Structural dynamics

Articles on this page:

• Difference between Normal and Attachment modes
• Blade torsion in different Bladed versions
• Bladed Support Structure vs Superelement approach
• Output blade and tower mode shapes
• Ill-conditioned stiffness or mass matrix
• Difference between Yaw Bearing and Tower Top loads
• Support structure "refine deflections"
• LSS shaft bending location
• Tower attachment mode shapes
• Define different mass on each blade
• Foundation stiffness matrix form
• "Refine Deflections" superseded by new functionality
• Rigid body mass tensor
• Tip-tower closest approach seems inaccurate
• Axis-angle representation in Bladed
• How do seismic accelerations work with foundations / PY curves / soil springs?
• Bladed doesn't find good initial conditions (e.g. blade deflections)
• Algorithm for calculating blade-to-tower distance
• Non-linear foundation forces only exact if load along x or y axis
• How to deal with the errors of a poorly defined structural model
• How to define a support structure which contains very high stiffness elements
• Why does support structure geometric stiffness not have an effect on tower frequencies in the Campbell diagram?
• Blade shear center axis orientation transformation

Problem

What is the difference between "normal" and "attachment" modes calculated in modal analysis?

How can normal modes calculated in other softwares be compared to those calculated in Bladed?

Solution

Blades

For the blades, only normal modes are calculated. The blade root is constrained, and then the eigenvector/value problem is solved.

Support structure (tower)

Attachment mode shapes are calculated by applying loads to the tower top and calculating the resulting nodal displacements. Tower tower is constrained at the proximal node* for this calculation. Such modes are sometimes referred to as “static” modes as they represent static deflection as a result of an applied unit force or moment.

Normal modes are calculated by constraining the nodes at the tower base and the tower top and then solving the eigenvector/value solution to find the “internal” vibration mode shapes.

For the support structure, the interpretation of the definition of "normal" modes can sometimes cause confusion. The conventional ‘normal’ modes of a support structure include free vibration modes where the top of the tower is free to move with no external forces on it. In Bladed, the ‘normal’ modes where the top of the tower is free to move are not calculated. The attachment modes are calculated instead which are more realistic as in reality the tower top will move due to the application of external forcing from the structure above it.

This means that if the free vibration ‘normal modes’ for the tower structure are calculated with only the tower base constrained, they will not match the mode frequencies calculated by Bladed.

Bladed also calculates “coupled” vibration modes in the Campbell diagram, that show how the normal and attachment modes combine into coupled vibration modes at a specific operating point. Typically, these coupled modes correspond well to normal modes calculated in other software, with the tower base constrained and the tower top free to move.

* The proximal node is the component (e.g. blade or tower) structural node to which the modal deflections are calculated relative to. For the blade, this is the blade root. For the support structure, the proximal node is and extra structural structural node at 0,0,0. The support structure foundations (either rigid or flexible) link the proximal node to the foundation nodes in the support structure.

Keywords

Mode shapes; Normal; Attachment; Modal analysis

Problem

What are the differences in blade torsion modelling in different Bladed versions?

Solution

• For Bladed 4.17 and later versions, please consult the online documentation (search for "geometric stiffness").
• For Bladed 4.16 and earlier versions, please refer to the Geometric stiffening options in Bladed document.

Keywords

Blade; Torsion

Problem

What advantages does Bladed’s coupled modelling of the turbine and support structure have over using a Superelement to model the support structure?

Solution

Both Bladed's standard fully integrated approach and the “superelement” approach use the Craig-Bampton method to calculate reduced mass and stiffness matrices (corresponding to support structure deflection mode shapes) in order to reduce simulation time. The standard method has some advantages over the superelement approach. The superelement method is sometimes invaluable however, in dealing with cases where the support structure cannot be created in Bladed or is kept confidential. For more details on Bladed's superelement feature, see the online documentation (or this document for Bladed 4.16 and earlier).

Bladed uses the Craig-Bampton method as a pre-processing step. However, as Bladed also retains the underlying support structure finite element model during the simulation, some modelling refinements compared to the “superelement” approach are possible.

Firstly, the deflected position of each individual member in the support structure can be taken into account at each time step, leading to coupling between structural motion and hydrodynamic loading. Secondly, the structural deflections can be used to provide a better estimate of structural response by calculating the additional stiffness due to structural displacements (called “stress stiffening” or “geometric stiffening”). Finally, retaining the detailed FE model allows Bladed to include a non-linear foundation model which can be important to properly evaluate foundation response.

In the “superelement” approach, Craig-Bampton mode shapes are calculated, but the detailed finite element model used to calculate the mode shapes is discarded. A reduced wave load must also be calculated as a pre-processing step, specifying the wave loading on the support structure assuming that the structure is stationary. The effect of structural motion on wave loading would therefore not be accounted for. Additionally, foundation properties must be included in the pre-calculated superelement, meaning that only linear (i.e. constant stiffness) foundation properties can be defined.

Keywords

Superelement; Support structure

Problem

Is it possible to output the exact mode shapes of blades and tower from Bladed?

Solution

It’s possible to find the blade and tower mode shapes in the .$PJ file.

• Bladed 4.7 and earlier
  They are located in the section MSTART RMODE.
  The blade modes are reported first. The line NBLADE gives the number of blade modes used, the line FREQ reports the frequency and so on.
  The mode shapes are given in the lines MD011, MD012… etc. The naming convention is such that the first two numbers is the mode number and the last digit is the direction. For example:
  Copy

  MD011 // mode 1, nodal x deflection  
  MD012 // mode 1, nodal y deflection  
  MD013 // mode 1, nodal z deflection  
  MD014 // mode 1, nodal x rotation  
  MD015 // mode 1, nodal y rotation  
  MD016 // mode 1, nodal z rotation  
  MD021 // mode 2, nodal x deflection  
  

• Bladed 4.8 and later
  This information is in the XML section under <TowerMode> for tower, or section <BladeModeContainer> for blades.
  Each six values represents a node displacement in the six degree of freedom.
  The mode shapes are normalised by a constant factor so that the maximum translational or rotational deflection is 1. The linear deflections are in meters and angular deflections in radians.

Keywords

Blade modes; Tower modes

Problem

Bladed sometimes reports an error during modal analysis about a stiffness or mass matrix being ill-conditioned.

What does this mean and how can this problem be resolved?

For example:

*** ERROR: mbflexbody.hpp(284): "Blade1-0" has singular or ill-conditioned stiffness matrix relating to free dofs. (Reciprocal condition number: 6.09387e-016)

*** ERROR: mbflexbody.cpp(818): "Blade1-0" - Singular or ill-conditioned mass matrix

Solution

The errors above are reporting mathematical difficulties when the stiffness or mass matrix for the blade is being created. Typically this is caused by having some very small and very large values together in a stiffness or mass matrix, making the problem difficult to solve numerically.

This error can be caused in various ways, but usually due to some non-physical structural definition being entered for the blade or tower. Some things to check are:

1. Check any warnings, as they can often indicate the problem.
2. Look for any physical impossibilities in the model, such as very low mass members, or very low stiffnesses. Remember to check torsional inertia and stiffness properties as well as mass and bending stiffness.
3. Ensure that there are no very small blade elements, as created by two blade stations very close together. A similar problem could be caused by a very small blade element being adjacent to a very large element.
4. For the tower, check that any rigid members are defined in Project Info, if desired. Very stiff members should be made rigid through Project Info rather than simply choosing a very high stiffness value.

Keywords

Ill-conditioned; Singular; Mass matrix; Stiffness matrix

Problem

Why are Yaw Bearing and Tower Top loads sometimes different even when the yaw angle is zero?

Solution

In Bladed 4.4 and earlier, there is a slight different in coordinate system between the tower loads and the yaw bearing loads even when the yaw angle is zero.

In the diagram below, the dotted line shows the deflected tower position. In Bladed 4.4 and earlier, the coordinate system for tower load output doesn’t rotate with deflections. From Bladed 4.5, the tower load output coordinate system does rotate with tower deflection, so there should be an exact match between tower and yaw bearing loads when yaw angle = 0.

In both Bladed 4.4 and 4.5, the coordinate system for yaw bearing loads does rotate with nacelle rotation, so only in Bladed 4.5 and later will you see an exact match in loads.

Keywords

Tower; Yaw Bearing

Problem

What does the support structure "Refine deflections" option in Calculation Outputs do?

Solution

There is an option in the support structure outputs to Refine deflections. With this option disabled, the tower deflection outputs are modal deflections. Modal deflections give a good estimate of overall tower motion, but may not be appropriate to calculate the small deflections at certain support structure stations, such as the foundations. With Refine deflections disabled, the foundation reactions are calculated by combining the modal deflections with the stiffness matrix provided for the foundation station. This can lead to a poor estimate of the foundation reaction loads given the applied loads on the rest of the turbine.

A good illustration of this problem is to consider a monopile tower without a vertical attachment mode. In this case, none of the tower vibration modes have a contribution in the vertical direction, so the tower node vertical displacements will always be zero. Therefore, the foundation reaction force in the vertical direction will always be zero, as the reactions are calculated from the modal deflections. In this case, the Refine deflections option would be needed to obtain correct foundation reaction loads.

With the Refine deflections feature enabled, the tower deflections are re-calculated at each output time step using the underlying finite element model with the external loads applied. The refined deflections give a more accurate estimate of the deflections at the foundation nodes, without being constrained only to fixed mode shapes, hence the foundation reaction forces will correctly balance the applied loads. In the case of non-linear foundations, there is also a static iteration between the refined deflections and the applied foundation load to more accurately calculate the non-linear foundation reaction force. Enabling the refine deflections option will therefore ensure that the applied loads and foundation reactions correspond correctly.

Note that, in all cases, the modal deflections are used to estimate the foundation loads when solving the structural system at each integrator time step. To use the refined deflections at every time step would require iteration on each time step, causing a significant increase in simulation time. The assumption with this modelling choice is that error in foundation load estimate due to using modal deflections doesn’t affect the overall turbine dynamics significantly. It is therefore reasonable to only calculate the foundation reaction loads based on refined deflection on each output time step.

Keywords

Support structure; Refined deflections

Problem

Where is the LSS bending hinge located relative to the hub centre?

Solution

This is summarised in the diagram below:

Keywords

LSS bending

Problem

How are the tower attachment mode shapes calculated?

Solution

The Craig-Bampton method uses a mixture of “normal” and “boundary” mode shapes.

• Boundary mode shapes are calculated by applying loads or displacements to the tower top and calculating the resulting nodal displacements. The tower is constrained at the tower base for this calculation. Such modes are sometimes referred to as “static” modes as they represent static deflection as a result of an applied unit loads or displacements.
• Normal modes are calculated by constraining the nodes at the tower base and the tower top and then solving the eigenvector/value solution to find the “internal” vibration mode shapes.

There are two different type of modes that could be calculated for the boundary modes

• Attachment modes, which are calculated by applying unit forces and moments (6 in total) at the nacelle attachment node. These mode shapes tend to include a mixture of rotation and translation at the nacelle attachment node.
• Constraint modes, which are calculated by applying unit translations and rotations (6 in total) at the nacelle attachment node. In this case, when 1 DoF is activated, the other 5 are constrained to not move.

Bladed uses attachment modes rather than constraint modes. However, once the attachment modes are calculated, the shapes are transformed in order to achieve a diagonal stiffness matrix. For the rotational modes, this transformation results in mode shapes with very little translation at the nacelle attachment node, which look somewhat like constraint modes. This is a slightly confusing situation where some of the Bladed modes look like constraint modes, and some look like attachment modes.

Keywords

Attachment modes; Constraint modes; Boundary modes

Problem

How can I define different mass distributions in each blade?

Solution

NOTE: This is a workaround which works for 4.8 and earlier - it's not applicable to 4.9 or subsequent versions. However, please note there will be a purpose-built solution in Bladed 5.

Firstly, there are two separate files to be aware of:

• powprod.$PJ – this is the turbine definition file that is written to disk for each calculation
• DTBLADED.IN – this is the input file for the calculation code dtbladed.exe. It is temporarily written to the installation directory when the calculation starts.

The two files have very similar formats but some slight differences. An important difference is that the $PJ file contains the inputs to calculate the ice mass on the blade, whereas the DTBLADED.IN file contains the actual mass of each blade including ice. This presents an opportunity to edit the ice mass on each blade manually.

Follow these instructions to define different mass on each blade:

1. Define some ice on at least one blade in the blade screen.
2. Start a calculation and you should see this window. Don’t press “Start” yet. (Don’t see this? Go to Tools > Preferences > select “warn when starting calculation”.)
   
   
   Leaving this window open means that you’ll be able to find the DTBLADED.IN file as described below. The file is deleted when the calculation completes.
3. Navigate to the installation directory and find the DTBLADED.IN file in the folder starting $$$$. Open the file DTBLADED.IN inside this folder.
   
   
   
   
4. In the DTBLADED.IN file, copy the block “MSTART BMASSMB” including the line “MEND”.
   
   
5. Paste the code in the Project Info Special Data box.
   
   
   
   
6. Disable the ice model in the blade screen.
   
   
7. Edit the parameter MASS in Project Info as you see fit. Note that the format is Member1End1, Member1End2, Member 2End1, Member2End2, ...
   
   So, there are (2*num_blade_elements) or equivalently (2_num_blade_stations-2) entries on each line.
   The blade mass distribution for each blade in Project Info will overwrite the blade mass defined in the blade screen.
   
   
8. Run the simulation.

Keywords

Mass blade

Problem

Foundation stiffness matrices often have a particular form, with all diagonal terms positive. There are also off diagonal (OD) terms coupling the translation and rotation terms. The off diagonals often have the same value but opposite sign. Why is this?

Solution

Stiffness matrices are basically derived by applying unit displacements of each degree of freedom individually and considering the restoring force that results from this displacement. So we can pose the question “if I impose x translation of a degree of freedom, what are the reaction forces” or equivalently “what applied forces and moments are required to give pure x translation”.

For the case of pure x deflection (no rotation) at the tip of a cantilever beam (or a lumped foundation) as sketched below, you’d need a positive x force and a negative y moment to make this deflection shape. This corresponds to column 1 of the stiffness matrix.

For the “pure rotation” case, you need to apply a positive y moment and a negative x force to make this shape. This is column 5 of the stiffness matrix.

So, we see that by inspecting the stiffness matrix you can answer the question “what force corresponds to a unit displacement of one degree of freedom”. However, you can’t (by simple inspection) answer the question “what displacement do I get by applying a unit force or unit moment” – for this you’d need to invert the stiffness matrix to give you a flexibility matrix, which you could inspect to answer that question.

In other words: you need to read the stiffness equation from right to left, as you multiply out the displacement and stiffness to get the forces and moments.

Keywords

Foundation stiffness matrix

Problem

In Bladed 4.8 and below, there is a "Refine Deflections" option in Tower Outputs for increasing accuracy of foundation deflections. It's been replaced by improved functionality in Bladed 4.9 and above called "Use finite element deflections for foundation loads".

Solution

In Bladed 4.9 and above, there is a checkbox called "Use finite element deflections for foundation loads" in the Additional Items screen, and there is no longer a "Refine deflections" checkbox in the Tower Outputs screen. Although superficially similar, these are completely different implementations and give different results. The earlier “refined deflections” can give erroneous results for non-linear foundations and in general we recommend that it should not be used. It doesn’t take account of the PY forces from FE deflections in the dynamic solution. The old method tries to calculate a more accurate foundation load after each time step, but the correction is not taken into account in the dynamic solution. This can lead to inconsistent and sometimes inaccurate results. "Use finite element deflections for foundation loads" includes the non-linear PY forces calculated using FE deflections in the dynamic solution, and therefore includes the dynamics from the non-linear foundation correctly. This method is documented in Section 3.7 of the Theory manual for Bladed 4.9 and later versions.

We therefore strongly recommend that you use Bladed 4.9 and later versions for accurate modelling of foundations that include non-linear PY forces.

Keywords

Refine deflections; FEM; Finite element; Foundations; Tower

Problem

Where can I find the assumed turbine rigid body mass tensor used by Bladed in the flexibility manager to calculate the uncoupled tower modes?

Solution

The mass tensor (AKA inertia tensor) is found in the "Inertial information" section of the .$VE output file.

Keywords

Mass tensor; Inertia tensor

Problem

Why is blade tip-to-tower closest approach not always exactly the minimum of the "Blade tip to tower surface" output value?

Clearly the “closest approach” should correspond exactly to the smallest value so far of the tip-to-tower instantaneous value. But sometimes simulations give results like the following, where the closest approach seems not to follow the instantaneous value very closely.

Overview: black line is blade tip to tower surface, red line is closest approach

Close-up showing the problem in detail: same colours

Solution

This is an artefact in the output time series, caused by the calculated values not being exactly in sync with the output values. In fact this value is being calculated correctly. You can confirm this by using a fixed-step integrator and ensuring that the output timestep is the same size as the integrator timestep.

Keywords

Closest approach; Tip to tower; Clearance

Problem

This article explains the axis-angle representation used in Bladed to represent node orientations. Users will interact with this orientation through a variety of Bladed inputs and outputs such as:

• The support structure deflection and support structure global motions output groups.
• The orientation of flexible body nodes (blades and support structure) and multibody nodes accessed via the external loads DLL.
• Inputting floating platform initial orientation in the "initial conditions" window.

This article explains some counter-intuitive results that may occur in particular for floating turbines with yaw rotations.

Solution

Bladed describes the orientation of support structure nodes using a representation known as axis-angle which is a vector of length 3. It is a method of representing rotation where the rotation is characterized by an axis of rotation and an angle. The axis is defined by the vector and the angle of rotation about the axis is given by the magnitude of the vector.

It is important to emphasise that the axis-angle is not equivalent to Euler angles. To explain this we consider two examples where the initial mooring position of a floating vertical cylinder is pitched.

Example 1

The platform is pitched by 10 deg about the global y-axis. This would be represented in Bryant angles (yaw, pitch, roll) as:

X: 0, Y: 10 deg, Z: 0 deg

An axis-angle would represent this rotation by

0, 10, 0 deg

Example 2

The platform is yawed by 180 deg about global z-axis and then pitched by 10 deg about the local y-axis. This would be represented in Bryant angles as:

X: 0, Y: 10 deg, Z: 180 deg

An axis-angle would represent this rotation by

15.6880337, 0, 179.3150457 deg

Counter intuitively the axis-angle has no component in the y-direction even though the platformed is pitched about the y-axis.

Keywords

Axis-angles; Orientation; Angles; Multibody; Floating

Problem

Earthquake simulations require the application of a seismic acceleration time history to the turbine support structure. How does this interact with any foundation soil springs that are used in the model?

Solution

Bladed's seismic model imposes a prescribed acceleration at all the foundation nodes. Where a non-rigid foundation is defined at a node, the acceleration is applied to the "ground" at one end of the theoretical soil spring, not to the tower node at the other end. If we simplify to one DoF and imagine it as a literal spring, it would look something like this:

Keywords

Earthquake; Seismic; P-Y curves; Soil springs; Foundations; Acceleration

Problem

Bladed can sometimes struggle to find the correct initial operating conditions (e.g. blade deflections, pitch angle), especially with some multi-part blade models. This can often be most clearly seen in Steady Calculations or Campbell Diagram initial conditions.

Example plot below:

Solution

Set the "initial conditions relaxation factor" to a value below 1 e.g. 0.4 in the "Additional Items" screen. (Available in 4.8.0.86 and later versions)

The initial deflections should then be reasonable as shown below:

Keywords

Blade deflections; Initial conditions

Problem

How is the closest approach of blade tip to tower calculated?

Solution

Keywords

Approach; Closest; Distance; Tower; Blade; Support structure

Problem

When non-linear foundations are present in the model, the correct reaction force is only calculated when the deflections are exactly along the global x or y directions.

Solution

The problem arises from the way Bladed calculates foundation loads from their components in the x and y directions, combined with the nonlinearity of the soil response. An illustrative example may help. The figure below shows a top view of a pile which undergoes a horizontal displacement of d metres in a direction 45° from the axes.

The foundations screen in Bladed allows non-linear soil stiffness characteristics to be defined as lookup tables.

The calculated restoring force is derived from displacement, via the force/displacement (F/d) curve for a given axis (x, y or z). For simplicity we will assume x-y symmetry, so that the curves for the x and y axes are the same. In the illustration below, a displacement of d metres corresponds to a restoring force of F2 Newtons.

Keywords

Non-linear foundations; P-Y curves; Soil springs; Foundation stiffness

Problem

Here is a list of errors indicate that part of the structure (blades, foundations, tower, or drivetrain/mounting flexibility if present) has a mass or stiffness matrix with some invalid entries.  How can these errors be resolved?

1. Error message:
   
2. Error message:
   Factorisation failed - Invalid non-positive definite matrix

Solution

These errors are typically caused by very small or very large values (or a combination of the two) in a stiffness or mass matrix, which can make it impossible to get an accurate solution to the multibody dynamics equations.

This error can be caused by several factors, the most common of which is the use of a non-physical structural definition for the blade or tower. In order to address this error:

1. Check any warnings, as they can often indicate the problem.
2. Look for any physical impossibilities in the model, such as very low mass members, or very low stiffnesses. Remember to check torsional inertia and stiffness properties as well as mass and bending stiffness.
3. Ensure that there are no very small blade elements, as created by two blade stations very close together.  A similar problem could be caused by a very small blade element being adjacent to a very large element.
4. For a support structure, check that any rigid members are defined in Project Info, if desired. Very stiff members should be made rigid through Project Info rather than simply choosing a very high stiffness value. Please refer to this article about how to define it in the "project info".
5. If the above doesn't yield a solution, it may help to narrow the problem down by switching off flexibility in one or more components and re-run to see which component is triggering the error.

Keywords

Factorisation; Non-positive definite matrix; Mass; Stiffness; Structural

Problem

Bladed modal analysis cannot cope with a support structure which contains too large a variation in element stiffness or mass. There is a limit on the stiffness values that can be used as explained in this article

Users may want to insert an offset node and therefore define a massless and rigid element. However this cannot be done by editing mass and stiffness of the element as it causes numerical problems like ill-conditioned matrices which cannot be used in the calculation. The solution is to use project info to define rigid elements.

Solution

1. Define low density dummy members in the "Tower" screen, for example like the member 153 in the following figure.
   
   
   
   
2. Go to "File" -> "Project Info" -> tick the option "Turbine calculations(dtbladed.exe)"-> click "Define".
   
   
   
   
3. In the "Special Data" screen, list all the dummy members using the following code. Then, the dummy members will be rigid. The stiffness property defined in the "Tower" screen will be replaced.
   
   
   
   

Keywords

Structural dynamics; Rigid members

Problem

Enabling "axial only" geometric stiffness on the support structure is expected to lower the tower natural frequencies, an effect known as "gravitational destiffening". Why can't I see this effect in the Campbell diagram?

Solution

Gravity is disabled by default in the Campbell Diagram and Linearisation calculations for onshore and fixed offshore turbines. The gravity is disabled to remove periodicity in the rotor, i.e. so that the linear system is the same at any azimuth angle, and a linear time invariant system can be generated for control design.

This means that the "axial" (vertical) load in the vertical tower members is zero (or close to zero) due to missing gravity load. The "axial only" geometric stiffness is proportional to the axial load in each member. So the geometric stiffness has no effect on the vertical tower members without gravity load.

To observe the gravitational destiffening effect, you can enable the gravity in "calculation options". However, this will also introduce unwanted periodicity into the system.

Keywords

Campbell; Tower; Support structure; Geometric stiffness

Problem

What setting should I choose for “'ignore blade shear center axis orientation transformation”?

Solution

This option allows users to control whether the orientation difference between the shear axis and neutral axis is taken into account in the blade cross sectional stiffness matrix. Full theoretical details can be found in the document Bend Twist Coupling in Bladed Beam Elements

The shear axis orientation transformation was originally implemented in Bladed to deal with a situation where blade designers added local cross section reinforcement typically near the blade root. Such reinforcement moves the elastic (bending) centre, but does not much affect the shear centre, and as such blade torsion should not change much when such local reinforcement is added. In order to reduce the sensitivity of torsion deflection to local blade design changes, a transformation was introduced that accounted for the orientation difference between the shear and neutral axes. This means that the beam torsion axis is around the shear axis orientation rather than around the neutral axis orientation.

However, in some blades, the shear centre axis can be non-smooth in the spanwise direction, as the centre is quite different between subsequent stations. This can result in the torsion axis (shear axis) being quite misaligned from the expected direction (i.e. roughly following the pre-bend blade local Z direction). As the torsion stiffness is low, the torsion axis direction can have a significant effect on the blade deflection. With the transformation enabled, for some blades, the torsional deflection on the blade can become non smooth and potentially non-physical. Therefore some blade designers prefer to assume that the torsion axis is parallel to the neutral axis, which is possible by selecting “'ignore blade shear center axis orientation transformation”.

It is the blade designer’s responsibility to make the choice on this setting depending on the blade properties, design and modelling approach used for the blade.

Note that this comparison to HAWC2 had the setting “'ignore blade shear center axis orientation transformation” activated in order to match the assumptions in HAWC2.

Keywords

Blade shear center axis orientation transformation