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Quadratic Tangles in Planar Algebras

In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors

The effect of delta 3 on a yawing HAWT blade and on yaw dynamics

A single degree of freedom aeroelastic computer model, WMSTAB3, was employed to perform a parametric analysis of HAWT blade behavior during yaw maneuvers. Over 1,000 different combinations of delta sub 3 and normal frequency were analyzed. The effect of delta sub 3 and flapping stiffness on flapping frequency, phase, and magnitude are discussed. The moments transmitted to the fixed system during yaw maneuvers were calculated and reduced to time constants of response to step changes in wind direction. The significance of the time constants for the configurations considered relative to yaw response rate and lag angle is discussed, along with their possible significance for large HAWT

Optimal design application on the advanced aeroelastic rotor blade

The vibration and performance optimization procedure using regression analysis was successfully applied to an advanced aeroelastic blade design study. The major advantage of this regression technique is that multiple optimizations can be performed to evaluate the effects of various objective functions and constraint functions. The data bases obtained from the rotorcraft flight simulation program C81 and Myklestad mode shape program are analytically determined as a function of each design variable. This approach has been verified for various blade radial ballast weight locations and blade planforms. This method can also be utilized to ascertain the effect of a particular cost function which is composed of several objective functions with different weighting factors for various mission requirements without any additional effort