NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Structural Design of a 

Horizontal-Axis Tidal Current 

Turbine Composite Blade

G.S. Bir, M.J. Lawson, and Y. Li

Presented at the ASME 30th International Conference on Ocean, 

Offshore, and Arctic Engineering

Rotterdam, The Netherlands

June 19-24, 2011

Conference Paper

NREL/CP-5000-50658

October 2011
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1

STRUCTURAL DESIGN OF A HORIZONTAL-AXIS TIDAL CURRENT TURBINE COMPOSITE 

BLADE

Gunjit S. Bir

National Renewable Energy 

Laboratory

Golden, CO, USA

Email: gunjit.bir@nrel.gov

Michael J. Lawson

National Renewable Energy 

Laboratory

Golden, CO, USA

Email: michael.lawson@nrel.gov

Ye Li

National Renewable Energy 

Laboratory 

Golden, CO, USA 

Email: ye.li@nrel.gov

ABSTRACT

This paper describes the structural design of a tidal turbine

composite blade. The structural design is preceded by two 

steps: hydrodynamic design and determination of extreme 

loads. The hydrodynamic design provides the chord and twist 

distributions along the blade length that result in optimal 

performance of the tidal turbine over its lifetime. The extreme 

loads, i.e. the extreme flap and edgewise loads that the blade

would likely encounter over its lifetime, are associated with 

extreme tidal flow conditions and are obtained using a

computational fluid dynamics (CFD) software. Given the blade 

external shape and the extreme loads, we use a laminate-theorybased structural design to determine the optimal layout of 

composite laminas such that the ultimate-strength and bucklingresistance criteria are satisfied at all points in the blade. The 

structural design approach allows for arbitrary specification of 

the chord, twist, and airfoil geometry along the blade and an 

arbitrary number of shear webs. In addition, certain fabrication 

criteria are imposed, for example, each composite laminate 

must be an integral multiple of its constituent ply thickness. In 

the present effort, the structural design uses only static extreme 

loads; dynamic-loads-based fatigue design will be addressed in 

the future. Following the blade design, we compute the 

distributed structural properties, i.e. flap stiffness, edgewise 

stiffness, torsion stiffness, mass, moments of inertia, elasticaxis offset, and center-of-mass offset along the blade. Such

properties are required by hydro-elastic codes to model the tidal 

current turbine and to perform modal, stability, loads, and 

response analyses.

INTRODUCTION

Extraction of energy from tidal currents, an untapped

renewable resource so far, is gaining increased attention. Tidal 

currents are an attractive source of renewable energy due to 

their predictability and high energy density. Recently, numerous 

technologies have been developed to convert the energy 

available within tidal currents into electrical power [1]. 

Horizontal-axis tidal turbines (HATTs) are perhaps the most 

mature and promising of the technologies and several 

companies (e.g. Marine Current Turbine, Verdant Power, and 

OpenHydro) have developed HATT prototypes that are 

currently undergoing testing. Nevertheless, as blade failures 

on a number of prototype devices have demonstrated, the 

ability to design HATT blades to withstand the expected 

hydrodynamic loads is critical. A HATT basically works on the 

same principle as does a horizontal-axis wind turbine. The 

HATT rotor blades convert the tidal current kinetic energy into 

the shaft mechanical energy and a generator converts this 

mechanical energy into electricity. Figure 1 shows a few 

examples of HATT configurations. These configurations differ 

in the type of support structure used for the turbine rotor. 

Fraenkel [1] discusses pros and cons of each configuration.

FIGURE 1. EXAMPLES OF HORIZONTAL-AXIS TIDAL 

CURRENT TURBINE (HATT) CONFIGURATIONS. EACH 

CONFIGURATION IS BEST SUITED FOR A PARTICULAR SEA 

DEPTH RANGE [1].

Irrespective of which configuration is used, the rotor blade is 

the key component that extracts energy from the tide and 

primarily dictates the performance, loads, and dynamics of the 

whole turbine system. Therefore, an efficient blade design is 

critical to the success of the HATT.
2

This paper focuses on the structural design of a tidal 

turbine composite blade. The structural design is preceded by 

two steps: hydrodynamic design and determination of extreme 

loads. The hydrodynamic design, discussed in the companion 

paper [2], provides the blade external shape, i.e. the chord and 

twist distributions along the blade, which result in optimal 

performance of the tidal turbine over its lifetime. The extreme 

loads, i.e. the extreme flap and edgewise loads that the blade 

would likely encounter over its lifetime, are associated with 

extreme tidal flow conditions and are determined using a 

computational fluid dynamics (CFD) software. Given the blade 

external shape and the extreme loads, we use a laminate-theorybased structural design to determine the optimal layout of 

composite laminas such that the ultimate-strength and bucklingresistance criteria are satisfied at all points in the blade. This

structural design approach allows for arbitrary specification of 

the chord, twist, and airfoil geometry along the blade and an 

arbitrary number of shear webs. In addition, certain fabrication 

criteria are imposed, for example, each composite laminate 

must be an integral multiple of its constituent ply thickness. In 

the present effort, the structural design uses only static extreme 

loads; dynamic loads-based fatigue design is not addressed. 

Following the blade design, we compute the distributed 

structural properties, i.e flap stiffness, edgewise stiffness, 

torsion stiffness, mass, moments of inertia, elastic-axis offset, 

and center-of-mass offset along the blade. Such properties are 

required by hydro-elastic codes to model the tidal current 

turbine and to perform modal, stability, loads, and response 

analyses.

THE TIDAL CURRENT TURBINE DESCRIPTION 

This paper considers a hypothetical monopole-supported 

550 kilowatt (kW) turbine shown in Figure 2; it is intended for 

deployment at the Northern Admiralty Inlet of Puget Sound. 

Table 1 lists the key design and operating specifications for the

turbine.

TABLE 1. TURBINE SPECIFICATIONS

Rated power 550 kW

Number of rotors 2

Rotor diameter 20 m

Number of rotor blades 2

Control type Variable speed, 

variable pitch

Hub diameter 2 m

Maximum rotor speed 11.5 rpm

Normal flow speed range 0.5–3.0 m/s

Hub height 18 m

Primary blade airfoil NACA 631-424

Water depth 33 m

The turbine has two 20-meter (m) diameter rotors. Each rotor 

has two blades and is mounted on a 2-m diameter hub. The 

blade design is optimized for a variable speed, variable pitch 

(VSVP) operation. A NACA 631-424 airfoil defines the primary 

shape of the turbine blade; this airfoil was selected because it 

provides a relatively large minimum pressure coefficient and

makes the blade resistant to cavitation. Also, NACA 63 series 

airfoils delay stall and are less sensitive to leading edge 

roughness than NACA 4 and 5 series airfoils. We assume a 

circular cross-section over the blade root length that is well 

suited to variable- pitch mechanism. The circular section

transitions to the NACA 631-424 airfoil shape at 20% of the 

blade span. It may be possible to improve the performance of 

the blade (i.e. increase power generation) by using different 

airfoil shapes over the blade length. We will explore this 

possibility in the future.

FIGURE 2A. SCHEMATIC OF THE MONOPOLE-SUPPORTED 

TIDAL CURRENT TURBINE. THE MONOPOLE IS DUG INTO 

THE SEABED AND THE TWIN ROTOR ASSEMBLY CAN 

SLIDE UP AND DOWN THE VERTICAL SHAFT.

FIGURE 2B. EACH ROTOR HAS TWO BLADES. THE BLADES 

SHED STRONG TIP VORTICES, AS SHOWN IN THIS 

COMPUTATIONAL FLUID DYNAMICS (CFD) SIMULATION, 

AND SIGNIFICANTLY INFLUENCE THE BLADE LOADS.
3

DESIGN APPROACH

Figure 3 summarizes the hydro-structural design of the 

HATT blade and computation of its structural properties. The 

green boxes identify the three main steps: hydrodynamic 

design, computation of extreme loads, and structural design. 

The following sections describe these steps.

HYDRODYNAMIC BLADE

DESIGN (using HAWT_Opt)

EXTREME LOADS COMPUTATION

( using CFD simulations)

STRUCTURAL BLADE DESIGN

(based on ultimate and 

buckling strength criteria)

Inputs: rotor diameter, 

tidal current conditions, 

airfoils geometries& 

aerodynamic coefficients

Composite material 

properties, material & load 

factors of safety, blade 

fabrication constraints

Extreme 

operating 

conditions

Blade external shape: chord 

& twist distribution along the 

blade

Optimal composite 

laminates layup inside the 

blade

Structural properties 

along the blade length Structural Analysis

FIGURE 3. STEPS USED IN THE AERO-STRUCTURAL 

BLADE DESIGN

HYDRODYNAMIC DESIGN

The turbine blade is designed for a hypothetical 550 kW 

turbine intended for deployment at the Northern Admiralty Inlet 

of Puget Sound. An acoustic Doppler current profiler survey at 

this site [3] shows the mean water velocity is approximately 1 

m/s, although velocities as high as 3 m/s occur during the tidal 

cycle. Table 1 presents the turbine’s specifications. The turbine 

has a 20-m diameter rotor comprised of a 2-m diameter hub and 

two blades. The blade design is optimized for a VSVP turbine 

that has a maximum rotation rate of 11.5 revolutions per minute

(rpm).

We used our recently developed numerical tool Harp_Opt 

[4,5] for the basic turbine blade design. Harp_Opt combines the 

blade element moment code WT_Perf [6] with a genetic 

algorithm to provide optimal blade twist angle and chord 

distribution along the blade for a specified objective function. 

The optimization objective for the blade design was to 

maximize tidal energy capture over the flow speed range 0.5–

3.0 m/s while limiting the turbine's maximum power output to

550 kW (the cavitation effects were ignored). Using this 

objective, Harp_Opt determined the blade chord and twist 

distribution along the blade (Figure 4). Note that the blade span 

location, r, with respect to the hub center has been normalized 

by R, the rotor radius. Figure 5 shows the computed optimal 

tip-speed ratio (TSR), rotor rotation speed, and optimal blade

pitch angle for each tidal current velocity. The TSR is defined 

as the ratio of the rotor tip speed and the mean tidal flow speed. 

Figure 6 shows how the rotor thrust and the blade root flap 

moment vary with the tidal current velocity.

FIGURE 4. OPTIMAL CHORD AND TWIST DISTRIBUTION 

ALONG THE BLADE

FIGURE 5. VARIATIONS OF OPTIMAL TIP-SPEED RATIO

(TSR), ROTOR SPEED, AND BLADE PITCH ANGLE WITH 

TIDAL FLOW VELOCITY.
4

 

FIGURE 6. VARIATION OF BLADE ROOT FLAP MOMENT 

AND ROTOR TORQUE WITH THE TIDAL CURRENT 

VELOCITY.

The chord and twist distribution, which HARP_Opt

computed at 30 sections along the blade, define the external 

shape of the blade (Figure 7).

FIGURE 7. AIRFOIL CHORD AND TWIST VARIATION ALONG 

THE BLADE

ESTIMATION OF EXTREME BLADE LOADS

Definition of Extreme Conditions

For structural design, it is imperative to know the

maximum loads the blade must withstand during its lifetime. 

We identified two extreme operating conditions (EOCs) during 

which the blade is expected to encounter maximum loads:

• Extreme operating condition 1 (EOC 1). The tidal 

current velocity becomes significantly higher than the 

normal velocity due to an extreme weather event. In 

this case, to prevent blade overloading, the turbine

control system automatically feathers the blades and 

engages the shaft brake to prevent rotor rotation. For

this condition, we assume that the tidal current can 

attain a velocity twice the maximum velocity

measured during the normal tidal cycle in the Northern 

Admiralty Inlet. The maximum velocity during a 

normal tidal cycle is approximately 3 m/s at hub 

height. Thus we considered current velocities up to 6 

m/s.

• Extreme operating condition 2 (EOC 2). The turbine 

is operating normally at the peak thrust and peak blade 

root flap moment operating condition (see Figure 6), 

which corresponds to 1.9 m/s tidal current speed, zero 

degree blade pitch angle, and 11.5 rotor rpm. The 

turbine then suddenly experiences a tidal gust due to 

the passage of a turbulent eddy that boosts the tidal 

current velocity to 2.85 m/s, which is 1.5 times the 

normal current velocity. The turbine control system is 

unable to pitch the blades quickly enough to shed the 

increased hydrodynamic loading associated with this 

event. Recent experimental measurements from the 

Puget Sound [7] suggest that velocity increments 

larger than 50% occurs rarely on the length scale of 

the turbine blades. Therefore, the choice of 1.5 times 

the normal speed as the extreme tidal current speed is 

quite conservative.

Extreme Loads Computation

To obtain extreme hydrodynamic loads on the blade, we 

simulated the extreme operating conditions, EOC 1 and EOC 2, 

using the CFD code STAR CCM+ (CD-Adapco; Melville, New 

York [8]). The computational grid (Figure 8) was generated 

using the STAR CCM+ grid generation utility and consisted of 

approximately 3 million polyhedral elements.

To simulate the rotation of the blades and the hub, we

rotated the model reference frame; this approach effectively 

simulated blade rotation without the need to physically rotate 

the computational grid by forming the Navier-Stokes equations 

in a frame that is rotating with the turbine.

FIGURE 8. COMPUTATIONAL GRID USED FOR 

COMPUTATIONAL FLUID DYNAMICS SIMULATIONS.

We took advantage of the 180 degree periodicity of the 

turbine rotor and only simulated one blade and half of the hub. 

Accordingly, a rotationally periodic boundary condition was 

applied across the bottom surface of the computational domain 

shown in Figure 8. A constant and spatially uniform velocity 

profile was specified over the front of the computational 

domain and a pressure outlet boundary condition was applied at 

the exit. Other external surfaces of the computational domain 
5

were specified as symmetry boundaries (i.e., slip boundaries) to 

decrease flow recirculation on the boundary surfaces, thus 

improving numerical stability. No-slip boundary conditions 

were applied on the surfaces of the blade and the hub.

Turbulence was modeled using the k-ω shear stress 

transport (SST) Reynolds-averaged Navier-Stokes (RANS) 

sub-grid scale model. The RANS equations were solved using a 

second-order-accurate finite-volume discretization scheme via a 

segregated algebraic multi-grid iterative solver. Simulations 

were judged to be converged when the residuals of the 

numerical solution stabilized and were reduced by 

approximately three orders-of-magnitude. Several global 

parameters, including rotor torque and thrust, were also 

monitored to insure convergence of the solution. Lawson et al.

[2] provide a more detailed description of the development and 

numerical verification of the CFD simulations.

The CFD simulations provide the flow field within the 

computational domain and also the blade pressure distribution 

(Figure 9) corresponding to the EOC. Spatial integration of the 

pressure distribution yields extreme load distributions, 

specifically the shearing forces and the bending moments, over 

the blade.

FIGURE 9. BLADE PRESSURE DISTRIBUTIONS FOR THE 

EXTREME OPERATING CONDITION, EOC 2. UNITS ARE IN 

PASCALS.

The structural design, described in the next section, considers 

only the flap and lag bending moments. Figure 10 shows the 

bending moment distributions along the blade for each EOC. 

These moments are first obtained in the global frame (shown in 

dotted lines). The global frame is a blade-section-attached 

frame, which does not twist with the blade and stays parallel to 

a hub-attached frame with one axis aligned with the blade pitch 

axis and another normal to the rotor plane. The bending 

moments are then transformed to a blade-section-attached local 

frame (shown in solid lines). The local frame has one axis 

aligned with the blade pitch axis and the other with the local 

chord line. Figure 10 indicates that both flap and lag bending 

moments are largest for EOC 2. Hydrodynamic loads from 

scenario 2, referenced to the local section frames, were used to 

design the internal structure of the 

blade.

FIGURE 10. FLAP AND LAG BENDING MOMENTS 

COMPUTED FOR THE TWO EXTREME OPERATING 

CONDITIONS, EOC 1 AND EOC 2.

STRUCTURAL DESIGN AND ANALYSIS

For the HATT blade structural design, we use a

computerized method that closely follows the one we 

developed earlier for the preliminary design of composite wind 

turbine blades [9]. The method allows for arbitrary 

specification of the chord, twist, and airfoil geometry along the 

blade and an arbitrary number of shear webs. Given the blade 

external geometry description and the design load distribution, 

the code uses ultimate-strength and buckling-resistance criteria 

to compute the optimal design thickness of load-bearing 

composite laminates at each blade span location. The code also 

includes an analysis option to obtain blade properties following 

blade design. These properties include bending stiffness, 

torsion stiffness, mass, moments of inertia, elastic-axis offset, 

and center-of-mass offset along the blade. Nonstructural 

materials—gelcoat, nexus, and bonding adhesive—are also 

included for computation of mass.
6

Figure 11 shows the assumed structural layout of 

composite materials within a typical blade cross section. The 

figure shows a three-cell blade section with two webs, but the 

code is applicable to a multi-cell section with an arbitrary 

number of webs. The outermost skin of a section consists of 

three layers: a gelcoat layer, a nexus layer, and a double-biasmaterial composite laminate. In this report, we define a 

laminate as a stack of plies, where a ply is a planar composite 

mat. The gelcoat outer layer provides a smooth surface, and 

although it is not a structural material, it can significantly 

contribute to the blade mass. Nexus is a soft-material mat that 

shields the rough surface of the underlying double-bias 

laminate and provides a relatively smooth but absorbent surface 

for the gelcoat. At the blade trailing edge, the double-bias 

laminate splits into two layers to accommodate a core material, 

such as foam, or honeycomb, as shown in Detail CC below. The 

core-material laminate augments the buckling strength of the 

trailing section of the blade.

Lining Unidirectional

Core

Nexus

Skin (DB)

Uni

Gelcoat

Skin (DB)

Lining

Uni

Core

BB

CC

AA

Boxspar

Lining

Boxspar

Detail AA Detail BB Detail CC

FIGURE 11. STRUCTURAL LAYUP OF COMPOSITE 

LAMINATES AT A TYPICAL BLADE SECTION.

A composite boxspar runs along the midsection of the 

blade and is attached to the skin double-bias layers at its upper 

and lower surfaces. The box-spar divides the blade interior into 

three cells, with the box-spar forming the mid-cell. A lining, 

typically a double-bias layer, covers the inside surface of each 

cell. As shown in Detail BB, the box-spar is made of 

unidirectional composite laminates with an embedded core 

material. Because of its good axial load-bearing capabilities, 

the unidirectional laminate provides most of the bending 

strength. The core material provides the buckling strength to the 

mid-cell. The two vertical sides of the box-spar serve as webs. 

Detail AA of Figure 11 shows the sequence of composite layers 

in each web.

Whereas the primary function of the unidirectional layers 

is to provide flexural strength, the functions of the double-bias 

layers are to provide shear strength and to prevent splaying of 

the unidirectional material. Computational effort is minimized 

by assuming that all double-bias plies are stacked in one 

laminate and all unidirectional plies are stacked in another 

laminate (Detail BB in Figure 11). In reality, the double-bias 

and unidirectional plies may be interspersed to form a single 

laminate. This interspersing of plies may have a significant 

effect on the blade structural integrity at the micro level. 

However, it will have little effect on the blade strength and 

properties predicted by the code, assuming the thickness of the 

combined stack is much smaller than the overall blade 

thickness, which usually is the case.

Figure 11 shows a box-spar configuration, which was used 

for the studies. A D-spar configuration may be obtained by 

simply moving the forward web to the leading-edge location, 

where its height automatically becomes zero. Depending on the 

loading environment and manufacturing considerations, a 

designer may opt for structural layouts different from the one 

shown in Figure 11. For example, for the webs, the designer 

might replace the unidirectional laminates with double-bias 

laminates, which provide higher shear strength. Some blade 

designs show the upper- and lower-surface unidirectional 

laminates extended somewhat beyond the web locations. 

Currently, we are surveying construction details of a few blades 

and consulting with tidal current blade designers to identify 

candidate layouts that are most likely to be used and we may 

extend our code to accommodate the additional layouts.

Technical Approach

The design objective is to size the thickness of the 

unidirectional laminate, double-bias laminate, and core material 

such that the blade has minimum weight and remains fail-safe 

under the extreme load distribution. For a conservative design, 

we assume that the gelcoat and the nexus are not load-bearing 

materials and, therefore, are not sized. The design is carried out 

using the ultimate-strength criterion, the buckling- strength 

criterion, and two trend-based relations. Details are provided 

in [9] and a summary is provided below.

To satisfy the ultimate-strength criterion, we first develop 

laminate-theory-based mathematical expression that relates 

axial stress at any point within the blade to the loading and 

composite material elastic properties at that point. We then 

impose a constraint to ensure that this stress does not exceed 

the allowable design stress for the composite material at that 

point. The allowable design stress for the material is its ultimate 

strength, compressive or tensile, multiplied by a material factor 

of safety.

To satisfy the buckling strength criterion, we use the 

following inequality:

τ υ ζ τ

π ζ τ τ σ ζ τ τ d zE z

b z d

panel top

panel bottom

panel top

panel bottom

∫ ∫

−

−

−

− − ≤

[1 ( ( , , ) )]

( , , ) ( , , ) 3.6 * 2

2

2

2

(1)

It states that the edge loading per unit peripheral length of a 

blade surface panel does not exceed the Euler buckling load for 

that panel. The left-hand side of this equation expresses the 

edge loading per unit peripheral length of a blade surface panel 

and it is obtained by integrating the axial compressive stresses 

over the thickness of a panel. The longitudinal z-axis is directed 

toward the blade tip and the ζ- and the τ-axes form the midsurface of the panel. The τ represents the distance of a material 

point in the panel from the z-ζ neutral surface. The right-hand 
7

side of equation (1) represents the critical buckling load of the 

panel (note that it is proportional to the panel flexural rigidity 

represented by the integral term on the right-hand side). E is the 

effective Young’s modulus in the longitudinal z direction and 

ν is the Poisson ’s ratio at the point (z,ζ,τ). We apply the 

buckling criterion to the mid-panel, which is the blade upper 

surface enclosed between the fore- and aft-webs, and to the 

trailing-edge panel, which is the blade upper surface enclosed 

between the aft-web and the trailing edge. The highly curved 

and short-length leading-edge panel is assumed to be bucklefree. For a conservative buckling analysis, we assume the panel 

edges parallel to the z-axis are simply supported, and the edges 

perpendicular to the z-axis are free. In reality, all edges would 

have a finite restraint to rotation due to the adjoining panels, 

and the buckling resistance would be somewhat enhanced. Also 

to keep the analysis simple, we ignore the nonlinear geometric 

and inelastic effects.

Compared to unidirectional-material, the double-bias 

material usually offers a much lower stiffness along the blade. 

Therefore, the ultimate-strength criterion would dictate that 

only the unidirectional-material be used, resulting in a zerothickness requirement for the double-bias material. Though the 

double-bias material does contribute to flexural rigidity, its 

prime role is to prevent splaying of the unidirectional plies, 

provide resistance to accidental denting of the blade surface, 

and provide shear strength. Because of the low torsion loads 

likely to be encountered by a typical wind blade, the shearstrength criteria also may not yield any requirement for the 

double-bias material. A rigorous relation governing double-bias 

material requirement for splay-prevention and dent-resistance is 

not available. We, therefore, consulted wind turbine blade 

designers and manufacturers and their input helped us 

formulate the following simple relation to compute the doublebias laminate thickness:

db max[ * max( , , , ), * ] panel panel 1 2 panel n db ply t mtsbypw w w w mdbplies t −− − − =  (2)

where wpanel-i is the width of panel i between webs i and i+1, 

tdb-ply is the ply thickness of the double-bias material, 

mdbplies is the minimum number of double-bias plies, and 

mtsbypw is the minimum double-bias-laminate-to-panel-width 

ratio. For mdbplies and mtsbypw, we used the values 3 and 

0.0025 respectively. These are typical values for the 10-m long 

wind turbine blades, but may be inadequate for similar size

marine turbine blades because of the crushing or impact loads 

from the surrounding water. We plan to consult marine blade 

designers to provide us with specific guidelines.

After satisfying the ultimate- and buckling-strength criteria 

described above, we increased the laminate thickness in the 

root area to allow secure attachment of the blade to the hub (see 

[9] for details). We also impose the design requirements that the

thickness of any laminate is an integer multiple of the thickness 

of the commercially available composite ply sheet.

Finally, we consider a filler material for the blade interior. 

Unlike a wind turbine blade, a marine turbine blade experiences 

substantial buoyancy forces due to the surrounding dense water. 

These forces act along the full length of the blade. Also, the 

direction of these large forces changes cyclically per each blade 

revolution resulting in fatigue damage. To minimize these 

cyclic forces, the blade should be made as neutrally buoyant as 

possible. Researchers have suggested filling the blade interior 

with water or with epoxy slurry, which has a comparable 

density to water.

Computation of Structural Properties

Using the composite laminates layup that results from the 

structural design, we compute the following structural 

properties along blade length: mass per unit length (m), flap 

stiffness (EIflap), lag stiffness (EIlag), axial stiffness (EA), torsion 

stiffness (GJ), and offsets of the elastic-axis (x_ea) and centerof-mass (x_cg) from the blade pitch axis. Each of these 

properties is a span-variant section property and is obtained by 

integrating either the materials density or the materials elastic 

parameters distributed over a specific section. The integral 

relations are quite simple and follow directly from the 

elementary mechanics of materials [10]. It may be mentioned 

that we ignore the effect of warping in the current formulation. 

In the near future, we plan to introduce Vlasov’s correction to 

account for the warping effects; this would yield improved 

estimates of torsion stiffness, particularly near the root area.

For computer evaluation of the various integrals that 

provide the structural properties, we discretize all the section 

laminates into a number of area segments along each section 

periphery. Based on the segment area, its distance and 

orientation with respect to the ξ- and η-axes, and the elastic 

moduli of the material enclosed by it, we determine its 

contribution to a particular section property. Contribution of all 

material segments is then added to yield the gross section 

property. In computing blade properties, we include the mass of 

the nonstructural materials, including gelcoat, nexus, and 

bonding adhesive. Also, at the blade root section, we take into 

account the mass contribution of bolts [9].

RESULTS

Design

To design the tidal current turbine composite blade, we 

followed steps outlined in the previous section. We first used 

HARP_Opt and obtained the blade external hydrodynamic 

shape, i.e. airfoil chord and twist distribution along the blade 

(Figure 4). The blade is 8.85-m long and has a circular cross 

section at the root with a diameter of 0.8 m. From the root to 

the 2.4-m span location, the blade section transitions from the 

circular shape into the NACA 631-424 airfoil shape. Outboard 

of this span location, the airfoil shape remains unchanged.

Next, we defined extreme operating conditions and, using a 

CFD code, computed the maximum loads the blade would 

encounter during its lifetime (Figure 10). Then we selected 

material properties using [11] and other handbooks. Table 2
8

lists the material properties: tply is the composite ply thickness, 

ρ is the material density, E is the effective modulus of elasticity 

in a direction parallel to the blade longitudinal axis, G is the 

shear modulus, σut is the ultimate allowable tensile stress, σuc is 

the ultimate allowable compressive stress, and ν is the 

Poisson’s ratio. The ultimate stresses are the mean values from 

coupon testing [11]. We applied a safety factor of 1.2 to the 

loads and a safety factor of 1.5 to the materials (to arrive at the 

allowable design stresses).

TABLE 2. BLADE MATERIAL PROPERTIES

Material tply

(mm )

ρ

(Kg/m3)

E

(Pa)

G

(Pa)

σut

(Pa)

σuc

(Pa)

ν 

Gelcoat 0.381 1664 -- -- -- -- --

Nexus 0.51 1830 -- -- -- -- --

Double-bias 0.53 1830 10.3E+9 8.0E+9 151 -174 0.3

Lining 0.53 1830 10.3E+9 8.0E+9 151 -174 0.3

Unidirectional 0.53 1860 37.0E+9 4.1E+9 986 -746 0.3

Core 3.125 128.1 -- -- -- -- 0.3

Next, we performed structural design, the final step in the 

design process, which yielded minimal thicknesses of the 

composite laminates and optimal location of the boxspar webs

such that minimal material is used while satisfying the ultimate 

and buckling-strength criteria.

Table 3 shows the design thicknesses of composite

laminates required at 74 sections along the blade. The optimal 

web locations are 12.8% and 56.0% of the chord length. The 

first column lists the blade section numbers and the second 

column lists the span location of those sections. The third 

column lists the chord lengths. The tsk, listed in the next 

column, is the design thickness of the double-bias skin material 

required at different blade stations. This thickness needs to be

augmented such that it becomes an integer multiple of the 

commercially available double-bias composite ply. The tskn

and nskin, listed in the next two columns, represent the 

augmented skin-laminate thickness and the number of plies 

required to obtain that thickness. The next three columns, with 

the headers tecore, tecoren, and ntecore, represent similar 

values for the core material (PVC foam) required at the blade 

trailing edge for resistance against buckling. The subsequent 

three columns, with the headers tuni, tunin, and nuni, represent 

corresponding values for the unidirectional material required in 

the box section. It is the unidirectional material that provides 

the majority of the bending stiffness and primarily meets the 

ultimate strength requirement. The tboxcore and ncore_bx

represent the core-material thickness and the number of core 

plies required in the boxspar to meet the buckling-strength 

criterion. The t_le, t_box, and t_te, listed in the last three 

columns, respectively represent the blade section wall thickness 

at its leading edge, mid section (spanned by the boxspar), and 

trailing edge parts. The wall thickness at any point on the blade 

surface is the sum of the thickness of gelcoat, nexus, and all 

composite laminas at that point.

It should be noted that additional unidirectional and 

double-bias materials are used over the inboard blade span for 

blade root reinforcement. This reinforcement is required to 

accommodate bolt inserts for blade attachment to the hub, to 

mitigate stress concentrations, and to provide smooth stress 

flow paths from the blade to the hub ([9] provides an empirical 

formula for the root design). The thickness of the reinforcement 

materials remains constant over a certain distance length from 

the blade root and then linearly tapers over the transition length, 

i.e., the length over which the blade section transitions from the 

circular shape to the regular airfoil shape. No core material is 

used over this blade-root region.

A close examination of the design results, listed in Table 3, 

suggests that the leading edge wall thickness might be too small 

for a tidal current turbine blade. While the shown thickness 

values are sufficient to meet the design criteria considered in 

the paper, these may not be adequate to withstand the crushing 

or impact loads from the water surrounding the blade. Specific 

design guidelines are being investigated to address this issue.

Finally, to make the blade near-neutrally buoyant, we 

consider water or epoxy slurry to fill the blade interior. A filler 

agent also helps reduce the fatigue-causing cyclic loads on the 

blade as discussed earlier. Though a filler does not contribute to 

the blade strength, it substantially increases the blade mass. The 

filler material also might mitigate buckling and crushing of the 

blade due to surrounding water; however, we did not consider 

these in the design.

Structural Properties

Next, using the composite layup that resulted from the 

blade design, we computed the span-variant structural 

properties. Table 3 lists these properties. The m is the mass per 

unit length; Ixx is the section mass moment of inertia about the 

chord; Iyy is the section mass moment of inertia about any axis 

normal to the chord and originating from the pitch axis; EIflap is 

the flap stiffness; EIlag is the lag stiffness or edgewise stiffness;

EA is the axial stiffness; GJ is the torsion stiffness; x_ea is the 

offset of the elastic-axis from the blade pitch axis; and x_cg is 

the offset of the section center of mass from the blade pitch 

axis. These offsets are positive if measured from the pitch axis 

toward the section leading edge. Note that the edgewise and 

torsion stiffness values dip around the 1.5-m span location. This 

is because both stiffness values are sensitive to the chord 

length (and are nearly proportional to the cube of the chord).

Moving inboard from this location, the chord length reduces 

and so do the edgewise and torsion stiffness values. Further 

inboard, the chord is the diameter of a circular section and 

remains constant, but the root reinforcement contributes 

substantially to the stiffness values. The slight dips in the mass 

and mass-inertia distribution seen in the table can be interpreted 

similarly (mass is roughly proportional to chord and massinertia is nearly proportional to the cube of the chord).

Table 5 provides a mass breakdown of the different materials 

used in the blade design. The contribution of mass of the bolt 

inserts and the filler material, though shown in the weight 

breakdown, is not included in section mass and inertia 

distributions shown in Table 4. The inserts behave more like a 

concentrated mass at the discreet root location rather than a 

distributed mass reflected in the tables.
9

After we account for the volume of the structural materials, 

the blade is left with a void of 24.9 m3 in its interior. We 

consider two options: filling the interior with water or with

epoxy slurry to achieve near-neutral buoyancy. The blade 

weight increases by 2402.7 kilograms (kg) if water is 

considered, by 2483.5 kg if epoxy slurry is considered. The 

resulting blade total weight becomes 2932.5 kg for water filler 

and 3213.2 kg for epoxy slurry filler (see Table 5).

CONCLUSIONS AND FUTURE WORK

We presented results of the preliminary structural design of 

a horizontal-axis tidal turbine composite blade. The results 

show the optimal location of webs and the minimum thickness 

requirement of different composite laminates that would satisfy 

the ultimate-strength and buckling-resistance criteria. We 

considered only the extreme static loads that the blade would 

likely encounter during its lifetime. Dynamic loads, fatigue, and 

stiffness criteria will be considered in the future.

A close examination of the design results showed that the 

leading edge wall thickness, while adequate to meet the 

buckling and strength criteria, might be too small to withstand

the crushing or impact loads from the water surrounding the 

blade. Specific design guidelines are being investigated to 

address this issue.

The design approach allows arbitrary twist, chord, and 

airfoil shape variation along the blade, but allows only a multicell boxspar. Though a boxspar design has been the choice by 

several HATT designers, we plan to extend our design code to 

accommodate a few more promising layouts. The materials we 

considered for the HATT design also appear adequate; however, 

we will critically assess other materials, which may be more 

suitable for HATT blades.

In the current preliminary design approach, we ignored 

warping and section in-plane distortion (Brazier effect). We 

have developed a code called PreComp [12], which accounts 

for these effects and also allows for arbitrary layup of 

composite laminates within the blade. However, its present 

capability is limited to computation of structural properties 

only. We plan to extend it to compute three-dimensional

stresses and also allow automated design. Following a 

PreComp-assisted preliminary design, we will use a finiteelement based analysis, such as NuMad [13], to refine the blade 

design and obtain a more accurate three-dimensional stress 

field.

REFERENCES

[1] Fraenkel, P., 2002. “Power From Marine Currents”. 

Proceedings of the Institution of Mechanical Engineers, Part 

A: Journal of Power and Energy, 216(1), pp. 1–14.

[2] Lawson, M. J., Li, Y., and Sale, D. C., 2011. “Development 

and Verification of a Computational Fluid Dynamics Model 

of a Horizontal Axis Tidal Current Turbine.” Proceedings of 

the 30th International Conference on Ocean, Offshore, and 

Arctic Engineering, Rotterdam, the Netherlands, June 19-

24, 2011.

[3] Polagye, B., and Thomson, J., 2010. “Tidal Energy 

Reference Model Inflow Conditions,” University of 

Washington, unpublished technical report.

[4] Sale, D. C., and Li, Y., 2010. “Preliminary Results From a 

Design Methodology and Optimization Code for Horizontal 

Axis Wind and Hydrokinetic Turbines.” Proceedings of the

29th International Conference on Ocean, Offshore, and 

Arctic Engineering, Shaghai, China, June 6-11, 2010.

[5] NWTC Design Code Harp_Opt, available at:

http://wind.nrel.gov/designcodes/simulators/HARP_Opt/, 

aceesed on December 15, 2010.

[6] NWTC Design Code WT_Perf, available at:

http://wind.nrel.gov/designcodes/simulators/wtperf/, 

aceesed on December 15, 2010.

[7] Thomson J., Polagye, B., Richmond, M., and Durgesh, V. 

“Quantifying Turbulence for Tidal Power Applications”, 

MTS/IEEE Oceans 2010, Seattle, WA September 20–23, 

2010.

[8] CD-Adapco, 2011, STAR CCM+ 5.06 User’s Guide.

[9] Bir, G. S. and Migliore, P., 2001, “A Computerized Method 

for Preliminary Structural Design of Composite Wind 

Turbine Blades.” Special November 2001 wind issue of the 

Journal of Solar Engineering. Also presented at the 2001 

AIAA/ASME Wind Energy Symposium, Reno, NV.

[10] Hodges, D. H. and Dowell, E. H., 1974, “Nonlinear 

Equations of Motion for the Elastic Bending and Torsion of 

Twisted Nonuniform Rotor Blades,” NASA TN D-7818.

[11] Mandell, J. F. and Samborsky, D. D., 1997, “DOE/MSU 

Composite Material Fatigue Database: Test Methods, 

Materials, and Analysis,” SAND97-3002, Sandia National 

Laboratories, Albuquerque, NM.

[12] Bir, G. S., 2006, “User's Guide to PreComp (Pre-Processor 

for Computing Composite Blade Properties)”, NREL Report 

No. TP-500-38929.

[13] Laird, D. L., 2001, “NuMAD User’s Manual”, 

SAND2001-2375, Sandia National Laboratories,

Albuquerque, NM.
10

TABLE 3. DESIGN THICKNESS REQUIREMENT FOR COMPOSITE LAMINATE AT DIFFERENT BLADE SECTIONS

Station sloc chord tsk tskn nskin tecore tecoren ntecore tuni tunin nuni tboxcore ncore_bx t_le t_box t_te

(m) (m) (mm) (mm) -- (mm) (mm) -- (mm) (mm) -- (mm) -- (mm) (mm) (mm)

1 0 0.8 5.64 5.83 11 0.00 0.00 0 31.99 32.33 61 21.78 7 7.25 61.46 7.25

2 0.075 0.823 5.64 5.83 11 0.00 0.00 0 31.99 32.33 61 24.25 8 7.25 64.58 7.25

3 0.15 0.847 5.64 5.83 11 0.00 0.00 0 31.99 32.33 61 26.65 9 7.25 67.71 7.25

4 0.225 0.871 5.64 5.83 11 0.00 0.00 0 31.99 32.33 61 29.00 10 7.25 70.83 7.25

5 0.3 0.894 5.64 5.83 11 0.00 0.00 0 31.99 32.33 61 31.29 11 7.25 73.96 7.25

6 0.375 0.95 5.64 5.83 11 0.00 0.00 0 31.99 32.33 61 36.59 12 7.25 77.08 7.25

7 0.45 1.006 5.64 5.83 11 0.00 0.00 0 31.99 32.33 61 41.72 14 7.25 83.33 7.25

8 0.525 1.062 5.48 5.83 11 19.36 21.88 7 31.05 31.27 59 0.00 0 7.25 38.52 29.13

9 0.6 1.118 4.97 5.30 10 20.82 21.88 7 28.14 28.62 54 0.00 0 6.72 35.34 28.60

10 0.675 1.185 4.39 4.77 9 22.50 25.00 8 24.88 24.91 47 3.39 2 6.19 37.35 31.19

11 0.75 1.252 3.78 4.24 8 24.19 25.00 8 21.42 21.73 41 13.90 5 5.66 43.02 30.66

12 0.825 1.319 3.16 3.18 6 26.15 28.13 9 17.91 18.02 34 24.43 8 4.60 47.62 32.73

13 0.9 1.386 2.58 2.65 5 27.83 28.13 9 14.64 14.84 28 31.04 10 4.07 50.16 32.20

14 0.975 1.442 2.53 2.65 5 29.01 31.25 10 14.36 14.84 28 33.03 11 4.07 53.29 35.32

15 1.05 1.498 2.48 2.65 5 30.19 31.25 10 14.05 14.31 27 34.86 12 4.07 55.88 35.32

16 1.125 1.554 2.48 2.65 5 31.37 34.38 11 14.08 14.31 27 36.77 12 4.07 55.88 38.45

17 1.2 1.61 2.51 2.65 5 32.55 34.38 11 14.22 14.31 27 38.67 13 4.07 59.01 38.45

18 1.275 1.633 2.51 2.65 5 33.04 34.38 11 14.22 14.31 27 39.46 13 4.07 59.01 38.45

19 1.35 1.657 2.51 2.65 5 33.54 34.38 11 14.24 14.31 27 40.25 13 4.07 59.01 38.45

20 1.425 1.681 2.52 2.65 5 34.03 34.38 11 14.28 14.31 27 41.04 14 4.07 62.13 38.45

21 1.5 1.704 2.55 2.65 5 34.53 37.50 12 14.43 14.84 28 42.12 14 4.07 62.66 41.57

22 1.575 1.694 2.58 2.65 5 34.31 34.38 11 14.62 14.84 28 41.76 14 4.07 62.66 38.45

23 1.65 1.683 2.62 2.65 5 34.08 34.38 11 14.82 14.84 28 41.40 14 4.07 62.66 38.45

24 1.725 1.673 2.65 3.18 6 33.59 34.38 11 15.03 15.37 29 37.11 12 4.60 57.47 38.98

25 1.8 1.662 2.70 3.18 6 33.37 34.38 11 15.31 15.37 29 36.77 12 4.60 57.47 38.98

26 1.875 1.651 2.73 3.18 6 33.14 34.38 11 15.44 15.90 30 36.57 12 4.60 58.00 38.98

27 1.95 1.64 2.75 3.18 6 32.92 34.38 11 15.58 15.90 30 36.21 12 4.60 58.00 38.98

28 2.025 1.63 2.77 3.18 6 32.69 34.38 11 15.71 15.90 30 35.86 12 4.60 58.00 38.98

29 2.1 1.619 2.80 3.18 6 32.46 34.38 11 15.85 15.90 30 35.50 12 4.60 58.00 38.98

30 2.25 1.598 2.80 3.18 6 32.02 34.38 11 15.85 15.90 30 34.80 12 4.60 58.00 38.98

31 2.4 1.577 2.85 3.18 6 31.58 34.38 11 16.12 16.43 31 34.16 11 4.60 55.41 38.98

32 2.55 1.556 2.80 3.18 6 31.13 31.25 10 15.85 15.90 30 33.38 11 4.60 54.88 35.85

33 2.7 1.534 2.75 3.18 6 30.67 31.25 10 15.56 15.90 30 32.66 11 4.60 54.88 35.85

34 2.85 1.513 2.69 3.18 6 30.23 31.25 10 15.25 15.37 29 31.91 11 4.60 54.35 35.85

35 3 1.492 2.63 2.65 5 30.06 31.25 10 14.93 15.37 29 34.88 12 4.07 56.94 35.32

36 3.15 1.471 2.58 2.65 5 29.62 31.25 10 14.59 14.84 28 34.05 11 4.07 53.29 35.32

37 3.3 1.45 2.51 2.65 5 29.18 31.25 10 14.25 14.31 27 33.21 11 4.07 52.76 35.32

38 3.45 1.429 2.45 2.65 5 28.72 31.25 10 13.90 14.31 27 32.47 11 4.07 52.76 35.32

39 3.6 1.407 2.39 2.65 5 28.27 31.25 10 13.54 13.78 26 31.63 11 4.07 52.23 35.32

40 3.75 1.386 2.32 2.65 5 27.83 28.13 9 13.16 13.25 25 30.80 10 4.07 48.57 32.20

41 3.9 1.365 2.26 2.65 5 27.39 28.13 9 12.78 13.25 25 30.11 10 4.07 48.57 32.20

42 4.05 1.344 2.19 2.65 5 26.93 28.13 9 12.39 12.72 24 29.28 10 4.07 48.04 32.20

43 4.2 1.322 2.12 2.12 4 26.75 28.13 9 11.99 12.19 23 32.42 11 3.54 50.11 31.67

44 4.35 1.301 2.04 2.12 4 26.30 28.13 9 11.58 11.66 22 31.45 11 3.54 49.58 31.67

45 4.5 1.279 1.97 2.12 4 25.85 28.13 9 11.16 11.66 22 30.72 10 3.54 46.45 31.67

46 4.65 1.257 1.90 2.12 4 25.38 28.13 9 10.74 11.13 21 29.75 10 3.54 45.92 31.67

47 4.8 1.235 1.82 2.12 4 24.92 25.00 8 10.31 10.60 20 28.78 10 3.54 45.39 28.54

48 4.95 1.214 1.74 2.12 4 24.47 25.00 8 9.87 10.07 19 27.81 9 3.54 41.74 28.54

49 5.1 1.192 1.66 2.12 4 24.02 25.00 8 9.41 9.54 18 26.85 9 3.54 41.21 28.54

50 5.25 1.17 1.59 1.59 3 23.82 25.00 8 8.96 9.01 17 30.37 10 3.01 43.27 28.01

51 5.4 1.148 1.59 1.59 3 23.36 25.00 8 8.48 8.48 16 29.18 10 3.01 42.74 28.01

52 5.55 1.125 1.59 1.59 3 22.89 25.00 8 7.99 8.48 16 28.44 10 3.01 42.74 28.01

53 5.7 1.103 1.59 1.59 3 22.41 25.00 8 7.50 7.95 15 27.25 9 3.01 39.09 28.01

54 5.85 1.081 1.59 1.59 3 21.94 25.00 8 7.01 7.42 14 26.06 9 3.01 38.56 28.01

55 6 1.058 1.59 1.59 3 21.47 21.88 7 6.51 6.89 13 24.86 8 3.01 34.90 24.89

56 6.15 1.035 1.59 1.59 3 20.98 21.88 7 6.01 6.36 12 23.64 8 3.01 34.37 24.89

57 6.3 1.012 1.59 1.59 3 20.50 21.88 7 5.51 5.83 11 22.41 8 3.01 33.84 24.89

58 6.45 0.989 1.59 1.59 3 20.01 21.88 7 5.00 5.30 10 21.17 7 3.01 30.19 24.89

59 6.6 0.966 1.59 1.59 3 19.53 21.88 7 4.50 4.77 9 19.92 7 3.01 29.66 24.89

60 6.75 0.943 1.59 1.59 3 19.04 21.88 7 3.99 4.24 8 18.65 6 3.01 26.00 24.89

61 6.9 0.92 1.59 1.59 3 18.56 18.75 6 3.49 3.71 7 17.37 6 3.01 25.47 21.76

62 7.05 0.896 1.59 1.59 3 18.05 18.75 6 3.01 3.18 6 16.05 6 3.01 24.94 21.76

63 7.2 0.872 1.59 1.59 3 17.55 18.75 6 2.53 2.65 5 14.71 5 3.01 21.29 21.76

64 7.35 0.848 1.59 1.59 3 17.04 18.75 6 2.06 2.12 4 13.35 5 3.01 20.76 21.76

65 7.5 0.824 1.59 1.59 3 16.54 18.75 6 1.61 2.12 4 12.91 5 3.01 20.76 21.76

66 7.65 0.8 1.59 1.59 3 16.03 18.75 6 1.18 1.59 3 11.57 4 3.01 17.10 21.76

67 7.8 0.776 1.59 1.59 3 15.53 15.63 5 0.77 1.06 2 10.25 4 3.01 16.57 18.64

68 7.95 0.751 1.59 1.59 3 15.00 15.63 5 0.40 0.53 1 9.20 3 3.01 12.92 18.64

69 8.1 0.726 1.59 1.59 3 14.47 15.63 5 0.41 0.53 1 8.86 3 3.01 12.92 18.64

70 8.25 0.701 1.59 1.59 3 13.95 15.63 5 0.50 0.53 1 8.52 3 3.01 12.92 18.64

71 8.4 0.676 1.59 1.59 3 13.42 15.63 5 0.41 0.53 1 8.17 3 3.01 12.92 18.64

72 8.55 0.651 1.59 1.59 3 12.89 15.63 5 0.58 1.06 2 8.38 3 3.01 13.45 18.64

73 8.7 0.626 1.59 1.59 3 12.37 12.50 4 0.57 1.06 2 8.00 3 3.01 13.45 15.51

74 8.85 0.601 1.59 1.59 3 11.84 12.50 4 0.65 1.06 2 7.63 3 3.01 13.45 15.51
11

TABLE 4. VARIATION OF STRUCTURAL PROPERTIES ALONG THE BLADE LENGTH

radius chord twist m Iyy Ixx x_cg x_ea GJ EA EIlag EIflap

(m) (m) (deg) kg/m kg-m kg-m (m) (m) MN-m2 MN MN-m2 MN-m2

0 0.8 12.86 204.67 1.28E+01 1.47E+01 0 0 7.09E+07 3.17E+09 2.52E+08 2.43E+08

0.075 0.823 12.86 208.4 1.37E+01 1.50E+01 -0.003 -0.003 7.37E+07 3.21E+09 2.69E+08 2.47E+08

0.15 0.847 12.86 211.61 1.45E+01 1.51E+01 -0.007 -0.007 7.60E+07 3.24E+09 2.84E+08 2.47E+08

0.225 0.871 12.86 214.67 1.54E+01 1.51E+01 -0.01 -0.01 7.81E+07 3.27E+09 3.00E+08 2.46E+08

0.3 0.894 12.86 217.58 1.63E+01 1.50E+01 -0.014 -0.014 8.00E+07 3.30E+09 3.15E+08 2.44E+08

0.375 0.95 12.86 225.16 1.87E+01 1.55E+01 -0.024 -0.024 8.70E+07 3.40E+09 3.59E+08 2.50E+08

0.45 1.006 12.86 233.16 2.12E+01 1.56E+01 -0.035 -0.035 9.33E+07 3.48E+09 4.03E+08 2.49E+08

0.525 1.062 12.86 170.33 5.00E+00 8.13E+00 0.054 0.076 5.42E+07 2.56E+09 1.12E+08 1.70E+08

0.6 1.118 12.86 157 4.98E+00 7.25E+00 0.045 0.069 5.11E+07 2.34E+09 1.11E+08 1.48E+08

0.675 1.185 12.86 143.82 4.96E+00 6.64E+00 0.032 0.058 4.92E+07 2.07E+09 1.10E+08 1.30E+08

0.75 1.252 12.86 132.24 4.92E+00 6.00E+00 0.017 0.045 4.68E+07 1.83E+09 1.07E+08 1.12E+08

0.825 1.319 12.86 114.73 4.64E+00 4.97E+00 0.004 0.032 3.95E+07 1.52E+09 9.56E+07 8.82E+07

0.9 1.386 12.86 100.4 4.28E+00 4.05E+00 -0.014 0.017 3.47E+07 1.25E+09 8.55E+07 6.72E+07

0.975 1.442 12.86 102.79 4.51E+00 3.96E+00 -0.03 0.003 3.66E+07 1.25E+09 9.15E+07 6.45E+07

1.05 1.498 12.86 102.57 4.58E+00 3.80E+00 -0.047 -0.013 3.82E+07 1.22E+09 9.53E+07 6.00E+07

1.125 1.554 12.86 103.84 4.65E+00 3.60E+00 -0.066 -0.029 4.01E+07 1.22E+09 1.01E+08 5.62E+07

1.2 1.61 12.86 105.25 4.70E+00 3.38E+00 -0.085 -0.047 4.21E+07 1.22E+09 1.06E+08 5.17E+07

1.275 1.633 12.86 105.32 4.66E+00 3.24E+00 -0.094 -0.054 4.28E+07 1.21E+09 1.08E+08 4.94E+07

1.35 1.657 12.86 105.35 4.60E+00 3.10E+00 -0.102 -0.062 4.36E+07 1.21E+09 1.10E+08 4.70E+07

1.425 1.681 12.86 106.24 4.58E+00 2.97E+00 -0.111 -0.07 4.44E+07 1.21E+09 1.12E+08 4.45E+07

1.5 1.704 12.86 108.87 4.61E+00 2.86E+00 -0.119 -0.077 4.56E+07 1.24E+09 1.16E+08 4.30E+07

1.575 1.694 12.53 107.1 4.48E+00 2.72E+00 -0.118 -0.076 4.44E+07 1.23E+09 1.13E+08 4.09E+07

1.65 1.683 12.2 105.97 4.35E+00 2.59E+00 -0.117 -0.075 4.32E+07 1.21E+09 1.10E+08 3.89E+07

1.725 1.673 11.87 108.92 4.05E+00 2.54E+00 -0.122 -0.077 4.75E+07 1.26E+09 1.15E+08 3.84E+07

1.8 1.662 11.54 107.65 3.91E+00 2.40E+00 -0.121 -0.076 4.62E+07 1.24E+09 1.12E+08 3.62E+07

1.875 1.651 11.265 108.63 3.93E+00 2.34E+00 -0.119 -0.075 4.54E+07 1.26E+09 1.11E+08 3.57E+07

1.95 1.64 10.99 107.57 3.81E+00 2.24E+00 -0.118 -0.074 4.42E+07 1.25E+09 1.09E+08 3.41E+07

2.025 1.63 10.715 106.51 3.70E+00 2.14E+00 -0.118 -0.074 4.31E+07 1.24E+09 1.06E+08 3.26E+07

2.1 1.619 10.44 105.46 3.59E+00 2.05E+00 -0.117 -0.073 4.20E+07 1.22E+09 1.03E+08 3.11E+07

2.25 1.598 9.97 103.75 3.42E+00 1.92E+00 -0.116 -0.072 4.02E+07 1.20E+09 9.84E+07 2.91E+07

2.4 1.577 9.5 102.8 3.28E+00 1.77E+00 -0.113 -0.07 3.85E+07 1.21E+09 9.54E+07 2.72E+07

2.55 1.556 9.105 98.97 3.05E+00 1.66E+00 -0.113 -0.07 3.67E+07 1.16E+09 8.96E+07 2.54E+07

2.7 1.534 8.71 97.6 2.93E+00 1.59E+00 -0.112 -0.069 3.52E+07 1.14E+09 8.59E+07 2.43E+07

2.85 1.513 8.365 94.46 2.71E+00 1.49E+00 -0.111 -0.068 3.35E+07 1.09E+09 8.06E+07 2.26E+07

3 1.492 8.02 90.61 2.78E+00 1.40E+00 -0.104 -0.064 2.86E+07 1.06E+09 7.34E+07 2.15E+07

3.15 1.471 7.725 86.87 2.54E+00 1.30E+00 -0.104 -0.064 2.72E+07 1.01E+09 6.87E+07 2.00E+07

3.3 1.45 7.43 83.9 2.35E+00 1.22E+00 -0.104 -0.064 2.58E+07 9.67E+08 6.42E+07 1.85E+07

3.45 1.429 7.17 82.66 2.24E+00 1.17E+00 -0.103 -0.063 2.46E+07 9.53E+08 6.14E+07 1.77E+07

3.6 1.407 6.91 79.74 2.07E+00 1.09E+00 -0.102 -0.063 2.33E+07 9.08E+08 5.72E+07 1.63E+07

3.75 1.386 6.68 75.71 1.88E+00 1.00E+00 -0.103 -0.062 2.21E+07 8.63E+08 5.33E+07 1.50E+07

3.9 1.365 6.45 74.56 1.79E+00 9.58E-01 -0.101 -0.062 2.11E+07 8.50E+08 5.09E+07 1.43E+07

4.05 1.344 6.245 71.78 1.64E+00 8.90E-01 -0.101 -0.061 1.99E+07 8.07E+08 4.73E+07 1.32E+07

4.2 1.322 6.04 66.81 1.62E+00 8.07E-01 -0.095 -0.058 1.64E+07 7.50E+08 4.12E+07 1.19E+07

4.35 1.301 5.86 64.17 1.48E+00 7.48E-01 -0.095 -0.058 1.54E+07 7.09E+08 3.81E+07 1.09E+07

4.5 1.279 5.68 62.49 1.39E+00 7.03E-01 -0.094 -0.057 1.47E+07 6.97E+08 3.62E+07 1.04E+07

4.65 1.257 5.515 59.92 1.26E+00 6.48E-01 -0.093 -0.057 1.38E+07 6.57E+08 3.33E+07 9.42E+06

4.8 1.235 5.35 56.94 1.15E+00 5.97E-01 -0.093 -0.056 1.29E+07 6.18E+08 3.06E+07 8.54E+06

4.95 1.214 5.2 53.91 1.02E+00 5.42E-01 -0.094 -0.056 1.21E+07 5.81E+08 2.81E+07 7.73E+06

5.1 1.192 5.05 51.54 9.14E-01 4.98E-01 -0.094 -0.056 1.13E+07 5.44E+08 2.58E+07 6.97E+06

5.25 1.17 4.91 47.2 9.09E-01 4.42E-01 -0.087 -0.052 8.90E+06 4.95E+08 2.17E+07 6.17E+06

5.4 1.148 4.77 44.95 8.16E-01 4.03E-01 -0.087 -0.052 8.28E+06 4.60E+08 1.97E+07 5.51E+06

5.55 1.125 4.64 44.07 7.69E-01 3.80E-01 -0.086 -0.051 7.80E+06 4.51E+08 1.85E+07 5.19E+06

5.7 1.103 4.51 41.33 6.69E-01 3.40E-01 -0.086 -0.051 7.24E+06 4.17E+08 1.68E+07 4.61E+06

5.85 1.081 4.385 39.2 5.92E-01 3.07E-01 -0.086 -0.051 6.70E+06 3.85E+08 1.51E+07 4.07E+06

6 1.058 4.26 36.22 5.10E-01 2.73E-01 -0.087 -0.052 6.19E+06 3.53E+08 1.36E+07 3.57E+06

6.15 1.035 4.145 34.2 4.44E-01 2.45E-01 -0.088 -0.052 5.71E+06 3.23E+08 1.21E+07 3.11E+06

6.3 1.012 4.03 32.23 3.84E-01 2.19E-01 -0.088 -0.052 5.25E+06 2.93E+08 1.08E+07 2.69E+06

6.45 0.989 3.915 29.84 3.17E-01 1.92E-01 -0.089 -0.053 4.82E+06 2.65E+08 9.55E+06 2.31E+06

6.6 0.966 3.8 27.99 2.67E-01 1.70E-01 -0.09 -0.054 4.41E+06 2.37E+08 8.42E+06 1.96E+06

6.75 0.943 3.685 25.75 2.11E-01 1.47E-01 -0.092 -0.055 4.03E+06 2.11E+08 7.39E+06 1.65E+06

6.9 0.92 3.57 23.68 1.73E-01 1.29E-01 -0.093 -0.056 3.67E+06 1.85E+08 6.45E+06 1.37E+06

7.05 0.896 3.46 21.99 1.36E-01 1.13E-01 -0.094 -0.058 3.32E+06 1.60E+08 5.57E+06 1.12E+06

7.2 0.872 3.35 19.94 9.29E-02 9.50E-02 -0.097 -0.061 2.99E+06 1.37E+08 4.77E+06 8.91E+05

7.35 0.848 3.24 18.38 6.34E-02 8.17E-02 -0.098 -0.065 2.69E+06 1.14E+08 4.05E+06 6.93E+05

7.5 0.824 3.13 17.86 5.81E-02 7.49E-02 -0.095 -0.063 2.46E+06 1.11E+08 3.72E+06 6.36E+05

7.65 0.8 3.015 16 2.58E-02 6.18E-02 -0.099 -0.068 2.19E+06 8.99E+07 3.11E+06 4.76E+05

7.8 0.776 2.9 14.31 7.61E-03 5.21E-02 -0.101 -0.077 1.92E+06 7.00E+07 2.56E+06 3.38E+05

7.95 0.751 2.785 12.59 -1.86E-02 4.17E-02 -0.106 -0.091 1.64E+06 5.11E+07 2.04E+06 2.19E+05

8.1 0.726 2.67 12.17 -1.68E-02 3.76E-02 -0.103 -0.088 1.48E+06 4.94E+07 1.84E+06 1.98E+05

8.25 0.701 2.55 11.75 -1.51E-02 3.38E-02 -0.099 -0.085 1.33E+06 4.77E+07 1.66E+06 1.78E+05

8.4 0.676 2.43 11.33 -1.36E-02 3.03E-02 -0.096 -0.082 1.19E+06 4.60E+07 1.49E+06 1.59E+05

8.55 0.651 2.305 11.69 -1.49E-04 2.96E-02 -0.087 -0.065 1.13E+06 5.87E+07 1.51E+06 1.98E+05

8.7 0.626 2.18 11.01 1.49E-03 2.63E-02 -0.084 -0.062 1.01E+06 5.65E+07 1.34E+06 1.76E+05

8.85 0.601 2.06 10.57 1.32E-03 2.32E-02 -0.08 -0.06 8.92E+05 5.42E+07 1.19E+06 1.56E+05
12

TABLE 5. BREAKDOWN OF THE BLADE MASS BY STRUCTURAL MATERIALS

Material Mass Blade filler option

Gelcoat 15.5 kg

Nexus 22.8 kg

Core (foam) 89.5 kg

Skin (double-bias plies) 120.1 kg

Lining (double-bias plies) 23.7 kg

Unidirectional plies 386.8 kg

Bond material 35.8 kg

Inserts for hub attachment 35.5 kg

Filler 2202.7 kg Water

2483.5 kg Epoxy Slurry

Total blade mass 2932.5 kg Water

3213.2 kg Epoxy Slurry