# Rotor Inertia computation

Dear all,
This question is regarding the rotor inertia reported in ElastoDyn summary file. And its computation.

I have taken the below formula01 and 02 from the ElastoDyn Source Code. Variable K stands for the blade number;
p%SecondMom(K) = p%SecondMom(K) + p%BElmntMass(J,K)*p%RNodes(J)*p%RNodes(J);
From the formula it seems the inertia of the blade is calculated about the rotor axis; i.e the variable p%SecondMom(K) represents the inertia of the Kth blade about rotor axis. Isnâ€™t it?

Formula02: Rotor Inertia (i.e the one reported in summary file) (Line:4774)
p%RotIner = p%RotIner + ( p%SecondMom(K) + p%BldMass (K)p%HubRad( 2.0p%BldCG(K) + p%HubRad ) )( p%CosPreC(K)**2 )
This is the total inertia of the system about the rotor axis. (That is inclusive of the Rotor shaft inertia about its own axis,
hub inertia about rotor axis, and inertia of blades about the rotor axis). Is this understanding correct?
Assume precone angle is zero, in which case the last term is equal to 1;
My question is, since p%SecondMom(K) already represent inertia of the blade about rotor axis (and NOT about the root of the blade) why are the extra terms needed in the formula02?
Also, why is the hub inertia and the term (gear ratio^2 *Generator inertia not included in the computation. Is it added at a different stage of computation? Thanks.

Regards,
Kumara

Dear Kumara,

Formula01 is the blade inertia about the blade root (not the rotor centerline), which is why the extra terms are needed in Formula02.

The parameter p%RotIner on the right-hand side of Formula02 includes the hub inertia before the blade inertia is added to it.

The generator inertia is not included in the rotor inertia written to the ElastoDyn summary file (but the generator inertia is included in the equations of motion).

Best regards,

Dear Jason,
Thanks for the clarification. It checks out now.

For RNode definition, I looked at the picture (below) and mistook as the distance from the rotor axis.

Instead I should have referred to the definition given in the later part of the FAST documentation as:
RNodes
These values are the distances of the analysis nodes from the rotor apex along the pitch axis,
which is not consistent with the YawDyn convention for 3-bladed turbines (but is consistent
for 2-bladed turbines). The analysis nodes are located at the centers of the blade segments. You
do not have complete freedom to put the RNodes anywhere you like. For instance, they cannot
be at the blade root or tip. It is also not always possible to alternate between nodes that are close
together and far apart. An easy way to ensure consistency is to divide the blade segments and then
compute the centers of the segments to use for the RNodes.

Regards,
Kumara

Dear Kumara,

That figure and description of RNodes are correct, but internally within the source code, the hub radius (HubRad) is subtracted from the values specified in the AeroDyn input file when setting the internal p%RNodes variable.

Best regards,

Thanks, Jason.

For the benefit of others, here is the formula for the p%RNodes: (Line 2432, ElastoDyn.F90 source file)
p%RNodes = BladeMeshData(K)%RNodes - p%HubRad ! Radius to blade analysis nodes relative to root ( 0 < RNodes( < p%BldFlexL ) (Convert RNodes to be relative to the hub)

Regards,
Kumara