I work on developing a similitude of wind blade of length 0.30 m to a prototype of 7m length.
I want to predict the deflection of the 7m blade to validate FE analysis. Because I cannot manufacture this prototype I need to apply Pi-Buckinghum Theorem to get the dimensionless ratio for the deflection.
The material of the 7m blade is orthotropic fiber glass composite and the material of the similitude is orthotropic ABS plastic.
Some professors said they have doubts about the possibility of this working due to size factor and difference in materials.
If you care about bending then I would start from the beam bending equation and non-dimensionalise that. Once you do that the appropriate scaling groups ought to just drop out naturally. You should then compare your model and simulation using the dimensionless variables.
Even for deflection only, the problem is the scalability of the load. You probably cannot assume, that aerodynamic load will be simply scaled.
The Pi theorem is a nice concept on preliminary stage of design, but later I suggest to switch to Finite Element model and CFD load computations.
Since you have FE package for the analysis, why bother to use PI theorem? Use the full scale in your FE model.
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