION TORSION 

There are, in general, five significant points on the blade section: 

mass center - Cg 

shear center - point about which no section torsional deflection is incurred with bending 

aerodynamic center - quarterchord 

control axis - axis defined by root fixation or pitch bearing 

blade axis - axis defined by original layout (placement and twist) of the blade airfoil 

shape (usually determined by construction considerations). 

Clearly the first three above are not necessarily straight line loci on the blade, but the last two are (Fig. 

1.4). For purposes of calculating the elastic twist the control axis was used. It is defined by the centroid 

of the blade root fixture as it would be if a pitching bearing were used. Then the elastic twist can be 

directly added or subtracted from the pitch angle changes. Thus, the four points that must be known or 

determined for each blade section are cg, shear center, aerodynamic center, and control axis. The cg's and 

shear centers are calculated in the section program above. The aerodynamic center is placed at the 

quarterchord, and the control axis is specified by the blade fixture. The section airfoil offsets, which 

locate these centers relative to each other are also input to the program. 

The section torsion that causes elastic twist is most easily calculated relative to the shear center of 

the section. This would be the "elastic axis" of a uniform blade. The above is true because torsion can be 

produced by a section force only if the line of action of the force does not pass through the shear center. 

Section moments then are all added together and must be resisted by an equal and opposite elastic moment at 

that section's shear center. The calculation then proceeds, introducing the section torsional stiffness GJ, 

which then gives the differential elastic twist for that section. To determine the total elastic twist, these 

section values must be integrated starting at the blade root. 

plane of 

rotation 

angle to 

principal 

axis 

ac,ca cg shear center 

FIG. 6.2 BLADE SECTION FREE BODY DIAGRAM 

The differential section steady torsional moments are shown in Figure 6.2, the section free body 

diagram (see Ref. 2 for a complete derivation): (Note: the offsets YI and YA have been simplified for 

clarity.) 

1. Aerodynamic forces in flapping (Fflap) and lead-lag (Fiead-lag) act at the aerodynamic 

center, with a moment arm to the shear center, YA cos0. 

2. Aerodynamic moment (Ma) acts at the aerodynamic center and is directly translated to the 

shear center. 
3. The primary centrifugal moment is due to the vertical force component (flapping deflection) 

and is simply the product of the section force r R* P dm times its moment arm from the 

shear center YI cose. 

4. The secondary centrifugal moment is due to the horizontal centrifugal force component, and 

comes from the vertical distribution of mass around the elastic axis; this is shown as Y1 a2 

dm in the free body diagram. This force is depicted in the following sketch: 

5. The third part of the centrifugal moment is the "tennis racket" or propeller moment, I, ~2 

8, where lo is the section pitching mass moment of inertia about the cg and 8 is the angle 

from the plane of rotation to the section's principal mass axis. Tennis racket moment is 

simply caused by a pitch (or a twist) rotation of the section mass away from the plane of 

rotation, which produces a centrifugal force couple on the mass elements above and below 

the plane of rotation tending to reduce pitch, This moment is zero when 8 = 0, or when the 

plane of rotation passes through the principal (major) mass axis of the blade (which is also 

referred to as the section principal axis of inertia). See the following sketch: 

These are the steady torsional moments acting on the section to produce local twist. These torsional 

moments are calculated in the second part of the STRESS ELASTIC program, and the deflections are then 

found and integrated to obtain the elastic twist distribution of the blade. The ~im~iified moment arms YI and 

YA from Figure 6.2 are not used in the program, which includes instead all the section moment arm 

contributions (e.g. x,y components). 
The section ballast weight contributions are done as separate calculations in the program to allow 

separate assessment of their effects by the blade designer. A ballast weight in the leading edge, for 

instance, adds to the tennis racket moment and has both the horizontal and vertical centrifugal components 

as above, again on their (new) moment arms to the shear center. [The basic tennis racket moment, if 

transposed to the shear center using the parallel axis theorem, confirms the horizontal centrifugal 

component described above (see Ref. Z).] 

Each elastic twist contribution is listed in the program output to assess its individual significance: 

Aerodvnamic Contribution includes torsion due to lift force, inplane aero force, and 

aerodynamic moment. 

Centrifuaal Contribution includes the basic section torsion due to horizontal and vertical 

centrifugal force (less ballast). 

Tennis Racket Contribution includes the basic section tennis racket torsion (less ballast). 

Ballast Contribution includes all the contributions of ballast weight, including 

centrifugal (horizontal and vertical) and additional tennis 

racket moment. 

AERODYNAMIC LOADS 

The aerodynamic section loads were calculated with a strip theory similar to the PROPPC code (Ref. 

7 and next section) since PROPPC has no section pitching moment calculation. The loads were output 

(expressed) as distributed load at the aerodynamic center (e.g. Win. or in.-lblin.) along the span. The 

airfoil c~/Cd section data were corrected by the aerodynamic consultant (S.J. Miley) to reflect airfoil 

deviations noted in the laboratory inspection of the blade airfoil section (Appendix 10.6). At and above 

stall no reliable theory exists; SERl had anticipated this and specified post-stall routines for the code (see 

Sec. 7.1). 

This is shown as an example to describe the format: 

Heading- "UTRC blade @ 30 mph load" 

rotor speed (Q) = 1 1.31 radlsec = 108 rpm 

pitch angle = 0 degrees 

coning angle = 5 degrees 

The output by station is listed from tip to root, station 1 to 11; this divides the blade into 10 equal 

segments. The top line shows the radius value measured from the tip to each station (thus the root value is 

the radius of the rotor: 192 in. or 16 ft). 

Blade section aerodynamic load is listed next, in X, Y, and Z directions (tension, lead-lag and flap) 

and pitching moment, all referenced to the quarterchord. These loads are the output of the aerodynamic 

strip theory. The remainder of this part gives the section stiffness and geometric properties. Bending and 

shear centers (elastic axis) are given next. It can be seen that this is a uniform blade; the values are 

constant for the outer 70% of the blade, which represents the pultrusion portion. The inner 30%, for the 

UTRC rotor, consists of a flexbeam with different properties, Weights, cg's, and moments of inertia are 

followed by a ballast weight section (for this blade the ballast is zero, as can be seen). Finally, the 

running "blade weight" line ends with the total blade weight (76.9 Ib), which was verified in the bench 

test. 

The aerodynamic flapping shear and bending moments are given next. [Note: these must be 

integrated from the tip, as shown.] The root values are the aerodynamic hub shear (400 Ib) and bending 

moment (54,367 inch-lb) for this condition. Next, the simple blade deflection is given, that would occur 

with the aerodynamic load alone (e.g., -0.2 in. inplane and 292 in. in flap) to compare with actual blade 

deflections. The final line of this part gives the flap deflection due to coning angle (e.g. 16.7 in. at the tip). 

These are the initial trial values of blade flap deflection. [Note: In this case the trial value is not realistic: 

292 in. of flap deflection is fwic;e the rotor radius! The linear beam assumptions have clearly been 

violated by the large airload at 30 mph; as seen below, the aeroelastic moment is largely counteracted by 

the centrifugal moment bringing the algorithm back into its assumption bounds.] 

The next four parts of the output list all the blade section pitching moments (in in.-lb, positive 

nose-down) : 

Aerodynamic pitching moment. 

Aerodynamic moment due to lift offset from shear center (total aerodynamic moment). 

Inertial centrifugal moment due to tennis racket effect. 

Inertial moment due to flap deflection. 

Inertial moment due to lead-lag deflection (total section inertial moment). 

Inertial moments due to ballast. 

Total section inertial moments due to tennis racket, flap deflection, lead-lag deflection. 

Total inertial moment. 

Total section moment, or the sum of the inertial and aerodynamic contributions 

1Notg: on this blade at the tip, the aerodynamic moment is 11 in.-lb nose up and the 

inertial moment 9.65 in.-lb nose down, yielding 1.4 in.-lb nose up net section 

moment.] 

The torsion is just the integration of the section moment distribution and appears next. Following 

is the elastic twist in degrees. [Note: this case, 30 mph, has only 0.25 degrees, nose up, elastic twist at 

the tip.] 

The following five lines give the blade structural reactions at each station: 

tension (Ib) 

lead-lag shear (Ib) 

iead-lag bending moment (in.-lb) 

flap shear (Ib) 

flap bending moment (in.-lb) 
The root values constitute the steady hub loading specification for this operating condition. This 

example shows the UTRC hub experiencing 2564 tb of centrifugal force (tension), 56 lb of lead-lag shear, 

8847 in.-lb of torque, 400 lb of flapping shear, and 4880 in.-lb of flap bending moment. 

Following the principal axis angle and the MIEI values, the blade flexural deflections are given in 

inches, for lead-lag and flapping. This blade has 0.52 in. of inplane deflection and 30 in. of flap deflection. 

The elastic twist denotes the torsional deflection of this blade. It can be seen that the bulk of the 

twist occurs in the softer flexbeam portion. This is more obvious in the other UTRC cases that experience 

greater elastic twist. 

Clearly, the centrifugal moments of this blade have reduced the tip deflection via centrifugal relief, 

which was the design intent. It should be noted that the flap deflection is not a straight line, since it 

represents the equilibrium position of a complex blade operating under complex aerodynamic and 

centrifugal loads. 

UTRC BLADE DEFLECTIONS 

The simplest blade is a uniform pultrusion connected to a torsionally flexible beam at its root (.30 

STA). The shear centers (elastic axis) and mass centers are collinear and likewise the inertial terms. The 

flap deflection and elastic twist for the UTRC blade are given in the Tables 6.1 and 6.2 below and plotted in 

Figures 6.4 and 6.5 for wind speeds from 10-70 mph (pitch = 0 degrees, coning = 5 degrees). 

TABLE 6.1 : UTRC FLAP DEFLECTION (in.) 

V,(mph) Root . Tip 

- -- --- 

TABLE 6.2: UTRC ELASTIC TWIST (DEGREES) 

VO (m~h) Root Tip 

The flap deflections (and lead-lag deflections not shown) are easy to understand. The aerodynamic 

bending moment increases with increasing wind speed, and the centrifugal moment does not. Therefore, the 

tip deflection increases as the aerodynamic moment increases. The static tip deflection due to straight 

coning angle is 16.7 inches (5 degrees); the 10 mph values above are less than this, indicating the 

centrifugal moment is dominating the aerodynamic moment at 10 mph. This is borne out by examining the 

root flap moment for these cases, reproduced here from the printouts: 

VO (m~h) Root Flap Moment (in-lb) 

The elastic twist is more complex. Not only do the gradients change along the blade, but also with 

wind speed; the tip elastic twist is large at 10 and 70 mph, but nearly nothing at 30 rnph. To discover the 

sources of this twist, each section moment must be examined over the range 10-70 mph. Referring to 

Tables 6.1 and 6.2: 

at 10 m~h: 

The 16.7 in. of static flap coning are reduced to 8.2 in. by centrifugal relief. Section twisting 

moments are dominated by the airfoil pitching moment (NACA 23012) and' the centrifugal moment 

due to flapping, both nose down. About one-third of this is offset by a nose-up lift moment due to 

aerodynamic center offset. The other section moments are negligible (tennis racket, lead-lag). The 

net nose-down moment amounts to 290 in.-tb of torsion at 0.30 STA, twisting the flexbeam about 

3.1 degrees. An additional 0.2 degrees of twist occurs in the much stiffer pultrusion portion of the 

blade. 

30 mph: (see Fig. 6.3): 

The airfoil pitching moment has not changed appreciably, but the lift offset moment is much greater 

since lift is much greater. Thus the net aerodynamic moment is now large and nose up. This is 

nearly offset by a large nose-down centrifugal moment, now made larger than above since the flap 

deflection is four times as great. Tennis racket and lead-lag are again negligible. The net elastic 

twist is slightly (0.25 degrees) nose up. 

60 m~h: 

The aerodynamic pitching moments have not changed drastically from above. But, the centrifugal 

flap-deflection moment has increased since there is greater flap bending. Now the net moment is 

again nose down, amounting to 290 in.-lb at 0.30 STA and yielding about 2.6 degrees of elastic 

twist. The distributions are not linear in any case since the net torsion is the sum of individual 

nonlinear values (e.g., lift, pitching moment, flap bending). 

6.7 ESI BLADE DEFLECTIONS 

The ESI blade was of vacuum-bagged, wood (Douglas fir), veneerlepoxy internal construction and 

was easily the stiffest blade tested. This rotor blade was in service at two operating speeds: 77 and 90 

rpm, corresponding to 54 and 85 kW rating; the rpm difference greatly affects the deflections via the 

inertial and aerodynamic loads. No ballast was used in either approach; however, two versions of the 

overspeed tip mechanism (tip flap) were used. These are depicted in Figure 5.19: the "regular tip" was a 
simple steel alloy flat plate on a hinged springhelease mechanism, and the "whisper tip" was a much 

larger fiberglass fairing over a larger baseplate and release mechanism. The regular tip weighed 10.06 lb 

and the whisper tip 17.44 lb, with the cg of the latter being forward of the former (1.22 in. vs. 5.93 in. 

aft of LE; see Fig. 5.19). 

TABLE 6.3: ESI TIP FLAP DEFLECTION 

77 rpm: no tip 26.7 31.5 35.8 38.8 40.5 41.1 41.9 

regulartip 25.5 29.9 33.9 36.7 38.3 38.9 39.6 

whisper tip 24.7 28.9 32.7 35.4 36.9 37.4 38.1 

90 rpm: no tip 25.4 30.7 35.7 39.9 42.7 44.3 44.9 

regular tip 24.0 28.8 33.4 37.2 39.7 41.1 41.7 

whisper tip 23.3 27.6 31.9 35.5 37.9 39.2 39.7 

TABLE 6.4: ESI TIP ELASTIC TWIST 

vo (m~h) 10 2 0 30 4 0 50 6 0 70 

77 rpm: no tip .I 1 .06 .OO -.03 -.02 .10 

regular tip .OO -.08 -.I5 -.20 -.I8 -.07 

whisper tip .25 -22 -1 9 17 -1 9 .31 

90 rpm: no tip .17 .10 .02 -.05 -.I0 -.05 

regular tip .02 -.08 -.I8 -.27 -.33 -.29 

whisper tip .35 .31 .27 .24 .2f -27 

No Tip: This case was run to separate the tip weight effects on the deflections. The static coning of 

5" gave 28.2 in. of flap deflection; at 10 mph the centrifugal relief again dominates, giving a negative root 

bending moment and a tip deflection less than the coned value. As wind speed increases, aerodynamic load 

increases, faster for the 90 rprn case. The flap deflections bear this out. The 90 rprn case has lower 

angles of attack at 10 - 30 mph, and as wind speed increases, the 77 rprn version stalls first and sheds 

airload. Thus the 90 rprn version has a higher eventual tip deflection (44.9 in.). However, this is still a 

small number since almost half of this value is due to static coning. The root bending moment for this 70 

rpm case is a huge 257,000 in.-lb (i.e. this is a 2067 lb flap shear load). This certainly must be a very 

stiff blade; for this highest load case, the root laminate strain is less than 1400 microstrain! The root 

tension (centrifugal force) is 8100 lb at 90 rpm. This is a further indication that the blade is not heavy. 

The elastic twist is always negligible for this blade and is dominated by the simple airfoil pitching 

moment (NACA 230XX variation airfoil). As would be expected the twist increases rapidly in stall, which 

can be clearly seen in the 77 rprn case at 60-70 mph. [Note: these twists are so small that a difference of 

only 1 in. of tip deflection reduces it by 70%; compare the 77 and 90 rpm, 10-mph case] 

Reaular Tip: Adding only 10 Ib to the tip at a chordwise position of 5.93 in. and some section moment of 

inertia are the only differences from the above values. As would be expected the centrifugal force at 90 

rprn (root tension) goes up from 8100 to 8840 Ib and the root bending moments decrease (e.g. 232,000 

vs. 257,000 in.-lb). Again the flap deflections are always less than the runs without tip weight. (Note: 

this is the traditional reason to add tip weight to helicopter blades -- to reduce tip deflection.] The root 

laminate strains are also less than before since the flexure is less than with no tip weight. 
The elastic twist is more complex. First, adding the weight to the tip is only part of the story; the 

additional section moment of inertia also depends on the chordwise distribution of the weights (e.g., tip 

parts; see Sec. 5.3.7). So each mechanism part had to be calculated independently to get the "ballast" 

moment of inertia. The elastic twist values are now clearly dominated by the tip ballast via centrifugal 

twisting moments. As can be seen in Figure 6.6, the elastic twist occurs almost entirely in the outer 2OoA 

of the blade. This is because the "ballast" has been added as a point load at the tip. This means that the tip 

twist is only an approximate indication of the overall blade effect, even though the highest airload occurs at 

the blade tip. Still these twists are small (0.33 degree or less). 

8 

(degrees) t 

STAT1 ON 

FIG. 6.6 ESI ELASTIC TWIST DISTRIBUTION 

The effect of stall can also be seen, as the 77 rpm (more stalled) blade at 60-70 mph has a nosedown twist compared to the 90 rprn (less stalled) blade. 

m: The whisper tip is about 7.5 Ib heavier than the regular tip. This increased tip weight 

reduces the flap deflection even more, and increases the root tension slightly (8100 Ib no tip, 8840 Ib 

regular, 9390 Ib whisper tip, at 90 rpm). The root bending moments are also reduced by the various tip 

weights (171,000 to 148,000 to 133,000 in.-lb). 

The other important difference is the cg location of the whisper tip. The additional weight is 

forward of the section cg and shear center; in fact it is almost on the leading edge (1.92 in. from LE). One 

would expect a far-forward tip mass to produce a large nose-down pitching moment with flap,deflection. 

This can be easily seen to be the case by looking at the elastic twist results in Table 6.4. All the twist is 

now nose down, and amounts to about 0.33 degree. Still this is a small value and would not be expected to 

affect performance very much. It does, however, produce section torsion which increases the laminate 

(veneer) shear strain. 

Some unpublished flight test strip chart data were available from ESI tests on the 90 rpm, whisper 

tip version (Ref. 26). They showed an average torsion at 0.90 STA to be about 50 ft-lb (600 in.-lb) 

nose-down at 20-25 mph. The calculations show for this condition: 90 rpm, whisper tip, 0.90 STA, 20 

rnph, a blade torsion of 36.9 ft-lb (443 in.-lb) nose-down, which compares very favorably with the data. 

CARTER BLADE DEFLECTIONS 

The Carter blade was by far the most complicated of the test series. This blade was made up of 

various laminates of vacuum-bagged glass reinforcements in an epoxy matrix. The makeup and detailed 

structural arrangement of the blade are fully described in Section 4.4. The flap and lag deflections and 

elastic twist for wind speeds of 10 - 70 rnph are given below in Tables 6.5, 6.6 and 6.7 for the operating 
value of 2.0". [Note: all deflections were corrected to the control axis (quarterchord) of the blade. Also 

the 50, 60, and 70 mph cases must be considered somewhat academic since the turbine does not operate at 

those wind speeds.] 

The clearest result seen is the increase of blade bending, both flapwise and edgewise, with 

increasing wind speed. The negative inplane deflections denote forward bending, i.e. positive torque on the 

rotor shaft. Realistically, with tip deflections of 6 ft, the blade can no longer be considered an actuator 

disk (e.g. as in PROPPC code) and some aerodynamic load relief due to flap bending must be occurring, This 

probably tends to reduce angles of attack, inplane loads, and the power output. So the power output 

calculations must all be suspect for this highly flexible blade above 30 mph. This discussion will, 

therefore, focus on the design and elasticity of the structure rather than the power output. 

TABLE 6.5: CARTER FLAP DEFLECTION (IN.) 

TABLE 6.6: CARTER LEAD-LAG DEFLECTION (IN.) 

Vo (mph) Root . Tip 

TABLE 6.7: CARTER ELASTIC TWIST (DEGREES) 

Vo (mph) Root . Tip 
Figure 6.7 shows the spanwise elastic twist and Figure 6.8 the pitching moment distributions of 

this blade for 10 and 30 mph; the corresponding distributions of section moment and the major 

constituents are also given in Table 6.8. 

3.0 

8 

(degrees) 

2.0 

1 .o 

0 

STATION 

FIG. 6.7 CARTER ELASTIC TWIST (1 0 AND 30 mph CASES) 

TABLE 6.8 : CARTER BMDE SECTION TORSION COMPONENTS 

Vo = 10 mph Root . Tip 

AERO PITCHING MOMENT 0 7.5 11.3 13.3 13.3 14.5 15.2 16.6 18.9 21.6 21.6 

UFT OFFSET 0 1.9 -.2 -2.3 -1.6 -4.2 -3.8 -2.4 -4.1 -8.7 -8.9 

TENNIS RACKET 0 -.I -.I -.I -1.3 -.6 -.4 -.3 -.2 -.4 -.4 

FIAP DEFLECTION 0 6.4 -.2 -.4 .7 9.1 7.8 7.4 8.9 12.8 10.8 

TOTALS: 9.8 10.8 10.6 11.2 18.4 18.7 21.1 23.3 24.9 22.9 

Vo = 30 mph Root . Tip 

-- - 

AEROPITCHINGMOMENT 0 14.5 14.3 14.3 14.0 13.8 14.5 16.9 19.5 22.1 22.1 

UFT OFFSET O -26.5 -23.9 -21.8 -20.2 -29.7 -25.2 -17.4 -26.9 -52.4 -50.0 

TENNIS RACKET 0 0 0 0 -1.3 -.6 -.4 -.3 -.2 -.4 -.4 

FLAP DEFLECTION 0 9.7 -.5 -.8 2.1 28.2 26.4 26.3 33.4 50.2 43.8 

TOTALS: -8.4 10.2 -8.4 -5.4 11.3 15.1 25.4 25.5 19.2 15.3 

10 m~h Case: The tip deflections are small for this case; the flap value is 15.1 in., which is less than the 

28 in. from coning, so the flap root moment is -live. The lead-lag moment is positive, or aft, indicating 

negative power output. 

Surprisingly, the elastic twist is the highest for any wind speed case: over 2" at the tip. Referring 

to Table 6.8 allows a closer look at the moment components. The angles of attack are in the lifting range, 

and there is substantial (nose-down) aeroelastic pitching moment all along the blade, since its large root 

chord and twist keep the aerodynamic values high. This indicates a well-designed blade, or one where all 

the blade sections operate close to the same angles of attack (i.e. "work together"). The next line in the 

table is moment due to lift offset, or quarterchord to elastic axis. This offset is appreciable, with the shear 
center being aft of the quarterchord (see Sec. 4.4). However this moment is small at 10 rnph owing to a 

relatively small lift value. 

lnertially (centrifugally) speaking, the only appreciable moment arises from flap coupling. Tennis 

racket and inplane coupling are small and can be neglected here (see line 3). The fourth line in Table 6.8 

shows that the flap coupling term is slightly nose-up inboard; this is due to the section cg being aft of the 

shear centers inboard. Outboard the situation is drastically reversed, since substantial lead ballast has 

been added to the leading edge (see Sec. 4.4). This has brought the cg forward of the shear center, which 

creates a nose-down flap coupling moment. The net result of all the terms is a substantiai nose-down 

moment, which causes substantial elastic nose-down elastic twist. 

All the section centers and the forces and moments are shown as free body diagrams in Figure 6.8 

for station 0.90. Referring to the figure: the small lift (2.0 Ib) acts through the aeroelastic offset (4.4 

in.) but is not enough to counter the aeroelastic pitching moment (21.6 in.-lb) and the centrifugal flap 

coupling moment (12.8 in.-lb), both of which are nose-down. The net result is a relatively smooth 

moment distribution which is always nose down (Fig. 6.9). 

10 MPH 

LIFT 11.3 

4 

-- 

HA CENTRIFUGAL MOMENT 

FIG. 6.8 CARTER SECTION FREE BODY DIAGRAMS 
NET MOMENT (INCH-tB/INCH) 

30 

NOSE 

DOWN 

20 - 

STATION 10 

NOSE I 

FIG. 6.9 CARTER PITCHING MOMENT DISTRIBUTION(10 AND 30 mph CASES) 

30 mph (;ase: For this case the tip deflections are much greater; this is a load case near the rated 

output of the turbine, and the tip deflection is over 5 feet. The root flap moment is 10,558 fi-lb; the flap 

shear is 2990 lb. The root lead-lag shear is 1824 lb, and the inplane moment (which gives rotor torque) 

is abut twice the size of the flap moment. Here is an illustration of the advantage of a flexible blade: this 

blade is flexible in the flap direction, so the loading is largely relieved by centrifugal force; the inplane 

stiffness is high, so the inplane deflection is low. Very little root load is relieved. 

Surprisingly, the elastic twist for this case is less than at 10 mph. The aerodynamic loads were 

much less. The reason can be seen in Figure 6.8, the lift force is much greater, thus the lift offset term is 

large. The flap coupling term is also larger (50.2 in.-lb) but it is practically canceled by the offset term. 

The net moment distribution can be seen in Fig 6.9; the moment relief due to lift is easily seen. 

Effect of Ballast: The effect of removing the ballast on the elastic twist can be seen in Figure 6.10, which 

shows the net section moment and elastic twist for the same blade but now with no lead ballast outboard. 

The elastic twist is now nose up rather than nose down as above. 

This is because the centrifugal moment is now much less because the weight is less and the cg is 

much farther aft (closer to the shear center). Referring to Figure 6.8, the free body diagram for 30 mph 

looks the same except now the centrifugal moment is only 2.9 in.-Mn. rather than 50.2 in.-lblin. (with 

ballast). With no ballast the nose-up lift offset dominates and the result is nose-up elastic twist. 

It is clear that the chordwise position of the ballast can be adjusted (slightly aft) to ~ornpw zero 

the elastic twist, if that becomes the wish of the designer. [Note: this would only be strictly true at one 

wind speed, since the lift vector changes and the centrifugal moment does not (except for flap deflection 

contribution)] 

Finally, the major designer's reason for the lead ballast can be easily seen in the flap defiection 

results. Without the ballast this flexible blade, under the 30 mph loading, would have a tip deflection of 

over 10 feet; by adding the ballast this tip deflection is reduced to 61 in. A secondary effect of reducing 

the flap deflection is to also reduce the flap coupling term above. 
7.0 PERFORMANCE CALCULATIONS AND RESULTS 

The last phase of the project used the adjusted twist distributions of the blades to determine the 

adjusted blade aerodynamic loading and wind turbine performance. We used the current PROPPC.FOR 

computer code and airfoil CL/C~ data sets specified by SERl and the consultation on aerodynamic corrections 

due to airfoil shape errors documented in the first phase. Adjusted rotor performance and loads were 

compared to unadjusted loads, and the aerodynamic loading set used to generate the elastic twist was 

adequately verified. 

7.1 : AERODYNAMIC CALCULATIONS 

This phase finally applied the elastic twist results to rotor performance calculations to modify the 

wind turbine performance and assess the effect of elastic twist. Four post-stall airfoil CllCd 

characteristic options were used, as specified by SERl (Fig 7.1 and Refs. 29-31): 

A Standard 2-D table data with flat plate stall algorithm. 

B. Standard 2-D table data with NACA 0012 stall values from wind tunnel test. 

C. Viterna post-stall synthesization routine. 

D. Viterna/Tangler post-stall routine. 

Each operating case was run for each of these, for each rotor, to determine the baseline performance. The 

cases were then rerun using the adjusted elastic twist results. Comparison of the post-stall synthesization 

routines can be seen in Figures 7.2, 7.3, and 7.4. The experimental 2-D lift and drag data which were 

input to PROPPC are shown in Table 7.1 

TABLE 7.1 : AIRFOIL LIFT AND DRAG DATA lNPUT TO PROPPC 

Carter 300: STA 1-5 NACA LS(1)-0417 STA 6-10 NACA LS(1)-0413 

ESI : STA 1-7 NACA 23024 STA 8 NACA 23021 STA 9 NACA 2301 8 STA t 0 NACA 2301 5 

UTRC 8: STA 3-1 0 NACA23112 (most of STA 3 is part of the flexbeam) 


POWER (W) 

~11r1r11111lr1rlll171 

5 10 15 20 25 

WINDSPEED (m/s) 

FIG. 7.4 CARTER: COMPARISON OF POST-STALL ROUTINES 

For the Carter 300, lift and drag data for the LS(1)-0417 and -0413 were used to approximate 

the sections, which varied from -0421 at the root to -0413 at the tip. The ESI 54 has a different airfoil 

(NACA 230XX) at each station, and was approximated by four airfoils. The problem here was that the 

inboard sections had up to 44% thickness and no experimental data were available; the thickest airfoil in 

the available literature, 24%. was used. Since the UTRC 8 was a constant chord, zero twist blade (NACA 

231 12), the lift and drag data were simpler. When the lift and drag data determined by Miley were used, 

section data from STA 6-1 0 were replaced for the Carter 300, 7-1 0 for the ESI, and all sections for the 

UTRC 8. Lift and drag coefficients from the static experimental data were used corresponding to the 

Reynolds numbers for all those stations. Tip and hub losses were included. All units were operated at 

essentially constant rpm. 

For each wind turbine, predicted power curves were obtained with the four different post-stall 

routines: flat plate, Viterna, Tangler, and 0012 experimental data. The output at each station (angles of 

attack, lift and drag coefficients, thrust, torque moments and power) were obtained for 5, 10, 15, 20, and, 

25 m/s. 

The Tangler and Viterna methods gave similar power outputs at high wind speeds for all three 

blades. Both methods predicted higher power than the flat plate and attached 0012 data, which is consistent 

with power curves obtained in the field. Even though the flat.pllate and attached 0012 data are included in 

the graphs, the data should be considered suspect in the post-stall region. None of the curves is smooth at 

high wind speeds because of the finite number of blade sections allowed in PROPPC. Twenty sections were 

used for the UTRC 8 and ten for the Carter 300 and ESI 54. 
OPEWTIONAL CASES CONSIDERED 

The performance results of the elastic twist calculations were finally compared with available field 

test results. These data were acquired from published sources and manufacturers' literature (see below). 

The field data were selected by reviewing key accuracy elements in field test such as 

a Anemometer locations and type (cup vs. prop vane) 

b. Wind turbulence measurements. 

c. Power or load transducers used. 

d. Binning and summing techniques. 

e. Averaging time. 

f. Number of readings taken. 

g - Drivetrain and generator loss model. 

The UTRC data came from two sources, a final report from Rocky Flats testing (Ref. 18) and the 

cumulative data collected at the AEVBorger Stripper Well site (Ref. 32). The Carter data came from a 

manufacturer's bulletin describing the Carter 300 (Ref. 33). The ESI data were extracted from a final 

report by Pacific Wind Energy, Inc. describing the Whiskey Run Windfarm (Refs. 34, 35). The data were 

all power curves with a known anemometer height and corrected to a standard atmospheric density. All 

curves were converted to metric units for both wind speed and power output. 

7.3: TURBINE POWER CURVE PERFORMANCE RESULTS 

Comparisons of field data and the computer models are given in Figures 7.5 - 7.7. 

POWER (kW) 

+ 

+ 

+ 

ROCKY FLATS TEST 

+ PROPPC 

Q ELAST. TWIST 

FIG. 7.5 UTRC POWER OUTPUT: COMPARISON OF FIELD TEST, PROPPC PREDICTIONS, AND ELASTIC TWIST 

7.3.1: UTRC8KWBLADE 

There is a large difference at high wind speeds for the UTRC 8 as predicted power output is around 

30 kW (Fig. 7.5). Also notice that the Viterna and Tangler post-stall calculations predict decreasing 

power at high wind speeds, in contrast to the fairly flat power curve from atmospheric testing. The lift and 

drag would have to be changed drastically to reduce the peak power to 15 kW, or the pitch needs to be 

changed. The lift and drag from the EPPLER Code (Appendix 10.6) over predicts the power output due to 

optimistic lift curve slopes at medium angles of attack, even at low wind speeds. 

Clearly the elastic twist of the UTRC 8 blade affects the power curve at wind speeds above 12 m/s 

(27 rnph), which helps to explain the discrepancy between tests and prediction. The elastic twist is nose 

down (Table 6.2), reducing angle of attack. The pendulurn/flexstrap root attachment was modeled in the 

study as a constant root pitch of 5' nose up, which is its operating equilibrium at rpm. 

7.3.2: ESI 54 S BLADE 

Power curves were obtained for two rotor speeds, 77 and 90 rpm (ESI 54s). The power curve 

from field data for the ESI 54s (90 rpm) is below the predicted output. Data obtained from the EPPLER 

Code (Appendix 10.6) also over predicts the power output. The lift and drag data were used for STA 7-8 

(.75 radius) and STA 9-10 (.95 radius), while STA 1-6 were left unchanged. The large discrepancy at 16 

m/s in the smoothness of the Miley curve is from the artificial connection of EPPLER Code data through 

angles of attack of -4" to 16". then the experimental data to 20" (same as before), and then the Tangler 

post-stall method. 

Figure 7.6 shows the ESI data for 90 rprn with the regular tip mechanism. The discrepancy 

between the PROPPC predictions and test data is still quite large. The effect of the elastic twist is 

negligible among all the cases of 77 and 90 rpm and the two tip mechanisms. Part, but by no means all, of 

the difference can be attributed to drivetrain and tip drag iosses, which were not accounted for in this case. 

7.3.3: CARTER300BLADE 

Predicted power vs. wind speed (Fig. 7.4) shows the characteristic leveling off at high wind speeds 

for the Tangler and Viterna methods. When the Tangler-predicted output is compared to the manufacturer's 

data, the field data show higher power output at low and high wind speeds. The predicted power using the 

lift and drag coefficients obtained from the EPPLER Code agree quite well with the calculated power curve 

using the experimental data. The Carter 300 blades closely matched the LS (1) airfoil offset 

specifications. 

Figure 7.7 shows the Carter 300 power curve comparisons, the manufacturer's test data, the 

PROPPC prediction (zero live twist), the prediction with elastic twist, and the power curve that would be 

obtained with zero ballast weight but including elastic twist. With no ballast weight the elastic twist is 

large and nose-up (e.g. 2.75" at 27 m/s [60 mph]) since the blade shear center (elastic axis) is at 

roughly 48% chord, outboard. This results in a large nose-up section moment due to quarterchord 

(aeroelastic lift) offset. Adding the ballast weight counteracts this with inertial moments resulting in 1.3' 

nose-down (Table 6.7). The effect of this much smaller elastic twist on the Carter power curve is to 

reduce the angle of attack at higher wind speeds. Still, in Figure 7.7, this effect cannot be clearly seen 

against the test curve. Again the drivetrain losses have not been accounted for, and presumably the 

predictions still do not match the test because of some other aerodynamic effect that is delaying stall and/or 

enhancing the output near the airfoil 2-D stall angles. 

7.4: DISCUSSION 

The PROPPC Code output by station shows how much each part of the blade contributes to the 

performance. All the blades stall progressively from the root as the wind speed increases, even the Carter 

300 which has a large twist (approaching a Glauert approximation). Looking more closely at the poststall methods, some observations can be made. 
First, for a given airfoil, different sections (blades) have a range of angles of attack depending on 

the wind speed. Combining these into a power curve, a smooth curve of lift and drag coefficients is obtained 

over a wide range of angles of attack, except for the flat plate method. 

Second, the lift and drag data are static data; the post-stall modifications are based on an averaging 

process. If those routines are attached at different terminal angles of attack of the static data, then the 

predicted power output changes. Both the Tangler and Viterna models should be investigated from angles of 

attack at the onset of stall rather than only at the end of the data input, which may be a fairer way of 

comparing stall. 

The PROPPC Code is sensitive to the input parameters. Lift and drag data were not available for all 

the airfoils for the range of Reynolds numbers needed, and also for the thick airfoils at the root. tf the 

actual airfoil is different from the airfoil specified, and/or the pitch or twist is incorrect, then the 

predicted output will be different from the measured field data, even for the pre-stall region of 

windspeeds. At 10 mls, the differences between the predicted (Tangler post-stall) and the atmospheric 

power are 13% for the Carter 300, 7% for the ESI 54S, and 10% for the UTRC 8. Even if the input data 

consistent with the actual blade characteristics, the prediction of power still must be considered 

suspect in the post-stall region. 
8.0 CONCLUSIONS 

8.1 : COMPARISON OF PREDICTED AND EXPERIMENTAL RESULTS 

Power output and blade loading are affected by the live "etastic twist" on flexible wind turbine 

blades. The aeroelastic analysis method developed during this project predicts substantial live twist which 

helps explain discrepancies observed between calculated and measured power curves. Still the 

discrepancies between predictions and test curves on stall-regulated turbines are significant, and 

presumably are due to some other aerodynamic phenomenon. 

8.2: USE OF METHOD FOR ANALYSIS OF COMPOSITE BLADES 

A secondary goal of this project was to develop a practical method of analyzing composite blades: one 

within the means and abilities of most wind turbine blade manufacturers. This necessarily means 

appropriately practical theoretical methods and complementary bench tests for verification, refinement, 

and quality control. This process was not straightforward since most composite blades have complex 

geometry (twist and taper), internal structure (laminate reinforcement and spars), and root attachment. 

8.3: USE OF METHOD FOR BLADE QUALITY CONTROL FOR MANUFACTURERS 

The experimental method developed at AEI has been presented in detail in this report. A 

conventional cantilever stand was used for all blades, and linear measurements were referenced to a simple 

laser-defined baseplane. Section angles were taken with a sensitive but readily obtainable mechanical 

clinometer, and results indicate a routine achievable accuracy of 0.1 degree. A key part of the method was 

sectioning a blade to check and verify the internal laminate geometry and ballast locations. For a properly 

constructed blade, the design specifications may be very close to the bench test. Frequencies and modes of 

vibration were measured on the test stand with SERl assistance, but even this could have been done in house 

with better instrumentation. 

In summary, the experimental methods developed in the project allow for practical verification of 

the predicted mass and stiffness properties of the blade, including the static bending deflections, static 

elastic twist, fundamental frequencies, and modes of vibration in flapping, lead-lag, and torsion. The 

aeroelastic model thus has the same static deflections, twist, modes, and frequencies of vibration as the 

actual blade. The blade testing procedure and codes permit practical standardized quality control, 

verification of blade design codes, and assessment of the static effects of ballast and tip mechanisms. For 

example, the actual mass and stiffness properties of the UTRC blade differed from the manufacturer's 

specifications by 21% (on running mass) to 49% (on torsional rigidity), for the ESI and Carter blades the 

differences were generally less than 10%. 

8.4: DESIGN IMPLlCATtONS OF RESULTS 

The elastic twist is greatly affected, via centrifugal moments, by the addition of ballast or tip 

weights. However, these effects may be beneficial if used correctly. The methodology used in this study 

enables designers of composite blades to assess the effect of adding structural elements, ballast, and tip 

mechanisms. Ultimately this could allow the tailoring of longitudinal and torsional section properties to 

exploit live twist to either enhance performance (e.g., delay stall) or reduce loading (e.g., promote stall). 

Also, the elastic axis of a composite blade can be changed dramatically by varying the type and amount of 

reinforcement, thereby changing the ratio of longitudinal modulus to shear modulus. These features may be 

used to advantage by FRP blade designers. Progress is being made in Great Britain in power limiting of 

vertical axis wind turbines by using "mirror" or "spiral" patterns of glass reinforcement (GRP) in just 

this way (Ref. 36). 
8.5: RECOMMENDATIONS FOR FURTHER WORK AND HAWT IMPROVEMENT 

Future beneficial work on elastic twist would "close the loop" by recalculating the aerodynamic 

loads with the elastic twist corrections in place, measuring the actual torsion on operating blades, and 

parametrically investigating the beneficial effects of live twist, particularly for the Carter-type blade. 

Other work could examine the calculated laminate flexural and shear strains, which must not be allowed to 

exceed allowable limits for a specified fatigue life, and which are particularly important at joints of 

dissimilar structural elements like root hubs. Finally, dynamic elastic twist and its effect on transient 

loads could be studied. 
9.0 REFERENCES 

J. L. Tangler and D. M. Somers, "Status of the Special-Purpose Airfoil Families", Proceedings, 

AWEA Conference, "Windpower '87, San Francisco, CA, Oct. 1987. 

D. M. Eggleston and F. S. Stoddard, wind Turbine Enaineerina Desian, Van Nostrand Reinhold, New 

York, 1987. 

F. S. Stoddard, "Structural Dynamics, Stability and Control of High Aspect Ratio Wind Turbines", 

UMass Alternative Energy Program, NTIS RFP-3027/67925/3533/79-7, Am herst, MA, 1979. 

L. J. Broutman and H. Kroch, Eds., Modern Com~osite Materials, Addison-Wesley, New York, 1967. 

G. Lubin, Ed., bndbook of Com~osites, Van Nostrand Reinhold, New York, 1982. 

Y. Stavsky and N. J. Hoff, "Mechanics of Composite Structures", in Composite Enaineering 

Laminates, A.G.H. Dietz, Ed., MIT Press, Cambridge, MA, 1969. 

J. L. Tangler, "A HAWT Performance Prediction Code for PCs: PROPPC", User's Guide, SERI, Golden, 

CO, Jan., 1987. 

K. L. Starcher, et al, "Modal Analysis of Six HAWT Blades", Alternative Energy Institute, WTSU, AEI 

87-2, Canyon, TX, Sept. 1987. 

L. J. Broutman, "Mechanical Behavior of Fiber-Reinforced Plastics", in Composite En~ineering 

bminates, op. cit. 

S. Jarosch, "Fatigue Properties and Test Procedures of GRP Plastic Rotor Blades", Proceedings, 

American Helicopter Society 25th Annual Forum, Washington D.C., May, 1 969. 

S. P. Timoshenko and J. M. Goodier, Theorv of Elasticitv, McGraw-Hill, New York, 1951. 

J. P. Den Hartog, a, A v n McGraw-Hill, New York, 1952. 

R. Rivello, Theorv and Analvsis of Fli~ht Structures, Addison-Wesley , New York, 1 975. 

J. P. Den Hartog, Mechanical Vibrations, 4th Ed., McGraw-Hill, New York, 1956. 

N. 0. Myklestad, "A New Method of Calculating Natural Modes of Uncoupled Bending Vibrations of 

Airplane Wings and other Types of Beams", Journal of Aeronautical Sciences, 155, 1 944. 

W. T. Thornsen, Vibration Theory and Agplication~, Prentice-Hall, 1965. 

M. A. Prohl, "A General Method For Calculating Critical Speeds of Flexible Rotors", ASME 

Tramtions, A-1 42, Sept. 1945. 

R. B. Taylor and M. C. Cheney, "UTRC 8KW Wind System: Phase II Test Technical Report", 

USDOE/Rocky Flats RFP-3232/2, Golden, CO, Feb. 1981. 

I. H. Abbott and A. E. Von Doenhoff, Theory of Wino Sections, Dover, New York, 1959. 
J. M. Salkind, et al., "Composite Materials: Testing and Design", ASTM STP497, Amer. Soc. Testing 

and Materials., 1972. 

R. Monroe, et a!., Personal Communications, Calculations and Engineering Drawings for ESI 54 

Blade, Gougeon Bros., Inc., Bay City, MI, July 1986. 

M. D. Zuteck, "Development and Manufacture of Wood Composite Wind Turbine Rotors", 

Proceedings, DOEINASA Workshop on Large HAWT, NASA Conf-810752, Cleveland, OH, July 1981. 

S. Lieblein, et al., "Design and Evaluation of Low-Cost Laminated Wood Composite Blades for Wind 

Turbines: Blade Design, Fabrication Concept and Cost Analysis", DOE..NASA/0101-1, NASA CR165463, Nov. 1982. 

R. F. Lark, et al., "Fabrication of Low-Cost MOD-OA Wood Composite Wind Turbine Blades", 

DOE/NASA/20320-45, NASA-TM-83323, Feb. 1983. 

R. H. Monroe, "Design and Development of Large WoodlEpoxy Wind Turbine Blades", Proceedings, 

AWEA Conference, "Windpower '87", San Francisco, CA, Oct. 1 987. 

C. P. Butterfield, et al., Personal Communication and Raw Field Test Data, ESI, Inc., Boulder, CO, 

1986. 

J. Carter, Jr., Personal Communications and Engineering Calculations, Carter Wind Systems, 

Burkburnett, TX, 1987. 

A.R.S. Bramwell, Helico~ter Dynamics, John Wiley and Sons, New York, 1976. 

1. A. Viterna and R. D. Corrigan, "Fixed Pitch Rotor Performance of Large HAWT", Proceedings, 

DOEINASA Workshop on Large HAWT, NASA Conference-81 0752, Cleveland, OH, July 1981. 

J. L. Tangler and C. Ostowari, "HAWT Post Stall Airfoil Characteristics Synthesization", DOE No. 

DE-AC04-76DP03533, Rocky Flats Test Center, Golden, CO, 1984. 

S. F. Hoerner, Fluid-Dvnamic Dra, Hoerner Fluid Dynamics, P.O. Box 342, Brick Town, NJ, 

08723, 1975. 

E. H. Gilmore, "Windpower to Assist in Stripper (Oil) Well Pumping", AEI/WTSU Report 85-1, 

Canyon, TX, Feb. 1985. 

D. M. Prossner, "Carter Wind Systems: Performance Results", Carter Wind Systems Press Release, 

Burkburnett, TX, May 1985. 

"ESI 54s Manufacturer's Specifications", ESI Inc., Boulder, CO, Aug. 1983. 

S. N. Walker and J. E. Wade., "Effects of Precipitation on Wind Turbine Performance", Pacific Wind 

Energy, SERVSTR-217-3287, March 1988. 

N. M. Karaolis, et al., "Passive Aerodynamic Control Using Composite Blades", Proceedings, BWEA 

Workshop on use of Composite Materials for Wind Turbines, ETSU-N-1 09, Harwell, UK, Nov. 

1987. 










































F1146-E(12/2004) 

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1. REPORT DATE (DD-MM-YYYY)

29-08-2006 

2. REPORT TYPE

subcontract report 

3. DATES COVERED (From - To)

August 1989 

5a. CONTRACT NUMBER

DE-AC36-99-GO10337 

5b. GRANT NUMBER

4. TITLE AND SUBTITLE

Determination of Elastic Twist in Horizontal Axis Wind Turbines 

(HAWTs) 

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

NREL/SR-500-12087 

5e. TASK NUMBER

WER6.7502 

6. AUTHOR(S)

F. Stoddard, V. Nelson, K. Starcher, B. Andrews 

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

F. Stoddard, V. Nelson, K. Starcher, B. Andrews, Alternative Energy 

Institute, West Texas State University, Canyon, Texas 

8. PERFORMING ORGANIZATION 

REPORT NUMBER

RL-6-06013 

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NREL 

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13. SUPPLEMENTARY NOTES

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14. ABSTRACT (Maximum 200 Words)

This report presents the results of a project at the Alternative Energy Institute that measured and calculated the 

elastic twist of three representative composite horizontal-axis blades. It covers the experimental method used to 

inspect and test the blades, the theory and computer programs used to develop semi-empirical analytical blade 

models, calculation of the steady elastic twist of the three blades in simulated operation, and comparison with actual 

field performance of the wind turbines. 

15. SUBJECT TERMS

wind energy; wind turbine; composite wind turbine blades; horizontal-axis blades 

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