### ElastoDyn local spanwise blade deflection transformation

Posted:

**Sun Jul 19, 2020 8:04 pm**Dear Jason,

With reference to a previous forum post https://wind.nrel.gov/forum/wind/viewtopic.php?f=3&t=2471, I'd like to understand how to transform spanwise deflections (for blade #i, strain gauge #j: SpnjTDxbi, SpnjTDybi, SpnjTDzbi, SpnjRDxbi, SpnjRDybi, SpnjRDzbi) from the blade local coordinate system (CS) to the blade root CS.

According to the old FAST user manual: "for BldGagNd array, a local CS is similar to the standard blade CS, but the x-axis and y-axis are aligned with the local principal axes and the local CS orient themselves with the deflected blade." So my understanding is that they differ by structural pretwist (StrctTwst in ElastoDyn) and prebend (BlCrvAng), as well as the local rotations.

Given the transformation formulation which was referenced in the previous post:

Is my understanding correct that, for blade #i, strain gauge #j:

{x, y, z} = {SpnjTDxbi, SpnjTDybi, SpnjTDzbi}

The following is to be plugged into the transformation matrix:

theta1 = SpnjRDxbi (in radians)

theta2 = BlCrvAng + SpnjRDybi (in radians)

theta3 = StrctTwst + SpnjRDzbi (in radians) (the second term is always 0 for ElastoDyn)

Then, to convert the local deflections to the blade root CS:

{X, Y, Z} = inverse(Transformation_Matrix) * {x, y, z}

Thank you in advance,

Jing

With reference to a previous forum post https://wind.nrel.gov/forum/wind/viewtopic.php?f=3&t=2471, I'd like to understand how to transform spanwise deflections (for blade #i, strain gauge #j: SpnjTDxbi, SpnjTDybi, SpnjTDzbi, SpnjRDxbi, SpnjRDybi, SpnjRDzbi) from the blade local coordinate system (CS) to the blade root CS.

According to the old FAST user manual: "for BldGagNd array, a local CS is similar to the standard blade CS, but the x-axis and y-axis are aligned with the local principal axes and the local CS orient themselves with the deflected blade." So my understanding is that they differ by structural pretwist (StrctTwst in ElastoDyn) and prebend (BlCrvAng), as well as the local rotations.

Given the transformation formulation which was referenced in the previous post:

Is my understanding correct that, for blade #i, strain gauge #j:

{x, y, z} = {SpnjTDxbi, SpnjTDybi, SpnjTDzbi}

The following is to be plugged into the transformation matrix:

theta1 = SpnjRDxbi (in radians)

theta2 = BlCrvAng + SpnjRDybi (in radians)

theta3 = StrctTwst + SpnjRDzbi (in radians) (the second term is always 0 for ElastoDyn)

Then, to convert the local deflections to the blade root CS:

{X, Y, Z} = inverse(Transformation_Matrix) * {x, y, z}

Thank you in advance,

Jing