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Pitching Moment Calculation
Dear all,
while exporting aero-loads from QBlade for a third-party FEM, I was startled as I saw that my hand calculations for pitching moment are way off from what the QBlade Blade Graph for “Pitching Moment [Nm/m]” displayed, or renormalized to [Nm] with multiplication of element width dr at the respective radius element.
I calculated the pitching moment about the elastic axis of my airfoil with the contribution of the aerodynamic pitch:
M_cm (r) = q(r) *Cm(r)* c(r)^2 *dr (note c(r)^2)
Together with the moment resulting from the lift force in the aerodynamic centre, offset from the elastic centre by dx:
M_cl (r) = q(r) * Cl(r)* c(r) *dr *dx
The total pitching moment at my element was expected to be the sum of the two listed components.
Pitching moment estimated by QBlade is about two OoM larger than my hand-calc with flipped sign.
Are there any other contributions taken into account for the calculation of the pitching moment at every blade element?
Which axis is the pitching moment defined about?
Why does it tend to (relatively) large positive values if the moment coefficient is negative and the contribution of the moment introduced by the offset lift vector is small?
Most importantly – If I need to access segment torsional loads at discrete radii, how should I proceed from here?
Thanks for any support and the thorough work in this forum,
Best regards
M
PS: was not sure about whether to chose this forum or the one about structural analysis, please move me to the right place if I happened to get lost 😉
Hi,
let me try to give you some detail on this topic:
In QBlade the aerodynamic pitching moment about the blade pitch axis / elastic axis is calculated internally as follows:
1. Compute the aerodynamic moment arm from the airfoil pitching-moment coefficient:
double arm = -Cm / Cn + 0.25;
- Cm = aerodynamic pitching-moment coefficient (reference: quarter–chord)
- Cn = normal force coefficient
- 0.25 represents the airfoil aerodynamic center (c/4 point in chord fraction about which Cm is defined)
2. Project this aerodynamic moment to the pitch / elastic axis
if (!std::isnan(arm) && arm != 0 && Cm != 0) Cm_pitch = -(arm – pAxis) * (Cn);
- pAxis is the pitch axis location (chordwise position in fraction of c)
- If no structural model exists → value from Blade Design (Advanced) module
- If a structural model is present → QBlade uses the elastic axis of the beam
- Cm_pitch is therefore already the total aerodynamic pitching moment coefficient about the axis used by the structural beam.
PitchMomentPerLength = Cm_pitch * 0.5 * fluidDensity * V_abs_squared * chord * chord;
- V_abs_squared is the the local relative velocity squared
So PitchMomentPerLength is the aerodynamic moment applied onto the structural beam, already referenced to the correct pitch/elastic axis and aerodynamic forces are applied directly at the beam centerline.
Now regarding thge sectional forces I would strongly recommend to extract them directly from the structural model using “sensor locations”, see:
https://docs.qblade.org/src/user/turbine/structure.html#loading-data-and-sensor-locations
You can find the resulting outputs in the structural timegraph or structural blade graph.
The aerodynamic load mapping and structural beam coupling have been extensively validated. A complete benchmark including sectional force comparison along a highly flexible 22 MW blade is documented here:
https://iopscience.iop.org/article/10.1088/1742-6596/2767/5/052042/pdf
I hope this helps to clear things up a bit.
Best regards,
David
Thank you David for your prompt clarification.
I ponder about an additional question, very basic but just to be sure.
Is the pitching moment positive counting sense the same as with the aerodynamic moment coefficient?
So a positive pitching moment will result in deformation that increases the angle of attack?
Thanks again,
Best regards
M
Quote from MDecker on 17. November 2025, 17:26Thank you David for your prompt clarification.
I ponder about an additional question, very basic but just to be sure.
Is the pitching moment positive counting sense the same as with the aerodynamic moment coefficient?
So a positive pitching moment will result in deformation that increases the angle of attack?Thanks again,
Best regardsM
I guess this answers my question well enough Global Coordinate System — QBlade Documentation 2.0.9.4 documentation Howdy
Hi,
By convention, a positive moment coefficient (Cm) refers to nose-up pitching moment.
If you output sectional moments in QBlade, these are defined within the local body axes – as defined in the part of the documentation that you references.
Best regards,
David
Quote from David on 18. November 2025, 13:27Hi,
By convention, a positive moment coefficient (Cm) refers to nose-up pitching moment.
If you output sectional moments in QBlade, these are defined within the local body axes – as defined in the part of the documentation that you references.
Best regards,
David
So then (referring to my initial post) if sectional pitching moment is positive, but moment coefficient Cm is negative, this has to be due to a negative
-(arm – pAxis)
Initially I thought it was unusual to see negative Cm yet positive pitching moment in the BEM analysis rotor and blade graph.
Hi,
The axial reaction moment (Z_l Mom. BLD pos x.xxx [Nm]) at a blade cross section is not generated solely by aerodynamic moments. It is the internal section resultant of all loads acting on the blade, including aerodynamic loads, elastic restoring moments, inertial forces and gravity.
Because all of these effects are coupled in the structural dynamics of a beam based multibody model, it is not straightforward to extract the pure aerodynamic contribution from the sectional reaction moment.
A way to approximate the aerodynamic contribution is to simulate the turbine under the same operating conditions, but with aerodynamic forces disabled. The difference between the sectional reaction moments in the full simulation and in the no-aero simulation then gives an estimate of the aerodynamic part of the reaction moment.
Best regards,
David
