I am attempting to estimate the blade root bending moment based on the first flapwise modal deflection. I am using values from the 5MW reference turbine. My Matlab code looks like this:

```
clear all; close all; clc;
% Load in blade information
[btable,ttable] = load5MWOC4SemiDistributed;
%%
% Load in OpenFAST simulation
load("5MW_OC4Semi_WSt_WavesWN_FAST_Results.mat");
t = sim_results.Time;
% Extract blade root moments
m1 = sim_results.RootMyb1;
% Extract modal displacement
fb1 = sim_results.Q_B1F1;
% Compute blade root moments from
m1calc = btable.FlpStff(1) * btable.ddFmode1(1) .* fb1;
% Plot comparison
figure
gca; hold on; box on;
plot(t,m1,'DisplayName','OpenFAST')
plot(t,3.25*m1calc*10^-3,'DisplayName','Estimated')
title('Blade 1 Root Flapwise Bending Moment')
xlabel('Time [s]')
ylabel('Moment [kN-m]')
legend
```

To estimate the root bending moment, I am using the following formula:

I have computed the curvature of the blade as the second derivative of the 1st flapwise mode shape (btable.ddFmode1). The blade flapwise stiffness is included via btable.FlpStff in units of Nm^2 (direct from FAST). The mode shape is generated using the normalized shape provided as polynomial coefficients in FAST.

I am comparing the results to RootMyb output from FAST in kN-m. What I am unsure of is that to get values to match, I require an additional factor of ~3.25 (suspiciously close to pi…), as seen in the code. Without this value, this is the result:

With the correction factor this is the result:

Am I misunderstaning the RootMyb output value?

Dear @Ian.Ammerman,

A similar question was asked and answered in the following forum topic: Root moment of blades verification from mode shape function.

Best regards,

Dear @Ian.Ammerman,

I am a user of OpenFAST and i am not from NREL staff. In addition to what Dr Jonkman said, the deflection in the formula you provided denoted “v” is the product of the mode shape and the blade tip displacement. So i assume you did not take the blade tip displacement into consideration right ?

Moreover, you should pay attention to the blade pitch angle governed by the blade pitch controller this influences the principle axis and so on… Furthermore, you should specify in which coordinate system of the blade you are computing your moment (see the documentation of FAST v7).

@Jason.Jonkman ,

Thank you for the note. My understanding of the mode shape and frequency shift due to these effects may be small enough for a good approximation. This is not intended to be a high-accuracy calculation. Perhaps if I generated the mode shapes directly rather than use the polynomial approximation.

@Riad.Elhamoud ,

First, on the formula - this is not the exact notation I am using. Admittedly I grabbed this shot from a textbook to show the relation I am using without trying to type it into inline text for ease of reading.

In that formula, “v” is the deflection at x along the blade, which is computed as q*phi(x) where q is the modal deflection. As a consequence,

d^2v/dx^2 = q*d^2phi/dx^2

Note in my code I multiply by “fb1” which is the modal deflection from OpenFAST.

From OpenFAST documentation, I am pulling the moment from the output “RootMyb” which is the root coordinate system of the blade:

I chose this coordinate system specifically such that blade pitch angle would be bypassed.

I have applied this method for the tower as well with excellent results. I am going to try again with mode shape vector I compute myself with a simple FEA script instead of the polynomial fit to see if that improves the result.

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