[BUG] blade inertia excluding inertia over span

[TheMercer]

pyBmodes version

1.60.0

Python version

3.11.8

How did you install pyBmodes?

pip install pybmodes (from PyPI)

Operating system

Window 11

What happened?

"Blade inertia = zeros is the rigid-RNA convention, not a dropped term. The blades are lumped as a translational point mass at the rotor apex, so their dominant contribution, the parallel-axis term N_bl · m_blade · apex², is in the tower-top tensor. Only the blades' own spanwise spin inertia is left out, which is what ElastoDyn does as well (the blade rotational dynamics live in their own DOFs, not the tower lump). The blade mass itself is integrated from the inertia_matrix mass-per-length over the span." Last issue I made, you responded

Stated is true for the code but I disagree for what is actually present in the model

What did you expect?

However, that assumes you was give the point mass at the hub of the blades and the inertia from parallel axis theorem was zero.

However i would argue the code is forgetting you have translation the point masses spanwise to the root of blade (actually to hub centre) which means we are missing N_bl · sum(m_blade_i · (r_i +hub_R)², which does add good amount of inertia. Yes you are still forgetting about I_o (spanwise spin inertia) which has already been explained why.

Take each blade inertia from translated masses to hub and do it same time in 3D/2D plane, so you don't have to do any rotations due to azimuth.

I believe there should be additional inertia from the section point mass translations

Minimal reproducer

N/a

Traceback or unexpected output

N/a

Anything else?

No response

[SMI-Lab-Inha]

You are right, and my previous answer was wrong on this point. Thanks for pushing on it.

I conflated two different terms. The point-mass-at-the-apex lumping captures the hub-to-tower-top translation (m_blades · apex²), but it does drop the rotor's own diametral inertia from the blade mass being spread along the span (the Σ mᵢ · rᵢ² you describe). That is not a small correction. On the IEA-22 blade:

• rotor diametral inertia ≈ 3.48e8 kg·m²
• vs the tower-top iyy the point-mass lump produced ≈ 1.42e8 kg·m²

so the missing term is about 2.5× what was there. For a rigid RNA lump that is a real error, and it is exactly why the tower modes came out stiff against your OrcaFlex rigid rotor.

Fixed in #131: the rotor is now assembled as a rigid body about the hub, diag([I_polar, I_polar/2, I_polar/2]) with I_polar = N_bl · ∫ (dm/ds) · r² ds and r = hub_radius + span·cos(cone), using the hub diameter and cone angle from the ontology when present. Exactly your "translate the section masses to the hub and sum in the rotor plane", with the 120° symmetry giving the I_polar / 2 diametral split so no azimuth is needed. Each blade's own sectional spin inertia (I_o) is still left out, as discussed. Mass and CM are unchanged.

This ships as 1.16.1. Thanks again for the careful catch.

[SMI-Lab-Inha]

And separately, thank you. The depth you go to here genuinely makes pyBmodes better. Across the last few issues you have found the edge cases that actually matter (the mudline clamp, the outfitting factor, and now the rotor span inertia) and you keep pushing until the physics is right rather than just plausible, backing it with real data every time. That is exactly the kind of feedback a young library needs, and it is hugely appreciated. Please keep it coming.

[TheMercer]

Thank you 😊, honestly couldn't do it without you making the library and having these conversations.

[SMI-Lab-Inha]

This is now released in 1.16.1, on both PyPI (pip install -U pybmodes) and conda-forge (building as we speak, on the channel shortly).

Thanks again for the careful report and for pushing back when my first answer was wrong. You were exactly right that the point-mass-at-apex lump dropped the rotor's own diametral inertia from the blade mass spread along the span, and on IEA-22 that missing term was about 2.5x what the lump carried, which is why the tower modes came out stiff against your rigid-rotor reference.

The rotor is now assembled as a proper rigid body about its centre of mass, diag([I_polar, I_diam, I_diam]) with I_polar = N_bl * integral(dm/ds * r^2 ds). While it was open, the fix also grew to cover a few things worth mentioning if you use it on other turbines: the lever folds in the coned hub radius (hub_radius + span)*cos(cone) (matching WISDEM/ElastoDyn), prebend and sweep, and the span is measured from the blade root so a reference_axis.z offset from zero behaves. Total RNA mass is unchanged, but the inertia and, for a coned rotor, the tower-top centre of mass shift a little relative to 1.16.0.

If anything still looks off against your OrcaFlex numbers, please do open another issue. Reports like this are what keep the modelling honest.